Matrix-valued Monge-Kantorovich Optimal Mass Transport

We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multivariable time-series. The "mass" represents energy at various frequencies whereas, in addition to a usual transportation cost across frequencies, a cost of rotation is also taken into account. We show that it is natural to seek the transportation plan in the tensor product of the spaces for the two matrix-valued marginals. In contrast to the classical Monge-Kantorovich setting, the transportation plan is no longer supported on a thin zero-measure set.Comment: 11 page

Probabilistic Kernel Support Vector Machines

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available on each datum. In the present paper, we specifically consider Gaussian distributions to model uncertainty. Thereby, our data consist of pairs $(x_i,\Sigma_i)$, $i\in\{1,\ldots,N\}$, along with an indicator $y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair. These pairs may be viewed to represent the mean and covariance, respectively, of random vectors $\xi_i$ taking values in a suitable linear space (typically $\mathbb R^n$). Thus, our setting may also be viewed as a modification of Support Vector Machines to classify distributions, albeit, at present, only Gaussian ones. We outline the formalism that allows computing suitable classifiers via a natural modification of the standard "kernel trick." The main contribution of this work is to point out a suitable kernel function for applying Support Vector techniques to the setting of uncertain data for which a detailed uncertainty description is also available (herein, "Gaussian points").Comment: 6 pages, 6 figure

Efficient robust routing for single commodity network flows

We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains with prescribed initial and final marginals. From a computational standpoint, viewing scheduling this way is especially attractive in light of the existence of an iterative algorithm to compute the solution. The present paper builds on [13] by introducing an index of efficiency of a transportation plan and points, accordingly, to efficient-robust transport policies. In developing the theory, we establish two new invariance properties of the solution (called bridge) \u2013 an iterated bridge invariance property and the invariance of the most probable paths. These properties, which were tangentially mentioned in our previous work, are fully developed here. We also show that the distribution on paths of the optimal transport policy, which depends on a \u201ctemperature\u201d parameter, tends to the solution of the \u201cmost economical\u201d but possibly less robust optimal mass transport problem as the temperature goes to zero. The relevance of all of these properties for transport over networks is illustrated in an example

Acceptance Corrections and Extreme-Independent Models in Relativistic Heavy Ion Collisions

Kopeliovich's suggestion [nucl-th/0306044] to perform nuclear geometry (Glauber) calculations using different cross sections according to the experimental configuration is quite different from the standard practice of the last 20 years and leads to a different nuclear geometry definition for each experiment. The standard procedure for experimentalists is to perform the nuclear geometry calculation using the total inelastic N-N cross section, which results in a common nuclear geometry definition for all experiments. The incomplete acceptance of individual experiments is taken into account by correcting the detector response for the probability of measuring zero for an inelastic collision, which can often be determined experimentally. This clearly separates experimental issues such as different acceptances from theoretical issues which should apply in general to all experiments. Extreme-Independent models are used to illustrate the conditions for which the two methods give consistent or inconsistent results.Comment: 4 pages, 1 figure, published in Physical Review

Condor services for the Global Grid:interoperability between Condor and OGSA

In order for existing grid middleware to remain viable it is important to investigate their potentialfor integration with emerging grid standards and architectural schemes. The Open Grid ServicesArchitecture (OGSA), developed by the Globus Alliance and based on standard XML-based webservices technology, was the first attempt to identify the architectural components required tomigrate towards standardized global grid service delivery. This paper presents an investigation intothe integration of Condor, a widely adopted and sophisticated high-throughput computing softwarepackage, and OGSA; with the aim of bringing Condor in line with advances in Grid computing andprovide the Grid community with a mature suite of high-throughput computing job and resourcemanagement services. This report identifies mappings between elements of the OGSA and Condorinfrastructures, potential areas of conflict, and defines a set of complementary architectural optionsby which individual Condor services can be exposed as OGSA Grid services, in order to achieve aseamless integration of Condor resources in a standardized grid environment

Promotion/Inhibition Effects in Networks: A Model with Negative Probabilities

Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between nodes is encoded in the sign of the corresponding entry of a sign-indefinite adjacency matrix, though the strength of such co-expression (i.e., the precise value of edge weights) cannot typically be directly measured. Herein we address the inverse problem to determine network edge-weights based on a sign-indefinite adjacency and expression levels at the nodes. While our motivation originates in gene networks, the framework applies to networks where promotion/inhibition dictates a stationary mass distribution at the nodes. In order to identify suitable edge-weights we adopt a framework of ``negative probabilities,'' advocated by P.\ Dirac and R.\ Feynman, and we set up a likelihood formalism to obtain values for the sought edge-weights. The proposed optimization problem can be solved via a generalization of the well-known Sinkhorn algorithm; in our setting the Sinkhorn-type ``diagonal scalings'' are multiplicative or inverse-multiplicative, depending on the sign of the respective entries in the adjacency matrix, with value computed as the positive root of a quadratic polynomial.Comment: 6 page