arXiv research

Polynomial-time algorithm for inferring high-dimensional linear regression from a single sample.

New MIP approach for efficient change-point detection.

New knots found that resist trace detection.

GLIMPS tackles abundant outlier detection in matched subspace detection.

We use Nathanson's $g$-adic representation of integers to relate metric properties of Cayley graphs of the integers with respect to various infinite generating sets $S$ to problems in additive number theory. If $S$ consists of all powers of a fixed integer $g$, we find explicit formulas for the smallest positive intege…

Detects handlebodies and mapping class extensions using bordered Floer homology.

Study grid homology of diagonal knots, finding key terms related to prime factors and decompositions.

For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots of unity arise in this manner.

New conic quadratic formulations improve outlier detection in regression models.

The paper connects three integer sequences to a knot polynomial.

Defines a new Rasmussen invariant over integers and improves knot slice genus bounds.

We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve this integer program, we propose a column generation formulation where the prici…

Research extends geodesic length function study to three holed sphere.

The rising popularity of intelligent mobile devices and the daunting computational cost of deep learning-based models call for efficient and accurate on-device inference schemes. We propose a quantization scheme that allows inference to be carried out using integer-only arithmetic, which can be implemented more efficie…

Analyzes biased random walks and corrupted intervals in adversarial settings.

New method for probabilistic modeling of integer submodular functions.

Invariant detects triple points in sphere immersions.

Integrally splits L-spectra of integers into simpler components.

The paper explores orthogeodesics on hyperbolic surfaces and their integer traces.

Enhances social spam detection using multi-level dependency of relational sequences.

Defines action on knot spaces using cacti and cubes.

Unified framework for intersectionally fair AI models using MIO.

A new metric MSD detects bias in datasets efficiently.

For each integral homology sphere $Y$, a function $Γ_Y$ on the set of integers is constructed. It is established that $Γ_Y$ depends only on the homology cobordism of $Y$ and it recovers the Frøyshov invariant. A relation between $Γ_Y$ and Fintushel-Stern's $R$-invariant is stated. It is shown that the value of $Γ_Y$ at…

Magnitude of manifolds linked to Riesz energies and beta functions.

The paper studies algebraic integer relations and sequences converging to 4.

For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective va…

Generic groups satisfy a chain condition for subgroups.

Study Betti and Hodge numbers of solvmanifolds from integer polynomials.

We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree $k$ of the positive Hermitian …

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer co…

The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones polynomial can be computed by a suitable (almost tight) state sum and the solution of a …

A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is propo…

PReNet detects seen and unseen anomalies using pairwise relations.

A new method detects communities in multi-relational networks.

We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3) TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given.

Image partitioning, or segmentation without semantics, is the task of decomposing an image into distinct segments, or equivalently to detect closed contours. Most prior work either requires seeds, one per segment; or a threshold; or formulates the task as multicut / correlation clustering, an NP-hard problem. Here, we …

The Euclidean cone metrics coming from q-differentials on a closed surface of genus g > 1 define an equivalence relation on homotopy classes of closed curves declaring two to be equivalent if they have the equal length in every such metric. We prove an analog of the result of Randol for hyperbolic metrics (building on …

Detects model changes in data streams using Ddim.

We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the mul…

Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outl…

Relational Graph Neural Networks improve fraud detection in Super-Apps.

Let $n$ be a nonnegative integer, we use ribbon $n-$graph diagrams and the Yamada polynomial skein relations to construct an algebra ${\mathcal Y}_n$ which is shown to be closely related to the Temerley-Lieb Algebra. We prove that the algebra ${\mathcal Y}_2$ is isomorphic to some quotient of a three variables polynomi…

The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (-2,3,6n \pm 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (…

We use quantum invariants to define a 3-manifold invariant j_p which lies in the non-negative integers. We relate j_p to the Heegard genus, and the cut number. We show that j_$ is an invariant of weak p-congruence.

We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot,…

A new framework combines CNN and GRU for better structural damage detection.

The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its relation to the integer valued Seiberg-Witten invariant.