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PubMed2006

Networks with given two-point correlations: hidden correlations from degree correlations.

This paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables, in which hidden variables correspond to desired node degrees. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node degrees. The observation supported by the depoissonization idea allows us to extract a distribution of hidden variables from a given node degree distribution. It completes the algorithm for generating uncorrelated networks that was suggested by other authors. In this paper we also carefully analyze the interplay between hidden attributes and node degrees. We show how to extract hidden correlations from degree correlations. Our derivations provide a mathematical background for the algorithm for generating correlated networks that was proposed by Boguñá and Pastor-Satorras.

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PubMed1976

Hidden genetic variability within electromorphs in finite populations.

The amount of hidden genetic variability within electromorphs in finite populations is studied by using the infinite site model and stepwise mutation model simultaneously. A formula is developed for the bivariate probability generating function for the number of codon differences and the number of electromorph state differences between two randomly chosen cistrons. Using this formula, the distribution as well as the mean and variance of the number of codon differences between two identical or nonidentical electromorphs are studied. The distribution of the number of codon differences between two randomly chosen identical electromorphs is similar to the geometric distribution but more leptokurtic. Studies are also made on the number of codon differences between two electromorphs chosen at random one from each of two populations which have been separated for an arbitrary number of generations. It is shown that the amount of hidden genetic variability is very large if the product of effective population size and mutation rate is large.

Codon↗
PubMed2001

Bell's theorem and the problem of decidability between the views of Einstein and Bohr.

Einstein, Podolsky, and Rosen (EPR) have designed a gedanken experiment that suggested a theory that was more complete than quantum mechanics. The EPR design was later realized in various forms, with experimental results close to the quantum mechanical prediction. The experimental results by themselves have no bearing on the EPR claim that quantum mechanics must be incomplete nor on the existence of hidden parameters. However, the well known inequalities of Bell are based on the assumption that local hidden parameters exist and, when combined with conflicting experimental results, do appear to prove that local hidden parameters cannot exist. This fact leaves only instantaneous actions at a distance (called "spooky" by Einstein) to explain the experiments. The Bell inequalities are based on a mathematical model of the EPR experiments. They have no experimental confirmation, because they contradict the results of all EPR experiments. In addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions; for instance, he assumes that the hidden parameters are governed by a single probability measure independent of the analyzer settings. We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.

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PubMed2002

Marginalized kernels for biological sequences.

MOTIVATION: Kernel methods such as support vector machines require a kernel function between objects to be defined a priori. Several works have been done to derive kernels from probability distributions, e.g., the Fisher kernel. However, a general methodology to design a kernel is not fully developed. RESULTS: We propose a reasonable way of designing a kernel when objects are generated from latent variable models (e.g., HMM). First of all, a joint kernel is designed for complete data which include both visible and hidden variables. Then a marginalized kernel for visible data is obtained by taking the expectation with respect to hidden variables. We will show that the Fisher kernel is a special case of marginalized kernels, which gives another viewpoint to the Fisher kernel theory. Although our approach can be applied to any object, we particularly derive several marginalized kernels useful for biological sequences (e.g., DNA and proteins). The effectiveness of marginalized kernels is illustrated in the task of classifying bacterial gyrase subunit B (gyrB) amino acid sequences.

Algorithms↗
PubMed2001

A possible loophole in the theorem of Bell.

The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results, these inequalities appear to prove that local hidden parameters cannot exist. This contradiction suggests to many that only instantaneous action at a distance can explain the Einstein, Podolsky, and Rosen type of experiments. We show that, in addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions that contribute to his being able to obtain the desired contradiction. For instance, Bell assumes that the hidden parameters do not depend on time and are governed by a single probability measure independent of the analyzer settings. We argue that the exclusion of time has neither a physical nor a mathematical basis but is based on Bell's translation of the concept of Einstein locality into the language of probability theory. Our additional set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does not permit Bell-type proofs to go forward.

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PubMed2003

Communication cost of simulating Bell correlations.

What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.

Journal Article↗
PubMed2005

Pre- and post-selection paradoxes and contextuality in quantum mechanics.

Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post-selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of the impossibility of a noncontextual hidden variable theory. This proof is obtained by considering all the measurements involved in the paradoxical effect--the preselection, the post-selection, and the alternative possible intermediate measurements--as alternative possible measurements at a single time.

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PubMed2003

Combinatorics and quantum nonlocality.

We use techniques for lower bounds on communication to derive necessary conditions (in terms of detector efficiency or amount of superluminal communication) for being able to reproduce the quantum correlations occurring in Einstein-Podolsky-Rosen-type experiments with classical local hidden-variable theories. As an application, we consider n parties sharing a Greenberger-Horne-Zeilinger-type state and show that the amount of superluminal classical communication required to reproduce the correlations is at least n(log((2)n-3) bits and the maximum detector efficiency eta(*) for which the resulting correlations can still be reproduced by a local hidden-variable theory is upper bounded by eta(*)</=8/n and thus decreases with n.

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PubMed2002

Local realistic model for the dynamics of bulk-ensemble NMR information processing.

We construct a local realistic hidden-variable model that describes the states and dynamics of bulk-ensemble NMR information processing up to about 12 nuclear spins. The existence of such a model rules out violation of any Bell inequality, temporal or otherwise, in present high-temperature, liquid-state NMR experiments. The model does not provide an efficient description in that the number of hidden variables grows exponentially with the number of nuclear spins.

Journal Article↗