Counting tripods on a flat torus using lattice point counting.
problem Counting finite BPS webs in flat torus geometry.
method Lattice point counting techniques in .
result Asymptotic counting result for tripods on the torus.
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48 results for “counting”
Flow Matching for Count Datastat.ML
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
Counting curves on orbifoldsmath.GT
New theorem counts curves on orbifolds.
problem Counting curves on surfaces.
method Applied Mirzakhani's theorem to orbifolds.
result Curve counting theorem extends to orbifolds.
A new method, Count-MORL, improves offline reinforcement learning by using state-action frequency.
problem Improving offline reinforcement learning performance.
method Integrates count-based conservatism into model-based offline reinforcement learning.
result The learned policy is near-optimal and outperforms existing methods.
Proposes a method to reconcile count time series forecasts.
problem No formal framework for probabilistic reconciliation of count time series.
method Generalizes Bayes' rule for reconciling real-valued and count variables.
result Improves forecast accuracy for count variables compared to Gaussian reconciliation.
Study geodesic paths on flat surfaces, comparing length and singularity counts.
problem Comparing geometric length and singularity counts on geodesic paths.
method Apply counting limit laws to infinite graphs and then to flat surfaces.
result Statistical comparison of geometric length and singularity counts on geodesic paths.
Graph neural networks struggle with counting certain substructures in graphs.
problem Detecting and counting specific substructures in graphs.
method Study of graph neural networks' ability to count attributed graph substructures.
result Graph neural networks like MPNNs, 2-WL, and 2-IGNs have limitations in counting certain substructures.
Counts arcs in surfaces, proving convergence of geodesic currents.
problem Counting arcs of the same type in compact surfaces and related geometries.
method Derives convergence of geodesic currents to prove arc counts.
result Proves convergence of geodesic currents, leading to arc counting results.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollmentsstat.ME
The paper proposes count echo state networks for forecasting graduate student enrollments.
problem Forecasting graduate student enrollments from historical data.
method Developed hierarchical count echo state networks and compared them to Poisson autoregressions and negative binomial models.
result Hierarchical negative binomial based echo state network is the superior model.
Counted essential surfaces in a knot's exterior, finding a unique pattern.
problem Counting essential surfaces in a knot's exterior.
method Counted essential surfaces by genus, using Euler totient function. Showed normal surfaces are connected by counting their components. Used Agol, Hass, and Thurston's tools to convert component counting into orbit counting.
result Found a unique pattern in the number of essential surfaces by genus.
The abstract reviews models for analyzing count data.
problem Challenges in analyzing count data with standard methods.
method Review of generalized linear models and multinomial models.
result Fundamental connections between multinomial and count models.
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.
problem Missing reports in panel count data.
method Functional EM algorithm for non-parametric counting process mean function estimation.
result Robust to misspecification of Poisson process assumption and missing completely at random.
Calegari, Marques, and Neves count minimal surfaces in hyperbolic manifolds.
problem Counting minimal surfaces in hyperbolic manifolds.
method Using a laminar measure concept.
result An idea of a proof for counting minimal surfaces.
Better neural arithmetic logic units improve cell counting model generalization.
problem Neural networks struggle with high cell counts outside training data range.
method Introduced Neural Arithmetic Logic Units (NALU) for arithmetic operations in existing architectures.
result Improved cell counting accuracy for higher numeric ranges with better generalization.
Counts minimal tori in Riemannian manifolds with 6 or more dimensions.
problem Counting minimal tori in Riemannian manifolds.
method Introduces a function to count minimal tori and shows invariance under metric perturbations.
result The count function is invariant under metric perturbations.
In recent scene recognition research images or large image regions are often represented as disorganized "bags" of features which can then be analyzed using models originally developed to capture co-variation of word counts in text. However, image feature counts are likely to be constrained in different ways than word …
Estimates point counts in Teichmüller space for mapping class groups.
problem Counting points in Teichmüller space under mapping class group actions.
method Quantitative estimates with power saving error terms for Teichmüller metric balls.
result Effectivizes asymptotic counting results of Athreya et al.
Proves quaternionic analog of Cartan's theorem and counts arithmetic chains.
problem Understanding transformations of quaternionic hyperbolic spaces.
method Analyzes chain-preserving transformations and arithmetic chains in quaternionic Heisenberg group.
result Proves analog of Cartan's theorem and provides counting and equidistribution results.
Counting is a fundamental task in biomedical imaging and count is an important biomarker in a number of conditions. Estimating the uncertainty in the measurement is thus vital to making definite, informed conclusions. In this paper, we first compare a range of existing methods to perform counting in medical imaging and…
Study shows how to count and equidistribute cusped Hitchin representations with entropy gaps.
problem Counting and equidistribution of cusped Hitchin representations.
method Renewal theorem of Kesseböhmer and Kombrink applied to count and equidistribute.
result Entropy gaps at infinity allow for counting and equidistribution results.
Enhances psyquandle counting invariants using cocycles.
problem Improving the counting invariant of pseudoknots and singular knots.
method Defining enhancements via biquandle 2-cocycles and new functions.
result New polynomial invariants that are proper enhancements and not determined by the Jablan polynomial.
We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. These formulae were conjectured by Hubert & Lelièvre. We show that these countings admit quasimodular forms as generating functions.
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two possible 4-node graphlets. The number of each graphlet, called graphlet count, i…
Marked Graph Mosaicsmath.GT
Enhances knot counting using mosaic diagrams.
problem Counting and classifying surface-links and knots.
method Marked graph diagrams and mosaic numbers.
result Established bounds on mosaic numbers for surface-links.
The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series …
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also inefficient for large count values and requires averaging over many samples to reduce …
We propose scalable methods to execute counting queries in machine learning applications. To achieve memory and computational efficiency, we abstract counting queries and their context such that the counts can be aggregated as a stream. We demonstrate performance and scalability of the resulting approach on random quer…
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time as the shape parameters of those at time , which are linked …
We consider involutory virtual biracks with good involutions, also known as symmetric involutory virtual biracks. Any good involution on an involutory virtual birack defines an enhancement of the counting invariant. We provide examples demonstrating that the enhancement is stronger than the unenhanced counting invarian…
We consider an agent's uncertainty about its environment and the problem of generalizing this uncertainty across observations. Specifically, we focus on the problem of exploration in non-tabular reinforcement learning. Drawing inspiration from the intrinsic motivation literature, we use density models to measure uncert…
The paper counts mapping classes by Nielsen-Thurston type, finding growth rates for different subsets.
problem Counting mapping classes in Teichmüller space with different subsets.
method Introduced complexity length to measure negative curvature of curve complexes.
result Growth rates for finite-order, reducible, and multitwists subsets.
Novel Bayesian method for high-dimensional count data prediction.
problem Count data in high-dimensional settings requires feature selection.
method Pseudo-Bayesian framework with scaled Student prior and exponential weights.
result Strong performance compared to Lasso in various settings.
New tribrackets defined to count link homotopy invariants.
problem Counting invariants of link homotopy.
method Defined -tribrackets and showed their invariants.
result Counting invariants for certain tribrackets are trivial.
Skew Brace Enhancementsmath.GT
Enhances knot counting invariant using skew braces.
problem Counting invariant for virtual knots and links.
method Introduces new invariants using skew brace structures.
result New invariants not determined by the counting invariant.
We define enhancements of the quandle counting invariant for knots and links with a finite labeling quandle Q embedded in the quandle of units of a Lie algebra \mathfrak{a} using Lie ideals. We provide examples demonstrating that the enhancement is stronger than the associated unenhanced counting invariant.
In this paper we examine a possible reason for the LSTM outperforming the GRU on language modeling and more specifically machine translation. We hypothesize that this has to do with counting. This is a consistent theme across the literature of long term dependence, counting, and language modeling for RNNs. Using the si…
p-SNE embeds Poisson count data into low dimensions preserving structure.
problem Embedding high-dimensional sparse Poisson data into a low-dimensional space.
method p-SNE (Poisson Stochastic Neighbor Embedding) using KL divergence and Hellinger distance.
result p-SNE recovers meaningful structure in real-world count datasets.
For a geometrically finite group Gamma of G=SO(n,1), we survey recent developments on counting and equidistribution problems for orbits of Gamma in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere countin…
Uniform counting formulas for orthogeodesics in Kleinian groups converge.
problem Counting orthogeodesics in Kleinian groups converging to a limit.
method Spectral gap of the limit manifold and geodesic flow mixing property.
result Asymptotically uniform counting formulas for orthogeodesics.
We study the combinatorial geometry of "lattice" Jenkins--Strebel differentials with simple zeroes and simple poles on and of the corresponding counting functions. Developing the results of M. Kontsevich we evaluate the leading term of the symmetric polynomial counting the number of such "lattice" Jenki…
Graphical estimation of count time series dependencies.
problem Estimating dependencies between multivariate count time series.
method Parameter-driven generalized linear model with l1-type regularization and MCEM algorithm.
result Characterization of disease spread interdependence and sources/sinks in Greater Mumbai.
The study counts Salem numbers linked to arithmetic hyperbolic orbifolds.
problem Bounding the proportion of Salem numbers in arithmetic lattices.
method Using results on the distribution of Salem numbers, classical methods for counting Pythagorean triples, and Gauss' lattice-counting argument.
result Improved bounds on the proportion of Salem numbers and strong exponential growth of averages.
Counting spheres in hyperbolic space with effective methods.
problem Counting spheres in Apollonian and Kleinian packings.
method Spectral methods and orbit counting, extending Kontorovich and Lax-Phillips techniques.
result Best-known effective error rate for sphere packing counting problems.
We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Al…
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
Counting curves on surfacesmath.GT
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface , and fix a number of points on its boundary. We ask: how many configurations of disjoint arcs are there on whose boundary is ? We find that thi…