arXiv research

Extends Young integral to Hölder differential forms in arbitrary dimensions.

New method improves curvature estimates for stable surfaces.

We show that geometric integrals of the type $\int_Ωf\, d g^1\wedge \, d g^2$ can be defined over a two-dimensional domain $Ω$ when the functions $f$, $g^1$, $g^2\colon \mathbb{R}^2\to \mathbb{R}$ are just Hölder continuous with sufficiently large Hölder exponents and the boundary of $Ω$ has sufficiently small dimensio…

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemanni…

Introduces Fitzpatrick losses, tighter than Fenchel-Young losses.

Young investors, especially students, dominate Indonesian stock exchanges.

We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any kno…

Study uses NLP to analyze emotions and challenges of young people with IDD.

This paper studies Fenchel-Young losses, a generic way to construct convex loss functions from a regularization function. We analyze their properties in depth, showing that they unify many well-known loss functions and allow to create useful new ones easily. Fenchel-Young losses constructed from a generalized entropy, …

Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure.…

Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be formulated as geodesic problems in curved spaces and spacetimes, and thus solving the de…

We construct complexes $P_{1^n}$ of Soergel bimodules which categorify the Young idempotents corresponding to one-column partitions. A beautiful recent conjecture of Gorsky-Rasmussen relates the Hochschild homology of categorified Young idempotents with the flag Hilbert scheme. We prove this conjecture for $P_{1^n}$ an…

We provide a draft of a theory of geometric integration of rough differential forms which are generalizations of classical (smooth) differential forms to similar objects with very low regularity, for instance, involving Hölder continuous functions that may be nowhere differentiable. Borrowing ideas from the theory of r…

Over the past decades, numerous loss functions have been been proposed for a variety of supervised learning tasks, including regression, classification, ranking, and more generally structured prediction. Understanding the core principles and theoretical properties underpinning these losses is key to choose the right lo…

We present a novel algorithm, Westfall-Young light, for detecting patterns, such as itemsets and subgraphs, which are statistically significantly enriched in one of two classes. Our method corrects rigorously for multiple hypothesis testing and correlations between patterns through the Westfall-Young permutation proced…

Study identifies clusters of EU countries with similar young mortality patterns.

Categorifies a skein relation for links colored by one-column Young diagrams.

Counterexample shows state-constrained optimal control problems can have Young measure gaps.

For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls), describe their structure and give a formulas fo the volume of the biggest of these domains. This paper is an attempt to generalize the classical isoperimetric inequality for the volume of the convex hull…

De Rham theorem extended to Orlicz cohomology.

The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and …

Model predicts cannabis use disorder risk for adolescents and young adults.

New method uses FY loss for better inverse optimization.

HZ transform applied to knot polynomials reveals hyperbolic knot structures.

We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations of the set of natural numbers. The Schur functions form a complete system of com…

Gradient descent converges with arbitrary stepsize for separable data under Fenchel-Young losses.

This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.

Foundation for robust finance using rough path theory.

New conditions prevent gaps in optimal control problems.

AR app enhances young children's understanding of Wudhu.

We show that the triply graded Khovanov-Rozansky homology of the torus link $T_{n,k}$ stablizes as $k\to \infty$. We explicitly compute the stable homology (as a ring), which proves a conjecture of Gorsky-Oblomkov-Rasmussen-Shende. To accomplish this, we construct complexes $P_n$ of Soergel bimodules which categorify t…

We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.

Algorithm calculates stable multiplicities in cohomology of configuration spaces.

Paper proposes new loss functions for training energy networks.

The paper calculates colored Jones polynomials for specific link configurations.

We determine the optimal strategies for purchasing term life insurance and for investing in a risky financial market in order to maximize the probability of reaching a bequest goal while consuming from an investment account. We extend Bayraktar and Young (2015) by allowing the individual to purchase term life insurance…

Study on droplet flow on uneven surfaces, proving existence and properties.

In the paper we give a compendium about theory of connection. We think that this compendium will be useful for young relativists.

We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams.

New categorified homology expressions for torus knots and links.

For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A.…

In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…

We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1)…

Study identifies risk factors for subsequent suicide attempts in youth.

Young isolated neutron stars (INS) most commonly manifest themselves as rotationally powered pulsars (RPPs) which involve conventional radio pulsars as well as gamma-ray pulsars (GRPs) and rotating radio transients (RRATs). Some other young INS families manifest themselves as anomalous X-ray pulsars (AXPs) and soft gam…

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove …

Unified model learns joint and individual features from brain imaging data.

Math model helps bees decide between winter survival and raising young.