Related papers: Holant clones and the approximability of conservat…

Given a countable transitive model of set theory and a partial order contained in it, there is a natural countable Borel equivalence relation on generic filters over the model; two are equivalent if they yield the same generic extension. We…

Clustering is a fundamental task in unsupervised learning. The focus of this paper is the Correlation Clustering functional which combines positive and negative affinities between the data points. The contribution of this paper is two fold:…

Code clones are similar code fragments that often arise from copy-and-paste programming. Neural networks can classify pairs of code fragments as clone/not-clone with high accuracy. However, finding clones in industrial-scale code needs a…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…

We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…

We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…

The following result has been shown recently in the form of a dichotomy: For every total clone $C$ on $\mathbf{2} := \{0,1\}$, the set $\mathcal{I}(C)$ of all partial clones on $\mathbf{2}$ whose total component is $C$, is either finite or…

In this paper the concept of $\mathbb{F}$-functorial of a finite group was introduced. These functorials have many properties of the Fitting subgroup of a soluble group and the generalized Fitting subgroup of a finite group. It was shown…

We give a full description of all sets of functions on the group $(\mathbb{ Z}_p, +)$ of prime order which are closed under the composition with the clone generated by $+$ from both sides. Thereby, we also get a description of all iterative…

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…

The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…

We investigate the structure of the lattice of clones on an infinite set X. We first observe that ultrafilters naturally induce clones; this yields a simple proof of Rosenberg's theorem: "there are 2^2^kappa many maximal (=precomplete)…

The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution their progeny, termed clones, which serve as…

In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions…

We show that every almost universal hash function also has the storage enforcement property. Almost universal hash functions have found numerous applications and we show that this new storage enforcement property allows the application of…

In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it…

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in terms of…

We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…