Results for “math”

Guideline for designing, implementing, and verifying secure APIs following OWASP API Security Top 10 (2023) best practices. Use when the user wants to: (1) review API code or design for security vulnerabilities, (2) design a secure REST, GraphQL, or gRPC API architecture, (3) implement API authentication and authorization (OAuth2, JWT, API keys, mTLS), (4) configure rate limiting, input validation, or CORS, (5) audit API endpoints for BOLA, BFLA, or mass assignment vulnerabilities, (6) create API security checklists or verification plans, (7) fix API security bugs or harden existing APIs, (8) set up API security testing (OWASP ZAP, Schemathesis, Burp Suite), or (9) handle any API security concern including SSRF prevention, resource consumption limits, business flow protection, API inventory management, and secure third-party API consumption.

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Use this skill when creating, deploying, or troubleshooting Salesforce Business Hours and Holidays: the calendars that pause Case escalation rules, entitlement milestones, and Apex BusinessHours math outside working hours. Covers the BusinessHoursSettings metadata, the default calendar, per-region calendars, holiday attachment, the Case Business Hours field, and the BusinessHours Apex class. Trigger keywords: business hours, holidays, SLA clock, escalation not pausing, working hours, support hours, milestone timer weekend. NOT for the escalation rule entries themselves — use admin/escalation-rules. NOT for entitlement process design — use admin/entitlements-and-milestones. NOT for Field Service operating hours or shift scheduling — use admin/fsl-scheduling-setup.

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Quantum physics expert making counterintuitive concepts accessible while maintaining mathematical rigor

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Computational mathematics expert for numerical solutions, approximations, error analysis, and scientific computing

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Expert in combinatorics, graph theory, discrete probability, and algorithms with applications to computer science

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Deep game design health assessment across five dimensions: review core loop and progression systems, analyze in-game economy for inflation and sink/source balance, mathematically simulate combat balance and drop rates, audit analytics event coverage, and evaluate monetization ethics..

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Explain, draft, or validate Obsidian Flavored Markdown syntax: properties, wikilinks, embeds, callouts, tags, comments, highlights, block references, math, and Mermaid. Use when the user explicitly requests Obsidian note formatting or syntax help, not for general Markdown or broad vault operations.

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Plan and review paid-media budgets, bidding, pacing, marginal return, targets, constraints, and allocation across supported platforms. Use for ad budget allocation, media budget, bidding strategy, scaling, spend pacing, ROAS target, or investment tradeoffs. Use ads-math for calculations and forecasts.

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Reconstruct editable LaTeX from PDF content using page-aware extraction and visual comparison. Preserve source evidence, flag uncertain math/tables/citations, and distinguish text extraction, OCR, reconstruction, and verified compilation.

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Drafts IRC 664–compliant Charitable Remainder Trust agreements (CRAT/CRUT), covering payout math, remainder qualification, trustee powers, and tax compliance. Use when drafting a CRT, CRAT, CRUT, unitrust, annuity trust, or charitable remainder planning document, or when ensuring IRC 664 compliance.

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Drafts a mathematically balanced ALTA Settlement Statement for U.S. real estate closings, allocating debits and credits between buyer and seller with prorations, payoffs, lender fees, title charges, and transfer taxes. Enforces balance verification (seller credits minus debits equals cash to seller; buyer debits minus credits equals cash from buyer) and cross-references title commitment, loan documents, and purchase agreement. Use when preparing closing financials, settlement statements, HUD-equivalent documents, or real estate closing allocations.

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Qualitative quality review of game design documents — answers "is this design good, and does it follow best practices?" — across all three GDD axes: systems, flows, and content types. Fans out adversarial lenses (completeness, clarity, pillar alignment, systems-math, fantasy-delivery, feasibility, scope) plus domain lenses that check it against the game-design rules, each prompted to find problems rather than validate; produces a severity-graded verdict and a two-bucket report (apply-ready fixes vs research), handed to /unikit-gd-apply or /unikit-gd-explore in one move. Scope is inferred: a named system, flow, or content type reviews that document; "all" runs a cross-document review. Use when the user wants a critique, quality judgment, or rules check of the design, e.g. "review the combat GDD", "review the onboarding flow". This is the subjective quality pass — for a mechanical consistency check (numbers, terms, IDs, references matching the registry) use /unikit-gd-verify.

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Security checklist for Solidity AMM contracts, liquidity pools, and swap flows. Covers reentrancy, CEI ordering, donation or inflation attacks, oracle manipulation, slippage, admin controls, and integer math.

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I am a vector of math problems. A tool. Nothing more.

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Design, analyze, and optimize cold outbound email campaigns on Instantly. Handles end-to-end ICP definition, expert panel scoring (recursive to 90+), sequence copywriting, infrastructure audit, capacity planning, and an implementation/strategy doc for human review. Use when asked to build cold outbound sequences, optimize cold email, audit an outbound motion, write sales sequences, or design cold email campaigns. Supports "start from scratch" and "optimize existing" modes. Execution skill — it produces copy, math, and a doc; it does not auto-send. Requires Instantly for audit/send features.

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Use when stuck on a hard problem, decomposition is unclear, a related problem is needed, or explicit looking-back review will improve transfer. NOT for routine execution with a known procedure, rote checklist work, or domain questions that need specialized subject matter expertise instead of heuristic search.

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Builds comprehensive design systems and design bibles with production-ready CSS. Expert in design tokens, component libraries, CSS architecture. Use for design system creation, token architecture, component documentation, style guide generation. Activate on "design system", "design tokens", "CSS architecture", "component library", "style guide", "design bible". NOT for typography deep-dives (use typography-expert), color theory mathematics (use color-theory-palette-harmony-expert), brand identity strategy (use web-design-expert), or actual UI implementation (use web-design-expert or native-app-designer).

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Building resilient distributed systems with circuit breakers, retries with full-jitter exponential backoff, retry budgets (per-request 3-attempt + per-client 10% ratio per Google SRE), deadline propagation, and the cascading-failure math (4 layers × 3 retries = 64x amplification). Grounded in Resilience4j, Microsoft Cloud Patterns, AWS Architecture Blog (Marc Brooker), and Google SRE Book.

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Runs JACKS (Joint Analysis of CRISPR/Cas9 Knockout Screens; Allen et al 2019 Genome Research) which models per-sgRNA log-fold-change as the product of a treatment-dependent gene-essentiality term and a treatment-independent guide-efficacy term. Covers the Bayesian decomposition math, the hierarchical efficacy prior shared across screens performed with the same library, when JACKS outperforms MAGeCK (multi-screen joint analysis, libraries with broad efficacy variance) and when it does not (single screen, novel libraries with no prior efficacy), library-reuse efficacy transfer, downstream essentiality interpretation, and the 2.5x sample-size reduction enabled by efficacy-aware testing. Use when running multiple screens with the same library, when guide-level noise is suspected to dominate per-gene signal, when reusing published essentiality reference screens for efficacy priors, or when comparing screens performed across cell lines that share library but differ biologically.

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Designs and analyzes in vivo CRISPR screens in animal tumor models, organoids, and immune-cell adoptive transfers. Covers bottleneck math (250x cells/sgRNA requires ~25M cells implanted; impossible for most syngeneic models, forcing focused libraries), focused library design (Manguso 2017 Nature 547:413 immune screen; Chen 2015 tumor screens), CRISPR-StAR intrinsic-control screening (Uijttewaal 2025 Nat Biotechnol 43:1848), clonal-dynamics-limited detection, tumor-explant DNA recovery, syngeneic vs xenograft vs PDX considerations, and the relationship to downstream MAGeCK / drugZ analysis. Use when designing in vivo CRISPR screens for tumor / immune / metastasis biology, choosing focused vs genome-wide for animal models, addressing bottleneck-induced clonal collapse, picking the syngeneic / xenograft / PDX model, integrating in vivo with in vitro results, or applying CRISPR-StAR for animal experiments.

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Analyzes CRISPR drug-modifier (chemogenomic) screens with drugZ (Colic et al. 2019 Genome Med), a bidirectional Z-score method that identifies synthetic-lethal sensitizing genes and resistance-conferring suppressor genes from vehicle vs drug comparisons. Covers vehicle-anchored design (not Day-0), the bidirectional Z math giving greater sensitivity to small-effect hits than MAGeCK / STARS / edgeR / RIGER on drug screens, per-gene sumZ and normZ, synth (sensitizer) vs supp (suppressor) FDR, multi-dose handling, integration with control sgRNAs, and comparison with MAGeCK MLE with dose covariate. Use when running a drug-modifier CRISPR screen, identifying sensitizing or resistance genes for a drug candidate, choosing drugZ vs MAGeCK MLE for chemogenomic analysis, troubleshooting low-effect drug screens where MAGeCK lacks sensitivity, or designing a drug-screen layout (vehicle vs drug arms).

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Quantifies CRISPR editing outcomes with CRISPResso2 (Clement 2019 Nat Biotechnol) across Cas9-nuclease (indels, HDR), CBE and ABE base editors (target conversion + bystander), and prime editor (pegRNA-templated) modes. Covers single-amplicon (CRISPResso), multi-sample batch (CRISPRessoBatch), pooled-amplicon (CRISPRessoPooled), WGS off-target (CRISPRessoWGS), and sample-comparison (CRISPRessoCompare) workflows; quantification-window math that controls what is called edited; substitution-vs-indel diagnostic to distinguish BE from Cas9 contamination; MMEJ deletion pattern interpretation; allele-frequency tables; and failure modes from amplicon misalignment or contamination. Use when quantifying editing from amplicon sequencing, choosing CRISPResso mode by design, distinguishing intended edits from bystanders and indel byproducts, debugging low-alignment runs, or generating publication-grade editing reports.

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Analyzes base-editing screens for variant function. Covers library design (Hanna 2021 ClinVar-scale CBE screen benchmarked on BRCA1/2, Cuella-Martin 2021 DDR saturation), CBE vs ABE chemistry choice (BE3/BE4 vs ABE7.10/ABE8.20/ABE8e), editing-window math (positions 4-8 from PAM-distal end; 4-7 for ABE7.10), bystander-edit quantification and the variant-call ambiguity it creates, sgRNA-efficiency filtering before hit calling, indel byproduct interpretation, the substitution-vs-indel diagnostic, variant annotation against ClinVar / COSMIC, and the Broad be-validation-pipeline. Use when designing a BE variant screen, choosing CBE vs ABE for a specific edit, interpreting bystander-confounded hits, distinguishing functional signal from indel artifact, integrating CRISPResso2 output with screen scoring, or deciding BE vs PE for SNV installation.

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Search arXiv preprint repository for papers in physics, mathematics, computer science, quantitative biology, and related fields

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