arXiv research

Novel algorithm solves optimal transport using evolving probability distributions and convolution.

Optimal transport learns Riemannian metrics for evolving probability measures.

Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolve according to a flow map. Such domains are said to be convecting. Here a transport theorem for nonconvecting domains evolving on an embedde…

We prove an optimal control on the time-dependent measure of a measurable set under a reparametrized Lagrangian mean curvature flow of almost calibrated submanifolds in a Calabi-Yau manifold. Moreover we give a classification of those Lagrangian translating solitons in $\mathbb{C}^m$ that evolve by this reparametrized …

dCMF models evolving patterns in multiway data with temporal dynamics.

Proposes standards for evaluating online machine learning methods in evolving data streams.

Kuroda and Nagai \cite{KN} state that the factor process in the Risk Sensitive control Asset Management (RSCAM) is stable under the Föllmer-Schweizer minimal martingale measure . Fleming and Sheu \cite{FS} and more recently Föllmer and Schweizer \cite{FoS} have observed that the role of the minimal martingale measure i…

A new method constrains PARAFAC2 for better pattern recovery.

Study mean curvature flow into evolving manifold with coupled flows.

New algorithms sample from complex path measures using neural networks.

Bayesian optimization of antibodies learns from immune system evolution.

This study examines whether the efficiency of cryptocurrency markets (Bitcoin and Ethereum) evolve over time based on Lo's (2004) adaptive market hypothesis (AMH). In particular, we measure the degree of market efficiency using a generalized least squares-based time-varying model that does not depend on sample size, un…

Establishes exponential contraction in Wasserstein distance on manifolds and flows.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any models that realistically cater to this phenomenon must exhibit two important p…

Paper tackles continuous transfer learning with evolving target domains.

We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangen- tial to the Ricci flow almost-everywhere along geodesics. To study spaces with geometric singularities, we consider this flow in the context of smooth manifolds with rough metri…

Study of filtering and smoothing in submanifolds of Euclidean space.

We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our model allows for contagious simultaneous jumps in credit ratings and provides flexib…

Model financial markets using information theory with a single parameter.

We consider some elementary aspects of the geometry of the space of probability measures endowed with Wasserstein distance. In such a setting, we discuss the various terms entering Perelman's shrinker entropy, and characterize two new monotonic functionals for the volume-normalized Ricci flow. One is obtained by a resc…

Stable topological summary captures evolving dependency structure in dynamic Bayesian networks.

The paper proves smooth convergence of evolving hypersurfaces to critical points.

This paper demonstrates the use of genetic algorithms for evolving: 1) a grandmaster-level evaluation function, and 2) a search mechanism for a chess program, the parameter values of which are initialized randomly. The evaluation function of the program is evolved by learning from databases of (human) grandmaster games…

Graphs evolve; GNNs learn from past tasks.

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proporti…

Proves upper bounds for heat kernels evolving on manifolds.

Establishes Calderón-Zygmund inequalities on evolving Riemannian manifolds.

The paper proposes a Gaussian mixture model for Hilbert-space-valued data.

Proposes tPARAFAC2 for tracking evolving patterns in time-evolving data.

We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for $\ell_1$-$…

Generative adversarial networks generate realistic, time-evolving high-resolution atmospheric fields.

Utilization of non-linear tools to characterize the state of development of the electricity markets in Italy and Greece. This is equivalent to testing the Efficient Market Hypothesis on these markets. The tools include a variety of complexity measures like Maximal Lyapunov and Hurst exponents and HHI index for market c…

Study improves $L^{\infty}$ estimates and extreme value behavior in stochastic differential games.

The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.

New algorithms ensure generated objects evolve and fill a distribution, unlike static neural networks.

Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect the community structure in time-evolving networks. However, due to significant comput…

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, there has not been a full investigation of evolving world economic networks with Markov chain formalism. Using the…

This paper demonstrates the use of genetic algorithms for evolving a grandmaster-level evaluation function for a chess program. This is achieved by combining supervised and unsupervised learning. In the supervised learning phase the organisms are evolved to mimic the behavior of human grandmasters, and in the unsupervi…

New method detects anomalies in computing centers' logs.

Method predicts how probability distributions evolve over time.

Although Deep Neural Networks have seen great success in recent years through various changes in overall architectures and optimization strategies, their fundamental underlying design remains largely unchanged. Computational neuroscience on the other hand provides more biologically realistic models of neural processing…

We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …

Derives new orthogonal coordinates for evolving surfaces and curves.

A new algorithm for K-means clustering in evolving data streams.

A non-Bayesian time-varying model is developed by introducing the concept of the degree of market efficiency that varies over time. This model may be seen as a reflection of the idea that continuous technological progress alters the trading environment over time. With new methodologies and a new measure of the degree o…

Improved online PCA algorithm learns from evolving norm of parameter vector.

We investigate the evolution of open curves with fixed endpoints under the curve shortening flow, which evolves curves in proportion to their curvature. Using a distance comparison of Huisken, we determine the long-term behavior of open curves with fixed endpoints evolving in certain convex domains on surfaces of const…