arXiv research

MaxSketch improves distinct counting in high-dimensional, noisy data streams.

Bayesian method estimates coverage from sketching imperfect data.

The paper explores privacy-preserving methods for counting unique elements in distributed settings.

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…

The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understood in the case of surfaces. For surfaces of revolution diffeomorphic to the sphere, a refinement of this problem was introduced by Borzellin…

We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be cons…

The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.

We tackle anomaly detection in sparse time series data.

New method counts boundary pieces in ReLU classifiers for better complexity measure.

The paper develops methods to estimate frequencies in large discrete data sets with improved coverage and robustness.

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex simple Lie group, we compute the dimension of apparent parabolic Teichm{ü}ller compon…

Minimal surfaces in lens spaces identified with specific counts.

Let $K$ be a polygonal knot in general position with vertex set $V$. A \emph{generic quadrisecant} of $K$ is a line that is disjoint from the set $V$ and intersects $K$ in exactly four distinct points. We give an upper bound for the number of generic quadrisecants of a polygonal knot $K$ in general position. This upper…

This article introduces vortex nerve complexes in CW (Closure finite Weak) topological spaces, which first appeared in works by P. Alexandroff, H. Hopf and J.H.C. Whitehead during the 1930s. A vortex nerve is a CW complex containing one or more intersecting path-connected cycles. Each vortex nerve has its own distincti…

The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference f…

Firms miscount their customers who stop buying without saying goodbye.

We extend asymptotic formulas for saddle connections on translation surfaces.

A faster Bayesian method for estimating spatial count data models.

By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced …

We propose a deep amortized clustering (DAC), a neural architecture which learns to cluster datasets efficiently using a few forward passes. DAC implicitly learns what makes a cluster, how to group data points into clusters, and how to count the number of clusters in datasets. DAC is meta-learned using labelled dataset…

We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\ge 3$ the number of…

We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in $\mathbb{C}^n$. Let $W_n$ be any sequence of virtual $S_n$-representations give…

We develop a recursive formula for counting the number of rectangulations of a square, i.e the number of combinatorially distinct tilings of a square by rectangles. Our formula specializes to give a formula counting generic rectangulations, as analyzed by Reading in [5]. Our computations agree with [5] as far as was ca…

New method groups genetic data into coherent topics for disease insights.

In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum $\mathcal{H} (α)$ of Abelian differentials. The first is the saddle connection Siegel-Veech constant $c_{\text{sc}}^{m_i, m_j} \big( \mathcal{H} (α) \big)$ counting saddle conne…

Anomaly detection identifies unusual malaria transmission patterns in Ghana.

Counting tripods on a flat torus using lattice point counting.

Enhanced symplectic quandle colorings detect causal structure in spacetime diagrams.

The study shows that symplectic Lefschetz fibrations can have infinitely many sections.

Flow Matching for count data improves sample quality and efficiency.

This paper defines ribbons and ribbon complexes in CW spaces and analyzes their topological properties.

Researchers found all embeddings of Kuratowski graphs on a double torus.

Finite resources limit false discovery rate control in structured hypothesis spaces.

New theorem counts curves on orbifolds.

A new method, Count-MORL, improves offline reinforcement learning by using state-action frequency.

Proposes a method to reconcile count time series forecasts.

Study geodesic paths on flat surfaces, comparing length and singularity counts.

Graph neural networks struggle with counting certain substructures in graphs.

Deviance-style normalization for sparse, jointly overdispersed count matrices

Counts arcs in surfaces, proving convergence of geodesic currents.

The paper proposes count echo state networks for forecasting graduate student enrollments.

Counted essential surfaces in a knot's exterior, finding a unique pattern.

The abstract reviews models for analyzing count data.

Counting objects in digital images is a process that should be replaced by machines. This tedious task is time consuming and prone to errors due to fatigue of human annotators. The goal is to have a system that takes as input an image and returns a count of the objects inside and justification for the prediction in the…

Proposes a robust EM algorithm for analyzing incomplete panel count data.

The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …

Calegari, Marques, and Neves count minimal surfaces in hyperbolic manifolds.

Quantum theory improves counting overlapping clusters.