Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

The Uncertain generalized probabilistic weighted average and its application in the theory of expertons

A new model for dealing with decision making under risk by considering subjective and objective information in the same formulation is here presented. The uncertain probabilistic weighted average (UPWA) is also presented. Its main advantage is that it unifies the probability and the weighted average in the same formulation and considering the degree of importance that each case has in the analysis. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases. The applicability of the UPWA is also studied and it is seen that it is very broad because all the previous studies that use the probability or the weighted average can be revised with this new approach. Focus is placed on a multi-person decision making problem regarding the selection of strategies by using the theory of expertons.

Comparing Random-based and k-Anonymity-Based Algorithms for Graph Anonymization

Recently, several anonymization algorithms have appeared for privacy preservation on graphs. Some of them are based on random-ization techniques and on k-anonymity concepts. We can use both of them to obtain an anonymized graph with a given k-anonymity value. In this paper we compare algorithms based on both techniques in orderto obtain an anonymized graph with a desired k-anonymity value. We want to analyze the complexity of these methods to generate anonymized graphs and the quality of the resulting graphs.

Matching stages of heavy-ion collision models

Heavy-ion reactions and other collective dynamical processes are frequently described by different theoretical approaches for the different stages of the process, like initial equilibration stage, intermediate locally equilibrated fluid dynamical stage, and final freeze-out stage. For the last stage, the best known is the Cooper-Frye description used to generate the phase space distribution of emitted, noninteracting particles from a fluid dynamical expansion or explosion, assuming a final ideal gas distribution, or (less frequently) an out-of-equilibrium distribution. In this work we do not want to replace the Cooper-Frye description, but rather clarify the ways of using it and how to choose the parameters of the distribution and, eventually, how to choose the form of the phase space distribution used in the Cooper-Frye formula. Moreover, the Cooper-Frye formula is used in connection with the freeze-out problem, while the discussion of transition between different stages of the collision is applicable to other transitions also. More recently, hadronization and molecular dynamics models have been matched to the end of a fluid dynamical stage to describe hadronization and freeze-out. The stages of the model description can be matched to each other on space-time hypersurfaces (just like through the frequently used freeze-out hypersurface). This work presents a generalized description of how to match the stages of the description of a reaction to each other, extending the methodology used at freeze-out, in simple covariant form which is easily applicable in its simplest version for most applications.

Impulse response recovery of linear systems through weighted cumulant slice

Identifiability of the so-called ω-slice algorithm is proven for ARMA linear systems. Although proofs were developed in the past for the simpler cases of MA and AR models, they were not extendible to general exponential linear systems. The results presented in this paper demonstrate a unique feature of the ω-slice method, which is unbiasedness and consistency when order is overdetermined, regardless of the IIR or FIR nature of the underlying system, and numerical robustness.

Scheduling an European basketball competition. An application of graph theory

The object of this project is to schedule a ctitious European basketball competition with many teams situated a long distances. The schedule must be fair, feasible and economical, which means that the total distance trav- eled by every team must be the minimal possible. First, we de ne the sport competition terminology and study di erent competition systems, focusing on the NBA and the Euroleague systems. Then we de ne concepts of graph theory and spherical distance that will be needed. Next we propose a com- petition system, explaining where will be allocated the teams and how will be the scheduling. Then there is a description of the programs that have been implemented, and, nally, the complete schedule is displayed, and some possible improvements are mentioned.

An efficient solver for weighted Max-SAT

We present a new branch and bound algorithm for weighted Max-SAT, called Lazy which incorporates original data structures and inference rules, as well as a lower bound of better quality. We provide experimental evidence that our solver is very competitive and outperforms some of the best performing Max-SAT and weighted Max-SAT solvers on a wide range of instances.

Edge matching puzzles as hard SAT/CSP benchmarks

Recently, edge matching puzzles, an NP-complete problem, have rececived, thanks to money-prized contests, considerable attention from wide audiences. We consider these competitions not only a challenge for SAT/CSP solving techniques but also as an opportunity to showcase the advances in the SAT/CSP community to a general audience. This paper studies the NP-complete problem of edge matching puzzles focusing on providing generation models of problem instances of variable hardness and on its resolution through the application of SAT and CSP techniques. From the generation side, we also identify the phase transition phenomena for each model. As solving methods, we employ both; SAT solvers through the translation to a SAT formula, and two ad-hoc CSP solvers we have developed, with different levels of consistency, employing several generic and specialized heuristics. Finally, we conducted an extensive experimental investigation to identify the hardest generation models and the best performing solving techniques.

An open source browser-based software tool for graph drawing and visualisation

In this research work we searched for open source libraries which supports graph drawing and visualisation and can run in a browser. Subsequent these libraries were evaluated to find out which one is the best for this task. The result was the d3.js is that library which has the greatest functionality, flexibility and customisability. Afterwards we developed an open source software tool where d3.js was included and which was written in JavaScript so that it can run browser-based.

WebGraphEd, an open source graph drawing editor for the web

WebGraphEd is an open source software for graph visualization and manipulation. It is especially designed to work for the web platform through a web browser. The web application has been written in JavaScript and compacted later, which makes it a very lightweight software. There is no need of additional software, and the only requirement is to have an HTML5 compliant browser. WebGraphEd works with scalable vector graphics (SVG), which it makes possible to create lossless graph drawings.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

Is the matching function Cobb-Douglas?

[cat] Estudiem les propietats teòriques que una funció d.emparellament ha de satisfer per tal de representar un mercat laboral amb friccions dins d'un model d'equilibri general amb emparellament aleatori. Analitzem el cas Cobb-Douglas, CES i altres formes funcionals per a la funció d.emparellament. Els nostres resultats estableixen restriccions sobre els paràmetres d'aquests formes funcionals per assegurar que l.equilibri és interior. Aquestes restriccions aporten raons teòriques per escollir entre diverses formes funcionals i permeten dissenyar tests d'error d'especificació de model en els treballs empírics.

Pointwise estimates for the Bergman kernel of the weighted Fock space

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^{2}(e^{-2\phi}) $ where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta\phi$.

Is the matching function Cobb-Douglas?

[cat] Estudiem les propietats teòriques que una funció d.emparellament ha de satisfer per tal de representar un mercat laboral amb friccions dins d'un model d'equilibri general amb emparellament aleatori. Analitzem el cas Cobb-Douglas, CES i altres formes funcionals per a la funció d.emparellament. Els nostres resultats estableixen restriccions sobre els paràmetres d'aquests formes funcionals per assegurar que l.equilibri és interior. Aquestes restriccions aporten raons teòriques per escollir entre diverses formes funcionals i permeten dissenyar tests d'error d'especificació de model en els treballs empírics.