Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such scenarios, we supplement the classical Fisher model of a market by introducing {\em transaction costs}. For every buyer $i$ and every good $j$, there is a transaction cost of \cij; if the price of good $j$ is $p_j$, then the cost to the buyer $i$ {\em per unit} of $j$ is p_j + \cij. This allows the same good to be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes $\epsilon$-approximate equilibrium prices and allocations in $O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations - where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum of the budgets of all the buyers

New techniques for the solution of linear systems by iterative methods

AbstractA new iterative method for the solution of linear systems, based upon a new splitting of the coefficient matrix A, is presented.The method is obtained by considering splittings of the type A = (A − M) + M, where M−1 is a symmetric tridiagonal matrix, and by minimizing the Frobenius norm of the iteration matrix so derived.Numerical examples are provided, showing that our algorithm improves the rate of convergence of Jacobi method, without increasing the order of magnitude of the computational efforts required

A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201

Using Elimination Theory to construct Rigid Matrices

The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in this family are distinct primitive roots of unity of orders roughly exp(n^2 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination theory of polynomial ideals. In particular, we use results on the existence of polynomials in elimination ideals with effective degree upper bounds (effective Nullstellensatz). Using elementary algebraic geometry, we prove that the dimension of the affine variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we use elimination theory to examine whether the rigidity function is semi-continuous.Comment: 25 Pages, minor typos correcte

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Detection of the mosquito-borne flaviviruses, West Nile, Dengue, Saint Louis Encephalitis, Ilheus, Bussuquara, and Yellow Fever in free-ranging black howlers (Alouatta caraya) of Northeastern Argentina

Several medically important mosquito-borne flaviviruses have been detected in Argentina in recent years: Dengue (DENV), St. Louis encephalitis (SLEV), West Nile (WNV) and Yellow Fever (YFV) viruses. Evidence of Bussuquara virus (BSQV) and Ilheus virus (ILHV) activity were found, but they have not been associated with human disease. Non-human primates can act as important hosts in the natural cycle of flaviviruses and serological studies can lead to improved understanding of virus circulation dynamics and host susceptibility. From July–August 2010, we conducted serological and molecular surveys in free–ranging black howlers (Alouatta caraya) captured in northeastern Argentina. We used 90% plaque-reduction neutralization tests (PRNT90) to analyze 108 serum samples for antibodies to WNV, SLEV, YFV, DENV (serotypes 1and 3), ILHV, and BSQV. Virus genome detection was performed using generic reverse transcription (RT)-nested PCR to identify flaviviruses in 51 antibody-negative animals. Seventy animals had antibodies for one or more flaviviruses for a total antibody prevalence of 64.8% (70/108). Monotypic (13/70, 19%) and heterotypic (27/70, 39%) patterns were differentiated. Specific neutralizing antibodies against WNV, SLEV, DENV-1, DENV-3, ILHV, and BSQV were found. Unexpectedly, the highest flavivirus antibody prevalence detected was to WNV with 9 (8.33%) monotypic responses. All samples tested by (RT)-nested PCR were negative for viral genome. This is the first detection of WNV-specific antibodies in black howlers from Argentina and the first report in free-ranging non-human primates from Latin-American countries. Given that no animals had specific neutralizing antibodies to YFV, our results suggest that the study population remains susceptible to YFV. Monitoring of these agents should be strengthened to detect the establishment of sylvatic cycles of flaviviruses in America and evaluate risks to wildlife and human health.Fil: Morales, Maria Alejandra. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Fabbri, Cintia M.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Zunino, Gabriel Eduardo. Universidad Nacional de General Sarmiento. Instituto del Conurbano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kowalewski, Miguel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia". Estación Biológica de Usos Múltiples (Sede Corrientes); ArgentinaFil: Luppo, Victoria C.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Enría, Delia A.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Levis, Silvana C.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Calderón, Gladys Ethel. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; Argentin