Health

Per-step and mean trophic transfer efficiencies from measured level values, with band grading, weakest transfer, and next-level projection.

Education

GFP reporter transfection scoring: efficiency = GFP+ / total × 100 with a Wilson 95% CI in single mode and per-replicate mean ± SD in replicate mode. Interpretation bands from excellent (≥70%) to low (<10%) with optimization hints. Wilson 1927 / Newcombe 1998 / Kim & Eberwine 2010 derived. Educational use only.

Development

Decode lexically sortable IDs losslessly with BigInt: ULID (Crockford base32), KSUID (base62), NanoID, MongoDB ObjectId, and Discord/Twitter/Sonyflake Snowflakes — with ISO timestamps, raw hex, bit-level field breakdowns and birthday-bound collision probabilities.

Health

Interpret the thyroid axis by pattern-reading TSH with FT4 and (optionally) FT3. Adult reference ranges: TSH 0.4–4.0 mIU/L, FT4 0.8–1.8 ng/dL (≈10–23 pmol/L), FT3 2.3–4.2 pg/mL (≈3.5–6.5 pmol/L). High TSH + low FT4 → overt primary hypothyroidism; high TSH + normal FT4 → subclinical hypothyroidism; low TSH + high FT4/FT3 → overt primary hyperthyroidism; low TSH + normal FT4 → subclinical hyperthyroidism, exogenous hormone, or resolving thyroiditis (check FT3 for T3 toxicosis); low/normal TSH + low FT4 → central hypothyroidism; high TSH + high FT4 → TSH-secreting adenoma or thyroid hormone resistance. Low FT3 with normal TSH/FT4 indicates low-T3 (non-thyroidal illness) syndrome. Units selectable for TSH, FT4, FT3. Derived from ATA 2014/2016, NACB 2002, Garber 2012, and MDCalc. Not medical advice.

Health

Calculate glucose/amino-acid/lipid delivery (grams and kcal), total and non-protein calories, the non-protein kcal:g nitrogen ratio and per-kg values from a parenteral nutrition prescription. Energy densities: dextrose 3.4 kcal/g, AA 4.0 kcal/g, lipid 20% ≈ 2.0 kcal/mL. Targets (ASPEN/ESPEN): 20–30 kcal/kg/day, protein 1.0–1.5 g/kg/day. This is a prescription-analysis aid, not a compounding recipe. Derived from ASPEN 2016, ESPEN 2019, McClave 2016, Mirtallo 2004. Not medical advice.

Health

Estimate the osmolality (mOsm/L) of a parenteral nutrition admixture to help choose peripheral vs central access. Sum-of-solute formula: Osm ≈ Dextrose(g/L)×5 + AA(g/L)×10 + Electrolytes. Thresholds: ≤ 900 peripheral; 900–1200 caution; > 1200 central. Lab-measured value is the gold standard. Derived from Mirtallo 2004, Pittiruti 2009, Dugan 2014. Not medical advice.

Health

Calculate Transferrin Saturation (TSAT) = Serum Iron / TIBC × 100% (matching units, µg/dL or µmol/L). Reference range ≈ 20–50% in men and 15–50% in women. TSAT < 20% (or < 15% in premenopausal women) indicates iron deficiency (iron-deficiency anemia from chronic blood loss, inadequate intake, malabsorption), and is highly specific when ferritin is also low. TSAT > 50% (> 45% premenopausal) indicates iron overload or ineffective erythropoiesis: hereditary hemochromatosis, thalassemia major, sideroblastic anemia, repeated transfusions, or excessive iron therapy. Note serum iron has diurnal variation (morning high, evening low) and is shifted by recent iron ingestion, infection/inflammation, and hepatic disease — interpret with ferritin and CRP. Derived from Camaschella Blood 2019, Guyatt 1992, and MDCalc. Not medical advice.

Text Processing

Line/word/char diff with ignore rules, three-way merge with conflict markers, and unified patch

Health

Predict the trough concentration Cmin from a measured peak concentration Cmax during therapeutic drug monitoring (TDM): Cmin = Cmax · e^(-kτ), where k = ln2 / t½ and τ is the time from the peak to the next dose. Inputs are the measured peak, the elimination half-life, and the dosing interval. Also reports the fraction of the peak remaining at the trough and the peak-to-trough drop. This tool takes a measured Cmax (the TDM workflow), unlike drug-half-life-dose (which derives C0 from Dose/Vd) and dosing-interval-designer (which outputs a dimensionless peak/trough ratio, not an absolute concentration). Valid for one-compartment first-order elimination with the peak measured post-distribution. Not medical advice.

Math & Numbers

Convert thermal resistance between K/W (kelvin per watt, SI base), °C/W (1 = 1 K/W, since Δ1 K = Δ1 °C exactly), and °F·h/BTU International Table (1 = 1.8956342 K/W). Converts via K/W to the target unit and lists the equivalent value in all three units for reference. Reference values: CPU heatsink ≈ 0.1–0.3, LED thermal path ≈ 5–20, natural convection ≈ 1 K/W.

Science

Propagate a spacecraft/satellite state vector (r₀, v₀) to time t₀+Δt under two-body gravity via the universal-variable (f-and-g) method, and derive the classical orbital elements

Math & Numbers

Convert thermal conductivity between W/(m·K) (watt per metre-kelvin, SI base, = W/(m·°C)), kcal/(m·h·°C) (1 = 1.1627778 W/(m·K)), and BTU/(hr·ft·°F) (1 = 1.7307347 W/(m·K)). Converts via W/(m·K) to the target unit and also lists the equivalent value in all three units for reference. Reference values: copper ≈ 401, aluminum ≈ 237, steel ≈ 50, water ≈ 0.6, air ≈ 0.026, insulation foam ≈ 0.03 W/(m·K).