Stress states collapse to Mohr circles on the σₙ–σₛ plane. - Hydrostatic pressure appears as a lone point; - Uniaxial compression or tension yields a single circle rooted at the origin; - Confined axial and triaxial fields generate nested circles whose diameters equal principal differences; - Pure shear centers at zero mean stress; - Differential stress is simply σ₁ − σ₃; - Pore pressure p_f shifts every circle leftward to give effective stress. Principal matrices sit beside each plot. From the same constructions, tectonicists forecast crustal faults and mining engineers gauge tunnel stability.

Approximating the Heaviside step function & its derivative with sigmoids Top: Smooth approximations to H(x) = 0 (x < 0), 1 (x > 0) using sigmoid(x; σ) = 1 / (1 + e^{-σ x}) for σ = 1 (orange), 2 (green), 4 (red), 8 (purple). Larger σ → sharper step. Bottom: Their derivatives d/dx [sigmoid] = σ ⋅ sigmoid(x; σ) ⋅ (1 − sigmoid(x; σ)) which converge to the Dirac delta δ(x) as σ → ∞. This Enables gradient-based optimization in neural networks and physics simulations where the true step function is non-differentiable.

Numbers rarely sit exactly at their average - the standard deviation formula shows the typical distance they stray from it. Population: σ = √[∑(xᵢ − μ)² / N] xᵢ = elements in population μ = population mean N = population size Sample: s = √[∑(xᵢ − x̄)² / (n − 1)] xᵢ = elements in sample x̄ = sample mean n = sample size The sample version is applied by bank risk analysts to measure day-to-day swings in currency exchange rates.

Backpropagation in a simple neural network. This diagram walks through the full process: > Forward pass with sigmoid activations σ > Mean squared error loss E > Backward pass computing gradients ∂E/∂z, ∂E/∂a, ∂E/∂w, and ∂E/∂b Clearly shows how error flows backward to update weights and biases using the chain rule.

What's the latest with Felix lending? Over the past week, deposits across Felix Vanilla + CDP have grown from $573M to $645M, up by ~12.6%, driven by continued HYPE growth. Stablecoin deposits have remained steady around $95-100M. Borrow demand remains healthy across the platform, with USDC Flagship at 4.32% APY and USDH Flagship at 5.11% APY as of today. Across Felix Vanilla, borrowing has continued to increase alongside that growth. Total borrows now stand at roughly $122M, with 6.7K active positions across Felix lending markets. Most borrow positions remain well-collateralized, with 4,241 positions above 1.35 HF. Only 104 positions currently sit in the 1.00-1.20 HF buffer range, with collateral at risk of liquidation at roughly $2.9M, or about 0.8% of total collateral. As far as DaR + CaR today, we monitor debt at risk and collateral at risk through real time scenario testing across the vault suite. Under a 3σ collateral drawdown, modeled DaR is about $1.58M and CaR about $2.15M. Even a 5σ shock remains fully liquidatable. Our DEX + orderbook monitoring makes sure ≤ 3σ swings do not threaten solvency. Supply utilization across Felix Vanilla sits now over 91% ($122m assets borrowed of $134m assets lent out). If interested in lending to the borrower base on Felix and looking for support, feel free to reach out. More information to come on spot equities borrow/lend.

Nom nom, I wanna eat up the whole world hehe (っ˘ڡ˘ς) 🥤🥗🍔🍗🍟🥓 𝙑𝙖𝙧𝙚𝙨𝙖 𝙂𝙚𝙣𝙨𝙝𝙞𝙣 𝙄𝙢𝙥𝙖𝙘𝙩 𝙛𝙤𝙧 𝙈𝙖𝙮 𝙋𝙖𝙩𝙧𝙚𝙤𝙣 #原神# #GenshinImpact#

🌙 Tonight's thesis — picks frozen Monday Jul 27 The index frame: SPX band 7,371–7,421, lean CALLS (skew +0.08) — the tape earns a bullish tilt. Fed-liquidity read: neutral (z -0.4, 20d -0.0). Standing back from: Hyperscalers (-4.3%/5d), Software (-2.4%/5d), Power / DC Infra (-2.2%/5d) — longs there are discounted until the 5-day trend itself recovers (a one-day pause is a dead-cat, the worst state in our backtest). The top of the book, and why: - CVX CALL (risk-adj vote +1.4) — Net edge here — running into CVX's upcoming catalyst (buy-the-rumor), though Energy is soft. (also: MACD) - MCD PUT (risk-adj vote -1.1) — Net edge here — fading MCD's momentum (though Defensive is bid today). (also: Wall Position) - NFLX CALL (risk-adj vote +1.1) — Net edge here — running into NFLX's upcoming catalyst (buy-the-rumor), as money rotates into Growth Tech. (also: 3-Day Up Streak) - BRK-B CALL (risk-adj vote +1.0) — Net edge here — running into BRK-B's upcoming catalyst (buy-the-rumor). (also: Pre-Event Run-up) Risk posture: 33 calls / 35 puts screened (puts carry a ×1.25 evidence bar — the tape drifts up). Every vote here is risk-adjusted (σ+β), liquidity-taxed, factor-capped at 3 per correlated complex, and stripped of earnings coin-flips. High conviction means diverse agreement per unit of risk, not loudness. The trade: buy ~3:50 PM ET, sell ~9:40 AM ET. 📋 The full board — 33 bet-up / 35 bet-down, ranked in the card 🐲 $SPX #Stocks# #OptionsTrading#

🦋 Celebrate $SKHYB on Aster: Hold & Share a $15,000 Prize Pool Hold the stock. Use the stock. Deposit $SKHYB into your Aster Perp account with Multi-Assets Mode on. It counts as collateral at up to 90% of market value, so you can trade any perp market against it without selling the stock. $SKHYB Spot is also live on Aster. 📋 Campaign Details - Campaign period: 2026-07-15 10:00 UTC to 2026-07-22 10:00 UTC - Prize pool: $15,000 in $SKHYB ✅ How to Qualify - Enable Multi-Assets Mode - Hold at least $100 worth of $SKHYB in your Aster Perp account - Trade at least $1,000 in perp volume during the campaign period. Any market you want 🎯 How Rewards Work - Score = Σ ($SKHYB balance × holding hours). Size and duration both count - Individual reward = (your score ÷ total score of all eligible participants) × $15,000 - Only full hours count. A balance held for 2.5 hours scores as 2 - Rewards below $1 worth of $SKHYB are not distributed. - Per-participant cap: 3% of the pool 🔍 What are bStocks? bStocks are tokenized securities issued by BTECH Holdings Ltd (ADGM), backed 1:1 by the underlying shares held with a regulated custodian. A bStock is not direct ownership of the stock, and is not an offer, solicitation, or investment advice. bStocks are not for distribution in the US, to US Persons, or in any other restricted jurisdiction. Investing involves risk. The value of your investment may go down and you may not get back the amount invested. Full risk disclosures and restricted jurisdictions: Details:

🚨 Claude Code made me 6 trading bots in 15 mins In the US alone, emotional retail traders lost more than $1.8 billion on liquidations While billions of amateur traders were staring at charts, overtrading, and getting wrecked on fees, a quiet group of algorithmic traders treated prediction markets like a hyper-liquid data engine They didn't guess outcomes -> they knew the structural price gaps in advance Here is how they did it, and why manual trading is completely dead: It's all about removing emotion and deploying cross-market statistical arbitrage Linear Spread Cointegration Formula: S_t = P_P,t - β * P_K,t - μ Ornstein-Uhlenbeck Continuous Dynamics Formula: dS_t = θ(μ - S_t)dt + σ dW_t Euler-Maruyama Discretization (MLE Calibration) Formula: S_t_i = S_t_i-1 * e^(-θΔt) + μ(1 - e^(-θΔt)) + ε_t Level 1 Order Book Imbalance (OBI) Formula: I_t = (V_b(t) - V_a(t)) / (V_b(t) + V_a(t)) Volume-Weighted Micro-Price Prediction Formula: P_micro(t) = P_mid(t) + I_t * (Δspread / 2) Cross-Venue Predictive Signal Optimization Formula: ΔP_Kalshi(t + δ) = f(I_Polymarket(t), P_micro,Polymarket(t) - P_micro,Kalshi(t)) In the era of advanced AI, the winner is not the one who guesses the score, but the one who lets automated systems execute with absolute patience and discipline. AI does the hard parts now -> you don't even need a CS degree to build this The full behind-the-scenes live system build is now available to the public 📝