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PubMed2002

Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states.

We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.

Journal Article↗
PubMed2003

Experimental test of the Kochen-Specker theorem with single photons.

Using the spontaneous parametric down-conversion process in a type-I phase matching beta-barium-borate crystal as a single photon source, we perform an all-or-nothing-type Kochen-Specker experiment proposed by Simon et al. [Phys. Rev. Lett. 85, 1783 (2000)]] to verify whether noncontextual hidden variables or quantum mechanics is right. The results strongly agree with quantum mechanics.

Journal Article↗
PubMed2003

Quantum states and generalized observables: a simple proof of Gleason's theorem.

A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple proof of the result, analogous to Gleason's theorem, that any quantum state is given by a density operator. As a corollary we obtain a von Neumann-type argument against noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.

Journal Article↗
PubMed2004

Preparing high purity initial states for nuclear magnetic resonance quantum computing.

Here we demonstrate how parahydrogen can be used to prepare a two-spin system in an almost pure state which is suitable for implementing nuclear magnetic resonance quantum computation. A 12 ns laser pulse is used to initiate a chemical reaction involving pure parahydrogen (the nuclear spin singlet of H2). The product, formed on the micros time scale, contains a hydrogen-derived two-spin system with an effective spin-state purity of 0.916. To achieve a comparable result by direct cooling would require an unmanageable (in the liquid state) temperature of 6.4 mK or an impractical magnetic field of 0.45 MT at room temperature. The resulting spin state has an entanglement of formation of 0.822 and cannot be described by local hidden variable models.

Journal Article↗
PubMed2005

Realization of Hardy's thought experiment with photons.

We present an experimental realization of Hardy's thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne-type inequality is derived and violated.

Journal Article↗
PubMed2006

Spin correlations of strongly interacting massive fermion pairs as a test of Bell's inequality.

We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin 1/2 hadrons from the decay of short-lived (tau<10;-21sec) 2He spin-singlet state, populated in the nuclear reaction 2H+;1H-->;2He+n. The novel features of this experiment are (a) the use of an 'event-ready' [corrected] detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full 2pi sr acceptance with a random "post selection" of the reference axes. The spin-correlation function is deduced to be S[exp](pi/4)=2.83+/-0.24stat+/-0.07sys. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of |S|<or=2 at a confidence level of 99.3%.

Journal Article↗
PubMed2001

Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.

It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.

Animals↗
PubMed2003

A taxonomy for spatiotemporal connectionist networks revisited: the unsupervised case.

Spatiotemporal connectionist networks (STCNs) comprise an important class of neural models that can deal with patterns distributed in both time and space. In this article, we widen the application domain of the taxonomy for supervised STCNs recently proposed by Kremer (2001) to the unsupervised case. This is possible through a reinterpretation of the state vector as a vector of latent (hidden) variables, as proposed by Meinicke (2000). The goal of this generalized taxonomy is then to provide a nonlinear generative framework for describing unsupervised spatiotemporal networks, making it easier to compare and contrast their representational and operational characteristics. Computational properties, representational issues, and learning are also discussed, and a number of references to the relevant source publications are provided. It is argued that the proposed approach is simple and more powerful than the previous attempts from a descriptive and predictive viewpoint. We also discuss the relation of this taxonomy with automata theory and state-space modeling and suggest directions for further work.

Classification↗
PubMed2002

Electromagnetic fields on a quantum scale. I.

This is the first in a series of two articles, the second of which provides an exact electro-magnetic field description of photon emission, absorption, and radiation pattern. Photon energy exchanges are analyzed and shown to be the triggered, regenerative response of a non-local eigenstate electron. This first article presents a model-based, hidden variable analysis of quantum theory that provides the statistical nature of wave functions. The analysis uses the equations of classical electro-magnetism and conservation of energy while modeling an eigenstate electron as a nonlocal entity. Essential to the analysis are physical properties that were discovered and analyzed only after the historical interpretation of quantum mechanics was established: electron non-locality and the standing electro-magnetic energy that accompanies and encompasses an active, electrically small volume. The standing energy produces a driving radiation reaction force that, under certain circumstances, is many orders of magnitude larger than currently accepted values. These properties provide a sufficient basis for the Schrödinger equation as a descriptor of non-relativistic eigenstate electrons in or near equilibrium. The uncertainty principle follows, as does the exclusion principle. The analysis leads to atomic stability and causality in the sense that the status of physical phenomena at any instant specifies the status an instant later.

Computer Simulation↗
PubMed2006

Independent component analysis reveals new and biologically significant structures in micro array data.

BACKGROUND: An alternative to standard approaches to uncover biologically meaningful structures in micro array data is to treat the data as a blind source separation (BSS) problem. BSS attempts to separate a mixture of signals into their different sources and refers to the problem of recovering signals from several observed linear mixtures. In the context of micro array data, "sources" may correspond to specific cellular responses or to co-regulated genes. RESULTS: We applied independent component analysis (ICA) to three different microarray data sets; two tumor data sets and one time series experiment. To obtain reliable components we used iterated ICA to estimate component centrotypes. We found that many of the low ranking components indeed may show a strong biological coherence and hence be of biological significance. Generally ICA achieved a higher resolution when compared with results based on correlated expression and a larger number of gene clusters with significantly enriched for gene ontology (GO) categories. In addition, components characteristic for molecular subtypes and for tumors with specific chromosomal translocations were identified. ICA also identified more than one gene clusters significant for the same GO categories and hence disclosed a higher level of biological heterogeneity, even within coherent groups of genes. CONCLUSION: Although the ICA approach primarily detects hidden variables, these surfaced as highly correlated genes in time series data and in one instance in the tumor data. This further strengthens the biological relevance of latent variables detected by ICA.

Algorithms↗
PubMed2000

The moon has four phases and that's what worries me.

The values held by health care administrators and inherent in the operation of the institution are of primary importance to the ministry of pastoral care. This narrative/story provides a case history in which the author recounts how these values change as administrators change. The results suggest that these values constitute one of the hidden variables that influenced the questionnaire results reported earlier in this work.

Attitude of Health Personnel↗
PubMed2000

On the relation between brain images and brain neural networks.

The relationship between brain images observed by PET and fMRI and the underlying neural activity is analysed using recent results on the detailed nature of averaged and synchronised activity of coupled neural networks and on a simplifying model of the level of blood flow caused by neural activity. The conditions on the coupled neural systems are specified that lead to structural equation models, giving support to analysis of the covariance structural equation modelling of brain imaging data. The relation between the resulting models and possible neural codes are analysed. Furthermore, a new form of structural equation model is derived, in which all neuronal activity arises as hidden variables. We discuss how the results of such analyses can be transported back to the domain of coupled temporally dynamic neural systems in the brain appropriate to EEG and MEG observations.

Brain↗
PubMed2006

Experimental design of time series data for learning from dynamic Bayesian networks.

Bayesian networks (BNs) and dynamic Bayesian networks (DBNs) are becoming more widely used as a way to learn various types of networks, including cellular signaling networks, from high-throughput data. Due to the high cost of performing experiments, we are interested in developing an experimental design for time series data generation. Specifically, we are interested in determining properties of time series data that make them more efficient for DBN modeling. We present a theoretical analysis on the ability of DBNs without hidden variables to learn from proteomic time series data. The analysis reveals, among other lessons, that under a reasonable set of assumptions a fixed budget is better spent on collecting many short time series data than on a few long time series data.

Algorithms↗
PubMed1997

Factor analysis using delta-rule wake-sleep learning.

We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variables-a factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake-sleep method, in which learning of the primary generative model is assisted by a recognition model, whose role is to fill in the values of hidden variables based on the values of visible variables. The generative and recognition models are jointly learned in wake and sleep phases, using just the delta rule. This learning procedure is comparable in simplicity to Hebbian learning, which produces a somewhat different representation of correlations in terms of principal components. We argue that the simplicity of wake-sleep learning makes factor analysis a plausible alternative to Hebbian learning as a model of activity-dependent cortical plasticity.

Factor Analysis, Statistical↗
PubMed2004

Modeling T-cell activation using gene expression profiling and state-space models.

MOTIVATION: We have used state-space models to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T-cell activation. State space models are a class of dynamic Bayesian networks that assume that the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be measured in a gene expression profiling experiment, e.g. genes that have not been included in the microarray, levels of regulatory proteins, the effects of messenger RNA and protein degradation, etc. RESULTS: Bootstrap confidence intervals are developed for parameters representing 'gene-gene' interactions over time. Our models represent the dynamics of T-cell activation and provide a methodology for the development of rational and experimentally testable hypotheses. AVAILABILITY: Supplementary data and Matlab computer source code will be made available on the web at the URL given below. SUPPLEMENTARY INFORMATION: http://public.kgi.edu/~wild/LDS/index.htm

Computer Simulation↗
PubMed2004

A Bayesian approach to reconstructing genetic regulatory networks with hidden factors.

MOTIVATION: We have used state-space models (SSMs) to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T cell activation. SSMs are a class of dynamic Bayesian networks in which the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be directly measured in a gene expression profiling experiment, for example: genes that have not been included in the microarray, levels of regulatory proteins, the effects of mRNA and protein degradation, etc. RESULTS: We have approached the problem of inferring the model structure of these state-space models using both classical and Bayesian methods. In our previous work, a bootstrap procedure was used to derive classical confidence intervals for parameters representing 'gene-gene' interactions over time. In this article, variational approximations are used to perform the analogous model selection task in the Bayesian context. Certain interactions are present in both the classical and the Bayesian analyses of these regulatory networks. The resulting models place JunB and JunD at the centre of the mechanisms that control apoptosis and proliferation. These mechanisms are key for clonal expansion and for controlling the long term behavior (e.g. programmed cell death) of these cells. AVAILABILITY: Supplementary data is available at http://public.kgi.edu/wild/index.htm and Matlab source code for variational Bayesian learning of SSMs is available at http://www.cse.ebuffalo.edu/faculty/mbeal/software.html.

Bayes Theorem↗
PubMed2005

Statistical determinants of dendritic morphology in hippocampal pyramidal neurons: A hidden Markov model.

Dendritic structure is traditionally characterized by distributions and interrelations of morphometric parameters, such as Sholl-like plots of the number of branches versus dendritic path distance. However, how much of a given morphology is effectively captured by any statistical description is generally unknown. In this work, we assemble a small number of standard geometrical parameters measured from experimental data in a simple stochastic algorithm to describe the dendrograms of hippocampal pyramidal cells. The model, consistent with the hidden Markov framework, is feedforward, local, and causal. It relies on two "hidden" local variables: the expected number of terminal tips in a given subtree, and the current path distance from the soma. The algorithm generates dendrograms that statistically reproduce all morphological essentials of dendrites observed in real neurons, including the distributions of branching and termination points, branch lengths, membrane area, topological asymmetry, and (assuming passive membrane parameters within physiological range) electrotonic characteristics. Thus, this algorithm and the small number of its morphometric parameters constitute a remarkably complete description of the dendrograms of hippocampal pyramidal cells. Specifically, it is found that CA3 and CA1 basal dendrites and CA3 apical dendrites can each be described as homogeneous morphological classes. In contrast, the accurate generation of CA1 apical dendrites necessitates the separate sampling of two types of branches, main and oblique, suggesting their derivations from different developmental mechanisms (terminal and interstitial growth, respectively). We further offer a plausible biophysical interpretation of the model hidden variables, relating them to microtubules and other intracellular resources.

Algorithms↗