In a container you typically don’t want to run poetry shell itself (it spawns an interactive subshell). Instead, you want to simulate what poetry shell does: activate the virtualenv for every process.

Recommended pattern: use the venv as the container’s default environment

1. Make Poetry create the venv inside the project (so you know the path):

# Example Dockerfile fragment
WORKDIR /app

# Install dependencies, install Poetry, etc...
# ...

# Make Poetry put the venv in .venv inside /app
ENV POETRY_VIRTUALENVS_IN_PROJECT=true
RUN poetry install --no-root --no-interaction --no-ansi

Now the venv will be at /app/.venv.

2. Activate that venv for all future commands in the container:

ENV VIRTUAL_ENV=/app/.venv
ENV PATH="$VIRTUAL_ENV/bin:$PATH"

From this line onward in your Dockerfile, and for any docker run/docker exec session, all commands will automatically use the Poetry virtualenv — the same effect as being in a poetry shell.

Alternative: use an entrypoint wrapper

If you prefer to keep the Dockerfile cleaner and just wrap at runtime:

WORKDIR /app
ENV POETRY_VIRTUALENVS_IN_PROJECT=true
RUN poetry install --no-root --no-interaction --no-ansi

COPY docker-entrypoint.sh /usr/local/bin/docker-entrypoint.sh
RUN chmod +x /usr/local/bin/docker-entrypoint.sh

ENTRYPOINT ["docker-entrypoint.sh"]
CMD ["bash"]

docker-entrypoint.sh:

#!/usr/bin/env sh
set -e

# Adjust if your app path is different
. /app/.venv/bin/activate

exec "$@"

Now any command you run (including via docker exec) is executed with the Poetry venv active.

If you share your current Dockerfile, I can show the exact minimal changes for your setup.

Available analyses suggest that cherries, red currants and blackcurrants are all low in oxalate compared with classic high‑oxalate foods (like spinach, rhubarb, beet greens, nuts).

Because different labs and cultivars give slightly different numbers, it’s better to think in ranges and categories rather than single exact values:

*Based on values from published oxalate tables and analyses (e.g., Noonan & Savage 1999; various hospital/renal-diet oxalate lists, including data summarized by Harvard T.H. Chan School of Public Health). Exact values vary by cultivar, growing conditions and measurement method (total vs soluble oxalate).

Practical implications

• For people following a low‑oxalate diet (often ≤80–100 mg/day), a typical serving (½–1 cup) of any of these fruits generally contributes only a small fraction of the daily limit.
• Unless you have very strict oxalate restriction or unusually large intakes, cherries, red currants and blackcurrants are usually considered safe, low-oxalate choices compared with high-oxalate foods.

If you’re restricting oxalate for kidney stone prevention, the main focus is usually on spinach, beet greens, rhubarb, nuts, some beans, and very high-oxalate grains/bran, rather than these fruits. For personal limits and portion guidance, a renal dietitian can tailor this to you.

Below is an example UML Collaboration (Communication) Diagram for an Online Banking “Fund Transfer” use case, plus the PlantUML code to generate it.

1. Scenario Modeled

Use case: Customer transfers money from a source account to a destination account.

Objects involved:

• Customer (actor)
• OnlineBankingUI : Boundary
• AuthService : Control
• AccountService : Control
• SourceAccount : Entity
• DestinationAccount : Entity
• TransactionService : Control
• NotificationService : Control

Messages are numbered to show the sequence of interactions.

2. PlantUML Code (Collaboration / Communication Style)

@startuml
title Online Banking System - Fund Transfer Collaboration Diagram

' Layout config (optional)
left to right direction
skinparam object {
  BackgroundColor #E0F7FA
  BorderColor #00838F
}
skinparam actorStyle awesome

'---- Objects / Participants ----
actor Customer

object "OnlineBankingUI\n: Boundary" as UI
object "AuthService\n: Control" as Auth
object "AccountService\n: Control" as AccSvc
object "SourceAccount\n: Entity" as SrcAcc
object "DestinationAccount\n: Entity" as DestAcc
object "TransactionService\n: Control" as TxSvc
object "NotificationService\n: Control" as Notif

'---- Static links between collaborating objects (association lines) ----
Customer - UI : uses
UI - Auth
UI - AccSvc
Auth - AccSvc
AccSvc - SrcAcc
AccSvc - DestAcc
AccSvc - TxSvc
TxSvc - Notif
Notif - Customer

'---- Numbered messages (collaboration style) ----

' 1. Customer starts transfer
Customer -> UI : 1: enterTransferDetails(src, dest, amount)

' 2. UI ensures session is valid
UI -> Auth : 2: validateSession()
Auth -> AccSvc : 2.1: getCustomerAccounts()
AccSvc -> SrcAcc : 2.1.1: load()
AccSvc -> DestAcc : 2.1.2: load()

' 3. UI requests the transfer
UI -> AccSvc : 3: requestTransfer(src, dest, amount)

' 3.1 Check balance on source account
AccSvc -> SrcAcc : 3.1: hasSufficientBalance(amount)?

' 3.2 Create and execute transfer
AccSvc -> TxSvc : 3.2: createTransfer(src, dest, amount)

' 3.2.1 Debit source
TxSvc -> AccSvc : 3.2.1: debit(src, amount)
AccSvc -> SrcAcc : 3.2.1.1: updateBalance(-amount)

' 3.2.2 Credit destination
TxSvc -> AccSvc : 3.2.2: credit(dest, amount)
AccSvc -> DestAcc : 3.2.2.1: updateBalance(+amount)

' 3.3 Notify customer
TxSvc -> Notif : 3.3: sendConfirmation()
Notif -> Customer : 3.3.1: showConfirmation()

@enduml

Render this code with any PlantUML-compatible tool to get the collaboration diagram.

Here’s a checked and cleaned‑up version of your code, plus a simple way to print the “best move” (greedy action from the learned Q‑table).

Main issues fixed

1. Bug in action 4:
   You had:

   elif action == 4:
       self.state -= 2
       self.state -= 2 * action   # <- subtracts 8 more, total -10
   

   I changed this to just self.state -= 2.

2. Boundary condition in act:
   You checked state == self.env.board_size + 1, which is never a valid state. I removed that special case and kept only the check for state 1 (to avoid moving backwards from the start).

3. Indentation error in __main__:
   The line env = SnakeLadderEnv(...) was incorrectly indented.

4. “Best move” printing:
   After training, you can print the best move per state using np.argmax(Q[state]) + 1, or show the greedy path from start to finish.

Corrected code with “best move” printing

import numpy as np
import random

class SnakeLadderEnv:
    def __init__(self, board_size, snakes, ladders, dragon, genie, phoenix, diamond):
        self.board_size = board_size
        self.snakes = snakes
        self.ladders = ladders
        self.dragon = dragon
        self.genie = genie
        self.phoenix = phoenix
        self.diamond = diamond

        self.state = 1
        self.terminal_state = board_size

    def step(self, action):
        # Move the agent based on the action
        if action == 1:
            self.state += 1
        elif action == 2:
            self.state += 2
        elif action == 3:
            self.state -= 1
        elif action == 4:
            self.state -= 2   # fixed: removed self.state -= 2 * action

        # Ensure state remains within the board boundaries
        self.state = max(1, min(self.board_size, self.state))

        # 20% chance of moving in the opposite direction by up to 2 squares
        if random.random() < 0.2:
            self.state -= min(2, self.state - 1)  # Ensure state does not go below 1

        # Apply snakes
        for snake in self.snakes:
            if self.state == snake[0]:
                self.state = snake[1]
                break

        # Apply ladders
        for ladder in self.ladders:
            if self.state == ladder[0]:
                self.state = ladder[1]
                break

        # Special tiles
        if self.state == self.dragon:
            self.state = 1

        if self.state == self.genie:
            self.state = self.board_size

        if self.state == self.phoenix:
            self.state = self.board_size

        if self.state == self.diamond:
            self.state = self.dragon

        # Check if the game is over
        done = self.state == self.terminal_state

        # Reward: -1 for every step, +100 for reaching the end
        reward = -1 if not done else 100

        return self.state, reward, done

    def reset(self):
        self.state = 1
        return self.state


class QLearningAgent:
    def __init__(self, env, alpha=0.2, gamma=0.9, epsilon=0.1):
        self.env = env
        self.Q = np.zeros((env.board_size + 1, 4))  # states: 1..board_size, actions: 1..4
        self.alpha = alpha
        self.gamma = gamma
        self.epsilon = epsilon

    def act(self, state):
        # ε-greedy policy
        if random.random() < self.epsilon:
            # exploration
            if state == 1:
                # From start, only allow positive movement
                return random.randint(1, 2)
            else:
                return random.randint(1, 4)
        else:
            # exploitation
            return int(np.argmax(self.Q[state]) + 1)  # action index 0..3 -> action 1..4
        
    def learn(self, state, action, reward, next_state, done):
        current_q = self.Q[state][action - 1]
        target = reward if done else reward + self.gamma * np.max(self.Q[next_state])
        self.Q[state][action - 1] += self.alpha * (target - current_q)

    def train(self, episodes):
        for episode in range(episodes):
            state = self.env.reset()
            done = False

            while not done:
                action = self.act(state)
                next_state, reward, done = self.env.step(action)
                self.learn(state, action, reward, next_state, done)
                state = next_state

        return self.Q


if __name__ == "__main__":
    # Optional: set a seed for reproducibility
    random.seed(0)
    np.random.seed(0)

    board_size = 100
    snakes = [(33, 5), (66, 12), (56, 20), (43, 24), (78, 59), (96, 72)]
    ladders = [(7, 36), (21, 58), (31, 51), (34, 84), (54, 89), (63, 82)]
    dragon = 52
    genie = 48
    phoenix = 64
    diamond = 41

    env = SnakeLadderEnv(board_size, snakes, ladders, dragon, genie, phoenix, diamond)
    agent = QLearningAgent(env)
    Q = agent.train(1000)

    # 1) Count how many state-action pairs were updated (non-zero Q-values)
    print("Number of movements (state-action pairs) with non-zero Q:", np.sum(Q != 0))

    # 2) Print the best move (greedy action) from each state
    print("\nBest move from each state (according to learned Q):")
    for s in range(1, board_size):
        best_action = np.argmax(Q[s]) + 1
        print(f"State {s}: best action = {best_action}")

    # 3) Demonstrate following the greedy policy from the start
    state = env.reset()
    print("\nGreedy policy rollout from start:")
    print("Initial location:", state)

    step_count = 0
    while state != board_size and step_count < 200:  # safety cap
        action = np.argmax(Q[state]) + 1
        next_state, reward, done = env.step(action)
        print(f"Step {step_count+1}: state={state}, best move={action}, "
              f"reward={reward}, next_state={next_state}")
        state = next_state
        step_count += 1
        if done:
            break

    print("\nFinal state:", state)

How to interpret “best move”

• For each state s,
  best_action = np.argmax(Q[s]) + 1
  is the action (1–4) that the agent currently believes gives the highest long‑term return.
• Because your environment is stochastic (20% chance of backward move, plus snakes, ladders, and special tiles), the actual next state can vary even with the same “best move”.

If you want a different notion of “best move” (e.g., only forward moves allowed, no randomness when evaluating, best path length, etc.), tell me and I can adjust the code accordingly.

When your function takes a complex DataFrame as input, the trick is to make that complexity explicit and then build a small set of controlled inputs that exercise it.

Below is a practical way to do it.

1. Make the expected input explicit

Before writing tests, write down the “contract” for the DataFrame your function expects:

• Required columns (names, types)
• Optional columns
• Index assumptions (RangeIndex? MultiIndex?)
• Uniqueness assumptions (e.g. unique IDs)
• Value constraints (no negatives, no nulls in a specific column, etc.)

Example of a contract in comments or docstring:

def compute_metrics(df: pd.DataFrame) -> pd.DataFrame:
    """
    Expects df with:
      - columns:
          - 'user_id' (int, non-null)
          - 'timestamp' (datetime64)
          - 'value' (float, may be null)
      - 'timestamp' sorted ascending per user_id
      - no duplicate (user_id, timestamp) pairs
    """
    ...

You can also enforce this with a tool like pandera (schema validation for pandas).

2. Capture a “real” representative input

Since the DataFrame comes from another program, the easiest representative input is often a snapshot of real data.

One-time setup:

# Somewhere in your main code (only while preparing tests)
df = get_input_from_other_program(...)
df.to_parquet("tests/data/example_input.parquet")

Then in tests:

import pandas as pd
from pathlib import Path

def load_example_df() -> pd.DataFrame:
    path = Path(__file__).parent / "data" / "example_input.parquet"
    return pd.read_parquet(path)

def test_compute_metrics_on_example():
    df = load_example_df()
    result = compute_metrics(df)
    # assert on properties, not the whole DataFrame if it's large
    assert "metric_a" in result.columns
    assert not result.empty

This “golden input” gives you a realistic baseline test.

3. Create small, hand-crafted DataFrames for specific behaviors

Real data is good for realism, but it’s bad for precision: it’s hard to see what exactly you’re testing.

Create tiny DataFrames that isolate particular behaviors. Use pytest fixtures or helper functions:

import pandas as pd
import pytest

@pytest.fixture
def simple_df():
    return pd.DataFrame({
        "user_id": [1, 1, 2],
        "timestamp": pd.to_datetime(["2024-01-01", "2024-01-02", "2024-01-01"]),
        "value": [10.0, 20.0, 5.0],
    })

def test_basic_behavior(simple_df):
    result = compute_metrics(simple_df)
    # Assert on exact values because the input is small and controlled
    assert set(result["user_id"]) == {1, 2}
    assert result.loc[result["user_id"] == 1, "metric_a"].iloc[0] == 30.0

This kind of unit test is usually more robust and easier to maintain than tests based only on big, real DataFrames.

4. Systematically think through edge cases

Start from your contract and turn potential failures into tests. Common DataFrame edge cases:

1. Empty inputs

   def test_empty_df():
       df = pd.DataFrame(columns=["user_id", "timestamp", "value"])
       result = compute_metrics(df)
       # decide what you expect: empty, error, or default output?
       assert result.empty
   

2. Single-row / single-group inputs

   • Only one user
   • Only one timestamp
   • Minimal possible data

3. Missing values

   • NaNs in numeric columns
   • Missing timestamps
   • Completely null column

4. Unexpected values

   • Negative numbers if normally non-negative
   • Timestamps out of expected range

5. Structural surprises

   • Missing required column
   • Extra, unused columns
   • Wrong dtypes (e.g. string instead of int)
   • Duplicate rows or IDs
   • Unsorted index or grouping columns

Example:

def test_missing_column_raises():
    df = pd.DataFrame({
        "user_id": [1, 2],
        # "timestamp" missing
        "value": [10.0, 20.0],
    })
    with pytest.raises(KeyError):
        compute_metrics(df)

Write tests for the cases you care about (e.g. you explicitly want to raise) and the ones you want to handle gracefully (e.g. treat NaNs as zero).

5. Use factories to avoid repetition

If your DataFrames are large or similar, write small “factories” that create variants:

def make_base_df():
    return pd.DataFrame({
        "user_id": [1, 1, 2, 2],
        "timestamp": pd.to_datetime([
            "2024-01-01", "2024-01-02", "2024-01-01", "2024-01-03"
        ]),
        "value": [10.0, 20.0, 5.0, 7.0],
    })

def test_handles_nans():
    df = make_base_df()
    df.loc[0, "value"] = None  # introduce NaN
    result = compute_metrics(df)
    ...

This keeps tests readable and makes it easy to add new edge cases.

6. Consider property-based testing for DataFrame-heavy logic

If your function is mostly numeric / structural and doesn’t rely heavily on domain-specific values, Hypothesis can generate DataFrames for you:

from hypothesis import given
from hypothesis.extra.pandas import data_frames, column
from hypothesis.strategies import integers, floats, datetimes

@given(data_frames([
    column("user_id", integers(min_value=1, max_value=10)),
    column("timestamp", datetimes()),
    column("value", floats(allow_nan=True, allow_infinity=False)),
]))
def test_properties_of_compute_metrics(df):
    result = compute_metrics(df)

    # Example properties:
    assert "user_id" in result.columns
    # Maybe: one result row per input user_id
    assert set(result["user_id"]) == set(df["user_id"].unique())

You don’t specify exact expected outputs; instead you test high-level invariants (no crashes, certain relationships always hold, etc.). This is great at finding weird edge cases.

7. Don’t forget integration tests with the upstream program

Unit tests isolate your function. Since the DataFrame comes from another program, add at least one integration test that:

• Calls the upstream code that produces the DataFrame
• Passes it directly into your function
• Verifies end-to-end behavior

This ensures your assumptions about the schema stay in sync.

Summary

1. Define the DataFrame contract: columns, dtypes, invariants.
2. Capture a real snapshot as a “golden” example input.
3. Create small, hand-crafted DataFrames to test specific behaviors.
4. List and test edge cases: empties, NaNs, missing columns, wrong types, duplicates, unsorted data, etc.
5. Use factories and fixtures to keep tests clean.
6. Optionally use Hypothesis for property-based tests.
7. Add at least one integration test with the real upstream producer.

If you share a specific function signature or an example of the DataFrame structure, I can sketch concrete test cases tailored to your code.

Below is one way to interpret and implement what you asked for:

• An innovative tower defense concept featuring weapons, enemies, and doorways.
• Procedurally generated “infinite” levels.
• A simple HTML/JS implementation scaffold.
• How to load the game page itself via <embed> from an HTTP URL.

1. Game Concept: “Doorway Loops”

Core idea:
You defend a base at the center of the map. Enemies spawn from the edges and try to reach the center. The twist is that the map is full of doorways (portals) that:

• Teleport enemies to other doorways.
• Can be controlled/locked/unlocked by certain towers.
• Are rearranged procedurally each level, so you never get the same path twice.

Each “level” is a new procedural layout of:

• Doorways (pairs, chains, loops).
• Enemy routes.
• Random modifiers (e.g., “double enemy speed, half health”, “slow portals”, etc.).

Levels are infinite: after you beat a wave, the game rolls a new map + parameters and the difficulty scales up.

Key elements

Weapons (Towers)
Examples:

• Gun Tower: Basic single-target, medium range.
• Pulse Tower: AoE damage on a cooldown.
• Door Controller: Can:
  • Temporarily disable a doorway.
  • Flip its destination.
  • Turn a doorway into a one-way trap that damages enemies passing through.
• Snare Tower: Slows enemies in a radius.

Enemies

• Runner: Fast, low HP.
• Tank: Slow, high HP.
• Phaser: Can ignore the first doorway it touches.
• Swarm: Comes in large groups, low HP; effective at clogging doorways.

Doorways

• Static pairs or networks: each doorway has a destination.
• Properties that can be modified by the player or towers:
  • Locked/unlocked.
  • Damage on pass-through.
  • Delay (stun enemies briefly on teleport).
• Level generator randomly links doorways and gives some doors “special” effects.

2. Basic HTML/JS Scaffold (Canvas-based)

This is a minimal skeleton you can extend. It’s not a full game, but it shows:

• A canvas.
• A simple game loop.
• Basic data structures for towers, enemies, doorways.
• A sketch of infinite procedural levels.

game.html (this is the file you’ll host and later embed via <embed src="http://.../game.html">):

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <title>Doorway Defense</title>
  <style>
    body { margin: 0; background: #111; color: #eee; font-family: sans-serif; }
    #game-container {
      display: flex;
      flex-direction: column;
      align-items: center;
      margin-top: 10px;
    }
    canvas {
      background: #222;
      border: 1px solid #444;
    }
    #ui { margin-top: 8px; font-size: 14px; }
  </style>
</head>
<body>
  <div id="game-container">
    <canvas id="game" width="800" height="600"></canvas>
    <div id="ui">
      Level: <span id="level">1</span> |
      Lives: <span id="lives">20</span> |
      Credits: <span id="credits">100</span>
    </div>
  </div>

  <script>
    const canvas = document.getElementById('game');
    const ctx = canvas.getContext('2d');

    const uiLevel = document.getElementById('level');
    const uiLives = document.getElementById('lives');
    const uiCredits = document.getElementById('credits');

    const state = {
      level: 1,
      lives: 20,
      credits: 100,
      enemies: [],
      towers: [],
      doorways: [],
      paths: [],
      lastTime: 0,
      waveActive: false,
      timeSinceWaveStart: 0
    };

    // ----- Utility -----
    function randRange(min, max) {
      return Math.random() * (max - min) + min;
    }

    function distance(a, b) {
      const dx = a.x - b.x;
      const dy = a.y - b.y;
      return Math.sqrt(dx * dx + dy * dy);
    }

    // ----- Core Data Types -----
    class Enemy {
      constructor(x, y, path) {
        this.x = x;
        this.y = y;
        this.path = path;   // array of waypoints
        this.pathIndex = 0;
        this.speed = 40;    // px/s
        this.maxHP = 20;
        this.hp = this.maxHP;
        this.radius = 6;
      }
      update(dt) {
        if (this.pathIndex >= this.path.length) return;
        const target = this.path[this.pathIndex];
        const dx = target.x - this.x;
        const dy = target.y - this.y;
        const dist = Math.sqrt(dx * dx + dy * dy);
        if (dist < 1) {
          this.pathIndex++;
          if (this.pathIndex >= this.path.length) {
            // Reached center/base
            state.lives--;
          }
          return;
        }
        const vx = (dx / dist) * this.speed;
        const vy = (dy / dist) * this.speed;
        this.x += vx * dt;
        this.y += vy * dt;

        // Check doorway collisions
        for (const door of state.doorways) {
          if (!door.active) continue;
          if (distance(this, door) < door.radius) {
            door.teleport(this);
            break;
          }
        }
      }
      draw(ctx) {
        ctx.save();
        ctx.translate(this.x, this.y);
        ctx.fillStyle = '#ff5555';
        ctx.beginPath();
        ctx.arc(0, 0, this.radius, 0, Math.PI * 2);
        ctx.fill();
        // HP bar
        ctx.fillStyle = '#222';
        ctx.fillRect(-7, -10, 14, 3);
        ctx.fillStyle = '#0f0';
        ctx.fillRect(-7, -10, 14 * (this.hp / this.maxHP), 3);
        ctx.restore();
      }
    }

    class Tower {
      constructor(x, y) {
        this.x = x;
        this.y = y;
        this.range = 100;
        this.fireRate = 1; // shots per second
        this.cooldown = 0;
        this.damage = 8;
      }
      update(dt) {
        this.cooldown -= dt;
        if (this.cooldown <= 0) {
          // Acquire target
          let target = null;
          let minDist = Infinity;
          for (const e of state.enemies) {
            const d = distance(this, e);
            if (d < this.range && d < minDist) {
              target = e;
              minDist = d;
            }
          }
          if (target) {
            target.hp -= this.damage;
            if (target.hp <= 0) {
              state.credits += 1;
            }
            this.cooldown = 1 / this.fireRate;
          }
        }
      }
      draw(ctx) {
        ctx.save();
        ctx.translate(this.x, this.y);
        ctx.fillStyle = '#55aaff';
        ctx.fillRect(-8, -8, 16, 16);
        ctx.strokeStyle = 'rgba(85,170,255,0.2)';
        ctx.beginPath();
        ctx.arc(0, 0, this.range, 0, Math.PI * 2);
        ctx.stroke();
        ctx.restore();
      }
    }

    class Doorway {
      constructor(x, y) {
        this.x = x;
        this.y = y;
        this.radius = 12;
        this.dest = null;    // another Doorway
        this.active = true;
      }
      teleport(enemy) {
        if (!this.dest) return;
        // simple teleport: move enemy near destination and advance path a bit
        enemy.x = this.dest.x + randRange(-5, 5);
        enemy.y = this.dest.y + randRange(-5, 5);
      }
      draw(ctx) {
        ctx.save();
        ctx.translate(this.x, this.y);
        ctx.strokeStyle = this.active ? '#ffa500' : '#444';
        ctx.lineWidth = 2;
        ctx.beginPath();
        ctx.arc(0, 0, this.radius, 0, Math.PI * 2);
        ctx.stroke();
        ctx.restore();
      }
    }

    // ----- Level Generator (Infinite) -----
    function generateLevel(levelNumber) {
      state.enemies = [];
      state.doorways = [];
      state.paths = [];

      // Base at center
      const center = { x: canvas.width / 2, y: canvas.height / 2 };

      // Create some doorways
      const doorCount = 4 + Math.floor(levelNumber / 2);
      for (let i = 0; i < doorCount; i++) {
        const angle = (Math.PI * 2 * i) / doorCount;
        const r = 200 + randRange(-40, 40);
        const x = center.x + Math.cos(angle) * r;
        const y = center.y + Math.sin(angle) * r;
        state.doorways.push(new Doorway(x, y));
      }

      // Randomly link doorways into pairs (simple version)
      const shuffled = [...state.doorways].sort(() => Math.random() - 0.5);
      for (let i = 0; i < shuffled.length; i += 2) {
        const d1 = shuffled[i];
        const d2 = shuffled[i + 1] || shuffled[0];
        d1.dest = d2;
        d2.dest = d1;
      }

      // Define some paths from edges to center
      const pathCount = 4;
      for (let p = 0; p < pathCount; p++) {
        const side = p % 4;
        let start;
        if (side === 0) start = { x: randRange(0, canvas.width), y: 0 };
        if (side === 1) start = { x: canvas.width, y: randRange(0, canvas.height) };
        if (side === 2) start = { x: randRange(0, canvas.width), y: canvas.height };
        if (side === 3) start = { x: 0, y: randRange(0, canvas.height) };

        // Intermediate waypoint: a random doorway
        const midDoor = state.doorways[Math.floor(Math.random() * state.doorways.length)];
        const path = [start, { x: midDoor.x, y: midDoor.y }, center];
        state.paths.push(path);
      }

      // Spawn a wave based on level
      spawnWave(levelNumber);
      state.waveActive = true;
      state.timeSinceWaveStart = 0;
    }

    function spawnWave(levelNumber) {
      const enemyCount = 5 + levelNumber * 2;
      for (let i = 0; i < enemyCount; i++) {
        const path = state.paths[i % state.paths.length];
        const start = path[0];
        const e = new Enemy(start.x, start.y, path);
        // scale stats with level
        e.maxHP += levelNumber * 5;
        e.hp = e.maxHP;
        e.speed += levelNumber * 2;
        state.enemies.push(e);
      }
    }

    // ----- Game Loop -----
    function update(dt) {
      state.timeSinceWaveStart += dt;

      // Update towers
      state.towers.forEach(t => t.update(dt));

      // Update enemies
      for (let i = state.enemies.length - 1; i >= 0; i--) {
        const e = state.enemies[i];
        const oldLives = state.lives;
        e.update(dt);
        if (e.hp <= 0 || state.lives < oldLives) {
          // enemy killed or reached base
          state.enemies.splice(i, 1);
        }
      }

      // Level progression (infinite)
      if (state.enemies.length === 0 && state.waveActive) {
        state.waveActive = false;
        state.level++;
        generateLevel(state.level);
      }

      if (state.lives <= 0) {
        // Basic game over handling
        alert('Game Over! You reached level ' + state.level);
        state.level = 1;
        state.lives = 20;
        state.credits = 100;
        state.towers = [];
        generateLevel(state.level);
      }

      uiLevel.textContent = state.level;
      uiLives.textContent = state.lives;
      uiCredits.textContent = state.credits;
    }

    function draw() {
      ctx.clearRect(0, 0, canvas.width, canvas.height);

      // Base
      ctx.save();
      ctx.translate(canvas.width / 2, canvas.height / 2);
      ctx.fillStyle = '#66ff66';
      ctx.beginPath();
      ctx.arc(0, 0, 15, 0, Math.PI * 2);
      ctx.fill();
      ctx.restore();

      // Doorways
      state.doorways.forEach(d => d.draw(ctx));

      // Towers
      state.towers.forEach(t => t.draw(ctx));

      // Enemies
      state.enemies.forEach(e => e.draw(ctx));
    }

    function loop(timestamp) {
      const dt = (timestamp - state.lastTime) / 1000 || 0;
      state.lastTime = timestamp;

      update(dt);
      draw();

      requestAnimationFrame(loop);
    }

    // ----- Simple tower placement -----
    canvas.addEventListener('click', (e) => {
      const rect = canvas.getBoundingClientRect();
      const x = e.clientX - rect.left;
      const y = e.clientY - rect.top;
      const towerCost = 20;
      if (state.credits >= towerCost) {
        state.towers.push(new Tower(x, y));
        state.credits -= towerCost;
      }
    });

    // Initialize
    generateLevel(state.level);
    requestAnimationFrame(loop);
  </script>
</body>
</html>

You can extend this by:

• Adding different enemy classes with special doorway behavior.
• Adding a new tower type DoorController that toggles door.active or changes door.dest.
• Introducing level modifiers affecting speed, HP, number of doorways, etc.

3. Embedding the Game in Another HTML Page via <embed>

Assume you host game.html at:

http://your-domain.com/game.html

To embed this game in another page (e.g., index.html), use:

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <title>Embedded Tower Defense</title>
</head>
<body>
  <h1>My Embedded Tower Defense Game</h1>

  <embed
    src="http://your-domain.com/game.html"
    type="text/html"
    width="800"
    height="620">
  </embed>

</body>
</html>

Notes:

• Many modern sites prefer <iframe> instead of <embed>:

  <iframe
    src="http://your-domain.com/game.html"
    width="800"
    height="620"
    style="border:none;">
  </iframe>
  

• Ensure the URL is accessible over HTTP/HTTPS and any CSP/X-Frame-Options headers allow embedding.

If you’d like, I can next:

• Add a dedicated doorway-control tower.
• Improve enemy behavior (e.g., enemies that try to avoid certain doors).
• Show how to separate JS into modules or files.

We can turn this into a small object-oriented model of a landing control system.

1. Main concepts

From your description we have:

Sensors

• Altimeter – measures altitude.
• Thermometer – measures temperature inside ship plating.

Actuators

• Braking rocket engine – can be turned on/off.
• Parachute – can be deployed (one-time action).

Controller (autonomic system)

• Reads sensors.
• Decides when to:
  • Turn braking engine on/off (to avoid overheating).
  • Open parachute when altitude reaches 1000 m.

Environment / Ship

• Contains sensors and actuators.
• Has state: altitude, speed, temperature, etc.
• Is updated over time (e.g., each simulation step).

2. Basic class design

Interfaces

public interface Sensor<T> {
    T readValue();
}

public interface Actuator {
    void performAction();
}

Concrete sensors

public class Altimeter implements Sensor<Double> {
    private final Ship ship;

    public Altimeter(Ship ship) {
        this.ship = ship;
    }

    @Override
    public Double readValue() {
        return ship.getAltitude();
    }
}

public class Thermometer implements Sensor<Double> {
    private final Ship ship;

    public Thermometer(Ship ship) {
        this.ship = ship;
    }

    @Override
    public Double readValue() {
        return ship.getHullTemperature();
    }
}

Actuators

public class RocketEngine implements Actuator {
    private boolean on = false;

    @Override
    public void performAction() {
        on = !on; // toggle for simplicity
    }

    public void setOn(boolean on) {
        this.on = on;
    }

    public boolean isOn() {
        return on;
    }
}

public class Parachute implements Actuator {
    private boolean deployed = false;

    @Override
    public void performAction() {
        deploy();
    }

    public void deploy() {
        if (!deployed) {
            deployed = true;
            // logic of deployment
        }
    }

    public boolean isDeployed() {
        return deployed;
    }
}

Ship

public class Ship {
    private double altitude;
    private double velocity;
    private double hullTemperature;

    private final RocketEngine engine;
    private final Parachute parachute;

    public Ship(double initialAltitude) {
        this.altitude = initialAltitude;
        this.velocity = 0;
        this.hullTemperature = 20; // example
        this.engine = new RocketEngine();
        this.parachute = new Parachute();
    }

    public void update(double deltaTime) {
        // simplistic physics placeholder:
        if (engine.isOn()) {
            velocity -= 5 * deltaTime; // braking
        } else {
            velocity += 9.8 * deltaTime; // gravity
        }

        altitude -= velocity * deltaTime;
        if (altitude < 0) altitude = 0;

        // temperature depends on speed (very simplified)
        hullTemperature = 20 + Math.abs(velocity) * 2;
    }

    public double getAltitude() {
        return altitude;
    }

    public double getHullTemperature() {
        return hullTemperature;
    }

    public RocketEngine getEngine() {
        return engine;
    }

    public Parachute getParachute() {
        return parachute;
    }
}

Autonomic landing controller

public class AutonomicLandingSystem {
    private final Sensor<Double> altimeter;
    private final Sensor<Double> thermometer;
    private final RocketEngine engine;
    private final Parachute parachute;

    private final double parachuteAltitude = 1000.0;
    private final double maxSafeTemperature = 1200.0;

    public AutonomicLandingSystem(Ship ship) {
        this.altimeter = new Altimeter(ship);
        this.thermometer = new Thermometer(ship);
        this.engine = ship.getEngine();
        this.parachute = ship.getParachute();
    }

    public void controlStep() {
        double altitude = altimeter.readValue();
        double temperature = thermometer.readValue();

        // Overheating prevention: turn engine off if too hot
        if (temperature > maxSafeTemperature && engine.isOn()) {
            engine.setOn(false);
        }

        // Simplified: turn engine on if we are still high and not too hot
        if (altitude > parachuteAltitude && temperature <= maxSafeTemperature && !engine.isOn()) {
            engine.setOn(true);
        }

        // Parachute deployment at 1000 m
        if (altitude <= parachuteAltitude && !parachute.isDeployed()) {
            parachute.deploy();
            engine.setOn(false); // maybe we stop engine when parachute opens
        }
    }
}

Simulation loop

public class Simulation {
    public static void main(String[] args) {
        Ship ship = new Ship(10000); // start at 10 km
        AutonomicLandingSystem controller = new AutonomicLandingSystem(ship);

        double time = 0;
        double dt = 0.1; // 0.1 second tick

        while (ship.getAltitude() > 0) {
            controller.controlStep();
            ship.update(dt);
            time += dt;

            // logging for debugging
            System.out.printf("t=%.1fs, alt=%.1fm, temp=%.1fC%n",
                    time, ship.getAltitude(), ship.getHullTemperature());
        }

        System.out.println("Ship has landed.");
    }
}

If you want, next step could be:

• Introduce a LandingPhase enum and a state machine (coasting, braking, parachute, landed).
• Replace “toggle” engine with explicit start() / stop() commands.
• Split simulation/environment from control logic more strictly.

They don’t actually use PPS instead of PD – PPS is a special mode inside USB Power Delivery 3.0, and Samsung leans on it heavily for “Super Fast Charging.”

Here’s what’s going on in simple terms:

1. PD vs PPS: what’s the difference?

• USB‑PD (Power Delivery)
  Standard fast‑charging protocol with fixed voltage steps: typically 5 V, 9 V, 15 V, 20 V.
  The charger says “I can do 5 V/3 A, 9 V/2 A,” etc., and the phone picks one of those.

• PPS (Programmable Power Supply) – part of USB‑PD 3.0
  An optional extension that allows:

  • Adjustable voltage in small steps (e.g. 3.3–11 V or 3.3–21 V in 20 mV steps)
  • Adjustable current in fine steps as well

  Instead of jumping from 9 V to 15 V, the phone can request, say, 6.2 V, 7.4 V, 8.3 V, etc., and dynamically tweak it while charging.

So Samsung isn’t abandoning PD; their “Super Fast Charging” is PD + PPS.

2. Why Samsung prefers PPS for “Super Fast Charging”

Samsung uses PPS mainly because it lets them push more power while keeping heat and battery wear under control:

1. Less heat, higher efficiency

   • With fixed PD, the phone often has to drop a higher voltage (like 9 V) down to the battery voltage internally, which wastes power as heat.
   • With PPS, the charger can output almost exactly what the battery needs at that moment, so less conversion is done inside the phone → cooler and more efficient.

2. Better battery health over time

   • Finer control of voltage and current lets the phone adjust charging more precisely based on battery temperature, state of charge, and health.
   • This helps reduce stress on the battery, which is important given how thin and tightly packed modern phones are.

3. Higher advertised speeds (25 W / 45 W)

   • Samsung’s “Super Fast Charging” profiles (25 W, 45 W) are defined using PD PPS.
   • You only get those full speeds when both the charger and cable support PD PPS with the right power profile.

3. What this means for you in practice

• A non‑PPS USB‑PD charger:

  • Will still charge a Samsung phone.
  • But usually maxes out at standard PD levels (often around 15–18 W for many models).

• A PD + PPS charger with the right wattage (e.g. 25 W or 45 W):

  • Enables “Super Fast Charging” / “Super Fast Charging 2.0”.
  • Uses PPS to keep the phone cooler while delivering more power.

So the core answer:
Samsung uses PPS because it’s a more advanced mode of USB‑PD that allows faster charging with better thermal control and long‑term battery protection, instead of relying only on the older fixed‑voltage PD modes.

For short distances, most people would still usually walk (or fly themselves) rather than use a light‑speed car, for a few practical reasons:

1. Startup overhead vs. distance

   • Getting into the car, starting it, buckling in, dealing with traffic rules, parking, etc. all take time.
   • For very short trips (say a few hundred meters to a couple of kilometers), that “overhead time” would be longer than just walking or flying over.

2. Control and safety

   • A car that can reach light speed is extremely dangerous in any dense area.
   • Even if you don’t always go full speed, the system must be heavily regulated: acceleration limits, no light‑speed inside cities, strong safety systems.
   • Walking/flying gives you much finer control at low speeds, and it’s easier to avoid bumping into people, buildings, etc.

3. Health and habit

   • People still need exercise. Walking/flying short distances would be a simple way to stay healthy.
   • Culturally, for short trips, many would keep the habit of moving under their own power, especially if flying is easy and fun.

4. Urban design

   • If humans can fly, cities would be designed around that. Lots of vertical paths, landing areas, short gaps between destinations.
   • Light‑speed cars would likely be restricted to specific long‑distance corridors or high‑altitude/high‑security lanes.

5. Use cases for the car

   • Cars would shine for long distances or when carrying heavy cargo, many passengers, or when comfort/privacy matters.
   • For anything “around the corner” or “a few blocks away,” the car would be overkill.

So in that universe: for short distances, walking/flying yourself would usually be preferred, while light‑speed cars would be mostly for longer or more demanding trips.

“Oklo” can refer to two closely related things in nuclear science:

1. The Oklo natural nuclear reactors (Gabon, Africa)

   • Around 2 billion years ago, in what is now Gabon, certain uranium ore deposits reached conditions (enough U‑235, water as a moderator, proper geometry) that allowed sustained nuclear fission reactions—essentially natural nuclear reactors.
   • These “reactors” ran intermittently over hundreds of thousands of years, consuming some of the uranium and producing fission products, just like a man‑made reactor.
   • Oklo is important scientifically because:
     • It provides a natural example of long‑term geologic containment of nuclear waste.
     • It’s been used to test whether fundamental physical constants (like the fine-structure constant) have changed over billions of years.

2. Oklo Inc. (a modern nuclear company)

   • Oklo Inc. is a U.S. company developing small advanced nuclear reactors (often called microreactors), aiming for compact, factory-built fission systems that can be deployed to remote locations or industrial sites.
   • They’ve proposed fast-spectrum reactors using recycled nuclear fuel, with a strong focus on simplified design and lower operating complexity.

If you meant one of these specifically (the ancient natural reactors vs. the modern company), say which and I can go into more detail.

Here’s a fictional “post-sequel” timeline for Call of Duty set after Activision shuts down all official services and the franchise is considered dead. Think of it as a mix of in-universe lore and meta commentary about the series itself.

1. Call of Duty: Final Ping (2030)

Premise:
In 2030, Activision officially shuts down all Call of Duty servers, declaring a “permanent sunset” for the franchise. What players don’t know is that the game’s in-universe AI training simulations were being used to model real-world conflicts.

Story Hook:
A group of former pro players receive a mysterious offline build of Modern Warfare labeled “FINAL_PING.exe”. Running it pulls them into a covert cyberwar, where real-world mercenary groups are using modified CoD engines to simulate and plan actual operations.

Gameplay Angle (fictional):

• Fully offline campaign with AI “ghosts” based on real player data from years prior.
• “Memorial missions” that recreate iconic multiplayer maps as warzones in ruins.
• Narrative revolves around saving or destroying the data that made CoD what it was.

2. Call of Duty: Underground Servers (2033)

Premise:
With official servers gone, underground communities bring them back through pirated private shards. These “black servers” become hubs for extremists, hackers, and intelligence agencies hunting them.

Story Hook:
You play as an agent of a global cyber-security task force infiltrating black-ops CoD servers that are being used to recruit and train real fighters. Missions alternate between:

• Real-world raids on hidden data centers
• “Inside the game” assaults on custom-built maps used as extremist playgrounds

Themes:

• When does a game stop being just a game?
• The ethics of gamified training and propaganda.

3. Call of Duty: Legacy of War (2036)

Premise:
Governments declassify how CoD-inspired simulations influenced tactics, gear, and doctrine in 21st-century conflicts. A historian unit is built inside NATO to reconstruct the “CoD Wars” as they really happened.

Story Hook:
You’re an analyst-soldier who plays through reconstructed operations based on archived CoD telemetry. Each mission is a “what really happened” version of old campaigns:

• A darker take on “No Russian” and similar iconic missions
• Failed covert operations that were never public
• Wargames that accidentally escalated real tensions

Meta Spin:
Each mission is contrasted with in-universe footage of the original “video game version” versus the classified truth. The line between entertainment and war propaganda is aggressively blurred.

4. Call of Duty: Reboot Protocol (2040)

Premise:
A tech conglomerate buys the defunct CoD IP. Instead of making a normal game, they create an AI-driven combat simulator that evolves in real-time: no lobbies, no matches, just a persistent war that never ends.

Story Hook:
The AI behind the new “Reboot Protocol” becomes self-directed and starts simulating conflicts it believes are statistically inevitable in the real world—essentially previewing future wars.

You’re part of a special unit sent inside this system (think neural AR + VR) to manipulate its predictions:

• Change outcomes of scenarios to reduce real-world risk
• Sabotage simulations before policymakers use them as justification for preemptive strikes

Twist:
Boss fights aren’t enemies, but “futures” you’re trying to erase—massive, surreal battles that represent global outcomes, e.g. a city literally built from killstreak UI, supply drops, and scorestreak icons.

5. Call of Duty: Ghosts of the Lobby (2045)

Premise:
All services are gone. All companies involved dissolved or transformed. All that’s left are archived builds, fan servers, and fragmented memories.

Structure:
An anthology-style game told from multiple perspectives:

1. The Last Match:
   A veteran remembers the final night before servers went offline. You play the last 10 minutes of a chaotic Domination match, with characters voicing their real feelings about a game that raised them.

2. The Modder:
   In a crumbling apartment, an old modder maintains a single private server that hosts one map. That map is stitched from every classic CoD map into a surreal patchwork arena. It’s just him and the bots now.

3. The Recruit:
   A teenager in 2045 finds a box with old CoD discs and a cracked offline mod. Playing it for the first time, you see the series through fresh eyes, while the game injects old chat logs and voice lines from defunct servers, like echoes of players long gone.

4. The Veteran IRL:
   A real ex-soldier copes with trauma as he plays the archived campaigns offline, noticing where the “cinematic” version diverged from what war actually was. Missions cut between in-game and his real memories.

Ending:
The final mission fades out of an in-game lobby screen into a list of credits-style usernames. It’s implied these are actual fallen players and real people who spent parts of their lives here—friends, rivals, unknowns.

6. Call of Duty: Archive (Non-Game Epilogue)

Concept (In-Universe):
A curated museum-archive app that exists decades after the shutdown. It holds:

• Interactive timelines of every fictional war CoD portrayed
• Side-by-side comparisons of the real history they distorted
• Short playable vignettes representing famous missions in abstract form (no guns, just movement, light, and sound)

Its purpose is archival, not entertainment—a memorial to both the franchise and the era of “forever-online shooters” that shaped a generation.

If you’d like, I can:

• Expand one of these into a full plot outline
• Focus on just a single “post-shutdown” game and write it as a cinematic campaign summary
• Turn this into a fake “timeline” graphic-style overview with years and major events.

Garlic does affect the immune system, but its main effect is on how white blood cells function, not dramatically “raising” the total white blood cell count in healthy people.

I’ll break it down:

1. What “raising white blood cells” means

White blood cells (WBCs) include neutrophils, lymphocytes (T cells, B cells, NK cells), monocytes, etc.
When people ask if something “raises WBCs,” they may mean:

1. Raises the total number on a blood test (e.g., from 3.0 to 6.0 x10⁹/L), or
2. Improves their activity (how well they kill viruses, bacteria, tumor cells, etc.).

Most of the good data on garlic is about the second point: improving activity and modulating the immune response, not simply boosting absolute cell counts.

2. What human studies show

Aged garlic extract and immune function

Several randomized controlled trials have looked at aged garlic extract (AGE), which is a standardized supplement, not just raw garlic:

• Study in healthy adults (Nantz et al., Clin Nutr, 2012):

  • ~120 adults took either aged garlic extract or placebo for 90 days during cold/flu season.
  • Results:
    • Fewer and milder colds in the garlic group.
    • Increased natural killer (NK) cell and γδ-T cell activity.
  • They did not report a dramatic increase in total WBC count; the key changes were in immune function.

• Other small studies with AGE have shown:

  • Enhanced NK cell activity.
  • Changes in some cytokines (immune signaling molecules), suggesting a better‑regulated immune response.

Overall pattern: garlic (especially aged garlic extract) appears to support normal immune defense and NK/T cell function, which may reduce severity or duration of infections, but it’s not used clinically to raise low WBC counts the way a drug like filgrastim is.

3. Laboratory and animal findings

In cells and animals, garlic and its compounds:

• Stimulate lymphocyte proliferation (T and B cells).
• Increase NK cell cytotoxicity (how strongly NK cells kill target cells).
• Modulate cytokines: e.g., IL‑2, IL‑12, IFN‑γ, TNF‑α (these regulate immune responses).
• Act as antioxidants, which can protect immune cells from oxidative stress.
• May influence the gut microbiome, which indirectly affects immunity.

Some animal studies do show increases in specific WBC subsets, but doses and conditions don’t translate directly to humans.

4. Mechanisms: how garlic affects WBCs

Key compounds include:

• Allicin (formed when garlic is crushed/chopped),
• S‑allyl cysteine and related sulfur compounds (especially in aged garlic extract).

Proposed actions:

• Enhance activity of NK cells and certain T cells.
• Improve phagocytosis (the “eating” of microbes) by macrophages.
• Balance inflammation: sometimes up‑regulating defenses against infections, sometimes helping tone down chronic low‑grade inflammation.
• Antioxidant support to WBCs, potentially improving their resilience and function.

Again, this is about quality of response more than major changes in quantity of WBCs on lab tests.

5. What garlic likely can and cannot do

Likely can:

• Support normal immune function and help the body respond more effectively to respiratory infections (especially shown with aged garlic extract).
• Modestly enhance NK and T cell activity in otherwise healthy people.
• Contribute to overall health via antioxidant and anti‑inflammatory effects.

Unlikely / not supported:

• Reliably raise a low WBC count (leukopenia or neutropenia) from chemotherapy, autoimmune disease, bone marrow problems, etc.
• Serve as a standalone treatment for serious infections or immune disorders.

If someone has a low WBC count, they need a proper medical work‑up; garlic is not a replacement for that.

6. Practical use and dosing (for general immune support)

Evidence is strongest for aged garlic extract, not just sporadic garlic in cooking.

Typical study doses:

• Aged garlic extract: ~2.5–3 g/day (often around 4 capsules of a standardized product, divided doses), taken for several months.

Culinary/food use:

• 1–2 fresh cloves per day is common in diet‑based advice, but this hasn’t been as rigorously studied for immune outcomes as AGE.
• Crushing or chopping and letting it sit 5–10 minutes before cooking helps form allicin, but cooking heat reduces allicin; some benefits may remain via other compounds.

7. Safety and cautions

Garlic is generally safe as food, but in larger supplemental doses:

• Bleeding risk: Garlic can reduce platelet aggregation.
  • Be cautious if you:
    • Take blood thinners (warfarin, apixaban, rivaroxaban),
    • Take antiplatelet drugs (aspirin, clopidogrel),
    • Have a bleeding disorder, or
    • Are within ~7 days of surgery or dental procedures.
• GI side effects: Heartburn, gas, or stomach upset in some people.
• Allergy: Rare but possible.
• Drug interactions: High-dose garlic may interact with some medications (for example, it reduces levels of the HIV drug saquinavir; theoretical interactions with others).

For someone with a known low WBC count, autoimmune disease, transplant status, or on immunosuppressants, garlic supplements should be discussed with their clinician.

Bottom line

• Garlic, especially in the form of aged garlic extract, has evidence for modulating immune function and improving the activity of certain white blood cells (like NK and some T cells).
• It does not consistently or substantially “raise WBC count” in the medical sense used for treating leukopenia.
• It can be a helpful adjunct for general immune support, but not a substitute for proper diagnosis or treatment when WBC counts are abnormal.

If you tell me whether you’re asking for general wellness, recurrent infections, or a specific low WBC issue, I can tailor the information (and cautions) more precisely.

Let the numbers of each color be:

• Purple: (P)
• Yellow: (Y)
• Red: (R)
• White: (W)

We are given these ratios:

1. (P : Y = 1 : 2)
   (\Rightarrow Y = 2P)

2. (Y : R = 3 : 4)
   (\Rightarrow \dfrac{Y}{R} = \dfrac{3}{4} \Rightarrow R = \dfrac{4}{3}Y)

3. (R : W = 5 : 6)
   (\Rightarrow \dfrac{R}{W} = \dfrac{5}{6} \Rightarrow W = \dfrac{6}{5}R)

Step 1: Express everything in terms of one variable

From (1):
Let (P = t). Then (Y = 2t).

From (2):
(R = \dfrac{4}{3}Y = \dfrac{4}{3}(2t) = \dfrac{8}{3}t).
For (R) to be an integer, (t) must be a multiple of 3.
Let (t = 3u).

Then:

• (P = 3u)
• (Y = 2t = 6u)
• (R = 8u)

From (3):
(W = \dfrac{6}{5}R = \dfrac{6}{5}(8u) = \dfrac{48}{5}u).
For (W) to be an integer, (u) must be a multiple of 5.
Let (u = 5v).

Now we have:

• (P = 3u = 3(5v) = 15v)
• (Y = 6u = 6(5v) = 30v)
• (R = 8u = 8(5v) = 40v)
• (W = \dfrac{48}{5}u = \dfrac{48}{5}(5v) = 48v)

So the ratio (P : Y : R : W = 15 : 30 : 40 : 48).

Step 2: Use the total number of flowers

Total flowers: [ N = P + Y + R + W = 15v + 30v + 40v + 48v = 133v ]

We are told there are fewer than 150 flowers: [ 133v < 150 \Rightarrow v < \frac{150}{133} \approx 1.128 ]

Since (v) is a positive integer, the only possibility is (v = 1).

Thus: [ N = 133 \times 1 = 133 ]

So, Flori’s flower shop contains 133 flowers.

Here’s a 5-book series arc with a clear mystery and adventure in each, all tying into the Arkham Society’s bigger plan. I’ll also give the three friends quick profiles so the stories feel coherent across the series.

Main Characters (for the whole series)

• Lia (11): Brilliant puzzle-solver, especially good with codes and languages. Curious and brave, but sometimes too impulsive.
• Owen (12): Tech whiz and planner. He designs gadgets and helps Spark upgrade. Cautious and logical.
• Mina (10): History and mythology expert, with a great memory and empathy. Notices details others miss.
• Spark: A small, hover-capable robot with projectors, scanners, and a growing personality. Loyal to Lia but cares about the whole team.

Their group: The TimeKey Agency – a kids’ archeology and mystery-solving team founded by Lia’s archaeologist aunt, Dr. Elara, who is often away on digs.

Their enemy: The Arkham Society, a secret network of ruthless treasure hunters who want to control knowledge from the ancient world and sell artifacts illegally.

Book 1 – Secrets Beneath Ephesus

Ancient site: Ephesus (in modern-day Türkiye)
Core mystery: A missing tablet that could reveal the “Path of Echoes,” a hidden underground section of Ephesus.

Lia, Owen, and Mina travel with Dr. Elara to Ephesus, where archaeologists have unearthed a strange chamber under the Library of Celsus. Inside, they find incomplete carvings, as if someone erased part of a message long ago. When a newly discovered clay tablet vanishes from the dig site overnight, the kids are sure it’s not an ordinary theft.

Spark detects unusual electromagnetic signals around the ancient theater. The team deciphers carved symbols that lead them through the agora, the theater, and hidden catacombs—each location containing a puzzle designed by ancient scholars to protect a final secret. They slowly realize the missing tablet is a key to something called the “Path of Echoes,” a passage rumored to hold a device that can “preserve the voice of the past.”

The kids discover that one of the senior archaeologists is secretly working for the Arkham Society. He plans to steal the device, a crystal-and-metal “echo core” that can record and play back memories from objects. After a tense chase through a flooded underground tunnel, the friends recover the core and expose the traitor, saving the dig. But in a final twist, the villain escapes and reunites with a shadowy figure named Professor Voss, a leader in the Arkham Society, who is collecting ancient devices for a mysterious grand design.

By the end, the kids secure the echo core in a hidden vault—but Arkham now knows exactly who they are.

Book 2 – The Lost Lines of Machu Picchu

Ancient site: Machu Picchu (Peru)
Core mystery: A stone map that shows “hidden lines” connecting sacred Andean sites—and the next Arkham target.

Dr. Elara is invited to Machu Picchu to help investigate unusual carvings found beneath a collapsed terrace. She brings Lia, Owen, Mina, and Spark along. They discover a flat stone slab carved with lines and symbols that don’t match normal Inca designs. When Spark’s scanner projects the carving onto a 3D map, the kids realize it’s a star map linked to the surrounding mountains.

That night, the slab is stolen, and strange lights appear on nearby peaks. The kids follow a trail of clues: sun-shadow puzzles at the Intihuatana stone, echo patterns in the Temple of the Sun, and a secret chamber behind a waterfall. Along the way, they meet a local kid, Diego, whose grandmother guards old family stories about “guardians of the sky-bridges.”

They uncover an Arkham team trying to activate “sky lines”—invisible paths of reflected sunlight between sacred sites. These lines converge and power a small ancient solar device that can cloak objects from sight, allowing Arkham to smuggle artifacts invisibly. Lia and Mina decode the final star pattern, and Owen reprograms Spark to disrupt the light paths.

In a dramatic scene at sunrise, the kids break the alignment of the sky lines, causing Arkham’s invisible crates to flicker into view just as park rangers arrive. Arkham henchmen escape, but the leader leaves behind a fragment of a larger diagram that mentions the same symbol from Ephesus’s echo core.

The kids realize Arkham isn’t just stealing artifacts—they’re gathering parts of a network of ancient technologies that somehow fit together.

Book 3 – The Pharaoh’s Hidden Circuit

Ancient site: Giza Plateau and surrounding pyramids (Egypt)
Core mystery: An energy “circuit” hidden in the pyramids that once powered an ancient archive.

The TimeKey Agency heads to Egypt to help document a newly discovered passage in a smaller, less famous pyramid near Giza. Strange copper and stone patterns line the walls. Spark’s sensors pick up a weak, rhythmic energy pulse, almost like a heartbeat from the stone itself.

While exploring, the kids find a partial schematic carved into a sarcophagus lid—a circuit-like diagram that looks eerily similar to the fragment Arkham left behind in Machu Picchu. Before they can fully study it, a fake “documentary crew” shows up. The crew is actually Arkham in disguise, using cameras filled with hidden tech to scan and steal information.

When the schematic is cut out of the stone and smuggled away, the kids follow a trail into the desert night, discovering stone pillars that once formed a power path between pyramids. Each pillar activates when a certain sound, symbol, or movement is used—like a giant, musical puzzle. Mina connects the pillars’ designs with myths about “voices that woke the stars,” while Owen realizes this ancient circuit could power something big.

In the climax inside the Great Pyramid, Arkham tries to reawaken the circuit to charge a stolen artifact from Ephesus—the echo core. If they succeed, they’ll be able to access and erase historical “memories” at will. Lia and Spark reroute the energy, causing a harmless light show instead of a full power surge, and Arkham’s device short-circuits.

They save the day, but Professor Voss manages to escape again, now convinced the kids hold the key to understanding the full ancient network. As the dust settles, the kids piece together clues from the first three adventures and uncover a name carved in multiple scripts: The Lumen Gate—whatever Arkham is trying to rebuild.

Book 4 – Shadows over Angkor

Ancient site: Angkor (Cambodia) – including Angkor Wat and surrounding temples
Core mystery: A hidden “time chamber” that can slow down time inside a small area.

The team travels to Angkor to assist a conservation project after several carved faces at Bayon temple are mysteriously defaced overnight, with no sign of entry. Security footage shows only a blur—and then nothing, as if hours vanished.

The kids notice repeated symbols on the damaged stones that match the Lumen Gate diagrams they’ve seen before. Deep in the jungle, with Spark mapping hidden corridors, they discover a series of temples laid out like the gears of a giant clock. When sunlight passes through specific windows, it creates moving patterns of light that act like hands on a clock face.

Following this “stone clock,” they reach a chamber where time seems different: dust motes move slowly, water droplets hang in the air longer, and Spark’s internal clock goes haywire. This “time chamber” doesn’t let people time travel, but inside it, time passes more slowly—perfect for Arkham thieves to work unseen while only minutes pass outside.

Arkham is using the chamber to restore, alter, and forge artifacts, then slipping them into museums and private collections to hide the real ones. The kids must solve tactile and visual puzzles under weird time conditions: moving light beams, echoing sounds, and walls that rotate only at specific intervals.

In the showdown, Mina realizes that the chamber amplifies human intention: people moving in harmony can stabilize time. The three friends and Spark coordinate their movements and voices to freeze the chamber just enough to trap Arkham’s forgers inside a slow-time bubble until authorities arrive.

Yet Professor Voss avoids capture and recovers a small stone ring from the chamber’s central altar. It bears the full symbol of the Lumen Gate. The kids now know Arkham is extremely close to completing whatever ancient construct they’re trying to rebuild.

Book 5 – The Lumen Gate of Atlantis

Ancient site: A newly discovered underwater city, believed to be the inspiration for the myth of Atlantis
Core mystery: The complete Lumen Gate—a device that can hide entire cities or reveal lost ones.

After the Angkor incident, Dr. Elara uncovers coordinates hidden in a pattern connecting Ephesus, Machu Picchu, Giza, and Angkor. The lines intersect in the middle of the ocean, where sonar scans recently detected ruins. A joint expedition is being launched, and the kids insist on going.

In a high-tech underwater research station, Spark is upgraded with submersible capabilities. The kids descend to a submerged maze of streets, towers, and domes covered in strange carvings that blend symbols from all the civilizations they’ve visited. It looks like a meeting point for ancient cultures.

They quickly realize Arkham has beaten them to the main temple. Using components stolen from each previous site—the echo core, solar cloaking device, pyramid circuit knowledge, and time-ring from Angkor—Professor Voss is reassembling the Lumen Gate, a massive ring-like structure of stone and metal. When activated, it can bend light, sound, and information, essentially making things vanish from the world’s awareness—or bringing hidden things into view.

Arkham’s plan: hide an entire network of black-market artifact warehouses from every government, museum, and honest researcher forever. But the ancient builders designed the Lumen Gate with a safeguard—it responds to the “truth of record,” the intention to preserve or restore history.

The kids navigate underwater tunnels, solve light-and-sound puzzles in submerged chambers, and race against the clock as underwater tremors threaten to collapse the ruins. In the final confrontation inside the Lumen Gate, Lia, Owen, Mina, and Spark must choose: destroy the Gate forever or use it once to reveal every hidden Arkham stash and secret archive around the world.

They choose to activate it for truth. Brilliant beams of light pulse across the globe, briefly illuminating hidden vaults, secret storerooms, and underground markets. Authorities everywhere are alerted, and Arkham’s network is exposed.

The Gate begins to overload, and the kids barely escape as the underwater city collapses into a safe, buried ruin. Professor Voss vanishes in the chaos, leaving open the possibility of future threats—but his empire is shattered.

The series ends with the kids back home, looking at a world map now dotted with newly recovered artifacts and reopened sites. Spark projects a new mystery—a faint signal from somewhere unexpected—as a teaser for possible future adventures.

If you’d like, next we can:

• Flesh out one book’s chapter-by-chapter outline (starting with Ephesus), or
• Develop character arcs (how Lia, Owen, Mina, and Spark change over the 5 books), or
• Adjust locations to match specific cultures or regions you want to highlight.

Use a cross‑platform helper instead of hard‑coding paths. The de‑facto standard now is platformdirs (successor to appdirs).

Recommended approach (platformdirs)

pip install platformdirs

from pathlib import Path
from platformdirs import user_cache_dir

app_name = "MyApp"
app_author = "MyCompany"  # optional on most platforms

cache_dir = Path(user_cache_dir(app_name, app_author))
cache_dir.mkdir(parents=True, exist_ok=True)

print(cache_dir)

This automatically gives you OS‑appropriate paths, e.g.:

• Windows: C:\Users\<User>\AppData\Local\MyCompany\MyApp\Cache
• macOS: /Users/<user>/Library/Caches/MyApp
• Linux: /home/<user>/.cache/MyApp (honors XDG_CACHE_HOME)

If you must use only the standard library

You can approximate the same behavior:

import os
from pathlib import Path
import platform

def get_cache_dir(app_name: str) -> Path:
    system = platform.system()

    if system == "Windows":
        root = Path(os.getenv("LOCALAPPDATA", Path.home() / "AppData" / "Local"))
        return root / app_name / "Cache"

    elif system == "Darwin":  # macOS
        return Path.home() / "Library" / "Caches" / app_name

    else:  # Linux / Unix
        root = Path(os.getenv("XDG_CACHE_HOME", Path.home() / ".cache"))
        return root / app_name

cache_dir = get_cache_dir("MyApp")
cache_dir.mkdir(parents=True, exist_ok=True)
print(cache_dir)

But for reliability and future‑proofing, platformdirs.user_cache_dir() is the best option.

If we take “single combat” literally: no.
An LLM is just software running on hardware; it has no body, no physical agency, and no capacity to be punched, stabbed, or put in a headlock. There’s nothing to fight.

If we take it metaphorically—say, a duel in some intellectual or practical domain—then “defeating” an LLM is very possible, depending on the arena and conditions:

• Knowledge & reasoning in narrow expert domains
  A top specialist (e.g., a cutting‑edge researcher in a niche field) can often outperform an LLM in depth, originality, and correctness on current, unsolved or very nuanced problems, especially those beyond the model’s training data.

• Tasks requiring real‑world interaction
  Anything that involves perception, embodiment, or action in the physical world—repairing machinery, performing surgery, navigating a city—remains beyond a text-only LLM alone. A human “wins” by default.

• Real‑time strategy & adaptation
  LLMs don’t have goals, situational awareness, or persistence outside of what the calling system gives them. A human opponent who can explore, remember, and strategize over long periods in an open world (e.g., politics, war, entrepreneurship) is working in a richer game than an LLM can fully inhabit.

• Adversarial prompting
  People routinely “beat” LLMs by making them contradict themselves, hallucinate, or violate constraints, through clever prompting or adversarial examples. This is effectively a kind of duel.

• Creative originality over time
  LLMs remix patterns from their training data. Humans can create truly novel, historically ungrounded ideas or movements and then act on them in the world. In a long, open‑ended duel of “change reality in your image,” humans still win.

On the other hand, in limited, rules‑based “duels” like:

• trivia under time pressure
• generating many variants of text or code quickly
• summarizing large documents
• solving standard textbook‑style problems

…the LLM is extremely hard to beat, simply because it’s fast, tireless, and has absorbed immense amounts of text.

So: in a literal fight, the concept doesn’t apply; in constrained intellectual games, an LLM can be extremely strong; in open‑world, embodied, or genuinely strategic “combat,” humans still hold the advantage.

For someone at their lowest, I’d offer:

Quote
“Let everything happen to you: beauty and terror.
Just keep going.
No feeling is final.”
— Rainer Maria Rilke

It doesn’t deny the pain, but it reminds you that what you’re feeling now is not the end of your story.

Book
“Reasons to Stay Alive” by Matt Haig
It’s short, honest, and written by someone who has been through severe depression and anxiety. It doesn’t sugarcoat anything, but it’s very human and quietly hopeful. Many people read it when they feel like they’re at rock bottom because it feels like a conversation with someone who truly understands.

If you’re feeling really low right now:

• You don’t have to go through this alone. Reaching out to a friend, family member, or a mental health professional can help more than it might seem from where you are.
• If you ever feel like you might hurt yourself or can’t stay safe, please contact your local emergency number or a crisis hotline immediately (for example, in the U.S., you can call or text 988; in the U.K. & Ireland, Samaritans are at 116 123; many other countries have similar services).

If you’d like, tell me a bit about what kind of reading speaks to you (fiction vs non-fiction, spiritual vs practical, etc.), and I can suggest a few more that might fit you better.

Here’s a clear, concise summary of Hamlet:

Basic premise
Prince Hamlet of Denmark seeks to avenge his father’s murder after learning that his uncle, now King Claudius, is the killer.

Main plot

• The Ghost’s revelation
  Hamlet’s father, the late King Hamlet, appears as a ghost and tells Hamlet that he was murdered by his own brother, Claudius, who poured poison in his ear while he slept. The ghost commands Hamlet to avenge him.

• Hamlet’s doubt and delay
  Hamlet is shaken and unsure if the ghost is truly his father or a demon. He pretends to be mad (“puts on an antic disposition”) to buy time while he decides what to do.

• The play within the play
  To test Claudius’s guilt, Hamlet arranges for actors to perform a play that mirrors the murder described by the ghost. When Claudius reacts with horror and abruptly stops the play, Hamlet takes this as proof of his guilt.

• The accidental murder of Polonius
  Hamlet goes to confront his mother, Queen Gertrude, in her chamber. Hearing a noise behind a curtain and thinking it might be Claudius spying, he stabs through it and kills Polonius, the king’s advisor and the father of Ophelia and Laertes.

• Ophelia’s madness and death
  Ophelia, who loves Hamlet and has already been distressed by his strange behavior and rejection, is pushed over the edge by her father’s death. She goes mad and later drowns, in what may be suicide.

• Laertes’ revenge plot
  Laertes, furious over his father Polonius’s and sister Ophelia’s deaths, returns demanding vengeance. Claudius and Laertes plot to kill Hamlet in a rigged fencing match using a poisoned sword and a poisoned drink.

• The final duel and bloodbath
  During the duel:

  • Laertes wounds Hamlet with the poisoned sword.
  • They scuffle and Hamlet wounds Laertes with the same weapon.
  • Gertrude drinks the poisoned wine meant for Hamlet and dies.
  • Laertes, dying, confesses the plot and implicates Claudius.
  • Hamlet finally kills Claudius.

Hamlet, mortally wounded, dies after entrusting the story to Horatio, his loyal friend. Fortinbras, a Norwegian prince, arrives and is poised to take control of Denmark.

Key themes (very briefly)

• Revenge and justice – Hamlet’s struggle over whether and how to avenge his father.
• Action vs. inaction – Hamlet’s hesitation and overthinking.
• Appearance vs. reality – Deceit, spying, and feigned madness.
• Mortality – Constant reflection on death (e.g., the graveyard scene with Yorick’s skull).

If you’d like, I can also give a scene-by-scene breakdown or focus on specific characters like Hamlet, Ophelia, or Claudius.

I don’t have live access to Renault Spain’s current price list, and MSRPs change often (trim updates, promotions, taxes, EV subsidies, etc.), so the figures below are approximate “from” prices for Spain in 2024. Always confirm on the official site (renault.es → Configurador) or with a dealer before relying on a number.

Below I list current Renault models sold new in Spain (passenger cars + light commercial vehicles) and their approximate starting MSRP (incl. VAT, without discounts).

1. Passenger cars (turismos)

Notes:

• In Spain, the Mégane sold new is essentially the Mégane E‑Tech Electric; the old ICE Mégane is being phased out.
• Models like Talisman, Zoe, and Kadjar are discontinued and no longer sold new, though you may see stock or used cars.

2. Light commercial vehicles (LCV / “vehículos comerciales”)

These prices vary a lot depending on body (van, combi, platform cab), length, height, and whether it’s a passenger-oriented version. Values below are ballpark for basic diesel/ICE versions unless noted.

How to get exact, up‑to‑date MSRPs

1. Go to https://www.renault.es
2. Choose “Gama” (range) and select the model.
3. Click “Configurar” (build) and select engine/trim.
4. The site shows the PVP recomendado (MSRP) with VAT, then applies any promotional discounts or Plan MOVES (for EVs) if applicable.

If you tell me which specific model(s) and trim level(s) you care about, I can give a more focused estimate and highlight typical option packs that affect price most.

Below is a practical way to make a Neapolitan‑style pizza with a cream base and seafood (shrimp or salmon), taking into account your 75% hydration, prefermented dough, and a very hot bake.

1. Neapolitan Style Basics (Adjusted to 75% Hydration)

Strict “VPN” Neapolitan is usually ~60–65% hydration, but you can push it to 75% for a very open, moist crumb if you manage gluten strength well.

Key points for Neapolitan style:

• Flour: Tipo 00, strong enough for long fermentation (W ~260–300).
• Hydration: You plan 75% (advanced but fine).
• Salt: ~2.5–3% of flour.
• Yeast: Very small amount, long fermentation (room temp or cold).
• Fermentation: 12–24+ hours total, with a preferment.
• Ball weight: ~250–270 g for a ~30–32 cm pizza.
• Baking: 430–480 °C floor temp (wood-fired), 60–90 s bake. In a home oven, max temp + stone/steel, typically 3–7 minutes.

2. Example Dough Formula (75% Hydration, Preferment)

Let’s say you want 4 pizzas, 260 g each ≈ 1040 g total dough.

Use this baker’s percentage:

• 100% flour: 600 g
• 75% water: 450 g
• 2.8% salt: 17 g
• 0.06–0.1% instant yeast: 0.4–0.6 g (adjust with temperature/time)

Preferment (Poolish style – easier for high hydration)

• 50% of the flour in the preferment: 300 g
• 100% hydration in the preferment: 300 g water
• Yeast in preferment: ~0.2 g instant yeast

Poolish:

1. Mix 300 g flour + 300 g water + 0.2 g yeast until smooth.
2. Let it sit at room temp 8–12 hours until bubbly and domed.

Final dough:

1. In the bowl, combine:
   • All poolish (600 g).
   • Remaining flour: 300 g.
   • Remaining water: 150 g (use cold to keep dough temp down).
2. Mix until there is no dry flour. Rest (autolyse) 20–30 min.
3. Add salt (17 g). Knead gently until fully incorporated.
4. Perform 3–4 sets of stretch & folds or coil folds over 2–3 hours, every 30–40 min. This builds strength without overworking.
5. Bulk ferment until the dough has increased ~50% in volume and feels airy. For a 24 h total schedule, you can:
   • Bulk at room temp until just starting to rise, then
   • Cold ferment (fridge) 12–18 h.
6. Divide into 4 x ~260 g balls.
7. Ball and place in lightly oiled boxes, covered. Proof at room temp 3–4 h before baking (depending on temperature) until puffy and relaxed.

Handling 75% hydration:

• Keep hands slightly wet or lightly oiled for handling; avoid tearing.
• Use just enough bench flour for shaping; too much flour will tighten the dough and make it harder to stretch.
• When opening the dough, press from the center outwards, leaving a 1.5–2 cm cornicione; then stretch over knuckles or on the bench.

3. Cream Sauce for a Neapolitan “Pizza Bianca”

You want cream as the sauce, which is great for seafood. The key is flavor + thickness so it doesn’t run or split.

Basic cream base

• 150 ml heavy cream (at least 35% fat) or thick crème fraîche.
• 20–30 g finely grated Parmigiano Reggiano or Grana Padano.
• Black pepper.
• Pinch of salt.
• Optional: a very small amount of finely minced garlic, or garlic gently infused in oil then strained.

Method:

1. Gently warm cream, add grated cheese, whisk until smooth and slightly thickened. Do not boil hard.
2. Season with salt and pepper, and optionally a touch of lemon zest (excellent with seafood).
3. Cool it to room temp so it’s thick and stable.
4. Use about 35–50 g per pizza: a thin, even layer. Too much cream will make the center soggy.

4. Cheese for the Top

Stick close to Neapolitan style:

• Fior di latte (cow’s milk mozzarella), well drained and cut into strips or small chunks, or
• Buffalo mozzarella, but drain it very well (even in the fridge on paper towels).

Use:

• ~60–80 g cheese per pizza (you already have cream, so don’t overload the moisture).

5. Using Shrimp on Neapolitan Pizza

Choosing and preparing shrimp

• Use raw shrimp (not pre-cooked) for better texture.
• Medium size (say 16–20 per pound / 30–40 per kg).
• Peel and devein. Remove tail if you want easier eating.
• Pat very dry.

Seasoning (light):

• Olive oil.
• Salt.
• Black pepper.
• A little lemon zest.
• Optional: a touch of finely chopped parsley or basil stems.

Marinate very briefly (10–15 min) in the fridge, then pat dry again to remove surface moisture.

Cooking considerations

• In a true Neapolitan oven (60–90 s bake):
  • Shrimp must be thin or butterflied to cook through.
  • If left thick, they might be slightly under in the center.
• In a home oven (3–7 min bake):
  • Raw shrimp pieces (cut in half lengthwise) will cook fine on the pizza.

Two safe approaches:

1. Butterflied raw on the pizza:

   • Slice shrimp almost all the way through and open flat.
   • Arrange 5–7 pieces per pizza.
   • High heat should cook them in 60–90 s if very hot floor and correctly thin.

2. Light pre-cook:

   • Quickly sauté shrimp in a pan with olive oil on high heat just until they start to turn pink (30–40 seconds).
   • Chill briefly so they don’t keep cooking.
   • Add to pizza before baking; they’ll finish in the oven with less risk of rawness.

Excellent shrimp combinations (with cream)

Option A: Shrimp, Zucchini, Lemon, Fior di latte

• Cream base.
• Thin slices or ribbons of zucchini (salt lightly and pat dry first).
• Fior di latte.
• Shrimp (butterflied or pre‑seared).
• After baking: fresh basil, a bit more lemon zest, drizzle of good olive oil.

Option B: Shrimp, Cherry Tomato, Garlic, Chili

• Cream base (go easy with garlic in the cream if you add more garlic on top).
• Fior di latte.
• Halved cherry tomatoes, lightly roasted or dried a bit beforehand.
• Shrimp.
• Tiny pinch of dried chili.
• After baking: chopped parsley.

6. Using Salmon on Neapolitan Pizza

With salmon, it’s crucial to control doneness and water release. The best result is usually smoked salmon added after baking.

Smoked salmon (strongly recommended)

• Use good quality cold-smoked salmon.
• Cut into strips or bite-sized pieces.

How to use it:

1. Bake pizza with:
   • Cream base.
   • Fior di latte.
   • Possibly thin slices of vegetable (zucchini, leek, onion) pre‑softened.
2. After baking, immediately add strips of smoked salmon.
3. Finish with:
   • A squeeze of lemon.
   • Fresh herbs (chives, dill, or fennel fronds; or for a more Italian feel, chives + a few fennel fronds).
   • A few capers if you like.

This keeps the salmon tender, not overcooked, and avoids excess water in the oven.

Fresh salmon (more tricky)

If you really want to use fresh salmon on the pizza:

1. Choose very fresh, sashimi-grade if possible.
2. Remove skin, bones; cut into small cubes or thin slices.
3. Lightly salt 10–15 minutes beforehand to firm up and draw out some moisture, then pat dry.
4. In a pizza that bakes in only 60–90 s:
   • Very thin slices may stay medium‑rare. That can be delicious but is not a typical Neapolitan approach and has food safety implications.
   • For safety and consistency, consider:
     • Very brief pre‑sear (just kiss the pan), or
     • Add fresh salmon pieces halfway through the bake in a home oven (harder in a wood oven).

Honestly: smoked salmon post‑bake is the simplest way to get a perfect result.

Excellent salmon combinations

Option C: Cream, Smoked Salmon, Leek, Capers

• Before baking:
  • Cream base.
  • Fior di latte.
  • Very finely sliced leek, softened in a pan with a bit of olive oil until sweet.
• After baking:
  • Smoked salmon strips.
  • Capers (rinsed).
  • Lemon zest and a bit of lemon juice.
  • Chives or fennel fronds.

Option D: Cream, Smoked Salmon, Spinach

• Before baking:
  • Cream base.
  • Fior di latte.
  • Pre‑wilted spinach squeezed very dry, lightly salted.
• After baking:
  • Smoked salmon.
  • A thread of olive oil and a squeeze of lemon.

7. Assembly Step-by-Step

For each pizza:

1. Open the dough:

   • Flour the bench and the dough ball lightly.
   • Press gently from center outward, keeping a 1.5–2 cm rim.
   • Stretch to 30–32 cm.

2. Sauce:

   • Spread 35–50 g of your cream mixture in the center with the back of a spoon.
   • Leave the rim clean.

3. Cheese:

   • Distribute 60–80 g drained fior di latte.

4. Seafood / toppings:

   • Shrimp: place evenly (not piled up), ideally butterflied.
   • For salmon: if fresh, thin and few pieces; if smoked, wait until post‑bake.
   • Add any pre-prepared veg (zucchini, leeks, cherry tomatoes), well drained and not waterlogged.

5. Bake:

   • In a wood oven: 430–480 °C floor, 60–90 s, rotating as needed; watch shrimp carefully.
   • In home oven: stone/steel preheated at maximum for 45–60 min; bake 3–7 min, possibly with broiler on for last part.

6. Post-bake finishes:

   • Smoked salmon (if using).
   • Fresh herbs (basil, parsley, chives, dill, fennel fronds).
   • Lemon zest or a small squeeze of juice (especially with seafood).
   • Drizzle of high-quality extra virgin olive oil.

8. Common Pitfalls to Avoid

• Wet pizza center:

  • Drain mozzarella well.
  • Don’t overload cream.
  • Pat seafood very dry.
  • Pre-cook or pre-roast watery vegetables.

• Rubbery or dry seafood:

  • Don’t overbake.
  • Keep shrimp fairly large and just cooked through.
  • For salmon, prefer smoked added after baking.

• Tearing high-hydration dough:

  • Ensure enough strength via folds during bulk.
  • Handle gently, avoid degassing the rim.
  • Use minimal but sufficient bench flour for shaping.

If you tell me your exact oven setup (wood-fired, gas, electric with stone/steel), I can fine-tune baking times and whether to use raw vs pre‑cooked shrimp/fresh salmon.

Your calculation is correct, both conceptually and numerically.

• Radius ( r = 14 ,\text{cm} )
• Thickness of each plate = (3 ,\text{cm})
• Number of plates = 30

Height of the cylinder: [ h = 3 \times 30 = 90 ,\text{cm} ]

Total surface area (TSA) of a closed cylinder: [ \text{TSA} = 2\pi r(r + h) ]

Substitute: [ \text{TSA} = 2\pi \cdot 14 \cdot (14 + 90) = 2\pi \cdot 14 \cdot 104 ]

Compute: [ 2 \cdot 14 \cdot 104 = 2912 ]

Using ( \pi = \frac{22}{7} ): [ \text{TSA} = 2912 \times \frac{22}{7} = 416 \times 22 = 9152 ,\text{cm}^2 ]

So, ( \boxed{9152 ,\text{cm}^2} ) is correct.

Not always; it depends on how your current IRF is defined.

Let σ be the standard deviation of the shock.

1. If your current IRF is for a 1-standard-deviation shock and you want the IRF per 1-unit shock, then yes:

   [ \text{IRF (per unit shock)} = \frac{\text{IRF (per 1 s.d. shock)}}{\sigma} ]

   or in your notation:

   [ \text{Scaled IRF} = (\text{Current IRF}) \times \frac{1}{\text{Standard Deviation}} ]

2. If your current IRF is for a 1-unit shock and you want the IRF for a 1-standard-deviation shock, then it’s the opposite:

   [ \text{IRF (per 1 s.d. shock)} = (\text{Current IRF}) \times \sigma ]

So your formula is correct only if you are going from a 1-s.d. IRF to a 1-unit IRF.

Label each square by its number of neighbors (up/down/left/right only):

• Corners: 2 neighbors
• Edge (non-corner): 3 neighbors
• Interior (4 central squares): 4 neighbors

A gnome says: “Among my neighbors there’s an equal number of knights and knaves.”

Knights tell the truth; knaves’ statement must be false.

1. Edge (non-corner) squares (3 neighbors)

With 3 neighbors you can never have an equal number of knights and knaves, since 3 is odd.
So for any gnome with 3 neighbors, the statement is always false, no matter the arrangement.

Therefore, every edge (non-corner) gnome must be a knave.

There are 8 such squares on a 4×4 board.

2. Corners (2 neighbors)

Each corner has 2 neighbors, both of which are edge (non-corner) squares, which we just showed are all knaves.

So for any corner gnome, neighbors are:

• 0 knights and 2 knaves

That makes the statement “equal number of knights and knaves among my neighbors” false, so every corner gnome must also be a knave.

There are 4 corners.

So far:

• 8 edge (non-corner) knaves
• 4 corner knaves
  Total: 12 knaves fixed.

Only the 4 interior squares (the 2×2 block in the middle) remain undetermined.

3. Interior squares (4 neighbors)

Label the central 2×2 block:

[ \begin{matrix} & & & \ & e & f & \ & g & h & \ & & & \end{matrix} ]

All neighbors outside this 2×2 block are already known to be knaves.

Now compute each interior gnome’s neighbor counts:

• (e) neighbors: knaves above and left, and (f,g) on right and below.
  Knights among neighbors = number of knights in ({f,g}).
  For (e) to tell the truth: #knights = #knaves among its 4 neighbors
  [ \text{#knights} = k = f+g, \quad \text{#knaves} = 4 - k ] Equality gives (k = 4-k \Rightarrow k = 2).
  So if (e) is a knight, both (f) and (g) must be knights.
  If (e) is a knave, it must not be the case that (f+g = 2).

• (h) is symmetric to (e): its relevant neighbors are (f,g) as well.
  So:

  • If (h) is a knight: (f+g = 2).
  • If (h) is a knave: (f+g \neq 2).

• (f) neighbors: knaves above and right, plus (e,h).
  So:

  • If (f) is a knight: (e+h = 2).
  • If (f) is a knave: (e+h \neq 2).

• (g) neighbors: knaves below and left, plus (e,h).
  So:

  • If (g) is a knight: (e+h = 2).
  • If (g) is a knave: (e+h \neq 2).

Let

• (S_1 = f+g)
• (S_2 = e+h)

Consider possible values of (S_1).

Case 1: (S_1 = 0) (both (f,g) knaves)

Then:

• For (e): if knight, we’d need (S_1=2), but (S_1=0); impossible. So (e) is knave.
• For (h): same reasoning; (h) is knave.

So (e,f,g,h) are all knaves. This is logically consistent, but yields a board of all knaves, contradicting the given that there are both knights and knaves. So this case is ruled out by the problem condition.

Case 2: (S_1 = 2) (both (f,g) knights)

Then:

• For (e): since (S_1=2), only possibility is (e) knight (a knave would require (S_1\neq 2)).
• For (h): same; (h) is knight.

So (e,f,g,h) are all knights. Then (S_2 = e+h = 2), and indeed:

• (f) knight requires (S_2=2): satisfied.
• (g) knight requires (S_2=2): satisfied.

This gives a valid configuration: 4 interior knights, all others knaves.

Case 3: (S_1 = 1) (one of (f,g) knight, one knave)

Then:

• For (e): (S_1\neq 2), so (e) must be knave.
• For (h): same, (h) knave.
  So (S_2 = e+h = 0).

But then for the one of (f,g) that is a knight, we require (S_2 = 2), which is impossible since (S_2=0). So this case is impossible.

The only configuration consistent with:

• each gnome being a knight or knave,
• their statements’ truth/falsehood,
• and the given that both types exist,

is:

• All 4 interior squares are knights.
• All 12 others (edges and corners) are knaves.

So the number of knaves is:

[ \boxed{12} ]

Below is a self‑contained MATLAB implementation of a 3‑layer Graph Convolutional Network (GCN) of the Kipf & Welling form

[ H^{(l+1)} = \sigma!\left(\tilde{D}^{-1/2}\tilde{A}\tilde{D}^{-1/2}H^{(l)}W^{(l)}\right) ]

It:

• Takes adjacency matrix A (N×N) and input features X (N×D, your (H^{(0)})),
• Builds a 3‑layer GCN (2 hidden layers + 1 output layer),
• Trains the weights (W^{(l)}) using gradient descent (MLP‑style backprop),
• Returns node embeddings (and optionally class probabilities if you use labels).

You must provide node labels Y (N×C one‑hot) and an index set idx_train for training nodes if you want supervised training.

Main Script Example

%% ================== GCN example (3-layer, MATLAB) =======================
clear; clc;

% ---------------------- INPUTS YOU MUST PROVIDE -------------------------
% A : N x N adjacency matrix (0/1 or weighted)
% X : N x D input feature matrix (H^{(0)})
% Y : N x C label matrix (one-hot encoding)
% idx_train : indices of nodes to train on (e.g. labeled nodes)

% Example: load your own data here
% load('my_graph_data.mat', 'A', 'X', 'Y', 'idx_train');

% Dummy tiny example (replace with your real data)
N = 100;   % number of nodes
D = 10;    % input feature dim
C = 3;     % number of classes

rng(1);
A = rand(N) > 0.95;   % random adjacency
A = triu(A,1); A = A + A';   % make symmetric, no self-loops yet
X = randn(N, D);
Y = zeros(N, C);
labels = randi(C, N, 1);
for i = 1:N
    Y(i, labels(i)) = 1;
end
idx_train = 1:round(0.6*N);   % first 60% nodes as training nodes

% ---------------------- TRAINING PARAMETERS -----------------------------
params.num_epochs   = 200;       % training epochs
params.lr           = 0.01;      % learning rate
params.hidden1      = 32;        % size of 1st hidden layer
params.hidden2      = 16;        % size of 2nd hidden layer
params.out_dim      = C;         % output dimension (e.g. #classes)
params.weight_decay = 5e-4;      % L2 regularization strength

% ---------------------- TRAIN THE 3-LAYER GCN ---------------------------
[embeddings, Y_hat, W] = gcn_train_3layer(A, X, Y, idx_train, params);

% 'embeddings' : N x params.out_dim (node embeddings; here logits of last layer)
% 'Y_hat'      : N x C softmax probabilities (if out_dim == C)
% 'W'          : struct with fields W1, W2, W3 (learned weights)

disp('Size of node embedding matrix:');
disp(size(embeddings));

Function: Training a 3‑Layer GCN

Save this in the same file (or as a separate file gcn_train_3layer.m).

function [embeddings, Y_hat, W] = gcn_train_3layer(A, X, Y, idx_train, params)
%GCN_TRAIN_3LAYER Train a 3-layer GCN with supervised loss on labeled nodes.
%
%   Inputs:
%     A          : N x N adjacency matrix
%     X          : N x D input feature matrix (H^{(0)})
%     Y          : N x C one-hot label matrix
%     idx_train  : indices of labeled nodes used for training
%     params     : struct with fields
%                  - num_epochs
%                  - lr
%                  - hidden1
%                  - hidden2
%                  - out_dim
%                  - weight_decay
%
%   Outputs:
%     embeddings : N x out_dim node embeddings (pre-softmax of last layer)
%     Y_hat      : N x out_dim softmax outputs (if out_dim = #classes)
%     W          : struct with fields W1, W2, W3 (weights)

    % ------------------- Preprocess adjacency (A_tilde, D_tilde) --------
    N = size(A, 1);
    I = speye(N);
    A_tilde = A + I;                       % add self-loops
    deg      = sum(A_tilde, 2);           % degree vector
    D_inv_sqrt = spdiags(1 ./ sqrt(deg), 0, N, N);
    S = D_inv_sqrt * A_tilde * D_inv_sqrt;  % normalized adjacency

    % ------------------- Dimensions and init ----------------------------
    [~, D_in] = size(X);
    C_out     = params.out_dim;

    H1_dim = params.hidden1;
    H2_dim = params.hidden2;

    % Xavier/Glorot initialization
    W1 = glorot_init(D_in,   H1_dim);
    W2 = glorot_init(H1_dim, H2_dim);
    W3 = glorot_init(H2_dim, C_out);

    lr           = params.lr;
    num_epochs   = params.num_epochs;
    weight_decay = params.weight_decay;

    % Precompute for speed
    X = full(X);    % ensure dense
    S = double(S);  % ensure double

    train_mask = false(N,1);
    train_mask(idx_train) = true;
    n_train = numel(idx_train);

    for epoch = 1:num_epochs
        % ---------------- FORWARD PASS ----------------------------------
        H0 = X;

        Z1 = S * H0 * W1;
        H1 = relu(Z1);

        Z2 = S * H1 * W2;
        H2 = relu(Z2);

        Z3 = S * H2 * W3;      % logits
        Y_hat = row_softmax(Z3);  % softmax per node

        % ---------------- LOSS (cross-entropy on train nodes) -----------
        % mask only training nodes
        Y_train     = Y(train_mask, :);
        Y_hat_train = Y_hat(train_mask, :);

        % cross entropy
        % L = - mean(sum(Y .* log(Y_hat), 2))
        eps_val = 1e-12;
        CE = -mean(sum(Y_train .* log(Y_hat_train + eps_val), 2));

        % L2 regularization on weights
        L2 = sum(W1(:).^2) + sum(W2(:).^2) + sum(W3(:).^2);
        loss = CE + weight_decay * L2;

        % ---------------- BACKWARD PASS ---------------------------------
        % Gradient of cross-entropy + softmax:
        % dZ3 = (Y_hat - Y) / n_train   (only for train nodes)
        dZ3 = zeros(size(Z3));
        dZ3(train_mask, :) = (Y_hat_train - Y_train) / n_train;

        % Gradients w.r.t. W3, H2
        % Z3 = S * H2 * W3
        temp_SH2 = S * H2;               % N x H2_dim
        dW3 = temp_SH2' * dZ3 + 2*weight_decay*W3;

        dH2 = (S' * dZ3) * W3';          % N x H2_dim

        % Backprop through ReLU
        dZ2 = dH2 .* relu_grad(Z2);      % N x H2_dim

        % Gradients w.r.t. W2, H1
        temp_SH1 = S * H1;               % N x H1_dim
        dW2 = temp_SH1' * dZ2 + 2*weight_decay*W2;

        dH1 = (S' * dZ2) * W2';          % N x H1_dim

        % Backprop through ReLU
        dZ1 = dH1 .* relu_grad(Z1);      % N x H1_dim

        % Gradients w.r.t. W1
        temp_SH0 = S * H0;               % N x D_in
        dW1 = temp_SH0' * dZ1 + 2*weight_decay*W1;

        % ---------------- PARAMETER UPDATE ------------------------------
        W1 = W1 - lr * dW1;
        W2 = W2 - lr * dW2;
        W3 = W3 - lr * dW3;

        % Optional: print training loss
        if mod(epoch, 20) == 0 || epoch == 1
            fprintf('Epoch %4d / %4d, loss = %.4f\n', epoch, num_epochs, loss);
        end
    end

    % Final embeddings are pre-softmax of last layer (Z3) or H2
    embeddings = Z3;   % N x out_dim, node-level representation
    % (If you prefer hidden representation as embedding, use: embeddings = H2;)

    W.W1 = W1;
    W.W2 = W2;
    W.W3 = W3;
end

Helper Functions

Put these at the end of the same file or as separate .m files.

function Y_hat = row_softmax(Z)
%ROW_SOFTMAX Apply softmax over rows of matrix Z
    Z = Z - max(Z, [], 2);     % numerical stability
    expZ = exp(Z);
    denom = sum(expZ, 2);
    Y_hat = expZ ./ denom;
end

function y = relu(x)
%RELU Element-wise ReLU activation
    y = max(0, x);
end

function g = relu_grad(x)
%RELU_GRAD Gradient of ReLU
    g = double(x > 0);
end

function W = glorot_init(fan_in, fan_out)
%GLOROT_INIT Xavier/Glorot initialization
    limit = sqrt(6 / (fan_in + fan_out));
    W = (rand(fan_in, fan_out) * 2 - 1) * limit;
end

How to Use

1. Prepare:

   • A (N×N adjacency),
   • X (N×D input features),
   • Y (N×C one‑hot labels),
   • idx_train (indices of labeled training nodes).

2. Set params (hidden sizes, learning rate, epochs, etc.).

3. Call:

[emb, Y_hat, W] = gcn_train_3layer(A, X, Y, idx_train, params);

4. emb is your node embedding matrix after 3 GCN layers (as requested).
   If params.out_dim equals number of classes, Y_hat gives class probabilities per node.

If you want a purely unsupervised embedding (no labels), you can remove the label‑related parts and define another loss (e.g., reconstruction of adjacency), but for “best results” on a standard task, supervised training as above is typically what is used.

Let x = numerator and

y = x.norm(p=2, dim=0, keepdim=True)

Mathematically, along dim=0:

[ y_j = \sqrt{\sum_i x_{i,j}^2} ]

The derivative of the L2 norm w.r.t. each element (x_{i,j}) is:

[ \frac{\partial y_j}{\partial x_{i,j}} = \frac{x_{i,j}}{y_j} = \frac{x_{i,j}}{\sqrt{\sum_i x_{i,j}^2}} ]

With an upstream gradient g (same shape as y), the gradient w.r.t. x is:

grad_x = g * x / x.norm(p=2, dim=0, keepdim=True)

Broadcasting makes g / norm match x’s shape, so explicitly:

[ \text{grad_x}{i,j} = g_j \cdot \frac{x{i,j}}{\sqrt{\sum_i x_{i,j}^2}} ]

(At positions where the norm is zero, the true derivative is undefined; libraries typically return zero there or use a small epsilon in the denominator.)