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Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…

Machine Learning · Statistics 2026-02-24 Naoya Hashimoto , Yuta Kawakami , Jin Tian

We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms are contained in…

Dynamical Systems · Mathematics 2019-09-24 Álvaro Castañeda , Ignacio Huerta

We enhance constrained-based data quality with approximate band conditional order dependencies (abcODs). Band ODs model the semantics of attributes that are monotonically related with small variations without there being an intrinsic…

Databases · Computer Science 2020-03-02 Pei Li , Michael Bohlen , Jaroslaw Szlichta , Divesh Srivastava

We study the construction of nonuniform tight wavelet frames for the Lebesgue space $L^2(\mathbb{R})$, where the related translation set is not necessary a group. The main purpose of this paper is to prove the unitary extension principle…

Functional Analysis · Mathematics 2022-07-14 Hari Krishan Malhotra , Lalit Kumar Vashisht

In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with…

Computational Complexity · Computer Science 2015-09-28 Chiel B. Ten Brinke , Frank J. P. van Houten , Hans L. Bodlaender

The standard Universal Approximation Theorem for operator neural networks (NNs) holds for arbitrary width and bounded depth. Here, we prove that operator NNs of bounded width and arbitrary depth are universal approximators for continuous…

Machine Learning · Computer Science 2021-09-24 Annan Yu , Chloé Becquey , Diana Halikias , Matthew Esmaili Mallory , Alex Townsend

We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…

Machine Learning · Computer Science 2022-08-04 David Witman , Alexander New , Hicham Alkendry , Honest Mrema

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

Combinatorics · Mathematics 2014-07-18 Giovanni Felici , Sokol Ndreca , Aldo Procacci , Benedetto Scoppola

We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…

Logic in Computer Science · Computer Science 2008-10-22 Alberto Momigliano , Frank Pfenning

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Machine Learning · Statistics 2020-07-08 Daniel Ting , Michael I. Jordan

Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…

Artificial Intelligence · Computer Science 2013-04-08 Piero P. Bonissone , David A. Cyrluk , James W. Goodwin , Jonathan Stillman

For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function…

Computational Complexity · Computer Science 2019-06-19 Stephan Wäldchen , Jan Macdonald , Sascha Hauch , Gitta Kutyniok

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

Optimization and Control · Mathematics 2022-04-22 Ashkan Mohammadi

This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free…

Computational Complexity · Computer Science 2025-06-17 Leah London Arazi , Amir Shpilka

We prove that a bounded open set U in Euclidean n-space has k-width less than C(n) Volume(U)^{k/n}. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in Euclidean space. In particular, we…

Differential Geometry · Mathematics 2007-05-23 Larry Guth

We use neural ordinary differential equations to formulate a variant of the Transformer that is depth-adaptive in the sense that an input-dependent number of time steps is taken by the ordinary differential equation solver. Our goal in…

Machine Learning · Computer Science 2020-10-23 Aaron Baier-Reinio , Hans De Sterck

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…

General Topology · Mathematics 2025-11-11 Xiao-Song Yang

We investigate the descriptional complexity of different variants of 1-limited automata (1-las), an extension of two-way finite automata (2nfas) characterizing regular languages. In particular, we consider 2nfas with common-guess…

Formal Languages and Automata Theory · Computer Science 2025-05-01 Bruno Guillon , Luca Prigioniero , Javad Taheri

Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…

Quantum Physics · Physics 2026-05-18 Namrata Manglani , Samrit Kumar Maity , Shashank Sharma , Soham Phulare , Sanjay Wandhekar

Binary neural networks (BNNs), where both weights and activations are binarized into 1 bit, have been widely studied in recent years due to its great benefit of highly accelerated computation and substantially reduced memory footprint that…

Computer Vision and Pattern Recognition · Computer Science 2021-01-01 Zhuo Su , Linpu Fang , Deke Guo , Dewen Hu , Matti Pietikäinen , Li Liu