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Showing 1411–1440 of 1709 reference entries

BiologyAlphaFold 3 predictions versus physical mechanism

AlphaFold 3 predicts biomolecular complex structures but reports limitations including clashes, stereochemistry errors and hallucinated regions.

Method
BiologyDiffusion-based design and independent validation

RFdiffusion generates proposed protein backbones and constrained designs.

Method
BiologyHDX opening energies and model assumptions

In the EX2 opening model, exchange rates constrain approximate opening free energies.

Method
BiologyMeasured protein landscapes: 2026 study

Ferrari and colleagues profile 5,778 small domains with multiplexed HDX-MS and compare 13 domains with site-resolved HDX NMR.

Empirical finding
BiologyDiffusion-driven instability and developmental patterns

Turing proposed that reacting and diffusing morphogens can destabilize an initially homogeneous equilibrium and generate patterned states.

Model
BiologyCell traction as an inverse mechanical problem

Traction microscopy infers forces from cell-induced substrate displacements using a substrate mechanics model.

Method
BiologyPredicting functional landscapes from structures

Predicting conformational free energies, kinetics and function from sequence/static structures remains an open research challenge.

Open question
BiologyProbabilistic immune-receptor histories

IGoR infers generative V(D)J models by considering alternative gene choices, deletions and insertions for each receptor sequence.

Model
BiologyGeneration probability versus immune selection

A receptor’s abundance or generation probability is not itself its antigen affinity.

Method
BiologyCalcium signals and calibrated spike inference

Calcium fluorescence is an indirect activity proxy, and spike inference depends on indicator dynamics, noise and the trained/calibrated model.

Method
BiologyGCaMP8 inference: 2026 benchmark

Rupprecht and colleagues benchmark GCaMP8 inference against simultaneous mouse-neocortical electrophysiology.

Empirical finding
BiologyAdult fly wiring: 2024 structural evidence

FlyWire reconstructs chemical-synapse wiring in a sampled adult female Drosophila brain using electron microscopy and proofreading.

Empirical finding
BiologyMICrONS structure–function evidence

MICrONS combines visual-response calcium imaging and dense electron-microscopy reconstruction in one mouse visual-cortical volume.

Empirical finding
BiologyForward evolutionary simulation and census timing

Forward simulators encode reproduction, mutation, recombination, selection and population regulation through a specified life cycle.

Model
BiologyNiche stabilization and neutral similarity

Niche differences and near-neutral fitness similarities can act concurrently in a competition–colonization model.

Model
BiologyEvolutionary synthesis and competing emphases

The 2014 point/counterpoint compares emphasis on developmental bias, plasticity, niche construction and broader inheritance with the view that evolutionary theory already integrates such evidence.

Model
BiologyIdentifying eco-evolutionary feedbacks

Ecological change and heritable trait change can influence one another, but parallel time-series changes do not identify their causal directions.

Open question
Earth & cosmosBayesian geophysical inverse problems

An inverse solution is a posterior distribution conditioned on observations, a forward operator, likelihood and prior.

Method
Earth & cosmosLinearized sensitivities and regularized resolution

Linearizing d=g(m) about m0 gives a sensitivity matrix J.

Method
Earth & cosmosSurface temperature retrieval and emissivity

Thermal radiance retrieval separates surface temperature from emissivity and atmospheric absorption/emission using a specified forward model and ancillary inputs.

Method
Earth & cosmosSAR displacement and stereo topography

Differential radar phase constrains displacement along the satellite line of sight after orbital, topographic and atmospheric corrections.

Method
Earth & cosmosEnsemble data assimilation

Ensemble assimilation estimates forecast-error covariances from model realizations and updates the state using observations and their error model.

Method
Earth & cosmosClimate detection, attribution and model evaluation

Fingerprinting compares observed patterns with simulated responses to specified forcing and internal-variability covariance.

Method
Earth & cosmosErtel potential vorticity and baroclinic instability

Dry atmospheric Ertel potential vorticity combines absolute vorticity and the potential-temperature gradient per unit density.

Method
Earth & cosmosReal seawater thermodynamics and density

TEOS-10 seawater calculations distinguish Absolute Salinity, Conservative Temperature and sea pressure.

Method
Earth & cosmosNonlinear seawater mixing and cabbeling

Mixing waters can change density through nonlinear temperature/salinity dependence even when each source has the same density at the reference pressure.

Method
Earth & cosmosNonideal mineral phase equilibrium

A mineral assemblage at specified pressure, temperature and bulk composition minimizes Gibbs energy subject to component balance.

Method
Earth & cosmosMineral thermodynamic databases and elastic inference

Combining mineral phase fractions with elastic properties can predict seismic velocities, but equilibrium databases and shear-modulus data have separate calibration domains.

Method
Earth & cosmosDiffusion, cooling and isotope closure

An apparent thermochronological age depends on diffusion kinetics, grain geometry and cooling history.

Method
Earth & cosmosInherited components, discordance and isotope uncertainty

U–Pb discordance can reflect common lead, radiogenic lead loss, initial daughter disequilibrium or mixtures of differently aged growth zones.

Method
MethodSource checked

Linearized sensitivities and regularized resolution

Earth & cosmos

Research context

research method · conditional · As of 2026-10-10

Linearizing d=g(m) about m0 gives a sensitivity matrix J.

Key knowledge

Linearizing d=g(m) about m0 gives a sensitivity matrix J. Weighted regularization selects a model using data covariance and prior penalties; the resolution operator indicates which parameter combinations the observations recover, rather than a universal spatial resolution.

Values and equations

d-g(m0) ≈ J δm; δm_hat = (J^T C_d^-1 J + C_m^-1)^-1 J^T C_d^-1 (d-g(m0)); R = (J^T C_d^-1 J + C_m^-1)^-1 J^T C_d^-1 J

m0
Linearization point and Gaussian prior mean
δm
Parameter perturbation with zero-mean Gaussian prior
J
Jacobian of the forward model
C_d
Positive definite observation covariance
C_m
Positive definite Gaussian prior covariance
R
Local model-resolution matrix

Conditions and scope

  • Local linearization can fail for multimodal or strongly nonlinear inversions.
  • Compare residuals, withheld data and regularization sensitivity; seismic paths and gravity/magnetic kernels have different null spaces.
  • Finite-dimensional zero-mean Gaussian observation noise and perturbation prior δm~N(0,C_m), with m0 the prior mean and invertible stated precision. A different prior mean requires an offset term; the displayed formula follows locally by completing the square.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. The Bayesian Approach to Inverse ProblemsDashti and StuartReference guidearxiv.orgRead source

Evidence and review

The Bayesian Approach to Inverse Problems: Sections 1.1–1.3 and 4: likelihood, regularization, posterior approximation (selected source body inspected).

2026-10-10 · Bounded source check of the recorded statement and conditions. This does not certify a unique physical model, reproduce the cited study or replace independent branch review.

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research-earth-linearized-resolution
Revision
research.1
Structured reference record
Postgraduate & research reference