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Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
We develop an alternative approach to this field, which was to a large extent developed by Verbeure et al. It is meant to complement their approach, which is largely based on a non-commutative central limit theorem and coordinate space…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
Recent theoretical ideas and observational claims suggest that the fine structure constant alpha may be variable. We examine a spectrum of models in which alpha is a function of a scalar field. Specifically, we consider three scenarios:…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <f(i)>: sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The…
A clustering outcome for high-dimensional data is typically interpreted via post-processing, involving dimension reduction and subsequent visualization. This destroys the meaning of the data and obfuscates interpretations. We propose…
Simple active models of matter recapitulate complex biological phenomena. The out-of-equilibrium nature of these models, however, often makes them beyond the reach of first-principle descriptions. This limitation is particularly perplexing…
As machine learning models become more accurate, they typically become more complex and uninterpretable by humans. The black-box character of these models holds back its acceptance in practice, especially in high-risk domains where the…
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…