arXiv research

New method estimates causal effects of multiple versions of treatment.

New method proves uniqueness in mean curvature flow.

New method reduces version space for CNNs, improving active learning performance.

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the …

New method for analyzing elliptic and parabolic equations.

New causal versions of MaxEnt and PIR avoid paradoxical probability updates.

The main results of the paper are Proposition 3 and 4 which provide an effective way to construct minimal hypersurfaces in a Euclidean space. We demonstrate our technique by several new examples. This note is English translation of an earlier draft version written (in Russian) in September 1999. The final version of th…

New Lipschitz de Rham theorem for $L_p$-cohomology.

Equations of motion of low-energy string effective actions can be conveniently described in terms of generalized geometry and Levi-Civita connections on Courant algebroids. This approach is used to propose and prove a suitable version of the Kaluza-Klein-like reduction. Necessary geometrical tools are recalled.

The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem …

Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type volatility at the macroscopic scale. One additional important feature of financial…

Improved analysis of UCBVI algorithm with better empirical performance.

New method disentangles high-order effects in feature importance.

We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it is always overestimated for OEX options, except for the shortest maturities wher…

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}.

RS-PINN uses randomized smoothing to speed up high-dimensional PDE simulations without sacrificing accuracy.

We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective isometric circle action. As an application of the classification we prove a version of the Borel conjecture for closed three-dimensional Alexandrov spaces with circle symmetry.

Proposes a new method to estimate variable importance in black box models, mitigating correlation effects.

We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the underlying surface. We use this to give an effective proof of a result regarding maps between curve complexes of surfaces induced by finite…

Solves nonlinear problems on metric structures through eigenvalue counting.

Transport demand is highly dependent on supply, especially for shared transport services where availability is often limited. As observed demand cannot be higher than available supply, historical transport data typically represents a biased, or censored, version of the true underlying demand pattern. Without explicitly…

A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of Riemannian metrics with positive Ricci curvature on an infinite subfamily of closed, sim…

In this paper, a novel racing environment for OpenAI Gym is introduced. This environment operates with continuous action- and state-spaces and requires agents to learn to control the acceleration and steering of a car while navigating a randomly generated racetrack. Different versions of two actor-critic learning algor…

Develops a sparsity-inducing Bayesian Causal Forest for estimating heterogeneous treatment effects.

In this work we present a technique to use natural language to help reinforcement learning generalize to unseen environments. This technique uses neural machine translation, specifically the use of encoder-decoder networks, to learn associations between natural language behavior descriptions and state-action informatio…

Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability distribution for the interventional distribution resulting from the action. In many case…

Cluster-DP improves differential privacy in randomized experiments by clustering data.

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string effective actions, the situation becomes more complicated due to the presence of t…

The paper updates methods for studying proper Dupin hypersurfaces in Lie sphere geometry.

Given a principal bundle $P\to M$ over a Riemannian manifold with compact structure group $G$, let us consider a stationary Yang-Mills connection $A$ with energy $\int_M |F_A|^2\le Λ$. If we consider a sequence of such connections $A_i$, then it is understood that up to subsequence we can converge $A_i\to A$ to a singu…

Paper tackles estimating individual treatment effects from observational data.

Paper explains learning property of logistic and softmax losses for balanced and imbalanced class data.

Proves effective Chen ranks conjecture for Koszul modules.

We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Na…

This study compares machine learning methods for high-cardinality categorical variables.

We analyze the effect of adding, removing, and moving basepoints on link Floer homology. We prove that adding or removing basepoints via a procedure called quasi-stabilization is a natural operation on a certain version of link Floer homology, which we call $CFL_{UV}^\infty$. We consider the effect on the full link Flo…

We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\in\mathrm{GL}_m(\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\geq0$ the matrix $AB^k$ is also quasi--unipotent. Then $A$ and $B$ have a…

Study adds memory effect to Solow-Swan model for more accurate economic growth modeling.

The multi-armed restless bandit problem is studied in the case where the pay-off distributions are stationary $\varphi$-mixing. This version of the problem provides a more realistic model for most real-world applications, but cannot be optimally solved in practice, since it is known to be PSPACE-hard. The objective of …

We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsváth-Szabó 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of su…

This article investigates the evolution of the Mexican stock market integration into the world market. First, we estimate the time-varying Mexican degree of market integration using an international conditional version of the CAPM with segmentation effects. Second, we study the structural breaks in this series. Finally…

Effective drilling and filling bounds for hyperbolic 3-manifolds.

The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.

Study shows how to effectively predict functions on manifolds using kernel methods.

The adaptive gradient online learning method known as AdaGrad has seen widespread use in the machine learning community in stochastic and adversarial online learning problems and more recently in deep learning methods. The method's full-matrix incarnation offers much better theoretical guarantees and potentially better…

It is shown how the generating functional method of De Dominicis can be used to solve the dynamics of the original version of the minority game (MG), in which agents observe real as opposed to fake market histories. Here one again finds exact closed equations for correlation and response functions, but now these are de…

In this paper we study Morse homology and cohomology with local coefficients, i.e. "twisted" Morse homology and cohomology, on closed finite dimensional smooth manifolds. We prove a Morse theoretic version of Eilenberg's Theorem, and we prove isomorphisms between twisted Morse homology, Steenrod's CW-homology with loca…

Study asset price bubbles using random matching and stochastic factors.