Algorithms For Such Models Research Articles

Compartmental spiking neuron model for pattern classification

One of the directions of development within the framework of the neuromorphic approach is the development of anatomically similar models of brain networks, taking into account the structurally complex structure of neurons and the adaptation of connections between them, as well as the development of learning algorithms for such models. In this work, we use the previously presented compartmental spike model of a neuron, which describes the structure (dendritic tree, soma, synapses) and behaviour (temporal and spatial signal summation, generation of action potential, stimulation and suppression of electrical activity) of a biological neuron. An algorithm for the structural organization of neuron models into a spike neural network is proposed for recognizing an arbitrary impulse pattern by introducing inhibitory synapses between trained neuron models. The dynamically adapting neuron models used are trained according to a previously proposed algorithm that automatically selects parameters such as soma size, dendrite length, and the number of synapses on each of the dendrites in order to induce a temporal response at the output depending on the input pattern encoded using a time window and temporal delays in the vector of single spikes arriving at a separate dendrite of a neuron. The developed algorithms are evaluated on the Iris dataset classification problem with four training examples from each class. As a result of the classification, separate disjoint clusters are formed, which demonstrates the applicability of the proposed spike neural network with a dynamically changing structure of elements in the problem of pattern recognition and classification.

Fundamental results for learning deterministic extended finite state machines from queries

Regular language inference, initiated by Angluin, has many developments, including applications in software engineering and testing. However, the capability of finite automata to model the system data is quite limited and, in many cases, extended finite state machine formalisms, that combine the system control with data structures, are used instead. The application of Angluin-style inference algorithms to extended state machines would involve constructing a minimal deterministic extended finite state machine consistent with a deterministic 3-valued deterministic finite automaton. In addition to the usual, accepting and rejecting, states of finite automaton, a 3-valued deterministic finite automaton may have “don't care” states; the sequences of inputs that reach such states may be considered as accepted or rejected, as is convenient. The aforementioned construction reduces to finding a minimal deterministic finite automaton consistent with a 3-valued deterministic finite automaton, that preserves the deterministic nature of the extended model that also handles the data structure associated with it. This paper investigates fundamental properties of extended finite state machines in relation to Angluin's language inference problem and provides an inference algorithm for such models.

Noise Removal from 3D Meshes: An Efficient Approach

The current methods for mesh denoising focus on models where all the vertices in the mesh are corrupted with low noise amplitudes.Some of these prevailing techniques would not provide the facility of denoising even when a small percentage of the vertices are corrupted with noise of very high amplitude. To solve the problem,we propose an efficient mesh denoising algorithm for such models in which vertices are corrupted with both high as well as low noise amplitudes. This proposed algorithm is divided into two phases.In the first phase, the corrupted vertices are detected by means of a filter called Localised Coordinate Variation filter. In the second phase, the corrupted vertices are abolished. The results revealed in this paper depicts the claims as mentioned above.

Efficient hbox {SMC}^2 schemes for stochastic kinetic models

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed-data likelihood. There has therefore been considerable attention given to the design of pseudo-marginal Markov chain Monte Carlo algorithms for such models. However, these methods are typically computationally intensive, often require careful tuning and must be restarted from scratch upon receipt of new observations. Sequential Monte Carlo (SMC) methods on the other hand aim to efficiently reuse posterior samples at each time point. Despite their appeal, applying SMC schemes in scenarios with both dynamic states and static parameters is made difficult by the problem of particle degeneracy. A principled approach for overcoming this problem is to move each parameter particle through a Metropolis-Hastings kernel that leaves the target invariant. This rejuvenation step is key to a recently proposed hbox {SMC}^2 algorithm, which can be seen as the pseudo-marginal analogue of an idealised scheme known as iterated batch importance sampling. Computing the parameter weights in hbox {SMC}^2 requires running a particle filter over dynamic states to unbiasedly estimate the intractable observed-data likelihood up to the current time point. In this paper, we propose to use an auxiliary particle filter inside the hbox {SMC}^2 scheme. Our method uses two recently proposed constructs for sampling conditioned jump processes, and we find that the resulting inference schemes typically require fewer state particles than when using a simple bootstrap filter. Using two applications, we compare the performance of the proposed approach with various competing methods, including two global MCMC schemes.

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Management Insights

A Parameterized Probabilistic Model of Network Evolution for Supervised Link Prediction

We introduce a new approach to the problem of link prediction for network structured domains, such as the Web, social networks, and biological networks. Our approach is based on the topological features of network structures, not on the node features. We present a novel parameterized probabilistic model of network evolution and derive an efficient incremental learning algorithm for such models, which is then used to predict links among the nodes. We show some promising experimental results using biological network data sets.

Parallel algorithms for Markov chain Monte Carlo methods in latent spatial Gaussian models

Markov chain Monte Carlo (MCMC) implementations of Bayesian inference for latent spatial Gaussian models are very computationally intensive, and restrictions on storage and computation time are limiting their application to large problems. Here we propose various parallel MCMC algorithms for such models. The algorithms' performance is discussed with respect to a simulation study, which demonstrates the increase in speed with which the algorithms explore the posterior distribution as a function of the number of processors. We also discuss how feasible problem size is increased by use of these algorithms.

Daily generation scheduling: quest for new models

This paper presents the need for adding transmission system representation in a conventional power system generation scheduling model. Given the complexity of developing solution algorithms for such models, the present study critically examines whether adding complexities to the simplified models viz., unit commitment and network flow models, is worthwhile, or the simplified models provide good approximation of the optimal generation schedule. Prototype model development and simple case studies for a capacity constrained test system shows there are major deviations in the generation schedules, load-shed requirement and spot prices obtained from the simple models and the complex model. The results indicate that research efforts towards algorithmic development for more accurate scheduling models are needed.

Optimal replacement for discrete additive damage models: Algorithm

A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another. The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold. Upon failure the system must be replaced by a new and identical one and a cost is incurred. If the system is replaced before failure, a smaller cost is incurred. In previous work, under some assumptions, we specified a replacement rule which minimizes the long-run (expected) average cost per unit time and possesses control limit property. In this paper, a general algorithm for such models is developed.

State Space Identification of Linear Deterministic Rainfall‐Runoff Models

Rainfall‐runoff models of the black box type abound in the water resources literature (i.e., transfer function, autoregressive moving average (ARMA), ARMAX, state space, etc.). The corresponding system identification algorithms for such models are known to be numerically efficient and accurate, leading in most cases to good parsimonious representations of the rainfall‐runoff process. Alternatively, every model in transfer function, ARMA, and ARMAX form has an equivalent state space representation. However, state space models do not necessarily have simple system identification algorithms, unless the system matrices are restricted to some canonical form. Furthermore, state space system identification algorithms that work with the rainfall/runoff data directly (i.e., covariance free), require initial conditions and are inherently iterative and nonlinear. In this paper we present a state space system identification theory which overcomes these limitations. One advantage of such a theory is that the corresponding algorithms are highly robust to additive noise in the data. They are referred to as “subspace algorithms” due to their ability to separate the signal subspace from the noise subspace. The main advantages of the subspace algorithms are the automatic structure identification (system order), geometrical insights (notions of angle between subspaces), and the fact that they rely on robust numerical procedures (singular value decomposition). In this paper, two algorithms are presented. The first one is a two‐step procedure, where the impulse response (unit hydrograph ordinates for the single‐input, single‐output case) are computed from the input/output data by solving a constrained deconvolution problem. These impulse response ordinates are then used as inputs for identifying the system matrices by means of a Hankel‐based realization algorithm. The second approach uses the data directly to identify the system matrices, bypassing the deconvolution step. The algorithms are tested with real data from the Voer catchment in Belgium.

Convergence in neural memories

One of the simplest optimization problems solved by Ising spin models of neural memory is associative memory retrieval. The authors study deterministic convergence properties of the Hopfield synchronous retrieval algorithm for such models. In this case a memory, stored in the network by an appropriate choice of connections, is retrieved by setting the neural outputs to the binary pattern of the recall key (probe) and allowing the network to converge to a stable state. Precise conditions are developed that ensure that all stored memories are fixed points of the retrieval algorithm. An orthogonality-nearness criterion is then obtained for a memory probe itself to be a stationary point and thus outside the error-correcting capability of the memory. A local stability result quantifies the spatial relationship required for fast convergence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Similarity of a Fourier transform generalization of the Earnshaw solution for planar waves to an interacting wave model for finite amplitude effects in sound beams

The Earnshaw solution for a finite amplitude planar wave, which displays amplitude dispersion, is valid for arbitrary excitation f(t) on a boundary. The form that results for small acoustic Mach numbers when f(t) is represented as the inverse of its Fourier transform F(ω) may be considered to be a coordinate straining of the linearized signal, in which the transformation has the appearance of a Fredholm integral equation in the frequency domain. In the case of an acoustic planar wave, the phase speed of all frequency components is the same, independent of frequency. A generalization of that result is obtained if one considers the possibility that the cumulative growth effect is an arbitrary function of distance. Rather than being an abstraction, this form is shown to be analogous to an earlier solution for finite amplitude sound beams [J. H. Ginsberg, H. C. Miao, and M. A. Foda, J. Acoust. Soc. Am. Suppl. 1 81, S25 (1987)]. The signal in that analysis was represented in terms of a spectrum of transverse wavenumbers, rather than frequencies, and the signal for each wavenumber was formed from interacting quasiconical waves, rather than a single planar wave. Nevertheless, the two problems share a common mathematical structure. A discussion of numerical algorithms for such models leads to some surprising observations regarding the implicit functional form of the Earnshaw solution. [Work supported by ONR.]

Predetermined and non-predetermined variables in rational expectations models

Abstract A new definition for a variable to be non-predetermined in a rational expectations model is given. Its current value is a function of current anticipations of future values of other variables. This definition is useful in solution algorithms for such models.