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Results for “Hidden variables”

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PubMed2004

Consciousness and quantum information processing: uncovering the foundation for a medicine of light.

Great progress has been made by Russian and German researchers in recent years (Popp, Voeikov, and others) to examine the biophysical aspects of biophotonic processes in humans. This paper suggests that there is a many-body reality to the way biophysical light interacts with the human self-organization of information that may be achieved by means of biomolecular, metabolic, or neural communication. These systems may merge as mobile energy relay systems similar to what is seen as qi processes in acupuncture science, suggesting a "holomovement" that seeks to confirm itself and increasingly retrieves and uses only the information that serves its exchanges with the environment. This coevolution of evolutionary process levels, expressed in process terms, can be seen as a foundation for a Medicine of Light integrating hidden variables in consciousness studies with functional differentiation and new findings in the biologic sciences.

Acupuncture Therapy↗

PubMed2004

Modeling and analysis of heterogeneous regulation in biological networks.

In this study, we propose a novel model for the representation of biological networks and provide algorithms for learning model parameters from experimental data. Our approach is to build an initial model based on extant biological knowledge and refine it to increase the consistency between model predictions and experimental data. Our model encompasses networks which contain heterogeneous biological entities (mRNA, proteins, metabolites) and aims to capture diverse regulatory circuitry on several levels (metabolism, transcription, translation, post-translation and feedback loops, among them). Algorithmically, the study raises two basic questions: how to use the model for predictions and inference of hidden variables states, and how to extend and rectify model components. We show that these problems are hard in the biologically relevant case where the network contains cycles. We provide a prediction methodology in the presence of cycles and a polynomial time, constant factor approximation for learning the regulation of a single entity. A key feature of our approach is the ability to utilize both high-throughput experimental data, which measure many model entities in a single experiment, as well as specific experimental measurements of few entities or even a single one. In particular, we use together gene expression, growth phenotypes, and proteomics data. We tested our strategy on the lysine biosynthesis pathway in yeast. We constructed a model of more than 150 variables based on an extensive literature survey and evaluated it with diverse experimental data. We used our learning algorithms to propose novel regulatory hypotheses in several cases where the literature-based model was inconsistent with the experiments. We showed that our approach has better accuracy than extant methods of learning regulation.

Algorithms↗

PubMed2002

Modelling regulatory pathways in E. coli from time series expression profiles.

MOTIVATION: Cells continuously reprogram their gene expression network as they move through the cell cycle or sense changes in their environment. In order to understand the regulation of cells, time series expression profiles provide a more complete picture than single time point expression profiles. Few analysis techniques, however, are well suited to modelling such time series data. RESULTS: We describe an approach that naturally handles time series data with the capabilities of modelling causality, feedback loops, and environmental or hidden variables using a Dynamic Bayesian network. We also present a novel way of combining prior biological knowledge and current observations to improve the quality of analysis and to model interactions between sets of genes rather than individual genes. Our approach is evaluated on time series expression data measured in response to physiological changes that affect tryptophan metabolism in E. coli. Results indicate that this approach is capable of finding correlations between sets of related genes.

Adaptation, Physiological↗

PubMed2005

Sorting points into neighborhoods (SPIN): data analysis and visualization by ordering distance matrices.

SUMMARY: We introduce a novel unsupervised approach for the organization and visualization of multidimensional data. At the heart of the method is a presentation of the full pairwise distance matrix of the data points, viewed in pseudocolor. The ordering of points is iteratively permuted in search of a linear ordering, which can be used to study embedded shapes. Several examples indicate how the shapes of certain structures in the data (elongated, circular and compact) manifest themselves visually in our permuted distance matrix. It is important to identify the elongated objects since they are often associated with a set of hidden variables, underlying continuous variation in the data. The problem of determining an optimal linear ordering is shown to be NP-Complete, and therefore an iterative search algorithm with O(n3) step-complexity is suggested. By using sorting points into neighborhoods, i.e. SPIN to analyze colon cancer expression data we were able to address the serious problem of sample heterogeneity, which hinders identification of metastasis related genes in our data. Our methodology brings to light the continuous variation of heterogeneity--starting with homogeneous tumor samples and gradually increasing the amount of another tissue. Ordering the samples according to their degree of contamination by unrelated tissue allows the separation of genes associated with irrelevant contamination from those related to cancer progression. AVAILABILITY: Software package will be available for academic users upon request.

Algorithms↗

PubMed1990

Animal models for osteoarthritis--ensuring experimental validity.

Confounding factors, bias factors and hidden variables affect the design of experiments involving animal models. In a frequently used dog model for osteoarthritis these can arise, for example, because of the influence of age, sex and breed of dog. Controls are required to investigate the progression of osteoarthritis even in experiments forming time series. However, there are no true controls in animal models for joint degeneration. Analysis of data collected from experiments involving animal models depends on the number of factors being varied. The number of animals influences the level of confidence associated with a result. Ignoring statistics can invalidate conclusions drawn from the experiments. Statistical considerations are also important in the presentation of results.

Animals↗

PubMed2004

Average path length in random networks.

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdös and Rényi (ER), evolving networks introduced by Barabási and Albert as well as random networks with asymptotic scale-free connectivity distributions characterized by an arbitrary scaling exponent alpha>2. Our result for 2 infinity there is a saturation effect for the average path length.

Journal Article↗

PubMed2006

Multispecies grand-canonical models for networks with reciprocity.

Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grand-canonical class of models reproducing the observed patterns of reciprocity by regarding single and double links as Fermi particles of different "chemical species" governed by the corresponding chemical potentials. Within this framework we find interesting special cases such as the extensions of random graphs, the configuration model, and hidden-variable models. Our theoretical predictions are also in excellent agreement with the empirical results for networks with well-studied reciprocity.

Journal Article↗

PubMed2006

Fluctuation-dissipation relations in complex networks.

In this paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing the susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of the self-organization of real systems into sparse structures with low susceptibility to random external disruptions. We also show that the ensembles of networks with a given degree sequence and networks characterized by two-point correlations are equivalent to random networks with hidden variables.

Journal Article↗

PubMed2006

Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation.

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.

Journal Article↗

PubMed2006

Effect of degree correlations on the loop structure of scale-free networks.

In this paper we study the impact of degree correlations in the subgraph statistics of scale-free networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the average number of Hamiltonian paths in a three-core of real world networks. We prove our results in the two-vertex correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.

Journal Article↗

PubMed2006

Network of epicenters of the Olami-Feder-Christensen model of earthquakes.

We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also an unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.

Journal Article↗

PubMed2000

Classical teleportation of a quantum Bit

Classical teleportation is defined as a scenario where the sender is given the classical description of an arbitrary quantum state while the receiver simulates any measurement on it. This scenario is shown to be achievable by transmitting only a few classical bits if the sender and receiver initially share local hidden variables. Specifically, a communication of 2.19 bits is sufficient on average for the classical teleportation of a qubit, when restricted to von Neumann measurements. The generalization to positive-operator-valued measurements is also discussed.

Journal Article↗

PubMed2000

Incompatibility of macroscopic local realism with quantum mechanics in measurements with macroscopic uncertainties

We show that quantum mechanics predicts a contradiction with local hidden variable theories for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new premise, macroscopic local realism.

Journal Article↗

PubMed2000

Inequalities for dealing with detector inefficiencies in greenberger-horne-zeilinger-type experiments

In this article we show that the three-particle Greenberger-Horne-Zeilinger theorem can be reformulated in terms of inequalities, allowing imperfect correlations due to detector inefficiencies. We show quantitatively that taking into account these inefficiencies, the published results of the Innsbruck experiment support the nonexistence of local hidden variables that explain the experimental results.

Journal Article↗

PubMed2000

Feasible "Kochen-Specker" experiment with single particles

We present a simple experimental scheme which can be used to demonstrate an all-or-nothing-type contradiction between noncontextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and Garcia-Alcaine, shows that even for a single particle, path and spin information cannot be predetermined in a noncontextual way.

Journal Article↗

PubMed2001

"All versus nothing" inseparability for two observers.

A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.

Journal Article↗

PubMed2001

Quantum communication between N partners and Bell's inequalities.

We consider a family of quantum communication protocols involving N partners. We demonstrate the existence of a link between the security of these protocols against individual attacks by the eavesdropper, and the violation of some Bell's inequalities, generalizing the link that was noticed some years ago for two-partners quantum cryptography. The arguments are independent of the local hidden variable debate.

Journal Article↗

PubMed2001

Multipartite bound entangled states that violate Bell's inequality.

We study the relation between distillability of multipartite states and violation of Bell's inequality. We prove that there exist multipartite bound entangled states (i.e., nonseparable, nondistillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.

Journal Article↗