New proof limits Jones polynomial values for quasi-alternating links.
problem Limits on Jones polynomial values for quasi-alternating links.
method Proved finitely many values of Jones polynomial for quasi-alternating links of a given determinant.
result Only finitely many quasi-alternating links have a given Jones polynomial.
Study eigenvalues of knot covers to bound knot properties.
problem Bounding knot genera, dealternating number, and alternation number.
method Minimal positive eigenvalues of double branched covers over spanning surfaces.
result Eigenvalue bounds provide estimates for knot properties.
Inertial proximal gradient algorithm shows monotonically decreasing values.
problem Optimizing functions with inertia.
method Proximal gradient algorithm with alternated inertia.
result Algorithm with alternated inertia achieves monotonically decreasing functional values.
Framework for sorting with diverse value models and valued assignment examples.
problem Sorting with diverse value models and valued assignment examples.
method Optimization model for constructing preference model from valued examples, regularization techniques, and efficient algorithm.
result Improved predictive ability and flexibility in classification performance.
New theory shows how learning algorithms can create a bias towards negative outcomes.
problem Negativity bias in adaptive learning algorithms.
method Generalization of the Hot Stove Effect to settings with negative estimates leading to smaller sample sizes.
result Negativity bias persists even when negative estimates do not lead to avoidance.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Paper finds periodic patterns in colored Jones polynomial values.
problem Understanding periodicity in colored Jones polynomial values.
method Investigated polynomial values at specific roots of unity and -1.
result Periodic patterns in polynomial values at certain substitutions.
New asymptotic e-values improve inference by eliminating data-dependent scaling inefficiency.
problem Data-dependent scaling inefficiency in existing asymptotic e-values.
method Drawing on Bentkus's near-optimal concentration inequalities, introduce Bentkus-type asymptotic e-values.
result Bentkus-type asymptotic e-values consistently deliver sharper inference than existing alternatives.
We solve a century-old conjecture about Alexander polynomials of special alternating links.
problem Fox's conjecture about unimodality of Alexander polynomial coefficients.
method Proving a multivariate generalization of the Alexander polynomial is Lorentzian.
result Alexander polynomial coefficients of special alternating links form a log-concave sequence.
We depart from the usual methods for pricing contracts with the counterparty credit risk found in most of the existing literature. In effect, typically, these models do not account for either systemic effects or at-first-default contagion and postulate that the contract value at default equals either the risk-free valu…
Study sharpens unlinking number bounds for special alternating links.
problem Determining the exact unlinking number for special alternating links.
method Analyzes links in the 3-sphere, focusing on special alternating links and their crossing changes.
result Sharp lower bounds for unlinking number realized by crossing changes in alternating diagrams.
It is a well known result from Thistlethwaite that the Jones polynomial of a non-split alternating link is alternating. We find the right generalization of this result to the case of non-split alternating tangles. More specifically: the Jones polynomial of tangles is valued in a certain skein module, we describe an alt…
This paper finds all prime alternating knots with minimal warping degree two.
problem Finding knots with minimal warping degree.
method Examined all prime alternating knots and determined those with minimal warping degree two.
result All prime alternating knots with minimal warping degree two were identified.
Alt-GNNs improve travel mode choice modeling by integrating graph neural networks with GEV models.
problem Capturing alternative dependence in discrete choice models with predefined, symmetric, and uniform dependence.
method Introducing Alternative Graph Neural Networks (Alt-GNNs) that embed alternative dependence within a unified framework.
result Alt-GNNs significantly improve predictive performance over benchmark models in travel mode choice datasets.
Paper proves existence of minimal surfaces with alternating multiple zeta values.
problem Existence and properties of minimal surfaces.
method Complex analytic methods to deform Lawson surfaces.
result Area of minimal surfaces ξ1,g is monotonically increasing in genus g. Paper connects link determinants to polytopes and arborescence counts.
problem Determining properties of alternating links using polytopes.
method Analyzed the relationship between alternating link determinants and root polytopes, and spanning arborescence counts.
result The number of spanning arborescences equals the determinant of an alternating link.
We classify all knot diagrams of genus two and three, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic v…
Expressing L-polynomials coefficients in terms of multiple zeta values.
problem Expressing L-polynomials coefficients in terms of multiple zeta values.
method Expressing L-polynomials coefficients in terms of multiple zeta values.
result Every monomial in the Pontryagin classes appears with a non-zero coefficient, with the expected sign.
We present an alternative to the pseudo-inverse method for determining the hidden to output weight values for Extreme Learning Machines performing classification tasks. The method is based on linear discriminant analysis and provides Bayes optimal single point estimates for the weight values.
Proposes a method to classify with matrix-valued predictors using penalized likelihood.
problem Classification with matrix-valued predictors.
method Penalized likelihood method with Kronecker product decomposition for precision matrix estimation.
result Outperforms competitors in classification accuracy, even when assumptions are violated.
New invariant for special alternating links based on graph Laplacian.
problem Developing an invariant for special alternating links.
method Using the Laplacian matrix of the Tait graph, invariant is defined.
result A specific quadratic trace expression is invariant under flype moves.
New invariants derived from Seifert graphs help distinguish alternating links.
problem Distinguishing alternating links from each other.
method Introducing new quantities derived from Seifert graphs of reduced alternating link diagrams and proving they are link invariants.
result These new invariants can easily distinguish many different alternating links, even large and complicated ones.
Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.
problem Identify optimal alternative with minimal extreme tail risk from unknown heavy-tailed distributions.
method Data-driven sequential sampling policies to maximize likelihood of selecting the optimal alternative.
result Proposed methods outperform existing approaches in identifying the optimal alternative.
We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representat…
New invariants for Turaev genus one links identified.
problem Defining invariants for Turaev genus one links.
method Signature determination from Kauffman states and coefficients of Jones polynomial.
result Signature of Turaev genus one knots determined by specific components and crossings.
Alternative proof of Alexander polynomial trapezoid conjecture using dimers.
problem Alexander polynomial trapezoid conjecture for special alternating links.
method Dimer model approach to Alexander polynomial.
result Shorter and more accessible proof of Azarpendar, Juhász, and Kálmán's result.
Algorithm identifies correct hypothesis from alternatives in bandit problems.
problem Efficiently identifying the correct hypothesis from a finite set of alternatives in structured stochastic multi-armed bandits.
method Frank-Wolfe Self-Play (FWSP) reformulates the game as a saddle-point problem, using a differential-inclusion argument to prove convergence.
result Convergence of the game value for best-arm identification in linear bandits, with uniform global convergence to the optimal value.
New proof of trapezoidal property for Alexander polynomials of special alternating links.
problem Proving trapezoidal property of Alexander polynomials for special alternating links.
method Analyzing vector configurations from matroids and totally positive matrices.
result Alexander polynomials of special alternating links exhibit log-concavity and trapezoidal properties.
It is known that alternative links are pseudoalternating. In 1983 Louis Kauffman conjectured that both classes are identical. In this paper we prove that Kauffman Conjecture holds for those links whose first Betti number is at most 2. However, it is not true in general when this value increases, as we also prove by fin…
We consider sequential decision making problems for binary classification scenario in which the learner takes an active role in repeatedly selecting samples from the action pool and receives the binary label of the selected alternatives. Our problem is motivated by applications where observations are time consuming and…
New invariant distinguishes all knots up to 10 crossings.
problem Classical knot invariants struggle with distinguishing all knots up to 10 crossings.
method Introducing a pair of integer polynomials associated with checkerboard planar graphs of minimal diagrams.
result The invariant distinguishes all knots up to 10 crossings.
A new formula predicts stock prices using median instead of mean for skewed distributions.
problem Erroneous predictions from expected value in skewed stock price distributions.
method Uses geometric mean or median for log-normal distribution, especially for long-term outcomes.
result More realistic prediction for heavy-tailed distributions of stock price variations.
A new method selects variables for random survival forests using maximally selected rank statistics.
problem Random survival forests can be biased in selecting variables, especially for non-linear effects.
method Use maximally selected rank statistics for variable selection in random survival forests, comparing on p-value scale.
result The new method outperforms other approaches in prediction performance and computational speed.
A new PCR method using SVD with sparse regularization.
problem Lack of response variable information in traditional PCR.
method One-stage SVD approach with two loss functions and sparse regularization.
result Obtains principal component loadings with response variable information.
X.S. Lin and O. Dasbach proved that the sum of the absolute value of the second and penultimate coefficients of the Jones polynomial of an alternating knot is equal to the twist number of the knot. In this paper we give a new proof of their result using Khovanov homology. The proof is by induction on the number of cros…
Paper proposes an alternative method to price American options using HJM approach.
problem Price American options efficiently and accurately.
method Utilizes HJM technique to model term structure of volatility for equity markets.
result Proposes a new value function, stopping criteria, and stopping time for American options.
New method calculates knot and link properties using state codes.
problem Determining the unoriented genus and crosscap number of prime alternating knots and links.
method Encoding states as tuples and using them to compute genus and crosscap number.
result Computed values for all such links through 14 crossings and knots through 19 crossings, identifying patterns.
The paper provides guarantees for an alternating minimization algorithm in dictionary learning.
problem Dictionary learning problem of factorizing samples into a basis and sparse vectors.
method Alternating minimization procedure switching between ℓ1 minimization and gradient descent. result Local convergence guarantees for the alternating minimization algorithm under a new matrix infinity norm condition.
STAT-SVD method reduces high-dimensional data sparsity, achieving optimal estimation.
problem Sparse tensor singular value decomposition for high-dimensional data.
method STAT-SVD method with double projection & thresholding scheme.
result STAT-SVD provides sharp thresholding criterion and minimax rate-optimal estimation.
Boosts Q-learning by using value function bounds.
problem Efficiently solving new tasks using past experience.
method Derives double-sided bounds on optimal value function and uses them to update Q-function.
result Boosted training performance through alternative Q-function update method.
Study Alexander polynomials of special alternating links and generalize Fox's conjecture.
problem Distinguish special alternating links up to isotopy using polynomial invariants.
method Combinatorial and discrete geometric properties of Alexander polynomials of special alternating links.
result Generalized Alexander polynomials of special alternating links can be expressed in terms of volumes of root polytopes of unimodular matrices.
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes values in a certain representation space. In this paper, we show that any algebrai…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, fo…
Value selection reduces model size while maintaining accuracy.
problem Space efficiency in model size reduction.
method Two probabilistic methods based on information theory's metric: PVS and P + VS.
result Value selection achieves balance between accuracy and model size reduction.
Alternative to p-values using machine learning techniques.
problem Traditional p-values in regression settings.
method Leave-one-out bootstrap for prediction error, modified to measure variable importance.
result VIMP index provides interpretable measure of variable effect size.
The paper calculates a knot invariant for 3-braid knots.
problem Calculating the concordance invariant for 3-braid knots.
method Constructing cobordisms between 3-braid knots and torus knots.
result Explicit formulas and values for the invariant υ(K) for 3-braid knots. Valid p-value for bounded random variables without distributional assumptions.
problem Calibration of predictive algorithms in a distribution-free setting.
method Built a super-uniform p-value based on a concentration inequality.
result Super-uniform p-value is tighter than existing alternatives.