A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Graph neural network using Beltrami flow for feature and topology evolution.
EvoNet predicts the evolution of dynamic graphs using a graph neural network and recurrent architecture.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
Differentiable NAS frameworks grow networks wider and deeper, revealing biases in wiring evolution.
CMS formulation solves Poincare conjecture for all dimensions.
I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of…
In this empirical paper, we investigate how learning agents can be arranged in more efficient communication topologies for improved learning. This is an important problem because a common technique to improve speed and robustness of learning in deep reinforcement learning and many other machine learning algorithms is t…
Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and topologically simpler, including also Boy surface (real projective plane), using a fam…
Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how traj…
We investigate topology and temporal evolution of the foreign currency exchange market viewed from a weighted network perspective. Based on exchange rates for a set of 46 currencies (including precious metals), we construct different representations of the FX network depending on a choice of the base currency. Our resu…
The FitzHugh-Nagumo equation provides a simple mathematical model of cardiac tissue as an excitable medium hosting spiral wave vortices. Here we present extensive numerical simulations studying long-term dynamics of knotted vortex string solutions for all torus knots up to crossing number 11. We demonstrate that FitzHu…
Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel 2-strand links. Within this family one can check topological invariance and under…
The paper analyzes diffusion condensation for data geometry and topology.
We solve the regularity problem for Milnor's infinite dimensional Lie groups in the -topological context, and provide necessary and sufficient regularity conditions for the (standard) -topological setting. We prove that the evolution map is -continuous on its domain the Lie gro…
This paper studies the Yang--Mills ASD equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and moreover it becomes an infinite dimensional and infinite entropy system. We study th…
Study of curve evolution in 2D space forms converging to a circle.
Study active nematic forces on curved surfaces, revealing new coupling mechanisms.
In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure: connected components (topological features of dimension 0), cycles (features of dime…
Enhanced neural network framework improves constraint satisfaction with topological conditioning.
This paper studies the topological properties of the World Trade Web (WTW) and its evolution over time by employing a weighted network analysis. We show that the WTW, viewed as a weighted network, displays statistical features that are very different from those obtained by using a traditional binary-network approach. I…
The Cheeger constant increases under Ricci flow on spheres.
GeoPhy uses geometric gradients to efficiently infer phylogenetic trees from molecular data.
The \emph{World Trade Web} (WTW), the network defined by the international import/export trade relationships, has been recently shown to display some important topological properties which are tightly related to the Gross Domestic Product of world countries. While our previous analysis focused on the static, undirected…
Study real algebraic curves on real del Pezzo surfaces using degeneration methods.
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible …
We connect topological changes that can occur in -space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the -dimensional spatial sectio…
CNN accurately reconstructs lattice topology with strong thermal fluctuations.
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered () model for interaction events fal…
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superst…
We present an empirical analysis of the network formed by the trade relationships between all world countries, or World Trade Web (WTW). Each (directed) link is weighted by the amount of wealth flowing between two countries, and each country is characterized by the value of its Gross Domestic Product (GDP). By analysin…
Current Deep Reinforcement Learning algorithms still heavily rely on handcrafted neural network architectures. We propose a novel approach to automatically find strong topologies for continuous control tasks while only adding a minor overhead in terms of interactions in the environment. To achieve this, we combine Neur…
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly i…
Bayesian topological learning improves EEG signal analysis for brain state classification.
This work develops agents to learn generalizable policies for dynamic network environments.
Financial networks have become extremely useful in characterizing the structure of complex financial systems. Meanwhile, the time evolution property of the stock markets can be described by temporal networks. We utilize the temporal network framework to characterize the time-evolving correlation-based networks of stock…
Study how knots occupy space using topological methods.
We construct smooth solutions to Ricci flow starting from a class of singular metrics and give asymptotics for the forward evolution. The singular metrics heal with a set of points (of codimension at least three) coming out of the singular point. We conjecture that these metrics arise as final-time limits of Ricci flow…
Proposes TSBP for matching topological signal distributions.
This review explores TDA and TDL beyond persistent homology.
Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities…
A new spinorial heat flow framework studies geometric degeneration on 3-manifolds.
A new method for state estimation on complex networks.
The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity, global existence and convergence of the flow in various ambient spaces and codimensio…
Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models ha…
Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlatio…
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block m…