New Method for Parameter Estimation in Probabilistic Models: Minimum Probability Flow

Neurons in vivo exhibit irregular firing, and some aspect of their firing pattern such as the degree of firing irregularity does not fluctuate greatly in time for individual neurons, while it differs among neurons [1]. By analyzing spike trains recorded from a variety of cortical areas, it has been revealed that neurons in motor-related cortical areas fire regularly while neurons in visual and prefrontal cortex fire randomly [2]. Here, the firing irregularity is defined as a variability of consecutive interspike intervals, independent of the firing rate. In those studies, the firing rate has been ignored, because it may fluctuate greatly in time depending on external stimuli or behavioral contexts of an animal. Though the neuronal firing rate may fluctuate with external stimuli, this does not necessarily mean that the rate is extrinsic and perfectly controllable; there could be some uncontrollable intrinsic aspect in the firing rate fluctuation. In this contribution, we go contrary to the above-mentioned studies, and attempt to characterize neuronal spike trains solely in terms of the firing rate, ignoring the firing irregularity. The key feature of neuronal spike trains we now pay attention to is dynamic mode of rate fluctuation, such that the rate either fluctuates smoothly in time or changes abruptly between several stationary states. We compare two different models of a fluctuating rate process for their goodness-of-fit with respect to spike trains recorded from single neurons in several cortical areas of rats. The first model is the state space model constructed under the Empirical Bayes method [3,4]. The generative inhomogeneous Poisson process is defined as the conditional distribution of the spike times ti≡t1,t2,...,tn given the rateλ(t), ptiλ(t)= ∏i=1nλ(ti)exp-∫ 0Tλ(t)dt. We give the prior distribution of λ(t) by incorporating the tendency of the rate to be flat, pλ(t)∝exp-β∫ 0Tdλ/dt2dt. The hyperparameter β is selected by the principle of maximizing the marginal likelihood, and then we obtain the maximum a posteriori (MAP) estimate for the rate λ⌢(t). The second alternative model is the Hidden Markov model (HMM) whose hidden states represent different rate states [5-7]. The number of states is selected with a variation Bayes method. In this way, two different estimations of the firing rate are obtained using the continuous state space model and the discrete HMM. We compare them for each spike train obtained from a neuron, and examine whether the continuous or discrete representation of the state transition is more plausible. Then, we examine how the different preferences are distributed in different cortical areas.

Load model plays important role in the dynamic simulation of power system. The time-varying property of load in short-time appears to be stochastic in long-term. Thus the approach in this paper to study the statistical regularity of load characteristic vector, based on probability distribution and statistics, gives references to the choice and application of load model and its parameters. This paper proposes the following approaches. First, the differential equation model is transformed into continuous state space model, and is solved for the time-domain response curve against step input. Second, the characteristic parameters of response curve, represented by [k/sub t/ T/sub f/,k/sub s/], are distilled as the characteristic vector of load property. 69 sets of effective sampling data from Yuzhuang substation of Cangzhou region in China were studied for the character parameters of load model, from which useful conclusions of the load model variety regularity have been got.

Efficient Gibbs Sampling for Markov Switching GARCH Models

The ITER Pulsed Power Electrical Network (PPEN) supplies the superconducting magnets and the Heating and Current Drive systems. During the experimental pulses, about several hundreds of seconds long, active power consumption of 500 MW and reactive one of 950 Mvar are foreseen. The ITER power supply system is very large and complex and a careful design is required to assure a safe operation. Stability of ITER PPEN has been already investigated in recent studies by numerical simulation and analytical methods. Now a new dynamic analytical model of the ITER power supply system is being developed, based on the state space theoretical approach, which allows the application of the linear control theory to study the stability of the whole system. For each subsystem of the ITER power supply a state space model has been developed, and in this paper the ac/dc converter model is presented and validated.

This paper presents the system identification and validation of Synchronous Buck Converter (SBC) models using both white-box and black-box approaches. The white-box method employs difference equations derived from continuous state-space models, while the black-box approach estimates second-order state-space representations. Models are experimentally validated against laboratory measurements, with accuracy quantified using the Normalized Root Mean Square Error (NRMSE). By analysing the trade-off between model fidelity and real-time feasibility, the study identifies the most accurate model for reliable real-time simulation and controller development.

The aerothermic process is a pilot scale heating and ventilation system. It is equipped with a heater grid and a centrifugal blower, fully connected through the Humusoft MF624 data acquisition system for real time control. The interaction between its main variables is considered as challenging for mono-variable controllers. An abrupt change in the ventilator speed might cause an undesirable disturbance in the air temperature representing a factor that must be managed to conserve energy. To annul the effect of this interaction, this paper presents an experimental comparison between three forms of the PID controller: the conventional PID controller, the PI-D controller and its decentralized version. A multi-variable continuous state space model is obtained from on-line experimental data. The outcome of the experimental results is that the main control objectives, such as set-point tracking and interactions rejection, are well achieved for the temperature and the air flow simultaneously.

The common practice in sign language recognition is to ?rst construct individual sign models, in terms of discrete state transitions, mostly represented using Hidden Markov Models, from manually isolated sign samples and then to use it to recognize signs in continuous sentences. In this paper we (i) propose a continuous state space model, where the states are based on purely image-based features, without the use of special gloves, and (ii) present an unsupervised approach to both extract and learn models for continuous basic units of signs, which we term as signemes, from continuous sentences. Given a set of sentences with a common sign, we can automatically learn the model for part of the sign, or signeme, that is least affected by coarticulation effects. While there are coarticulation effects in speech recognition, these effects are even stronger in sign language. The model itself is in term of traces in a space of Relational Distributions. Each point in this space represents a Relational Distribution, capturing the spatial relationships between low-level features, such as edge points. We perform speed normalization and then incrementally extract the common sign between sentences, or signemes, with a dynamic programming framework at the core to compute warped distance between two subsentences. We test our idea using the publicly available Boston SignStream Dataset by building signeme models of 18 signs. We test the quality of the models by considering how well we can localize the sign in a new sentence. We also present preliminary results for the ability to generalize across signers.

Issues in sampling and estimating continuous-time models with stochastic disturbances

The obstructed diffusion of proteins in the plasma membrane is studied using computer simulation and an analysis using spatial tessellation and percolation theory. The membrane is modeled as a two-dimensional space with fixed hard disc obstacles, and the proteins are modeled as hard discs. The simulations show a transition from normal to anomalous diffusion as the area fraction, phim, of obstacles is increased and to confined diffusion for area fractions above the pecolation threshold, which occurs for phim=0.22. A Voronoi tessellation procedure is used to map the continuous space system onto an effective lattice model, with the connectivity of bonds determined from a geometric criterion. The estimate of the percolation threshold obtained from this lattice model is in excellent agreement with the simulation results, although the nature of the dynamics in the continuous space model is different from lattice models. At high obstacle area fractions (but below the percolation threshold), the primary mode of transport is a hopping motion between voids, consistent with experiment. The simulations and analysis emphasize the importance of structural correlations between obstacles.

A high coordination lattice was recently introduced for the simulation of coarse-grained rotational isomeric state (RIS) model chains. This second nearest neighbor diamond (2nnd) lattice is formed by connecting every other site on a tetrahedral lattice. Monte Carlo simulations of polyethylene (PE) melts have recently been performed on the 2nnd lattice by incorporating the intramolecular short range interactions from the RIS model and the long range interactions using a potential derived from an averaging procedure of the Mayer function in the expansion for the second virial coefficient. In the present work, the reverse mapping of specific snapshots from the coarse-grained PE melt back to the fully atomistic representation in continuous space is demonstrated. Reverse mapping is, essentially, determining the location of intermediate backbone atoms that are not represented on the 2nnd lattice but exist on the diamond lattice. In certain situations, the new locations of two intermediate atoms may coincide, leading to an unrealistic local conformation with infinite energy. Although these collapse situations are rare in the case of PE, they still present a problem in finding an energetically acceptable snapshot, which can be further subject to energy minimization in continuous space. These local collapse phenomena can be avoided by taking into consideration the geometry of the underlying tetrahedral lattice during coarse-grained simulations. Consequently, specific snapshots from bulk PE simulations are reverse mapped and their energy is minimized. The cohesive energy densities of these energy-minimized snapshots are very close to the experimental values reported in the literature.

The derivation of certain pandemic bounds

This paper considers the optimization problem for partially observable Markov decision processes (POMDPs) with the continuous state, observation, and action spaces. POMDPs with the discrete spaces have emerged as a promising approach to the decision systems with imperfect state information. However, in recent applications of POMDPs, there are many problems that have continuous states, observations, and actions. For such problems, due to the infinite dimensionality of the belief space, the existing studies usually discretize the continuous spaces with the sufficient or nonsufficient statistics, which may cause the curse of dimensionality and performance degradation. In this paper, based on the sensitivity analysis of the performance criteria, we have developed a simulation-based policy iteration algorithm to find the local optimal observation-based policy for POMDPs with the continuous spaces. The proposed algorithm needs none of the specific assumptions and prior information, and has a low computational complexity. One numerical example of the complicated multiple-input multiple-output beamforming problem shows that the algorithm has a significant performance improvement.

Metapopulation models and stepping-stone models in genetics are based on very different underlying dispersal structures, yet it can be difficult to distinguish the behaviour of the two kinds of models. We demonstrate a striking qualitative difference in the equilibrium behaviour possible with these two kinds of dispersal. If, in a local patch, there are multiple stable equilibria (and consequently an unstable equilibrium), we demonstrate that, for the spatial system with a metapopulation structure, at equilibrium every patch has to be near one of the stable equilibria. This contrasts with the clinal structure possible with a stepping-stone or continuous space model; thus the result can be used to deduce qualitative information about the form of dispersal from observations of allele frequencies.

State and local organizations see adding to raw agricultural commodities as the solution to unemployment in rural areas, financial stress in agriculture, and deterioration of rural infrastructure. Adding value is viewed as a key strategy for economic development. Many assumptions are often made, such as, the location of economic activities is not optimal, markets will expand to absorb added processing capacity, and allocations of raw commodities to finished products are inefficient. These assumptions may have some validity. Agricultural economists can play an important role in identifying those activities which add value and those which reduce value. An analysis with negative results may not be greeted with enthusiasm, but it is just as important as the discovery of a star performer. Most states, communities, and firms cannot afford many mistakes. The paper by Capps, Fuller, and Nichols (CFN) provides a useful framework for assessing value-adding activities. This framework is quite similar to that used in feasibility studies during the 1960s (French, pp. 152-54). For those analyzing value-adding opportunities, it would be useful to review some of the earlier empirical work. I agree with the factors identified by CFN as being most important for determination of regional activities, so my comments will expand on some of their themes. The coefficients of localization proposed by CFN are certainly plausible and may be a useful device for teaching decision makers. However, they are probably too crude for use as decision aids. The coefficients are not independent of the degree of regional aggregation. Decision makers need to understand that something is not wrong if their regional share is below average. Even where there is economic reason to expect a higher share, its attainment may be difficult. Barriers include excess capacity for processing many commodities and reluctance of firms to make new investments if current facilities are economical. Much value is now added offshore, and this means that the scope of analysis cannot be confined to the United States. Continuous space models (French, pp. 154-55) might be used to capture the interrelations among processing economies of size, raw product assembly costs, and finished product distribution costs described by CFN. Such models could be used to determine the

The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian spacetime potentials W as solutions u to the multiplicative stochastic heat equation [Formula: see text] with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponential behavior of u is studied via its almost sure Lyapunov exponent λ = limt→∞t-1log u(t, x), which is proved to exist, and is estimated as a function of β and κ for β2κ-1bounded below: positivity and nontrivial upper bounds are established, generalizing and improving existing results. In discrete space λ is of order β2/ log (β2/κ) and in continuous space it is between β2(κ/β2)H/(H+1)and β2(κ/β2)H/(1+3H).