arXiv research

The paper examines special Q-nets that terminate after a finite number of Laplace steps.

Circular nets with spherical parameter lines have geometric properties related to Darboux cyclides and terminating Laplace sequences.

The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develo…

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delau…

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of correspondin…

Efficiently simulates SABR model with novel sampling methods.

We study the problem of utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset. The asset price dynamics follow a diffusion process with regime-switching coefficients modeled by a continuous-time finite-state Markov chain. We consider an inves…

In this paper, we give a lower bound of Bergman kernels for a sequence of almost Kähler-Einstein Fano manifolds, or more general, a sequence of Fano manifolds with almost Kähler-Ricci solitons. This generalizes a result by Donaldson-Sun, Tian for Kähler-Einstein manifolds sequence with positive scalar curvature. As an …

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. W…

The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on an annulus than on any other surface of revolution in $\mathbb{R}^3$ with the same boundary. This is established by defining a sequence of shrinking cylinders about the axis of symmetry and proving that flattening a surface outside of each cylinde…

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into complex projective space or the inversion of a minimal…

Study of line congruences for Appell's rank-4 hypergeometric functions.

We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the we…

Study eigenvalues and shapes, proving sharp inequalities for Steklov eigenvalues.

Develops a method for causal inference in recurrent event data with terminal failure.

We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the…

In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this kind of problem, we consider to minimize the variances of the investm…

We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, c…

Study approximates sub-Riemannian structures with Riemannian metrics and analyzes spectral convergence.

Study two types of singular Kähler-Einstein metrics on complex varieties.

Variational method for eigenvalues on manifolds.

Bayesian context trees capture complex dependencies in categorical sequences.

We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a fund/agent investing in futures markets. We offer some preliminary remarks about stat…

Optimizes metrics on surfaces for eigenvalues.

Let $(M,g)$ be a connected, closed, orientable Riemannian surface and denote by $λ_k(M,g)$ the $k$-th eigenvalue of the Laplace-Beltrami operator on $(M,g)$. In this paper, we consider the mapping $(M, g)\mapsto λ_k(M,g)$. We propose a computational method for finding the conformal spectrum $Λ^c_k(M,[g_0])$, which is d…

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on price move directions. Our goa…

The paper classifies Willmore 2-spheres in $S^n$.

This manuscript studies manifolds-with-boundary collapsing in the Gromov-Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The main result e…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the m…

Recurrent models can produce infinite sequences, causing bias; new methods prevent this.

We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We consider three main applications: Conditional Gibbs measures on compact spaces, …

We approximate the spectral data (eigenvalues and eigenfunctions) of compact Riemannian manifold by the spectral data of a sequence of (computable) discrete Laplace operators associated to some graphs immersed in the manifold. We give an upper bound on the error that depends on upper bounds on the diameter and the sect…

Machine learning and data mining techniques have been used extensively in order to detect credit card frauds. However, most studies consider credit card transactions as isolated events and not as a sequence of transactions. In this article, we model a sequence of credit card transactions from three different perspectiv…

A new method optimizes neural sequence models for better task performance.

We consider the space KR(n,F) of Kahler-Ricci solitons on n-dimensional Fano manifolds with Futaki invariant bounded by F. We prove a partial C^0 estimate for KR(n,F) as a generalization of the recent work of Donaldson-Sun for Fano Kahler-Einstein manifolds. In particular, any sequence in KR(n,F) has a convergent sub…

In this short paper, we improve the result of Phong-Song-Sturm on degeneration of Fano Kähler-Ricci solitons by removing the assumption on the uniform bound of the Futaki invariant. Let $\mathcal{KR}(n)$ be the space of Kähler-Ricci solitons on $n$-dimensional Fano manifolds. We show that after passing to a subsequence…

Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose a generic theoretical framework consisting of three key GS components: simplex …

To improve the efficient frontier of the classical mean-variance model in continuous time, we propose a varying terminal time mean-variance model with a constraint on the mean value of the portfolio asset, which moves with the varying terminal time. Using the embedding technique from stochastic optimal control in conti…

The Volterra Heston model is used to price American options.

We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every move of the sequence. This conditional setting leads to a possibility of irreve…

Machine learning and data mining techniques have been used extensively in order to detect credit card frauds. However, most studies consider credit card transactions as isolated events and not as a sequence of transactions. In this framework, we model a sequence of credit card transactions from three different perspect…

Study improves regularity estimates for harmonic maps into ellipsoids.

In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common -- the policy. The termination condition is usually trained to optimize a control obj…

Bayesian framework for sphere regression using Gaussian fields.

The paper analyzes network models with binary values and sub-Gamma noise, deriving asymptotic properties.

We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by Carr [Review of Financial Studi…

This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued function through a sequence of strategically selected q…