arXiv research

we construct a properly embedded minimal surface in the flat product R^2*S^1 which is quasi-periodic but is not periodic.

In this article we consider the motion of relativistic strings in the Minkowski space $\textbf{R}^{1+n}$. Those surfaces are known as a timelike minimal surface, and described by a system with $n$ nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the $n$…

New method detects change points in quasi-periodic signals without supervision.

Paper proposes TBSD for efficient anomaly detection in textured images.

The M and A transactions represent a wide range of unique business optimization opportunities in the corporate transformation deals, which are usually characterized by the high level of total risk. The M and A transactions can be successfully implemented by taking to an account the size of investments, purchase price, …

In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2.

We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.

This work uses QPGPs to improve ILC performance in repetitive tasks.

By and large the behavior of stochastic gradient is regarded as a challenging problem, and it is often presented in the framework of statistical machine learning. This paper offers a novel view on the analysis of on-line models of learning that arises when dealing with a generalized version of stochastic gradient that …

The paper explores the geometry of level lines of quasiperiodic functions with many periods.

Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remarkable system of quasi-linear equations which turns out to be a Rich system of conservation laws. This reduces the question of integrability to the question of existence of smooth (q…

For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such a…

Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichmüller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the…

Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.

In this paper, we study two classes of planar self-similar fractals $T_\varepsilon$ with a shifting parameter $\varepsilon$. The first one is a class of self-similar tiles by shifting $x$-coordinates of some digits. We give a detailed discussion on the disk-likeness ({\it i.e., the property of being a topological disk}…

The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. …

Debate over the existence of branches in the stellar activity-rotation diagrams continues. Application of modern time series analysis tools to study the mean cycle periods in chromospheric activity index is lacking. We develop such models, based on Gaussian processes, for one-dimensional time series and apply it to the…

In this paper we consider Monge-Ampère equations on compact Hessian manifolds, or equivalently Monge-Ampère equations on certain unbounded convex domains $Ω\subseteq \mathbb{R}^n$, with a periodicity constraint given by the action of an affine group. In the case where the affine group action is volume-preserving, i.e.,…

Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations which describe the motion of financial prices with respect to real world probabi…

In this paper we present a continuous time dynamical model of heterogeneous agents interacting in a financial market where transactions are cleared by a market maker. The market is composed of fundamentalist, trend following and contrarian agents who process information from the market with different time delays. Each …

Let G be a connected Lie group, LG its loop group, and PG->G the principal LG-bundle defined by quasi-periodic paths in G. This paper is devoted to differential geometry of the Atiyah algebroid A=T(PG)/LG of this bundle. Given a symmetric bilinear form on the Lie algebra g and the corresponding central extension of Lg,…

Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.

The paper constructs a symplectic groupoid for a specific Poisson structure.

Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.

We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus $a$. For the standard structure $a=1$, the chains are well-known and are closed curves. We show that for almost all other values of the modulus $a$ either two or three ty…

Zero-energy orbits in the Kepler-Heisenberg problem are self-similar and stratify into three families.

In this article we study the topology of a family of real analytic germs $F \colon (\mathbb{C}^3,0) \to (\mathbb{C},0)$ with isolated critical point at 0, given by $F(x,y,z)=f(x,y)\bar{g(x,y)}+z^r$, where $f$ and $g$ are holomorphic, $r \in \mathbb{Z}^+$ and $r \geq 2$. We describe the link $L_F$ as a graph manifold us…

Spectral methods predict long-term signals from linear and nonlinear systems.

Automatic music transcription (AMT) aims to infer a latent symbolic representation of a piece of music (piano-roll), given a corresponding observed audio recording. Transcribing polyphonic music (when multiple notes are played simultaneously) is a challenging problem, due to highly structured overlapping between harmon…

Mechanical devices such as engines, vehicles, aircrafts, etc., are typically instrumented with numerous sensors to capture the behavior and health of the machine. However, there are often external factors or variables which are not captured by sensors leading to time-series which are inherently unpredictable. For insta…

Classifies minimal surfaces of finite genus in 3D space.

Unified framework for intermittent demand forecasting using renewal processes.

In this paper we address the question of the existence of a model for the string 2-group as a strict Lie-2-group using the free loop group $LSpin$ (or more generally $LG$ for compact simple simply-connected Lie groups $G$). Baez-Crans-Stevenson-Schreiber constructed a model for the string 2-group using a based loop gro…

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …

Imitative and contrarian behaviors are the two typical opposite attitudes of investors in stock markets. We introduce a simple model to investigate their interplay in a stock market where agents can take only two states, bullish or bearish. Each bullish (bearish) agent polls m "friends'' and changes her opinion to bear…

Pitch or fundamental frequency (f0) extraction is a fundamental problem studied extensively for its potential applications in speech and clinical applications. In literature, explicit mode specific (modal speech or singing voice or emotional/ expressive speech or noisy speech) signal processing and deep learning f0 ext…

The paper proposes a method to improve Bayesian inference for periodic data using data-driven priors.

In this paper we consider a conjecture formulated by the second author in occasion of the 1998 ICM in Berlin (arXiv:math/9807034v2). This conjecture states the equivalence, for a Fano variety $X$, of the semisimplicity condition for the quantum cohomology $QH^\bullet(X)$ with the existence condition of full exceptional…