Maximum Entropy Approaches to Living Neural Networks

One well-recognized problem in three-dimensional (3D) confocal microscopic images is that the intensities in deeper slices are generally weaker than those in shallower slices. The loss of intensity with depth hampers both qualitative observation and quantitative measurement of specimens. Two major types of methods exist to compensate for this intensity loss: the first is based on the geometrical optics inside the specimen, and the second applies an empirical parametric intensity decay function (IDF) of depth. A common feature shared by both methods is that they are parameter-dependent. However, for the optics-based method there are as yet no fully automated parameter-setting approaches; and for the IDF method the traditional profile-fitting approach cannot provide proper parameters if the presumed IDF model does not match the experimental intensity-depth profile of the 3D image. In this paper, we propose a novel maximum-entropy (ME) approach to fully automated parameter-setting. In principle the ME approach is suitable for any compensation method as long as it is parameter-dependent. The basic assumption is that without intensity loss an ideal 3D image should be generally homogeneous with respect to depth and this axial homogeneity can be represented by the entropy of a normalized intensity-depth profile. Experiments on real confocal images showed that such a profile was consistent with visual evaluation of axial intensity homogeneity and that the ME approach could provide proper parameters for both compensation methods mentioned above. Moreover, for the IDF method, experiments on both real and simulated data showed that the ME approach could provide more precise parameters than with traditional profile-fitting. The Appendix provides a proof that under certain conditions the global maximization of the profile-entropy is guaranteed.

Empirical evidence of scaling behaviors in neuronal avalanches suggests that neuronal populations in the brain operate near criticality. Departure from scaling in neuronal avalanches has been used as a measure of distance to criticality and linked to brain disorders. A distinct line of evidence for brain criticality has come from thermodynamic signatures in maximum entropy (ME) models. Both of these approaches have been widely applied to the analysis of neuronal data. However, the relationship between deviations from avalanche criticality and thermodynamics of ME models of neuronal populations remains poorly understood. To address this question, we study spontaneous activity of organotypic rat cortex slice cultures in physiological and drug-induced hypo- or hyper-excitable conditions, which are classified as critical, subcritical and supercritical based on avalanche dynamics. We find that ME models inferred from critical cultures show signatures of criticality in thermodynamic quantities, e.g. specific heat. However, such signatures are also present, and equally strong, in models inferred from supercritical cultures—despite their altered dynamics and poor functional performance. On the contrary, ME models inferred from subcritical cultures do not show thermodynamic hints of criticality. Importantly, we confirm these results using an interpretable neural network model that can be tuned to and away from avalanche criticality. Our findings indicate that maximum entropy models correctly distinguish subcritical from critical/supercritical systems. However, they may not be able to discriminate between avalanche criticality and supercriticality, although they may still capture a number of important features from neuronal data.

This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes only and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author. [Approved for Public Release; Distribution Unlimited Case 19-1301. Copyright 2019, The MITRE Corporation.]This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes onl...

SAXS Ensemble Refinement of ESCRT-III CHMP3 Conformational Transitions

Location‐only and use‐availability data: analysis methods converge

A maximum entropy approach to adaptive statistical language modelling

The variations of the b coefficient in the frequency-magnitude relationship for earthquakes which occurred at Mt. Etna from 01/01/90 to 31/12/92 are analyzed; the completeness threshold for our earthquakes catalogue is M = 2.30. The b values calculated using the Maximum Entropy Principle (MEP) are compared to those obtained by conventional methods of Least Squares (LS) and Maximum Likelihood (ML). All the differences among the b values computed using these methods, and the reasons for these differences, are discussed and examined. In particular, our results show that the b values obtained by MEP are lower than the others calculated using LS and ML; this implies that, on the average, LS and ML underestimate the seismic hazard at Mt. Etna. Moreover, temporal variations of bMEP are more evident than the corresponding ones of bLS and bML; indeed, in some cases the trend of bMEP variation is opposite those of bLS and bML. A significant correlation between temporal variations of the volcanic activity and the b values is evident only if the MEP is used; this means that, if b temporal variations are analyzed in order to detect changes in the volcano dynamics and predict the eruptions, the maximum entropy approach should be preferred. Finally, the observed pattern of bMEP temporal variations with regard to the changes in the volcanic activity is consistent with the hypothesis of a compressive stress field acting on Mt. Etna.

Stochastic methods have been typically used for the design and operations of hydraulic infrastructure. They allow decision makers to evaluate existing or new infrastructure under different possible scenarios, giving them the flexibility and tools needed in decision making. In this paper, we present a novel stochastic streamflow simulation approach able to replicate both temporal and spatial dependencies from the original data in a multi‐site basin context. The proposed model is a multi‐site extension of the modified Fractional Gaussian Noise (mFGN) model which is well‐known to be efficient to maintain periodic correlation for several time lags, but presents shortcomings in preserving the spatial correlation. Our method, called Weighted‐mFGN (WmFGN), incorporates spatial dependency into streamflows simulated with mFGN by relying on the Cholesky decomposition of the spatial correlation matrix of the historical streamflow records. As the order in which the decomposition steps are performed (temporal then spatial, or vice‐versa) affects the performance in terms of preserving the temporal and spatial correlation, our method searches for an optimal convex combination of the resulting correlation matrices. The result is a Pareto‐curve that indicates the optimal weights of the convex combination depending on the importance given by the user to spatial and temporal correlations. The model is applied to a number of river basins in Chile, where the results show that the WmFGN approach maintains the qualities of the single‐site mFGN, while significantly improving spatial correlation.

A prototype of a computerized patient record

Various seismic deconvolution operators can be determined by estimating a seismic wavelet and subsequently designing an appropriate inverse filter which converts the wavelet to a spike. Seismic wavelets and deconvolution operators must be estimated in a time adaptive sense due to the nonstationarity of the seismic trace. The wavelet estimation methods considered in this paper either use the assumption of a minimum phase wavelet and a random impulse response, or the assumption that the wavelet cepstrum is readily separable from the cepstrum of the seismic trace. The former assumption is required in using the Hilbert transform and Wiener‐Levinson wavelet estimations, while the latter assumption is used in homomorphic deconvolution. These wavelet estimates can be used in the design of multichannel Wiener and Kalman deconvolution operators. Multichannel usage of homomorphic deconvolution can also be implemented through various types of cepstral stacking.The discussion of deconvolution filter design focuses on the problems of filter length, degree of prewhitening, and nonstationarity. In designing time adaptive deconvolution filters, the autocorrelation function can be used to monitor the nonstationarity of the seismic trace. The autocorrelation function, which is used in the computation of least squares inverse filters, can be estimated in an optimum fashion by using the maximum entropy method. Differences between minimum phase Wiener deconvolution and maximum entropy deconvolution become more pronounced for shorter data gates. As a result, the maximum entropy approach is preferred for time adaptive deconvolution.In this paper, the performance of various wavelet estimators and inverse filters is discussed using real and synthetic seismic data. Discussions of homomorphic deconvolution and maximum entropy prediction error filtering are merged with descriptions of conventional approaches to deconvolution.

Multi-label classification with local pairwise and high-order label correlations using graph partitioning

Inducing Gamma Oscillations and Precise Spike Synchrony by Operant Conditioning via Brain-Machine Interface

Maximum-entropy approach with higher moments for solving Fokker–Planck equation

This paper describes an analysis of 1H-1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM.

Regression is one of the most widely used of all statistical tools. Linear modelling in its widest sense is both well developed and well understood, and there is in addition a variety of useful techniques for checking the assumptions involved. However, there are cases where such models cannot be applied because of intrinsic nonlinearity in the data. Nonparametric regression aims to provide a means of modelling such data. Even where the suitability of linear models has not yet been brought into question, smoothing techniques are still useful by enhancing scatterplots to display the underlying structure of the data, without reference to a parametric model. This can in turn lead to further useful suggestions of, or checks on, appropriate parametric models. In this chapter, the main ideas of nonparametric regression are introduced and illustrated on several different types of data. The emphasis throughout is on the exploration of data, although technical and inferential issues will be raised for discussion in later chapters.