DSpace Collection:
http://hdl.handle.net/2117/3741
Tue, 22 Jul 2014 13:39:19 GMT2014-07-22T13:39:19Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoOn the nucleolus of 2 × 2 assignment games
http://hdl.handle.net/2117/21814
Title: On the nucleolus of 2 × 2 assignment games
Authors: Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves
Abstract: We provide explicit formulas for the nucleolus of an arbitrary assignment game with two buyers and two sellers. Five different cases are analyzed depending on the entries of the assignment matrix. We extend the results to the case of 2 × m or m × 2 assignment games.Fri, 28 Feb 2014 15:22:22 GMThttp://hdl.handle.net/2117/218142014-02-28T15:22:22ZMartínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las NievesnoTeoria de jocs, Assignació de recursos, Matemàtica financera, Models matemàtics, Estudis de viabilitat, Game theory, Ressource allocation, Business mathematics, Mathematical models, Feasibility studiesWe provide explicit formulas for the nucleolus of an arbitrary assignment game with two buyers and two sellers. Five different cases are analyzed depending on the entries of the assignment matrix. We extend the results to the case of 2 × m or m × 2 assignment games.A procedure to compute the nucleolus of the assignment game
http://hdl.handle.net/2117/21811
Title: A procedure to compute the nucleolus of the assignment game
Authors: Martínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las Nieves
Abstract: The assignment game introduced by Shapley and Shubik (1972) [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.Fri, 28 Feb 2014 15:06:04 GMThttp://hdl.handle.net/2117/218112014-02-28T15:06:04ZMartínez De Albeniz, Javier; Rafels Pallarola, Carlos; Ybern Carballo, M. de Las NievesnoAssignment game, Core, NucleolusThe assignment game introduced by Shapley and Shubik (1972) [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.Kirchhoff indexes of a network
http://hdl.handle.net/2117/8290
Title: Kirchhoff indexes of a network
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, Margarida
Abstract: In this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger
operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures
of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with
symmetries, specifically for weighted wagon-wheels and circular ladders.Wed, 21 Jul 2010 08:33:04 GMThttp://hdl.handle.net/2117/82902010-07-21T08:33:04ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel; Mitjana Riera, MargaridanoIn this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger
operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures
of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with
symmetries, specifically for weighted wagon-wheels and circular ladders.A formula for the Kirchhoff index
http://hdl.handle.net/2117/1247
Title: A formula for the Kirchhoff index
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n-th Formula.Wed, 17 Oct 2007 14:55:49 GMThttp://hdl.handle.net/2117/12472007-10-17T14:55:49ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoKirchhoff index, effective resistance, equilibrium measureWe show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n-th Formula.Application of the forces' method in dynamic systems
http://hdl.handle.net/2117/1246
Title: Application of the forces' method in dynamic systems
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We present here some applications of the Forces's method in dynamic systems. In particular, we consider the problem of the approximation of the trajectories of a conservative system of point masses by means of the minimization of the action integral and the computation of planar central configurations.Wed, 17 Oct 2007 14:33:10 GMThttp://hdl.handle.net/2117/12462007-10-17T14:33:10ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuelnodynamic systems, forces' method, choreographiesWe present here some applications of the Forces's method in dynamic systems. In particular, we consider the problem of the approximation of the trajectories of a conservative system of point masses by means of the minimization of the action integral and the computation of planar central configurations.Computational cost of the Fekete problem
http://hdl.handle.net/2117/1241
Title: Computational cost of the Fekete problem
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We present here strong numerical and statistical evidence of the fact that the Smale's 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the 2-sphere satisfying the Smale's conditions can be identified with a computational cost of approximately O(N^10})Thu, 11 Oct 2007 16:42:31 GMThttp://hdl.handle.net/2117/12412007-10-11T16:42:31ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoFekete points, Smale's 7th problemWe present here strong numerical and statistical evidence of the fact that the Smale's 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the 2-sphere satisfying the Smale's conditions can be identified with a computational cost of approximately O(N^10})Characterization of symmetric M-matrices as resistive inverses
http://hdl.handle.net/2117/1168
Title: Characterization of symmetric M-matrices as resistive inverses
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do that we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite
Schrödinger operator which ground state is determined by the its lowest eigenvalue and the corresponding positive eigenvector. We also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric M-matrices. The key tool is the definition of the effective resistance with respect to a nonnegative value and a weight. We prove that these effective resistances verify similar properties to those satisfied by the standard effective resistances which leads us to carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric M-matrices. Moreover we pay special attention on those generalized inverses identified with Green operators, which in particular
includes the analysis of the Moore-Penrose inverse.Wed, 01 Aug 2007 19:30:23 GMThttp://hdl.handle.net/2117/11682007-08-01T19:30:23ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoSchrödinger operator, M-matrices, generalized inverses, Green kernels, Moore-Penrose inverse, effective resistance, Kirchhoff indexWe aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do that we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite
Schrödinger operator which ground state is determined by the its lowest eigenvalue and the corresponding positive eigenvector. We also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric M-matrices. The key tool is the definition of the effective resistance with respect to a nonnegative value and a weight. We prove that these effective resistances verify similar properties to those satisfied by the standard effective resistances which leads us to carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric M-matrices. Moreover we pay special attention on those generalized inverses identified with Green operators, which in particular
includes the analysis of the Moore-Penrose inverse.Potential Theory for boundary value problems on finite networks
http://hdl.handle.net/2117/589
Title: Potential Theory for boundary value problems on finite networks
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We aim here at analyzing self-adjoint boundary value problems
on finite networks associated with positive semi-definite
Schrödinger operators. In addition, we study the existence
and uniqueness of solutions and its variational formulation.
Moreover, we will tackle a well-known problem in the framework
of Potential Theory, the so-called condenser principle. Then,
we generalize of the concept of effective resistance between
two vertices of the network and we characterize the Green
function of some BVP in terms of effective resistances.Fri, 01 Dec 2006 17:44:29 GMThttp://hdl.handle.net/2117/5892006-12-01T17:44:29ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoDiscrete Potential Theory, Combinatorial Laplacian, Schrödinger operator, Boundary value problems, Effective resistance, Green functionWe aim here at analyzing self-adjoint boundary value problems
on finite networks associated with positive semi-definite
Schrödinger operators. In addition, we study the existence
and uniqueness of solutions and its variational formulation.
Moreover, we will tackle a well-known problem in the framework
of Potential Theory, the so-called condenser principle. Then,
we generalize of the concept of effective resistance between
two vertices of the network and we characterize the Green
function of some BVP in terms of effective resistances.Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks
http://hdl.handle.net/2117/588
Title: Bounds on the first non-null eigenvalue for self-adjoint boundary value problems on networks
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: We aim here at obtaining bounds on the first non-null eigenvalue for self-adjoint boundary value problems on a weighted network by means of equilibrium measures, that includes the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of
distance-regular graphs, and we show that the bounds obtained are better than the known until now.Fri, 01 Dec 2006 17:29:22 GMThttp://hdl.handle.net/2117/5882006-12-01T17:29:22ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoNetworks, Self-adjoint eigenvalue problems, Discrete laplacian, Equilibrium measures, Distance-regular graphsWe aim here at obtaining bounds on the first non-null eigenvalue for self-adjoint boundary value problems on a weighted network by means of equilibrium measures, that includes the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some known examples. In particular, we emphasize the case of
distance-regular graphs, and we show that the bounds obtained are better than the known until now.Regular boundary value problems on a path throughout Chebyshev Polynomials
http://hdl.handle.net/2117/587
Title: Regular boundary value problems on a path throughout Chebyshev Polynomials
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: In this work we study the different types of regular boundary value
problems on a path associated with the Schrödinger operator. In
particular, we obtain the Green function for each problem and we
emphasize the case of Sturm-Liouville boundary conditions. In
addition, we study the periodic boundary value problem that
corresponds to the Poisson equation in a cycle. In any case, the
Green functions are given in terms of Chebyshev polynomials since
they verify a recurrence law similar to the one verified by the
Schrödinger operator on a path.Fri, 01 Dec 2006 17:06:32 GMThttp://hdl.handle.net/2117/5872006-12-01T17:06:32ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoDiscrete Schrödinger operator, boundary value problems, paths, Chebyshev polynomials, Green functionsIn this work we study the different types of regular boundary value
problems on a path associated with the Schrödinger operator. In
particular, we obtain the Green function for each problem and we
emphasize the case of Sturm-Liouville boundary conditions. In
addition, we study the periodic boundary value problem that
corresponds to the Poisson equation in a cycle. In any case, the
Green functions are given in terms of Chebyshev polynomials since
they verify a recurrence law similar to the one verified by the
Schrödinger operator on a path.Vector Calculus on weighted networks
http://hdl.handle.net/2117/494
Title: Vector Calculus on weighted networks
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
Abstract: In this work we study the different type of regular boundary value
problems on a path associated with the Schr\"odinger operator. In
particular, we get the Poisson kernel and the Green function for
each problem and we emphasize the cases of Dirichlet, Neumann, Mixed
and periodic problems. In any case, the Poisson kernel and the Green
function are given in terms of second and third kind Chebyshev
polynomials since they verify a recurrence law similar to the one
verified by the Sch\"odinger operator on a path.Mon, 02 Oct 2006 17:59:53 GMThttp://hdl.handle.net/2117/4942006-10-02T17:59:53ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés MarcosnoDiscrete operators, Discrete green identity, Vector calculus, Network cohomologyIn this work we study the different type of regular boundary value
problems on a path associated with the Schr\"odinger operator. In
particular, we get the Poisson kernel and the Green function for
each problem and we emphasize the cases of Dirichlet, Neumann, Mixed
and periodic problems. In any case, the Poisson kernel and the Green
function are given in terms of second and third kind Chebyshev
polynomials since they verify a recurrence law similar to the one
verified by the Sch\"odinger operator on a path.Fekete points in non-smooth surfaces
http://hdl.handle.net/2117/493
Title: Fekete points in non-smooth surfaces
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: In this paper we present a procedure for the estimation of the Fekete points on a
wide variety of non-regular objects in $R^3$. We understand the problem of the Fekete
points in terms of the identification of good equilibrium configurations for a potential energy that depends on the relative position of N particles. Although the procedure that we present here works well for different potential energies, the examples showed refer to the electrostatic potential energy, that plays an special role in Potential Theory and Physics. The objects for which our procedure has been designed can be described basically as the finite union of piecewise regular surfaces and curves. For the determination of a good starting configuration for the search of the Fekete points on such objects, a sequence of approximating regular surfaces must be constructed.
The numerical experience carried out until now suggests that the total computational
cost of the obtaining of a nearly optimal configuration with the procedure
introduced here is less than $N^3$ independently of the object considered.Mon, 02 Oct 2006 17:34:51 GMThttp://hdl.handle.net/2117/4932006-10-02T17:34:51ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoFekete points, Optimization, Non-smooth surfaces, Riesz KernelsIn this paper we present a procedure for the estimation of the Fekete points on a
wide variety of non-regular objects in $R^3$. We understand the problem of the Fekete
points in terms of the identification of good equilibrium configurations for a potential energy that depends on the relative position of N particles. Although the procedure that we present here works well for different potential energies, the examples showed refer to the electrostatic potential energy, that plays an special role in Potential Theory and Physics. The objects for which our procedure has been designed can be described basically as the finite union of piecewise regular surfaces and curves. For the determination of a good starting configuration for the search of the Fekete points on such objects, a sequence of approximating regular surfaces must be constructed.
The numerical experience carried out until now suggests that the total computational
cost of the obtaining of a nearly optimal configuration with the procedure
introduced here is less than $N^3$ independently of the object considered.Estimation of Fekete points
http://hdl.handle.net/2117/492
Title: Estimation of Fekete points
Authors: Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Abstract: In this paper we present a new method to estimate Fekete points on surfaces.
Although our method works in a general setting, we concentrate on its application to
the unit sphere because it is the prototype problem and in the unit cube because its
singularity. The algorithm we present here is very simple and it is based in a physical
interpretation of the behavior of a system of particles when they search for a minimal
energy configuration. Moreover, the algorithm is efficient and robust independently of the surface and the kernel used to define the energy. The algorithm allows us to work with a great number of particles, for instance, in less than a day of calculation time, we have obtained a good configuration for 50000 particles in the unit sphere without using symmetry properties and with a conventional PC.Mon, 02 Oct 2006 17:20:08 GMThttp://hdl.handle.net/2117/4922006-10-02T17:20:08ZBendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José ManuelnoFekete points, Optimization, Equilibrium distributions, Regular surfacesIn this paper we present a new method to estimate Fekete points on surfaces.
Although our method works in a general setting, we concentrate on its application to
the unit sphere because it is the prototype problem and in the unit cube because its
singularity. The algorithm we present here is very simple and it is based in a physical
interpretation of the behavior of a system of particles when they search for a minimal
energy configuration. Moreover, the algorithm is efficient and robust independently of the surface and the kernel used to define the energy. The algorithm allows us to work with a great number of particles, for instance, in less than a day of calculation time, we have obtained a good configuration for 50000 particles in the unit sphere without using symmetry properties and with a conventional PC.