scholarly journals On blockers in bounded posets

2001 ◽  
Vol 26 (10) ◽  
pp. 581-588 ◽  
Author(s):  
Andrey O. Matveev
Keyword(s):  
Boolean Lattice ◽  
Bounded Poset ◽  
Finite Set ◽  
Bounded Posets

Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed.

scholarly journals n-Permutability is not join-prime for n ≥ 5

2020 ◽  
Vol 30 (08) ◽  
pp. 1717-1737
Author(s):  
Gergő Gyenizse ◽  
Miklós Maróti ◽  
László Zádori
Keyword(s):  
Primal Algebra ◽  
Bounded Poset ◽  
Finite Set ◽  
Near Unanimity

Let [Formula: see text] be the variety generated by an order primal algebra of finite signature associated with a finite bounded poset [Formula: see text] that admits a near-unanimity operation. Let [Formula: see text] be a finite set of linear identities that does not interpret in [Formula: see text]. Let [Formula: see text] be the variety defined by [Formula: see text]. We prove that [Formula: see text] is [Formula: see text]-permutable for some [Formula: see text]. This implies that there is an [Formula: see text] such that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties. In fact, it follows that [Formula: see text]-permutability where [Formula: see text] runs through the integers greater than 1 is not prime in the lattice of interpretability types of varieties. We strengthen this result by making [Formula: see text] and [Formula: see text] more special. We let [Formula: see text] be the 6-element bounded poset that is not a lattice and [Formula: see text] the variety defined by the set of majority identities for a ternary operational symbol [Formula: see text]. We prove in this case that [Formula: see text] is 5-permutable. This implies that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties whenever [Formula: see text]. We also provide an example demonstrating that [Formula: see text] is not 4-permutable.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Novel Simplified Implementation of Finite-Set Model Predictive Control for Power Converters

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jose J. Silva ◽  
Jose R. Espinoza ◽  
Jaime A. Rohten ◽  
Esteban S. Pulido ◽  
Felipe A. Villarroel ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Power Converters ◽  
Finite Set

scholarly journals Robust Universal Inference

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 773
Author(s):  
Amichai Painsky ◽  
Meir Feder
Keyword(s):  
Robust Estimation ◽  
Minimax Estimator ◽  
Worst Case ◽  
Capacity Theory ◽  
Alternative Approach ◽  
True Model ◽  
Finite Set ◽  
Universal Prediction ◽  
Estimation Scheme

Learning and making inference from a finite set of samples are among the fundamental problems in science. In most popular applications, the paradigmatic approach is to seek a model that best explains the data. This approach has many desirable properties when the number of samples is large. However, in many practical setups, data acquisition is costly and only a limited number of samples is available. In this work, we study an alternative approach for this challenging setup. Our framework suggests that the role of the train-set is not to provide a single estimated model, which may be inaccurate due to the limited number of samples. Instead, we define a class of “reasonable” models. Then, the worst-case performance in the class is controlled by a minimax estimator with respect to it. Further, we introduce a robust estimation scheme that provides minimax guarantees, also for the case where the true model is not a member of the model class. Our results draw important connections to universal prediction, the redundancy-capacity theorem, and channel capacity theory. We demonstrate our suggested scheme in different setups, showing a significant improvement in worst-case performance over currently known alternatives.

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

On procrustean mean shapes and the shape of the means

1996 ◽  
Vol 28 (2) ◽  
pp. 336-337
Author(s):  
Hulling Le
Keyword(s):  
Statistical Models ◽  
Nuisance Parameters ◽  
Finite Set

Two sets of k labelled points, or configurations, in ℝm are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

scholarly journals A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 767
Author(s):  
Alexandra Băicoianu ◽  
Cristina Maria Păcurar ◽  
Marius Păun
Keyword(s):  
Approximation Method ◽  
Finite System ◽  
Countable System ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Finite Systems ◽  
Fractal Interpolation Function ◽  
Fractal Interpolation Functions ◽  
Finite Set ◽  
Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

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