Search results for "Relational algebra"
showing 10 items of 20 documents
Spectral Properties of Partial *-Algebras
2010
We continue our study of topological partial *algebras focusing our attention to some basic spectral properties. The special case of partial *-algebras of operators is examined first, in order to find sufficient hints for the study of the abstract case. The outcome consists in the selection of a class of topological partial *-algebras (partial GC*-algebras) that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*-algebra.
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
A decomposition theorem for compact-valued Henstock integral
2006
We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.
Caristi Type Selections of Multivalued Mappings
2015
Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.
Parameter subset selection for the dynamic calibration of activated sludge models (ASMs): experience versus systems analysis.
2007
In this work we address the issue of parameter subset selection within the scope of activated sludge model calibration. To this end, we evaluate two approaches: (i) systems analysis and (ii) experience-based approach. The evaluation has been carried out using a dynamic model (ASM2d) calibrated to describe nitrogen and phosphorus removal in the Haaren WWTP (The Netherlands). The parameter significance ranking shows that the temperature correction coefficients are among the most influential parameters on the model output. This outcome confronts the previous identifiability studies and the experience based approaches which excluded them from their analysis. Systems analysis reveals that parame…
Fault diagnosis and modeling of the liquids packaging process. A research based on Petri Nets
2008
Searching for solutions to manufacture industries, which every day deal with problems of faults in their process, that generate economics and humans main losses, an algorithm to construct a Petri Nets based model and diagnoser to isolate and fault detection of discrete events systems is presented. This algorithm is developed in a real process of liquids packaging, where we can see that its implementation allows detecting individuals, simultaneous and dependents faults. The process to construct the model and diagnoser is systematic and useful, and it reduces the problems of combinational explosion, which is the main problem present in other investigations. This research has an excellent proj…
Combinatorial proofs of two theorems of Lutz and Stull
2021
Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…
Social Influence Maximization in Hypergraphs
2021
This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold diffusion model defined on an input graph with node thresholds, quantifying the hardness to influence each node. The goal is to find the smaller set of items that can influence the whole network according to the diffusion model defined. This study generalizes the TSS problem on networks characterized by many-to-many relationships modeled via hypergraphs. Specifically, we introduce a linear threshold diffusion process on such …
Implementing an ATL model checker tool using relational algebra concepts
2014
Alternating-Time Temporal Logic (ATL) is a branching-time temporal logic that naturally describes computations of open systems. An open system interacts with its environment and its behavior depends on the state of the system as well as the behavior of the environment. ATL model-checking is a well-established technique for verifying that a formal model representing such a system satisfies a given property. In this paper we describe a new interactive model checker environment based on algebraic approach. Our tool is implemented in client-server paradigm. The client part allows an interactive construction of ATL models represented by concurrent game structures as directed multi-graphs. The se…
Solar neutrino detection in liquid xenon detectors via charged-current scattering to excited states
2020
We investigate the prospects for real-time detection of solar neutrinos via the charged-current neutrino-nucleus scattering process in liquid xenon time projection chambers. We use a nuclear shell model, benchmarked with experimental data, to calculate the cross sections for populating specific excited states of the caesium nuclei produced by neutrino capture on $^{131}$Xe and $^{136}$Xe. The shell model is further used to compute the decay schemes of the low-lying $1^{+}$ excited states of $^{136}$Cs, for which there is sparse experimental data. We explore the possibility of tagging the characteristic de-excitation $\gamma$-rays/conversion electrons using two techniques: spatial separation…