Super-resolution of X-ray CT images of rock samples by sparse representation: applications to the complex texture of serpentinite.

X-ray computed tomography (X-ray CT) has been widely used in the earth sciences, as it is non-destructive method for providing us the three-dimensional structures of rocks and sediments. Rock samples essentially possess various-scale structures, including millimeters to centimeter scales of layering and veins to micron-meter-scale mineral grains and porosities. As the limitations of the X-ray CT scanner, sample size and scanning time, it is not easy to extract information on multi-scale structures, even when hundreds meter scale core samples were obtained during drilling projects. As the first step to overcome such barriers on scale-resolution problems, we applied the super-resolution technique by sparse representation and dictionary-learning to X-ray CT images of rock core sample. By applications to serpentinized peridotite, which records the multi-stage water-rock interactions, we reveal that both grain-shapes, veins and background heterogeneities of high-resolution images can be reconstructed through super-resolution. We also show that the potential effectiveness of sparse super-resolution for feature extraction of complicated rock textures.

Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis-Hastings Method.

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis-Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis-Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.

Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches.

Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. It is important to specify the kinetics of heterogeneous reactions in order to elucidate the microscopic elementary processes and predict the macroscopic future evolution of the system. In this study, we propose a data-driven method based on a sparse modeling algorithm and sequential Monte Carlo algorithm for simultaneously extracting substantial reaction terms and surface models from a number of candidates by using partial observation data. We introduce a sparse modeling approach with non-uniform sparsity levels in order to accurately estimate rate constants, and the sequential Monte Carlo algorithm is employed to estimate time courses of multi-dimensional hidden variables. The results estimated using the proposed method show that the rate constants of dissolution and precipitation reactions that are typical examples of surface heterogeneous reactions, necessary surface models, and reaction terms underlying observable data were successfully estimated from only observable temporal changes in the concentration of the dissolved intermediate products.

Estimation of neuronal dynamics based on sparse modeling.

Elucidating neural dynamics is one of the important subjects in neuroscience. To elucidate nonlinear dynamics of single neurons, it is important to extract nonlinear membrane currents from many types of membrane current candidates. In this study, we propose a sparse modeling method for estimating a conductance-based neuron model from observed data, by extracting necessary membrane currents from multiple candidates. We show using simulated data that our proposed sparse modeling approach with different sparsity levels for distinct membrane currents extracts only necessary membrane currents from candidates more accurately, compared with least-squares method and sparse method with uniform sparsity level.

Microglia Enhance Synapse Activity to Promote Local Network Synchronization.

Microglia are highly motile immunoreactive cells that play integral roles in the response to brain infection and damage, and in the progression of various neurological diseases. During development, microglia also help sculpt neural circuits, via both promoting synapse formation and by targeting specific synapses for elimination and phagocytosis. Microglia are also active surveyors of neural circuits in the mature, healthy brain, although the functional consequences of such microglia-neuron contacts under these conditions is unclear. Using in vivo imaging of neurons and microglia in awake mice, we report here the functional consequences of microglia-synapse contacts. Direct contact between a microglial process and a single synapse results in a specific increase in the activity of that contacted synapse, and a corresponding increase in back-propagating action potentials along the parent dendrite. This increase in activity is not seen for microglia-synapse contacts when microglia are activated by chronic lipopolysaccharide (LPS) treatment. To probe how this microglia-synapse contact affects neural circuits, we imaged across larger populations of motor cortical neurons. When microglia were again activated by LPS (or partially ablated), there was a decrease in the extent to which neuronal activity was synchronized. Together, our results demonstrate that interactions between physiological or resting microglia and synapses in the mature, healthy brain leads to an increase in neuronal activity and thereby helps to synchronize local populations of neurons. Our novel findings provide a plausible physical basis for understanding how alterations in immune status may impact on neural circuit plasticity and on cognitive behaviors such as learning.

Putative Neural Network Within an Olfactory Sensory Unit for Nestmate and Non-nestmate Discrimination in the Japanese Carpenter Ant: The Ultra-structures and Mathematical Simulation.

Ants are known to use a colony-specific blend of cuticular hydrocarbons (CHCs) as a pheromone to discriminate between nestmates and non-nestmates and the CHCs were sensed in the basiconic type of antennal sensilla (S. basiconica). To investigate the functional design of this type of antennal sensilla, we observed the ultra-structures at 2D and 3D in the Japanese carpenter ant, Camponotus japonicus, using a serial block-face scanning electron microscope (SBF-SEM), and conventional and high-voltage transmission electron microscopes. Based on the serial images of 352 cross sections of SBF-SEM, we reconstructed a 3D model of the sensillum revealing that each S. basiconica houses > 100 unbranched dendritic processes, which extend from the same number of olfactory receptor neurons (ORNs). The dendritic processes had characteristic beaded-structures and formed a twisted bundle within the sensillum. At the "beads," the cell membranes of the processes were closely adjacent in the interdigitated profiles, suggesting functional interactions via gap junctions (GJs). Immunohistochemistry with anti-innexin (invertebrate GJ protein) antisera revealed positive labeling in the antennae of C. japonicus. Innexin 3, one of the five antennal innexin subtypes, was detected as a dotted signal within the S. basiconica as a sensory organ for nestmate recognition. These morphological results suggest that ORNs form an electrical network via GJs between dendritic processes. We were unable to functionally certify the electric connections in an olfactory sensory unit comprising such multiple ORNs; however, with the aid of simulation of a mathematical model, we examined the putative function of this novel chemosensory information network, which possibly contributes to the distinct discrimination of colony-specific blends of CHCs or other odor detection.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Free-energy landscape and nucleation pathway of polymorphic minerals from solution in a Potts lattice-gas model.

Metastable minerals commonly form during reactions between water and rock. The nucleation mechanism of polymorphic phases from solution are explored here using a two-dimensional Potts model. The model system is composed of a solvent and three polymorphic solid phases. The local state and position of the solid phase are updated by Metropolis dynamics. Below the critical temperature, a large cluster of the least stable solid phase initially forms in the solution before transitioning into more-stable phases following the Ostwald step rule. The free-energy landscape as a function of the modal abundance of each solid phase clearly reveals that before cluster formation, the least stable phase has an energetic advantage because of its low interfacial energy with the solution, and after cluster formation, phase transformation occurs along the valley of the free-energy landscape, which contains several minima for the regions of three phases. Our results indicate that the solid-solid and solid-liquid interfacial energy contribute to the formation of the complex free-energy landscape and nucleation pathways following the Ostwald step rule.

Higher-order spike triggered analysis of neural oscillators.

For the purpose of elucidating the neural coding process based on the neural excitability mechanism, researchers have recently investigated the relationship between neural dynamics and the spike triggered stimulus ensemble (STE). Ermentrout et al. analytically derived the relational equation between the phase response curve (PRC) and the spike triggered average (STA). The STA is the first cumulant of the STE. However, in order to understand the neural function as the encoder more explicitly, it is necessary to elucidate the relationship between the PRC and higher-order cumulants of the STE. In this paper, we give a general formulation to relate the PRC and the nth moment of the STE. By using this formulation, we derive a relational equation between the PRC and the spike triggered covariance (STC), which is the covariance of the STE. We show the effectiveness of the relational equation through numerical simulations and use the equation to identify the feature space of the rat hippocampal CA1 pyramidal neurons from their PRCs. Our result suggests that the hippocampal CA1 pyramidal neurons oscillating in the theta frequency range are commonly sensitive to inputs composed of theta and gamma frequency components.

Measurement of infinitesimal phase response curves from noisy real neurons.

We sought to measure infinitesimal phase response curves (iPRCs) from rat hippocampal CA1 pyramidal neurons. It is difficult to measure iPRCs from noisy neurons because of the dilemma that either the linearity or the signal-to-noise ratio of responses to external perturbations must be sacrificed. To overcome this difficulty, we used an iPRC measurement model formulated as the Langevin phase equation (LPE) to extract iPRCs in the Bayesian scheme. We then simultaneously verified the effectiveness of the measurement model and the reliability of the estimated iPRCs by demonstrating that LPEs with the estimated iPRCs could predict the stochastic behaviors of the same neurons, whose iPRCs had been measured, when they were perturbed by periodic stimulus currents. Our results suggest that the LPE is an effective model for real oscillating neurons and that many theoretical frameworks based on it may be applicable to real nerve systems.

Switch of encoding characteristics in single neurons by subthreshold and suprathreshold stimuli.

Spike-triggered analysis is a statistical method used to elucidate encoding properties in neural systems by estimating the statistical structure of input stimulus preceding spikes. A recent numerical study suggested that the profile of the spike-triggered average (STA) changes depending on whether the mean input stimuli are subthreshold or suprathreshold. Here we analytically verify the difference between subthreshold STA and suprathreshold STA by using the spike response model (SRM). We show by moment expansion that the suprathreshold STA is proportional to the first derivative of the response kernel, and that the subthreshold STA is expressed by a linear combination of the response kernel and its first derivative. We verify whether the analytical results obtained from the SRM can be applied to a multicompartment model with Hodgkin-Huxley type dynamics.

An analytic solution of the cable equation predicts frequency preference of a passive shunt-end cylindrical cable in response to extracellular oscillating electric fields.

Under physiological and artificial conditions, the dendrites of neurons can be exposed to electric fields. Recent experimental studies suggested that the membrane resistivity of the distal apical dendrites of cortical and hippocampal pyramidal neurons may be significantly lower than that of the proximal dendrites and the soma. To understand the behavior of dendrites in time-varying extracellular electric fields, we analytically solved cable equations for finite cylindrical cables with and without a leak conductance attached to one end by employing the Green's function method. The solution for a cable with a leak at one end for direct-current step electric fields shows a reversal in polarization at the leaky end, as has been previously shown by employing the separation of variables method and Fourier series expansion. The solution for a cable with a leak at one end for alternating-current electric fields reveals that the leaky end shows frequency preference in the response amplitude. Our results predict that a passive dendrite with low resistivity at the distal end would show frequency preference in response to sinusoidal extracellular local field potentials. The Green's function obtained in our study can be used to calculate response for any extracellular electric field.

Steep decrease in the specific membrane resistance in the apical dendrites of hippocampal CA1 pyramidal neurons.

Specific membrane resistance (R(m)), distributed non-uniformly over the dendrite, has a substantial effect on neuronal information processing, since it is a major determinant in subthreshold-synaptic integration. From experimental data of dendritic excitatory postsynaptic potential (EPSP) spread, we previously reported that non-uniform R(m) distribution in hippocampal CA1 pyramidal neurons could be expressed as a step function. However, it remains unclear how steeply R(m) decreases. Here, we estimated the R(m) distribution using sigmoid function to evaluate the steepness of decrease in R(m). Simulations were performed to find the distribution which reproduced experimental voltage responses to extracellular electric field applied to CA1 slices, in contrast to the EPSP spread. Distribution estimated from the responses to electric field was a steep-sigmoid function, similar to that from the EPSP spread. R(m) in distal dendrite was estimated to be < or approximately 10(3.5) Omegacm(2) whereas that in proximal dendrite/soma was > or approximately 10(4.5) Omegacm(2). Our results not only supported previous studies, but, surprisingly, implied that R(m) decreases at a location more distal, and that distal dendrite was leakier, than previous estimates by other groups. Simulations satisfactorily reproduced the responses to two distinct perturbations, suggesting that steep decrease in R(m) is reliable. Our study suggests that the non-uniform R(m) distribution plays an important role in information processing for spatially segregated synaptic inputs.

MAP estimation algorithm for phase response curves based on analysis of the observation process.

Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.

Statistical mechanics of lossy compression for nonmonotonic multilayer perceptrons.

A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize a treelike committee machine (committee tree) and a treelike parity machine (parity tree) whose transfer functions are nonmonotonic. The scheme performance at the infinite code length limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate the Shannon bound. The Almeida-Thouless stability of the replica symmetric solution is analyzed, and the tuning of the nonmonotonic transfer function is also discussed.

Estimated distribution of specific membrane resistance in hippocampal CA1 pyramidal neuron.

It has been suggested that dendritic membrane properties play an important role in a synaptic integration. In particular, the specific membrane resistance, one of membrane properties, has been reported to be non-uniformly distributed in a single neuron, although the spatial distribution of the specific membrane resistance is still unclear. To reveal its non-uniformity in dendrite, we estimated the spatial distribution of specific membrane resistance in a single neuron, based on voltage imaging data, observed optically in hippocampal CA1 slices. As the optically recorded data, we used bi-directional propagations of subthreshold excitatory postsynaptic potentials in dendrite, which were not be reproduced numerically with uniform-specific membrane resistance. By numerical simulations for multi-compartment models with non-uniformity of specific membrane resistance, we estimated that the distribution obeys a step function; the optically recorded data were consistently reproduced for the distribution with a steep decrease in the specific membrane resistance at the distal apical dendrite, which occurs 300-500 microm away from the soma. In the estimated distribution, the specific membrane resistance at the distal side is less than about 10(3) Omegacm(2), whereas the resistance at the proximal side is greater than about 10(4) Omegacm(2). This result implies that the specific membrane resistance decreases drastically at the distal apical dendrite in hippocampal CA1 pyramidal neuron.