Related papers: Ordinal Decompositions and Extreme Selections
This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was…
We consider a coset construction of minimal models. We define it rigorously and prove that it gives superconformal minimal models. This construction allows to build all primary fields of superconformal models and to calculate their…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…
A tie-point of a compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. Set-theoretically a tie-point of N* is an ultrafilter whose dual maximal ideal can be…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very…
Computer vision systems in real-world applications need to be robust to partial occlusion while also being explainable. In this work, we show that black-box deep convolutional neural networks (DCNNs) have only limited robustness to partial…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Recently, there has been intense research in proposing and developing various methods for constructing high-order exceptional points (EPs) in dissipative systems. These EPs can possess a number of intriguing properties related to, e.g.,…
In the framework of convolutional neural networks that lie at the heart of deep learning, downsampling is often performed with a max-pooling operation that only retains the element with maximum activation, while completely discarding the…
Exceptional points are complex-valued spectral singularities that lead to a host of intriguing features such as loss-induced transparency - a counterintuitive process in which an increase in the system's overall loss can lead to enhanced…
Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…
We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical \v{S}arkovski\u{i}…
Multi-hop reading comprehension requires not only the ability to reason over raw text but also the ability to combine multiple evidence. We propose a novel learning approach that helps language models better understand difficult multi-hop…