arXiv research

Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.

Given a sub-hyperbolic semi-rational branched covering which is not CLH-equivalent a rational map, it must have the non-empty canonical Thurston obstruction. By using this canonical Thurston obstruction, we decompose this dynamical system in this paper into several sub-dynamical systems. Each of these sub-dynamical sys…

Commonly used limit order book attributes are empirically considered based on NASDAQ ITCH data. It is shown that some of them have the properties drastically different from the ones assumed in many market dynamics study. Because of this difference we propose to make a transition from "Statistical" type of order book st…

Proposes dynamic model type recommendation for OLP technique.

Paper explains dynamics of homeomorphisms to mapping tori geometry.

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the cond…

Two heuristics solve dynamic multiple travelling salesmen problems.

Typilus predicts types for Python programs using neural networks.

Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.

The present paper contains an interpretation and generalization of Novikov's theory of Morse type inequalities for 1-forms in terms of Conley's theory for dynamical systems.

Paper addresses reward hacking in preference optimization, proposing POWER-DL to improve AI alignment.

Enhances RL in target domains with limited data using augmented return.

We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS$^3$ for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS$^3$, which yields a classification of FDS$^3$'s. Secondly, for each type of the classification, we construct concrete examples of FDS$^3$…

Constructs algorithms to recognize and classify 2D surfaces.

The aim of this paper is to show that the dynamics of $L^p$ heat semigroups ($p>2$) on a symmetric space of non-compact type is very different from the dynamics of the $L^p$ heat semigroups if $p\leq 2$. To see this, it is shown that certain shifts of the $L^p$ heat semigroups have a chaotic behavior if $p>2$ and that …

This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.

New numerical method for non-linear asset price model with CEV volatility.

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.

We focus on the topology and dynamics of minimal sets and Levi-flats in surfaces of general type. Our method relies on the ergodic theory of Riemann surfaces laminations: we use harmonic measures and Lyapunov exponents. Our first result establishes that minimal sets have large Hausdorff dimension when a leaf is simply …

Graph Hawkes Neural Network forecasts evolving graph sequences.

This paper finds a global surface of section in dynamically convex L(p,p-1) using ECH.

We study the problem of dynamic assortment personalization with large, heterogeneous populations and wide arrays of products, and demonstrate the importance of structural priors for effective, efficient large-scale personalization. Assortment personalization is the problem of choosing, for each individual (type), a bes…

Study magnetic Hamiltonian systems with constraints, deriving Hamilton-Jacobi equations.

We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The fir…

Develops path integral for spiked tensor model dynamics.

Elman-type RNNs converge to globally optimal solutions in the mean-field regime.

Book explores infinite translation surfaces, challenging traditional geometry.

In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly, we derive precisely the geometric constraint conditions of the induced distribu…

Modeling Bitcoin prices and media attention using jump-type processes.

Paper tackles anomaly detection and RCA in dynamical systems using ICODE Networks.

The paper explores the geometry of holomorphic flows and orbits.

Unified product Lie groups and their quotient spaces are analyzed for dynamics.

New dynamic allocation methods for multi-armed bandit models.

Spotify improves content mix using contextual bandits.

Li-York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the 2-dimensional disk. In this case a periodic orbit is specified by a braid type and on the se…

Study dynamic matching in heterogeneous networks using ODE model.

In this paper, we study the herding phenomena in financial markets arising from the combined effect of (1) non-coordinated collective interactions between the market players and (2) concurrent reactions of market players to dynamic market signals. By interpreting the expected rate of return of an asset and the favorabi…

The paper studies automorphisms of free groups with a North-South dynamics.

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …

In this paper, we give precisely the geometric constraint conditions of canonical symplectic form and regular reduced symplectic forms for the dynamical vector fields of a regular controlled Hamiltonian (RCH) system and its regular reduced systems, which are called the Type I and Type II of Hamilton-Jacobi equations. A…

Paper bridges quantum and classical mechanics for open systems.

The partially observable hidden Markov model is an extension of the hidden Markov Model in which the hidden state is conditioned on an independent Markov chain. This structure is motivated by the presence of discrete metadata, such as an event type, that may partially reveal the hidden state but itself emanates from a …

Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users give similar ratings and that similar items garner similar ratings. This paradigm h…

Derives formula for skew stickiness ratio in asset price and volatility dynamics.

In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e. systems dynamically equivalent to linear control systems, the advantage of this a…

Study on order book dynamics with uniform catastrophes, explaining volatility and trends.

SympFormer accelerates attention blocks using inertial dynamics on density spaces.