The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.
We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Particle Gibbs Sampling method, which alternately samples coalescent times conditioned on coalescent tree structures, and tree…
We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate o…
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
Study of first passage percolation on hyperbolic groups, showing velocity and coalescence.
problem Understanding the geometry and dynamics of first passage percolation on hyperbolic groups.
method Investigation of first passage times on Cayley graphs of Gromov-hyperbolic groups with i.i.d. random passage times.
result Existence and almost sure constancy of velocity in almost every direction on the boundary of the group.
Linear-cost unbiased estimates for complex models via couplings.
problem High-dimensional Bayesian models with crossed effects and matrix factorization.
method Coupled Gibbs samplers for linear computational cost.
result Unbiased posterior estimates at linear cost.
Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens when the charge difference is sufficiently small. However, Ristenpart et al disc…
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural re…
Develops a variational method for ultrametric phylogenetic trees.
problem Accurate and efficient approximation of posterior distributions over trees in Bayesian phylogenetics.
method Variational Bayesian approach based on coalescent times of a single-linkage clustering.
result Achieves competitive accuracy with significantly fewer gradient evaluations.
New definition of angular momentum avoids supertranslation ambiguity.
problem Supertranslation ambiguity in angular momentum calculations.
method Derived from quasilocal angular momentum and defined at null infinity.
result First supertranslation-invariant definition of angular momentum.
PipeDream-2BW accelerates large model training by 20x with minimal memory usage.
problem Training large models requires memory beyond single accelerator capacity.
method Pipeline parallelism, weight gradient coalescing, double buffering.
result Accelerates large model training by up to 20x.
The LORACs prior improves latent representation interpretability in VAEs.
problem Learning interpretable latent representations in VAEs.
method Flexible Bayesian nonparametric hierarchical clustering prior based on TMC for VAEs.
result Improved interpretability and practical performance of latent space.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Bayesian Neural Networks detect gravitational wave events with high accuracy and real-time potential.
problem Detecting and identifying the full duration of compact binary coalescence events in gravitational wave data.
method Integrating Bayesian approach into a CLDNN classifier that combines CNN and LSTM for event detection and uncertainty estimation.
result Successfully detected all seven BBH events in LIGO Livingston O2 data with high accuracy.
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…
Study models Indian stock market using hyperbolic geometry for market stability and volatility analysis.
problem Identifying market stability and volatility in the Indian stock market.
method Modelled as a heterogeneous scale-free network, embedded in a 2D hyperbolic space, applied coalescent embedding, hyperbolic kmeans, and Bollinger Band analysis.
result Clusters in the embedded network better represent market communities than Euclidean clusters, allowing for early detection of market changes.
We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebra…
Extends ML fairness to handle minority groups over time.
problem Limitations of existing fairness criteria.
method Performative Distributionally Robust Optimization.
result Improves fairness for minority groups over time.
Random trees emerge from geodesics in hyperbolic groups.
problem Understanding geodesics in hyperbolic groups.
method Surveying known properties and constructing random trees.
result Rich random geometry of emerging trees.
New RL approach builds short ancestral recombination graphs.
problem Building short ancestral recombination graphs (ARGs).
method Reinforcement Learning applied to genetic sequences.
result RL can build ARGs as short as heuristic algorithms.
In distributed function computation, each node has an initial value and the goal is to compute a function of these values in a distributed manner. In this paper, we propose a novel token-based approach to compute a wide class of target functions to which we refer as "Token-based function Computation with Memory" (TCM) …
Proposes a method to balance imbalanced image datasets using capsule-GAN.
problem Imbalanced datasets challenge deep learning techniques.
method Capsule-GAN, combining GANs and capsule networks, addresses imbalance by generating minority class samples.
result Improves learning from imbalanced data with fewer parameters.
Feature Squeezing is a recently proposed defense method which reduces the search space available to an adversary by coalescing samples that correspond to many different feature vectors in the original space into a single sample. It has been shown that feature squeezing defenses can be combined in a joint detection fram…
Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
problem Understanding the geometry and uniqueness of geodesics in FPP on hyperbolic groups.
method Analyzing random geodesic trees and exceptional directions in the context of FPP on hyperbolic groups.
result The set of exceptional directions has strictly smaller Hausdorff dimension than the boundary, and hence has measure zero.
We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above this space. These are real manifolds with corners. We then study the space of constant curvature metrics on this Riemann surface with prescribe…
GrateTile optimizes CNN feature map storage for efficient data access.
problem Efficient storage and access of sparse CNN feature maps.
method Divides feature maps into uneven-sized subtensors, compresses and stores them in a compressed yet accessible format.
result Average 55% DRAM bandwidth reduction with minimal indexing overhead.
We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i.d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic co…
The paper proves convergence of WDVV potentials and semisimplicity of Frobenius manifolds.
problem Convergence of WDVV potentials and semisimplicity of Frobenius manifolds.
method Analytical proof of integrable deformations of meromorphic connections and application to Frobenius manifolds.
result Convergence of semisimple formal Frobenius manifolds to analytic manifolds.
Transforming cylindrical packings into bicontinuous surfaces.
problem Understanding the early development of bicontinuous structures in plant plastids.
method Geometric modeling and computational simulations of cylinder packings.
result Specific cylinder packings with cubic symmetry transform into TPMS.
New algorithm learns mixtures of any constant number of Gaussians robustly.
problem Learning mixtures of Gaussians with robustness guarantees.
method New method using differential operations on generating functions to prove polynomial identifiability.
result First provably robust algorithm for mixtures of any constant number of Gaussians.
Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its propert…
Unified 3D R-matrices from quantum cluster algebra.
problem Constructing new solutions to the tetrahedron equation.
method Symmetric butterfly quiver, quantum cluster algebra, quantum dilogarithms, q-Weyl algebra.
result Unified 3D R-matrices from various sources.
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts exponential distribution of income between individuals. We also present new approach to…
Extends convex clustering to graph-structured data.
problem Handling graph-structured data with convex clustering.
method Formulates a convex objective and uses a proximal dual algorithm for efficient recovery.
result Demonstrates the effectiveness of the method on real-life datasets.
A new method for detecting anomalies in large, high-dimensional data streams using probabilistic forest models.
problem Challenges in detecting anomalies in large, high-dimensional data.
method Probabilistic Mondrian Pólya Forests for summarizing data and estimating underlying probability density.
result State-of-the-art performance with interpretable anomaly scores.
Study shows a universal local obstruction to the Samuelson condition for tangent Lagrangian 2-webs.
problem Obstruction to the Samuelson condition for tangent Lagrangian 2-webs.
method Local analysis of tangent lines and their intersection maps.
result A universal local phenomenon produces a nonzero mixed derivative, obstructing the Samuelson condition.
Deep neural network predicts black hole merger remnants with high accuracy.
problem Estimating the properties of black hole merger remnants.
method Trained on a dataset of binary black hole simulations, a deep neural network predicts mass and spin with high precision.
result The network predicts remnant black hole mass and spin with errors less than 0.04% and 0.3% respectively, and reduces errors in precessing cases to half.
Introduces Space Fortress to test RL algorithms' context and time sensitivity.
problem RL benchmarks lack context-dependent shifts and temporal sensitivity.
method Introduces Space Fortress as a new RL benchmark.
result Existing RL algorithms fail on Space Fortress due to context insensitivity and reward sparsity.
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self tran…
Study on network flow singularities, focusing on Type-0 singularities.
problem Understanding singularities in network flow evolution.
method Analysis of curvature evolution and junction behavior.
result Bounded curvature for Type-0 singularities in network flow.
Kolmogorov-Arnold network improves GW catalog posterior construction.
problem Efficiently constructing posterior distributions for GW catalogs.
method Using the Kolmogorov-Arnold network to create lightweight neural density estimators.
result Kolmogorov-Arnold network achieves superior interpretability and accuracy in posterior construction.
Paper classifies solutions to oriented associativity equations on flat F-manifolds.
problem Classifying quasi-homogeneous formal power series solutions.
method Introducing monodromy local moduli and solving Riemann-Hilbert-Birkhoff problem.
result Formal germs of flat F-manifolds are convergent if not strictly doubly resonant.
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms…
VFPred combines signal processing and machine learning for VF detection from short ECG signals.
problem Detecting Ventricular Fibrillation from short ECG signals.
method VFPred uses Empirical Mode Decomposition, Discrete Time Fourier Transform, and Support Vector Machine.
result VFPred achieves high sensitivity and specificity even from short 5-second signals.
The perennial problem of "how many clusters?" remains an issue of substantial interest in data mining and machine learning communities, and becomes particularly salient in large data sets such as populational genomic data where the number of clusters needs to be relatively large and open-ended. This problem gets furthe…
Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…