The paper extends the Manhattan curve concept to complex dynamics and studies its relation to multiplier spectra.
problem Understanding the growth rate of lengths of closed geodesics in complex dynamics.
method Defining and studying the Manhattan curve for holomorphic endomorphisms of CPk and relating it to multiplier spectra. result The Manhattan curve for two holomorphic endomorphisms is related to the correlation number of their multiplier spectra.
Study shows exact dimensionality and regularity of manifolds for specific groups.
problem Exact dimensionality and regularity of manifolds for relatively Anosov groups.
method Dynamical methods, including finite and mixing of Bowen–Margulis–Sullivan measures.
result Manifolds are C1-regular and growth indicator is strictly concave. The Manhattan curve connects metrics of hyperbolic groups, showing rigidity.
problem Understanding the relationship between different metrics on hyperbolic groups.
method Ergodic theory of topological flows and analysis of Patterson-Sullivan measures.
result The Manhattan curve is a straight line if and only if metrics are roughly similar.
In this paper, we extend the construction of pressure metrics to Teichmüller spaces of surfaces with punctures. This construction recovers Thurston's Riemannian metric on Teichmüller spaces. Moreover, we prove the real analyticity and the convexity of Manhattan curves of the finite area type-preserving Fuchsian represe…
This study uses Twitter to analyze traveler behavior in Manhattan.
problem Analyzing traveler behavior using social media data.
method Systematic method to extract displacement information from geo-tagged tweets.
result Twitter reveals unique demographics and travel behavior patterns.
A method for camera calibration using heatmap regression for fisheye images.
problem Accurate and robust camera angle estimation from fisheye images in the Manhattan world.
method Heatmap regression to detect directions of labeled image coordinates, simultaneous rotation and fisheye distortion recovery.
result Our method outperforms conventional methods on large-scale datasets and with off-the-shelf cameras.
Strict concavity proven for growth indicator function of certain groups.
problem Proving strict concavity of growth indicator function for specific groups.
method Smoothness of Manhattan hypersurface and critical-exponent map.
result Strict concavity of growth indicator function for relatively Anosov groups.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
Paper refines cross-lingual word embeddings using Manhattan norm.
problem Sensitivity of ℓ2 norm loss function to outliers in CLWEs. method Post-processing step using ℓ1 norm to improve CLWEs. result The ℓ1 refinement substantially outperforms state-of-the-art baselines. New method proves length spectrum rigidity in various geometric settings.
problem Length spectrum rigidity in geometric settings.
method Combination of dynamical systems and geometric group theory.
result Provides concise proofs and extends classical results.
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and WTH to model the Poisson noise or the Gaussian noise.…
The paper studies the correlation of Hilbert lengths for convex projective surfaces.
problem Understanding the correlation of Hilbert lengths for convex projective surfaces.
method Asymptotic formula for free homotopy classes with renormalized Hilbert length.
result The correlation number is not uniformly bounded away from zero but can be larger than a uniform strictly positive constant.
Geodesics and boundaries found for metric structures on hyperbolic groups.
problem Understanding the space of metric structures on hyperbolic groups.
method Outer automorphism invariant geodesic bicombing and boundary construction.
result Boundary contains well-known pseudo metrics and rigidity results.
Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online factorization and partition of implicit large-scale networks based on observati…
The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the "richest" countries are examined. Four types of "distances" are calculated.Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best charac…
Using publicly available traffic camera data in New York City, we quantify time-dependent patterns in aggregate pedestrian foot traffic. These patterns exhibit repeatable diurnal behaviors that differ for weekdays and weekends but are broadly consistent across neighborhoods in the borough of Manhattan. Weekday patterns…
A Discriminative Deep Forest (DisDF) as a metric learning algorithm is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. The case of the fully supervised learning is studied when the class labels of individual training examples are …
In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set…
Study analyzes Airbnb booking lead times during global crises using a new metric.
problem Disruptions in booking behaviors during global crises affect forecasting accuracy.
method Normalized L1 (Manhattan) distance to assess lead time divergences.
result Identified two-phase disruption: abrupt change at pandemic onset followed by partial recovery.
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
The rise in popularity of major social media platforms have enabled people to share photos and textual information about their daily life. One of the popular topics about which information is shared is food. Since a lot of media about food are attributed to particular locations and restaurants, information like spatio-…
Generative modeling on metric graphs using neural optimal transport
problem Deep generative modeling for continuous probability distributions on metric graphs
method Embedding graph into smooth ambient space, solving entropic Kantorovich problem, projecting back onto graph
result Generator is graph-supported
Study confirms fractional norms and quasinorms do not help overcome curse of dimensionality.
problem Overcoming the curse of dimensionality in machine learning.
method Systematic testing of fractional norms and quasinorms (p<1) on classification problems.
result Distance concentration behavior is qualitatively the same for all norms and quasinorms as dimensionality increases.
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Man…
This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states is characterized by the nonnegative rank of the Markov transition mat…
State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propos…
In this paper, a novel joint transmit power and resource allocation approach for enabling ultra-reliable low-latency communication (URLLC) in vehicular networks is proposed. The objective is to minimize the network-wide power consumption of vehicular users (VUEs) while ensuring high reliability in terms of probabilisti…
The article proposes modified Gower's coefficients for handling mixed type variables in nearest neighbor methods.
problem Handling mixed type variables in nearest neighbor methods, especially imputation and statistical matching.
method Suggests modifications to the Gower's distance for interval and ratio scaled variables to address unbalanced contributions and outlier sensitivity.
result Improved distance calculations reduce the unbalanced contribution of different variable types and attenuate outlier effects.
MuJAM learns traffic signal control policies that generalize to unseen intersections and traffic conditions.
problem Lack of transferability in reinforcement learning methods for traffic signal control.
method Model-based graph reinforcement learning with explicit coordination and generalization to both cyclic and acyclic constraints.
result MuJAM outperforms existing methods in zero-shot and larger transfer settings.
IG-RL learns adaptive traffic signals for any network, outperforming existing methods.
problem Adaptive traffic signal control for large networks with combinatorial state and action spaces.
method Graph-Convolutional Networks for decentralized, flexible control.
result IG-RL generalizes to new networks and traffic conditions without additional training.
Study of group actions on CAT(0) cube complexes, focusing on marked length spectra.
problem Comparing marked length spectra of group actions on CAT(0) cube complexes.
method Use of finite-state automata and thermodynamic formalism for suspension flows over subshifts of finite type.
result Prove that the Manhattan curve is analytic and convex, and a straight line if and only if marked length spectra are homothetic.
We prove contractibility of VR complexes for integer lattices up to dimension 5.
problem Contractibility of Vietoris-Rips complexes for integer lattices.
method Analyzing the homotopy type and contractibility of VR complexes for integer lattices.
result Contractibility of VR complexes for integer lattices up to dimension 5.
Extends Tian theorem to Vaisman manifolds for approximations.
problem Approximating Vaisman metrics by immersions/embeddings.
method Study Vaisman metrics on compact manifolds.
result Extend Tian's theorem to Vaisman manifolds.
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with (2n+s)-dimensional s−contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient c…
Study on a new type of manifolds that generalize almost C-manifolds.
problem Understanding weak nearly C-manifolds and their properties.
method Analyzing conditions for local Riemannian product structures and characterizing specific dimensions.
result Conditions for a weak nearly C-manifold to become locally a Riemannian product and characterization of specific dimensions.
Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.
problem Understanding the equivalence between stabilized convex symplectic manifolds and flexible Weinstein manifolds.
method Analyzing the homotopy type and symplectic properties of the manifolds.
result Stabilized convex symplectic manifolds are symplectomorphic to flexible Weinstein manifolds.
New class of complex manifolds defined, properties studied.
problem Understanding properties of complex manifolds.
method Introduced and studied wHHR manifolds, proved metric equivalence.
result Bergman and Kobayashi metrics are biLipschitz equivalent for wHHR Stein manifolds.
A selfsimiar manifold is a Riemannian manifold (M,g) endowed with a homothetic vector field ξ. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian ma…
Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.
problem Embedding 3-manifolds smoothly in 5-manifolds.
method Homotopy and small homotopy to achieve smooth embeddings.
result Locally flat embeddings are homotopic to smooth ones.
The study provides a structure theorem for a new class of noncompact 3-manifolds.
problem Understanding a new class of noncompact 3-manifolds.
method Proved a structure theorem for irreducible open graph manifolds.
result A canonical 'reduced' decomposition of irreducible open graph manifolds along embedded, incompressible 2-tori.
Condition for intersection of real flag manifolds in complex flag manifold.
problem Intersection conditions of real flag manifolds in a complex flag manifold.
method Condition given in terms of symmetric triad, antipodal intersection proven.
result Intersection of real flag manifolds is antipodal.
The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.
problem Exploring new types of manifolds in general relativity.
method Generalization of existing manifolds and construction of specific examples.
result Existence and properties of extended quasi-Einstein manifolds with solitons.
Conditions for flat manifolds as cusp cross-sections in arithmetic hyperbolic manifolds.
problem Determining when a flat manifold can be a cusp cross-section in arithmetic hyperbolic manifolds.
method Analyzing rational representations of holonomy groups and quasi-arithmetic manifolds.
result Conditions for a flat manifold to appear as a cusp cross-section in every commensurability class of arithmetic hyperbolic manifolds.
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.
Study on 3D manifolds with specific tensor structures and their properties.
problem Characterizing 3D Riemannian manifolds with tensor structures.
method Investigation of locally conformal Riemannian product manifolds and their associated structures.
result Conditions for additional structures to be parallel and properties of almost Einstein and Einstein manifolds.
New manifold type PNDP-manifold defined with Einstein warped product structure.
problem Defining manifolds with non-standard dimensions.
method Einstein warped product manifold with special base and fiber structures.
result PNDP-manifolds are Einstein warped product manifolds with specific base and fiber properties.
Optimal inequalities for systole, inradius, and volume in hyperbolic 3-manifolds
problem Establishing optimal inequalities relating systole, inradius, and volume in hyperbolic 3-manifolds
method Using systole-volume inequalities for extremal manifolds
result Extremal manifolds for systole, inradius, and volume are identified
The paper explores F-manifolds and metrics, constructing canonical structures.
problem Understanding relationships between F-manifolds and metrics.
method Construction of canonical flat F-manifolds and homogeneous Riemannian F-manifolds.
result Construction of a canonical flat F-manifold associated to an arbitrary Riemannian F-manifold.