arXiv research

Study axisymmetric surfaces in Euclidean space for energy minimization.

New method optimizes policies in non-stationary environments.

In this paper, we perform statistical segmentation and clustering analysis of the Dow Jones Industrial Average time series between January 1997 and August 2008. Modeling the index movements and log-index movements as stationary Gaussian processes, we find a total of 116 and 119 statistically stationary segments respect…

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…

The paper proves optimal smoothness for certain Lagrangian graphs with specific Hölder continuity.

We characterize stationary solutions to McKean-Vlasov equations on the circle.

This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is that when a nonparame…

This paper introduces SRPR for robust phase retrieval with smoothed loss functions.

We give a new proof of Witten asymptotic conjecture for Seifert manifolds with non vanishing Euler class and one exceptional fiber. Our method is based on semiclassical analysis on a two dimensional phase space torus. We prove that the Witten-Reshetikhin-Turaev invariant of a Seifert manifold is the scalar product of t…

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure oscillates in that region, commonly around a single point. In this paper, we devel…

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrica…

Paper tackles non-stationary kernelized bandits with near-optimal algorithm.

Smooth solutions found for Hamiltonian stationary equations in low dimensions.

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show that SGD with constant rates can be effectively used as an approximate posterio…

The covariance of a stationary process $X$ is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. The…

Study of asymptotics of meromorphic 3D-index as q approaches 1.

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with non-stationary process…

Formula calculates Riemann-Roch number for singular symplectic quotients.

Given an odd vector field $Q$ on a supermanifold $M$ and a $Q$-invariant density $μ$ on $M$, under certain compactness conditions on $Q$, the value of the integral $\int_{M}μ$ is determined by the value of $μ$ on any neighborhood of the vanishing locus $N$ of $Q$. We present a formula for the integral in the case where…

We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a uniformly distributed random variable) defined on a closed, bounded interval Ω\subset …

We prove that the density function of the gradient of a sufficiently smooth function $S : Ω\subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of $φ=\exp\left(\frac{i…

In this paper we explore the functional correlation approach to operational risk. We consider networks with heterogeneous a-priori conditional and unconditional failure probability. In the limit of sparse connectivity, self-consistent expressions for the dynamical evolution of order parameters are obtained. Under equil…

Noise balance theory explains SGD's behavior in neural networks.

Observer learns optimal policy from learner's actions without rewards.

Study uses topological signatures to quantify financial market complexity.

The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…

We prove a Morrey-type theorem for Hamiltonian stationary submanifolds of $\mathbb{C}^{n}$. Namely, if $L$ $\subset$ $\mathbb{C}^{n}$ is a $C^{1}$ Lagrangian submanifold with weakly harmonic Lagrangian phase $θ,$ then $L$ must be smooth. In the process we also discuss a local version of the equation, which is a nonline…

The paper analyzes convergence in SGD with momentum and proposes a diagnostic test.

Study analyzes price change patterns across different market capitalizations using Markov chains.

New GLB algorithm handles non-stationary data with forgetting.

In this article, we give a rough, and so not complete yet, proof of Kashaev's conjecture, that is, the volume conjecture for hyperbolic knots, where the hyperbolicity equations associated to knot diagrams appear as the stationary phase equations for Kashaev's invariants.

New algorithm helps escape saddle points in optimization problems.

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

We give new methods for computing the coefficients of the asymptotic expansions of the kernel of Berezin-Toeplitz quantization obtained recently by Ma-Marinescu, and of the composition of two Berezin-Toeplitz quantizations. Our main tool is the stationary phase formula of Melin-Sjöstrand.

We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemeister torsion is used as a density on the moduli space of flat connecti…

We propose a novel online learning algorithm for Restricted Boltzmann Machines (RBM), namely, the Online Generative Discriminative Restricted Boltzmann Machine (OGD-RBM), that provides the ability to build and adapt the network architecture of RBM according to the statistics of streaming data. The OGD-RBM is trained in…

Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.

SAMoSSA combines mSSA and AR for accurate time series analysis.

A new model for generating point processes with complex geometries.

Study the singular limit of a boundary reaction equation, showing energy concentration and varifold support.

DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.

Study bandit problems under censorship, estimating performance loss.

Study classifies stock price data into stationary and non-stationary periods for mechanical trading.

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many body systems…

We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation introduces statistical arbitrages that traders exploit by adapting their trading strat…

We investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double contour integrals. These integral formulae allow us to propose a formula for the leadi…

The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters advancing conventional randomized approaches constrained with a fixed scope of rand…

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S^2, then the singular sets of stationary map…