Related papers: Analytic clones
The aggregated journal-journal citation matrix derived from the Journal Citation Reports 2001 can be decomposed into a unique subject classification by using the graph-analytical algorithm of bi-connected components. This technique was…
We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of $K$-means applied in the image space while addressing its clustering performance issues.…
There has been growing interest in developing accurate models that can also be explained to humans. Unfortunately, if there exist multiple distinct but accurate models for some dataset, current machine learning methods are unlikely to find…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
We discuss the history and uses of the parallel census technique---an elegant tool in the study of certain computational objects having polynomially bounded census functions. A sequel will discuss advances (including Cai, Naik, and…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
The multiplicative fragment of Linear Logic is the formal system in this family with the best understood proof theory, and the categorical models which best capture this theory are the fully complete ones. We demonstrate how the Hyland-Tan…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
Data clones are defined as multiple copies of the same data among datasets. Presence of data clones between datasets can cause issues such as difficulties in managing data assets and data license violations when using datasets with clones…
We propose a novel taxonomy for bias evaluation of discriminative foundation models, such as Contrastive Language-Pretraining (CLIP), that are used for labeling tasks. We then systematically evaluate existing methods for mitigating bias in…
We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data…
In this paper we give an ordinal analysis of a set theory with $\Pi_{1}$-Collection.
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…
In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$.…
We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.