arXiv research

New method clusters strong and weak views effectively, improving performance by up to 40%.

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 paper extends Cartan development to infinite dimensional Lie groups.

In this paper, a type of integrable evolution equation--the generalized Landau-Lifshitz equation into $S^n$ is considered. We deal with this equation from a geometric point of view by rewriting it in a geometric form. Through the geometric energy method, we show the global well-posedness of the corresponding Cauchy pro…

This reviews the econophysics activities in Belgium from my admittedly biased point of view. Unknown historical notes or facts are presented for the first time explaining the aims, whence evolution of the research papers and friendly connections with colleagues. Comments on endeavors are also provided. The lack of offi…

We introduce certain spherically symmetric singular Ricci solitons and study their stability under the Ricci flow from a dynamical PDE point of view. The solitons in question exist for all dimensions $n+1\ge 3$, and all have a point singularity where the curvature blows up; their evolution under the Ricci flow is in sh…

Differentiable NAS frameworks grow networks wider and deeper, revealing biases in wiring evolution.

Paper proposes an alternative to MCMC for sampling in energy-based models.

We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector. The flow stems from a geometrically natural action containing kinetic and internal energy terms. As the mean curvature of the hypersurface is the main drivi…

Using the mechanics of creep in material sciences as a metaphor, we present a general framework to understand the evolution of financial, economic and social systems and to construct scenarios for the future. In a nutshell, highly non-linear out-of-equilibrium systems subjected to exogenous perturbations tend to exhibi…

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…

Unified view of surfaces in R^n using Gauss map, caustics, and quadratic forms.

This paper proves certain quasi-Einstein manifolds are rigid under Ricci flow.

We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the f…

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…

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is…

Geometrically revisits Dupin cyclidic systems using evolving circles and cyclides.

A discrete method approximates hyperbolic curvature flow in the plane.

A powerful mathematical method for the investigation of the properties of dynamical systems is represented by the Kosambi-Cartan-Chern (KCC) theory. In this approach the time evolution of a dynamical system is described in geometric terms, treating the solution curves of a dynamical system by geometrical methods inspir…

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends…

Taxi demand prediction has recently attracted increasing research interest due to its huge potential application in large-scale intelligent transportation systems. However, most of the previous methods only considered the taxi demand prediction in origin regions, but neglected the modeling of the specific situation of …

Study chaotic dynamics in social stratification models leading to thermalization and turbulence.

This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by an exponential randomized Brownian bridge (rBb) and consider various prior dist…

A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.

Paper explores solving HJB equations using neural networks.

Survey of diffusion and optimal transport methods in machine learning.

We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). To justify $W^F$ from a fundamental point of view, we embed this …

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thu…

An explicit construction of surfaces with flat normal bundle in the Euclidean space (unit hypersphere) in terms of solutions of certain linear system is proposed. In the case of 3-space our formulae can be viewed as the direct Lie sphere analog of the generalized Weierstrass representation of surfaces in conformal geom…

Derives effective continuous dynamics for adaptive SGD methods.

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these network…

The production and consumption of information about Bitcoin and other digital-, or 'crypto'-, currencies have grown together with their market capitalisation. However, a systematic investigation of the relationship between online attention and market dynamics, across multiple digital currencies, is still lacking. Here,…

InstanceFlow visualizes classifier confusion over training epochs.

An almost Kähler structure on a symplectic manifold $(N, ω)$ consists of a Riemannian metric $g$ and an almost complex structure $J$ such that the symplectic form $ω$ satisfies $ω(\cdot, \cdot)=g(J(\cdot), \cdot)$. Any symplectic manifold admits an almost Kähler structure and we refer to $(N, ω, g, J)$ as an almost Käh…

The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…

Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature. We use a first principles approach to explain LR and RP, and show a connection …

Study material evolution using groupoids to track intrinsic properties.

The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtrati…

Study shows large extra dimensions are hidden from view by black holes.

We give an extensive treatment of the Constant Mean Curvature (CMC) Einstein flow from the point of view of the Bel-Robinson energies. The article, in particular, stresses on estimates showing how the Bel-Robinson energies and the volume of the evolving states control intrinsically the flow along evolution. The treatme…

In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $ξ$ in a risk-conservative way relative to a family of probability measures $\mathcal{P}$. We first describe the evolutio…

The paper studies circular evolutes and involutes of framed curves in Euclidean space.

The paper studies curve evolution using the PLR equation and its solutions.

New bidirectional model predicts magnetohydrodynamics fields and estimates uncertainty.

The paper defines evolutes and involutes for framed curves and their properties.

Generative Adversarial Network (GAN) is a current focal point of research. The body of knowledge is fragmented, leading to a trial-error method while selecting an appropriate GAN for a given scenario. We provide a comprehensive summary of the evolution of GANs starting from its inception addressing issues like mode col…

MonoFlow rethinks GANs using Wasserstein gradient flows.

Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.