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Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…

Knots are abundant in globular homopolymers but rare in globular proteins. To shed new light on this long-standing conundrum, we study the influence of sequence on the formation of knots in proteins under native conditions within the…

In previous papers, the author realized the following principle for many knot theories: if a knot diagram is complicated enough then it reproduces itself, i.e., is a subdiagram of any other diagram equivalent to it. This principle is…

Using the symmetric monoidal closed category structure of the category of measurable spaces, in conjunction with the Giry monad which we show is a strong monad, we analyze Bayesian inference maps and their construction in relation to the…

In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes. This is then applied to finding topologically meaningful maps between simplicial complexes, which in…

The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…

Mammography and ultrasound are extensively used by radiologists as complementary modalities to achieve better performance in breast cancer diagnosis. However, existing computer-aided diagnosis (CAD) systems for the breast are generally…

This paper addresses the $\epsilon$-close parameter tuning problem for Bayesian Networks (BNs): find a minimal $\epsilon$-close amendment of probability entries in a given set of (rows in) conditional probability tables that make a given…

One of the central problems in the classification of individual test sequences (e.g. genetic analysis), is that of checking for the similarity of sample test sequences as compared with a set of much longer training sequences. This is done…

To better understand the theoretical behavior of large neural networks, several works have analyzed the case where a network's width tends to infinity. In this regime, the effect of random initialization and the process of training a neural…

Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…

We define homotopy-theoretic invariants of knots in prime 3-manifolds. Fix a knot J in a prime 3-manifold M. Call a knot K in M concordant to J if it cobounds a properly embedded annulus with J in MxI, and call K J-characteristic if there…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Several recent works encourage the use of a Bayesian framework when assessing performance and fairness metrics of a classification algorithm in a supervised setting. We propose the Uncertainty Matters (UM) framework that generalizes a…

Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into…

We present a novel method for neural network quantization that emulates a non-uniform $k$-quantile quantizer, which adapts to the distribution of the quantized parameters. Our approach provides a novel alternative to the existing uniform…

Open set recognition problems exist in many domains. For example in security, new malware classes emerge regularly; therefore malware classification systems need to identify instances from unknown classes in addition to discriminating…

Data mining techniques have been used by researchers for analyzing protein sequences. In protein analysis, especially in protein sequence classification, selection of feature is most important. Popular protein sequence classification…

This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.