The paper proposes a new co-training method using information theory.
problem Predicting future sensations from past ones.
method Introduces a co-training objective based on mutual information.
result The method improves mutual information between past and future sensations.
Confirmation bias leads to biased estimates in noisy data analysis.
problem Confirmation bias affects scientific conclusions in noisy data environments.
method Investigation of confirmation bias in Gaussian mixture models using K-means and EM algorithms.
result Estimates from algorithms are biased and resemble initial hypotheses, not the noise.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
The paper confirms two groups of gamma-ray bursts using a new nonparametric metric.
problem Determining the number of inherent groups in gamma-ray bursts.
method A new nonparametric interpoint distance-based measure, combined with clustering methods.
result Confirms two groups of short and long gamma-ray bursts.
Paper predicts transaction confirmation time in Ethereum blockchain using machine learning.
problem Estimating transaction confirmation time in Ethereum blockchain.
method Uses machine learning, specifically Random Forest Regressor and Multilayer Perceptron, to predict transaction confirmation time.
result Proposed model shows improved accuracy in predicting transaction confirmation time compared to statistical models.
The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or…
Procedure confirms covariate balance anytime from unlabeled data.
problem Ensuring covariate balance in sequential data.
method Time-uniform confidence sequences for continuous monitoring.
result Probability of false confirmation controlled.
Study confirms conjecture about Kähler metrics on smooth minimal models.
problem Behavior of constant scalar curvature Kähler metrics on smooth minimal models.
method Analysis of metrics in a neighborhood of the canonical class.
result Convergence to singular Kähler Einstein metric in the canonical class.
Study confirms asymptotic behavior of logarithmic balanced metric near infinity.
problem Asymptotic behavior of logarithmic balanced metric near infinity.
method Non-trivial refinement of tools from previous work.
result Partial confirmation of conjecture on asymptotic behavior.
The paper confirms a conjecture linking link bipyramid volume and Mahler measure.
problem Link bipyramid volume and Mahler measure relationship for alternating links.
method Using isoradial graphs and spanning trees on lattices, the authors confirm the conjecture for two examples and calculate five more.
result The conjecture is confirmed for specific examples of alternating links.
Paper confirms Whitehead's conjecture for aspherical 2-complexes.
problem Whitehead's conjecture about aspherical 2-complexes.
method Argument on ribbon sphere-links, generalized for aspherical 2-complexes.
result Whitehead's conjecture confirmed for aspherical 2-complexes.
Proves a local analytic Bertini theorem confirming a conjecture.
problem Analytic Bertini theorem in local generality.
method Full generality proof of the local analytic Bertini theorem.
result Confirms a conjecture by Boucksom in local analytic settings.
The AJ conjecture, formulated by Garoufalidis, relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been confirmed for all torus knots, some classes of two-bridge knots and pretzel knots, and most cabled knots over torus knots. The strong AJ conjecture, formulated by Sikora, relat…
A Gaussian mixture model improves generalization for long-tailed data.
problem Optimizing generalization for rare data in long-tailed distributions.
method Suggested Gaussian mixture model and comparison of linear vs. nonlinear classifiers.
result Nonlinear classifiers outperform linear ones for long-tailed data.
Numerical study confirms Brennan's conjecture for a counterexample to Thurston's K=2 conjecture.
problem Thurston's K=2 conjecture and Brennan's conjecture in planar domains. method Numerical analysis of a specific counterexample to Thurston's conjecture.
result The counterexample does not contradict Brennan's conjecture.
Mitigates confirmation bias in SSL by adjusting pseudo labels dynamically.
problem Confirmation bias in semi-supervised learning leads to errors in pseudo labels.
method TaMatch framework adjusts scaling ratio to debias pseudo labels and dynamically adjusts target distribution.
result TaMatch significantly outperforms existing methods in SSL tasks.
Improved county-level COVID-19 forecasting model using LSTM and data augmentation.
problem Accurately forecasting county-level COVID-19 cases to optimize medical resources.
method Adapted TDEFSI-LONLY model, utilized LSTM, data augmentation, and inter-county mixing.
result CLEIR-Net model provides better forecasts than TDEFSI-LONLY.
Study improves model robustness in noisy datasets.
problem Instance-specific label noise in robust classification tasks.
method Coordinated Sparse Recovery (CSR) method introduces a collaboration matrix and confidence weights to reduce generalization error.
result CSR and CSR+ significantly reduce generalization error compared to existing methods.
Perelman's proof confirmed, new method uses 4D topology.
problem Confirming the classical Poincaré conjecture.
method 4D topology, spun torus-knots, ribbonness, disk-chord system, Bing's result.
result Homotopy 3-sphere is diffeomorphic to the 3-sphere.
Local Clustering improves semi-supervised learning models.
problem Improving semi-supervised learning models with limited labeled data.
method Local Clustering (LC) method to mitigate confirmation bias in Mean Teacher (MT) model.
result Adding LC loss to MT improves model performance on semi-supervised benchmark datasets.
The paper confirms a conjecture about compact unitary manifolds with non-empty fixed points.
problem Bounding the dimension of compact unitary manifolds with non-empty fixed points.
method The approach involves confirming Kosniowski's conjecture for almost complex manifolds under specific weight conditions.
result The conjecture is confirmed for manifolds with specific types of weights.
Bayesian approach to selecting data for machine learning.
problem Iterative data selection in machine learning algorithms.
method Embedding data selection into decision theory and deriving Bayes-optimal criteria.
result Mitigates confirmation bias in data selection.
Researchers confirm conjecture for complex nilmanifolds in higher dimensions.
problem Confirming the conjecture for compact Hermitian manifolds with constant holomorphic sectional curvature.
method Focused on complex nilmanifolds, proving the conjecture for these specific manifolds.
result The conjecture is confirmed for complex nilmanifolds in higher dimensions.
Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.
problem Hamilton-Tian conjecture for specific Sasakian manifolds.
method Sasaki-Ricci flow, compact transverse Fano Sasakian 5-manifolds, klt foliation singularities.
result Confirmed Hamilton-Tian conjecture for compact transverse Fano Sasakian 5-manifolds.
Proves Juhl formulas for curved Ovsienko--Redou operators, confirming conjectures.
problem Formal self-adjointness of curved Ovsienko--Redou operators and their linear analogues.
method Proves Juhl type formulas for curved Ovsienko--Redou operators and their linear analogues.
result Confirms two conjectures of Case, Lin, and Yuan on formal self-adjointness.
Holomorphic maps of degree one are biholomorphic, confirming a partial order.
problem Understanding the partial order of holomorphic maps.
method Analyzing holomorphic maps of positive degree between compact complex manifolds.
result Holomorphic maps of degree one are biholomorphic.
Synthetic learning improves neonatal brain MRI segmentation robustness.
problem Challenges in neonatal brain MRI segmentation due to image contrast and anatomical variations.
method Synthetic learning model trained on few T2-weighted volumes, then enhanced with motion artifacts and over-segmentation.
result Synthetic learning robust to image contrast and improves segmentation of both T1- and T2-weighted images.
This work explains how linear representations in large language models arise from training objectives and gradient descent.
problem Understanding the origins of linear representations in large language models.
method A latent variable model to abstract and formalize concept dynamics, combined with analysis of the softmax cross-entropy objective and gradient descent.
result Linear representations emerge when learning from data matching the latent variable model, and this simple structure suffices to yield linear representations.
Studying Binomial and Gaussian return dynamics in discrete time, we show how excess volatility can be traded to create growth. We test our results on real world data to confirm the observed model phenomena while also highlighting implicit risks.
Gradient descent on LSE objectives implicitly performs EM, leading to collapse without volume control.
problem Gradient collapse in autoencoders without volume control.
method Introduced a single-layer encoder with an LSE objective and InfoMax regularization for volume control.
result Gradient--responsibility identity holds exactly; LSE alone collapses; variance prevents dead components; decorrelation prevents redundancy.
Anytime-valid confirmation of label-shift corrections
problem Small-batch scientific deployments with scarce labeled outcomes
method Conditional e-value and martingale-based rule
result Nonnegative martingale and anytime-valid confirmation rule
Study examines how COVID-19 affected India's exchange rates and stock market.
problem Impact of COVID-19 on India's financial markets during and after lockdown.
method Secondary data analysis using VAR models across different phases of lockdown and unlock.
result Increase in confirmed cases does not significantly affect exchange rate and stock market.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
The paper studies graphs minimizing Dirichlet energy with analytic boundaries, confirming a conjecture about singularities.
problem Understanding the singularities of area-minimizing currents with real analytic boundaries.
method Analyzing multi-valued graphs with real analytic interfaces that minimize Dirichlet energy.
result Dirichlet energy-minimizers with analytic boundary singularities are discrete in 2 dimensions, confirming a conjecture by B. White.
Paper confirms conjecture for specific Lie algebras.
problem Fino-Vezzoni conjecture on Lie algebras with abelian ideals of codimension two.
method Analyzes unimodular Lie algebras with abelian ideals of codimension two.
result Confirms the Fino-Vezzoni conjecture for this specific class of Lie algebras.
Totally nonnegative flag varieties are shown to be regular CW complexes.
problem The structure of totally nonnegative flag varieties.
method Confirmation through CW complex structure and homeomorphism of positroid cells.
result Totally nonnegative flag varieties are regular CW complexes.
Quantum framework explains human choices in ambiguity and risk.
problem Testing human choices in ambiguity and risk.
method Quantum-theoretic framework for decision-making under uncertainty.
result Quantum framework faithfully models human choices in ambiguity and risk.
The paper confirms a conjecture about the fundamental groups of ends of certain noncompact manifolds.
problem Understanding the fundamental groups of ends of noncompact manifolds with specific curvature properties.
method Analyzing the universal cover and using the concept of visibility manifolds.
result The fundamental group of each end of a manifold is almost nilpotent if its universal cover is a visibility manifold.
Pseudo-label selection affects semi-supervised learning performance.
problem Selection of pseudo-labeled data impacts semi-supervised learning's generalization performance.
method Embedding pseudo-label selection into decision theory, deriving a novel selection criterion based on posterior predictive.
result BPLS (Bayesian pseudo-label selection) outperforms traditional methods in overfitting-prone data.
Study confirms conjecture on extremal length of hyperbolic metrics.
problem Determining the extremal length of hyperbolic metrics on Riemann surfaces.
method Analyzes the topology of closed hyperbolic Riemann surfaces to find extremal lengths.
result Extremal length is topology-dependent and has a specific upper bound.
Research confirms a conjecture about complex manifolds with total Betti number three.
problem Understanding the minimal total Betti number of closed almost complex manifolds.
method Analyzing properties of almost complex manifolds and using topological results.
result The only simply connected closed complex manifold with total Betti number three is the complex projective plane.
Research confirms non-trivial knots in S^3 do not admit purely cosmetic surgeries.
problem Non-trivial knots in S^3 do not admit purely cosmetic surgeries.
method Analysis of JSJ-structures to confirm Gordon's conjecture.
result Connected sums of knots do not admit purely cosmetic surgeries.
Confirming operator characterization on smooth manifolds.
problem Characterizing an operator on smooth sections of tangent bundles.
method Using algebraic axioms and H^1(M, R) = {0} assumption.
result Operator can be characterized universally for any smooth manifold.
We confirm the square-root law of market impact on Apple Inc. using a large dataset.
problem Testing the square-root law of market impact on a single U.S. large-cap equity.
method Using a full market-by-order feed, we reconstruct metaorders and calibrate impact using the square-root formula.
result The square-root law is confirmed with a prefactor of 0.34, consistent with worldwide data.
Study confirms rough volatility in S&P500 options, with Hurst parameter 0.3.
problem Confirming rough volatility in financial markets using option data.
method Analyzed implied volatility approximations of spot volatility using S&P500 options.
result Found Hurst parameter of 0.3 for S&P500 options, slightly larger than historical data.
New method confirms Ricci iteration converges to Kähler-Einstein metrics.
problem Confirming the conjecture that the Ricci iteration converges to Kähler-Einstein metrics.
method Using Perelman's convergence theory for the Ricci flow, the article confirms the conjecture for the Ricci iteration.
result The Ricci iteration converges to Kähler-Einstein metrics, providing a new method of uniformization of the Riemann sphere.
The study confirms two cases of the convex body isoperimetric conjecture in the plane.
problem The least perimeter to enclose a given area inside a unit disk is greater than inside any other convex set.
method Examined symmetric domains and perturbations of the unit disk.
result Two cases of the convex body isoperimetric conjecture are confirmed.
The Strominger conjecture is confirmed for compact Hermitian manifolds in 2D and special higher dimensions.
problem Determining conditions for a Hermitian metric to be Kähler based on the Strominger connection's curvature.
method Analyzing the Strominger connection's holomorphic sectional curvature in compact Hermitian manifolds.
result The Strominger conjecture is confirmed in 2D and special higher dimensions.