Counting orbits for Anosov groups with specific functionals.
problem Counting orbits for relatively Anosov groups with linear functionals.
method Equidistribution results and previous counting results for periods.
result Generalization of earlier work on Anosov groups.
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 C2. result Asymptotic counting result for tripods on the torus.
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.
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.
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.
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.
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.
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.
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
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 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…
Study equidistribution for flows on geometrically finite convergence group actions.
problem Counting, mixing and equidistribution for flows on geometrically finite convergence group actions.
method Establishing results for finite BMS measures on flow spaces associated to geometrically finite convergence group actions.
result Results apply to flow spaces associated to relatively Anosov groups.
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…
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.
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.
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 …
Study on counting orbits and Poincaré series for specific hyperbolic metrics.
problem Counting orbits and analyzing Poincaré series for strongly hyperbolic metrics.
method Combining ergodic theory techniques with topological flows and symbolic dynamics.
result Obtained orbital counting results and described the domain of analyticity for Poincaré series.
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 (t−1) as the shape parameters of those at time t, which are linked …
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately IR2log22(I) non-zero counts. 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.
We study the combinatorial geometry of "lattice" Jenkins--Strebel differentials with simple zeroes and simple poles on CP1 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…
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.
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 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.
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.
We derive a sharp cusp count for finite volume complex hyperbolic surfaces which admit smooth toroidal compactifications. We use this result, and the techniques developed in [DiC12], to study the geometry of cusped complex hyperbolic surfaces and their compactifications.
The paper counts geodesic loops on surfaces without conjugate points.
problem Counting geodesic loops on surfaces of genus at least 2 without conjugate points.
method Proves asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points.
result Generalizes classical counting results and sector theorems for surfaces of strictly negative curvature.
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.
Anosov groups study matrix coefficients and orbit counting in symmetric spaces.
problem Anosov groups and their matrix coefficients in symmetric spaces.
method Asymptotic analysis of matrix coefficients and higher rank measures.
result Asymptotic behavior of matrix coefficients and orbit counting results.
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface S, and fix a number of points F on its boundary. We ask: how many configurations of disjoint arcs are there on S whose boundary is F? We find that thi…
Neuro# learns heuristics to speed up #SAT solvers.
problem Efficiently solving #SAT problems for large industrial instances.
method Learning branching heuristics to improve #SAT solver performance.
result Neuro# reduces step count and wall-clock time on diverse problem families.
Continuing the program of math.SG/0012067 and math.SG/0310450, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into reducible components. In cases where a corresponding analogue of the Gromov-Tau…
Paper tackles NP-complete subgraph isomorphism counting problem.
problem Counting subgraph isomorphisms in large graphs.
method Learning framework that augments representation learning architectures and iteratively attends pattern and target graphs.
result Scalable learning approach counts subgraph isomorphisms in linear time.
A Gauss diagram is a simple, combinatorial way to present a knot. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting (with signs and multiplicities) subdiagrams of certain combinatorial types. These formulas generalize the calculation of a linking number by coun…
Paper proposes a method to estimate uncertainty in counting tasks in medical imaging.
problem Estimating uncertainty in counting tasks for medical imaging.
method Proposes and tests a method for calculating predictive intervals as an output of a multi-task network.
result Demonstrates the effectiveness of the technique on histopathological cell counting and white matter hyperintensity counting.
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.
Warped DLMs improve forecasting for count time series.
problem Limited options for modeling count time series data.
method Introduces a semiparametric methodology using warping of Gaussian DLMs.
result Demonstrates improved forecasting capabilities for count time series.
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.
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension 2. We prove a Mertens' formula for the integer points over a quadratic imaginary num…
Quantum theory improves counting overlapping clusters.
problem Counting overlapping clusters in machine learning.
method Applied quantum theory using path integral technique.
result Quantum theory provides a robust statistical method for counting clusters.
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.
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
problem Handling high-dimensional and sparse binary and count data with traditional tensor decompositions.
method ENTED uses nonparametric Gaussian processes and sparse orthogonal variational inference to handle binary and count tensors.
result ENTED outperforms traditional methods in binary and count tensor completion tasks.
Let P be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various P-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
New bootstraps improve speed and accuracy for graph count functionals.
problem Efficiently counting subgraphs in large graphs.
method Developed two types of multiplier bootstraps: a fast, approximate linear one and a quadratic one for denser graphs.
result Both bootstraps provide valid inference and higher-order accuracy under different graph sparsity conditions.
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting su…