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Register a new userSynthesis models in a probabilistic framework: metrics of fitting
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M. Cervino
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In general, synthesis models provide the mean value of the distribution of possible integrated luminosities, this distribution (and not only its mean value) being the actual description of the integrated luminosity. Therefore, to obtain the closest model to an observation only provides confi- dence about the precision of such a fit, but not information about the accuracy of the result. In this contribution we show how to overcome this drawback and we propose the use of the theoretical mean-averaged dispersion that can be produced by synthesis models as a metric of fitting to infer accurate physical parameters of observed systems.
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The theory interest group in the International Virtual Observatory Alliance (IVOA) has the goal of ensuring that theoretical data and services are taken into account in the IVOA standards process. In this poster we present some of the efforts carried out by this group to include evolutionary synthesis models in the VO framework. In particular we present the VO tool PGos3, developed by the INAOE (Mexico) and the Spanish Virtual Observatory which includes most of public SSP models in the VO framework (e.g. VOSpec). We also describe the problems related with the inclusion of synthesis models in the VO framework and we try to encourage people to define the way in which synthesis models should be described. This issue has implications not only for the inclusion of synthesis models in the the VO framework but also for a proper usage of synthesis models.
We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical calculus of PGMs and TNs exhibits many similarities, with discrete undirected graphical models (UGMs) being a special case of TNs. However, more general probabilistic TN models such as Born machines (BMs) employ complex-valued hidden states to produce novel forms of correlation among the probabilities. While representing a new modeling resource for capturing structure in discrete probability distributions, this behavior also renders the direct application of standard PGM tools impossible. We aim to bridge this gap by introducing a hybrid PGM-TN formalism that integrates quantum-like correlations into PGM models in a principled manner, using the physically-motivated concept of decoherence. We first prove that applying decoherence to the entirety of a BM model converts it into a discrete UGM, and conversely, that any subgraph of a discrete UGM can be represented as a decohered BM. This method allows a broad family of probabilistic TN models to be encoded as partially decohered BMs, a fact we leverage to combine the representational strengths of both model families. We experimentally verify the performance of such hybrid models in a sequential modeling task, and identify promising uses of our method within the context of existing applications of graphical models.
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate generation of new data.
Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic polynomial time, in some cases even finding the optimal solution in probabilistic polynomial time given access to an oracle for factoring integers. In this paper, we present a common mathematical structure underlying all results related to the exact synthesis of qubit unitaries known to date, including Clifford+T, Clifford-cyclotomic and V-basis gate sets, as well as gates sets induced by the braiding of Fibonacci anyons in topological quantum computing. The framework presented here also provides a means to answer questions related to the exact synthesis of unitaries for wide classes of other gate sets, such as Clifford+T+V and SU(2) level k anyons.
We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash market equilibria and other optimal strategies in various situations ranging from competition of two identical firms to firms of different sizes and firms which improve their efficiency.
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