arXiv research

The paper generalizes rigidity results for contact Anosov flows with bunching assumption.

We refine a metric bunching estimate for pinched manifolds.

Golden L surface has unbounded bunching of saddle connections

Improved algorithm for modular links provides upper volume bounds.

Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a realistic roulette is not ideal: the probabilities of realisation of different …

This paper tackles post-trade allocation inefficiencies and presents a uniform return allocation method.

Paper simplifies link classification in 3-sphere using braids and templates.

The financial crisis of 2007/08 caused catastrophic consequences and brought a bunch of changes around the world. Interest rates that were known to follow or behave similarly of each other diverged. Furthermore, the regulation and in particular the counterparty credit risk began to to be considered and quantified. Cons…

We develop new algorithms for approximating extremal toric Kähler metrics. We focus on an extremal metric on $\mathbb{CP}^{2}\sharp2\overline{\mathbb{CP}}^{2}$, which is conformal to an Einstein metric (the Chen-LeBrun-Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various g…

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $δ$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…

Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In this paper, we generalize Yau's conjecture on some numerical invarian…

Financial institutions have massive computations to carry out overnight which are very demanding in terms of the consumed CPU. The challenge is to price many different products on a cluster-like architecture. We have used the Premia software to valuate the financial derivatives. In this work, we explain how Premia can …

Introduces resemblance structure for large scale geometry.

Proves simplicity of Lyapunov exponents for specific Anosov flows.

The paper develops time-uniform inference methods for stochastic approximation parameters.

To collectively forecast the demand for ride-sourcing services in all regions of a city, the deep learning approaches have been applied with commendable results. However, the local statistical differences throughout the geographical layout of the city make the spatial stationarity assumption of the convolution invalid,…

The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.

This paper addresses the identification of insurance models with multidimensional screening where insurees have private information about their risk and risk aversion. The model includes a random damage and the possibility of several claims. Screening of insurees relies on their certainty equivalence. The paper then in…

Proposes a method to generate high-quality candlestick data for financial trading.

Nowadays, CAPTCHAs are computer generated tests that human can pass but current computer systems can not. They have common usage in various web services in order to be able to detect a human from computer programs autonomously. In this way, owners can protect their web services from bots. In addition to visual CAPTCHAs…

Stochastic gradient descent (SGD) has achieved great success in training deep neural network, where the gradient is computed through back-propagation. However, the back-propagated values of different layers vary dramatically. This inconsistence of gradient magnitude across different layers renders optimization of deep …

A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,α)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $α:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of $\mathbb{T}^n$ on $A$. In this…

Although the Nash theorem solves the isometric embedding problem, matters are inherently more involved if one is further seeking an embedding that is well-behaved from the standpoint of submanifold geometry. More generally, consider a Lipschitz map $F:M^m\to\mathbb R^n$, where $M^m$ is a Hadamard manifold whose curvatu…

Study on reinsurance decisions using mean-variance criterion with irreversible contracts.

Authorship identification is a process in which the author of a text is identified. Most known literary texts can easily be attributed to a certain author because they are, for example, signed. Yet sometimes we find unfinished pieces of work or a whole bunch of manuscripts with a wide variety of possible authors. In or…

Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the falling accuracy effect of dealing with huge number of features in typical learning …

Federated learning algorithm improves with intermittent client availability.

The biggest problem with the methods of machine learning used today in business analytics is that they do not generalize well and often fail when applied to new data. One of the possible approaches to this problem is to enrich these methods (which are almost exclusively based on statistical algorithms) with some intrin…

In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometr…

Tasks such as search and recommendation have become increas- ingly important for E-commerce to deal with the information over- load problem. To meet the diverse needs of di erent users, person- alization plays an important role. In many large portals such as Taobao and Amazon, there are a bunch of di erent types of sea…

ABM automates feature engineering and variable selection for loss-based models.

Proposes a weaker faithfulness assumption for causal discovery.

Paper simplifies balancing weights by relaxing outcome assumptions.

Study finds rigidity of biconservative hypersurfaces in space forms without curvature assumptions.

Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG) models. In many applications, feedback naturally arises and directed graphical models …

Paper relaxes independence assumption for non-centered data.

New algorithm estimates causal effects for non-Gaussian data.

For many interesting tasks, such as medical diagnosis and web page classification, a learner only has access to some positively labeled examples and many unlabeled examples. Learning from this type of data requires making assumptions about the true distribution of the classes and/or the mechanism that was used to selec…

The paper clarifies the distinction between CATE and ITE under ignorability assumptions.

New assumptions and algorithm solve offline two-player zero-sum Markov games.

The paper relaxes assumptions for analyzing stochastic optimization algorithms.

Unified parametric assumption improves convergence guarantees for nonconvex optimization.

Revisits causal inference identifiability with positivity assumption.

Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treat…

Emputation learns imputation models guided by missingness assumptions.

A new learning method uses data to learn from large model sets.

The paper bounds and identifies joint probabilities in causal inference with monotonicity assumptions.

There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness of the regression function (or the boundary between classes) and the margin…