Information-theoretic semi-supervised metric learning via entropy regularization.

Science.gov (United States)

Niu, Gang; Dai, Bo; Yamada, Makoto; Sugiyama, Masashi

2014-08-01

We propose a general information-theoretic approach to semi-supervised metric learning called SERAPH (SEmi-supervised metRic leArning Paradigm with Hypersparsity) that does not rely on the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize its entropy on labeled data and minimize its entropy on unlabeled data following entropy regularization. For metric learning, entropy regularization improves manifold regularization by considering the dissimilarity information of unlabeled data in the unsupervised part, and hence it allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Moreover, we regularize SERAPH by trace-norm regularization to encourage low-dimensional projections associated with the distance metric. The nonconvex optimization problem of SERAPH could be solved efficiently and stably by either a gradient projection algorithm or an EM-like iterative algorithm whose M-step is convex. Experiments demonstrate that SERAPH compares favorably with many well-known metric learning methods, and the learned Mahalanobis distance possesses high discriminability even under noisy environments.

Balancing Two-Player Stochastic Games with Soft Q-Learning

OpenAIRE

Grau-Moya, Jordi; Leibfried, Felix; Bou-Ammar, Haitham

2018-01-01

Within the context of video games the notion of perfectly rational agents can be undesirable as it leads to uninteresting situations, where humans face tough adversarial decision makers. Current frameworks for stochastic games and reinforcement learning prohibit tuneable strategies as they seek optimal performance. In this paper, we enable such tuneable behaviour by generalising soft Q-learning to stochastic games, where more than one agent interact strategically. We contribute both theoretic...

Stochastic microstructure characterization and reconstruction via supervised learning

International Nuclear Information System (INIS)

Bostanabad, Ramin; Bui, Anh Tuan; Xie, Wei; Apley, Daniel W.; Chen, Wei

2016-01-01

Microstructure characterization and reconstruction have become indispensable parts of computational materials science. The main contribution of this paper is to introduce a general methodology for practical and efficient characterization and reconstruction of stochastic microstructures based on supervised learning. The methodology is general in that it can be applied to a broad range of microstructures (clustered, porous, and anisotropic). By treating the digitized microstructure image as a set of training data, we generically learn the stochastic nature of the microstructure via fitting a supervised learning model to it (we focus on classification trees). The fitted supervised learning model provides an implicit characterization of the joint distribution of the collection of pixel phases in the image. Based on this characterization, we propose two different approaches to efficiently reconstruct any number of statistically equivalent microstructure samples. We test the approach on five examples and show that the spatial dependencies within the microstructures are well preserved, as evaluated via correlation and lineal-path functions. The main advantages of our approach stem from having a compact empirically-learned model that characterizes the stochastic nature of the microstructure, which not only makes reconstruction more computationally efficient than existing methods, but also provides insight into morphological complexity.

Stochastic sensitivity analysis and Langevin simulation for neural network learning

International Nuclear Information System (INIS)

Koda, Masato

1997-01-01

A comprehensive theoretical framework is proposed for the learning of a class of gradient-type neural networks with an additive Gaussian white noise process. The study is based on stochastic sensitivity analysis techniques, and formal expressions are obtained for stochastic learning laws in terms of functional derivative sensitivity coefficients. The present method, based on Langevin simulation techniques, uses only the internal states of the network and ubiquitous noise to compute the learning information inherent in the stochastic correlation between noise signals and the performance functional. In particular, the method does not require the solution of adjoint equations of the back-propagation type. Thus, the present algorithm has the potential for efficiently learning network weights with significantly fewer computations. Application to an unfolded multi-layered network is described, and the results are compared with those obtained by using a back-propagation method

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

Science.gov (United States)

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Stochastic Learning and the Intuitive Criterion in Simple Signaling Games

DEFF Research Database (Denmark)

Sloth, Birgitte; Whitta-Jacobsen, Hans Jørgen

A stochastic learning process for signaling games with two types, two signals, and two responses gives rise to equilibrium selection which is in remarkable accordance with the selection obtained by the intuitive criterion......A stochastic learning process for signaling games with two types, two signals, and two responses gives rise to equilibrium selection which is in remarkable accordance with the selection obtained by the intuitive criterion...

Learn-and-Adapt Stochastic Dual Gradients for Network Resource Allocation

OpenAIRE

Chen, Tianyi; Ling, Qing; Giannakis, Georgios B.

2017-01-01

Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of Lagrange multipliers in network resource allocation, a novel learn-and-adapt stochastic dual gradient (LA-SDG) method is developed in this paper to learn the sample-optimal Lagrange multiplier from historical data, and accordingly adapt the upcoming resource...

Learning regularization parameters for general-form Tikhonov

International Nuclear Information System (INIS)

Chung, Julianne; Español, Malena I

2017-01-01

Computing regularization parameters for general-form Tikhonov regularization can be an expensive and difficult task, especially if multiple parameters or many solutions need to be computed in real time. In this work, we assume training data is available and describe an efficient learning approach for computing regularization parameters that can be used for a large set of problems. We consider an empirical Bayes risk minimization framework for finding regularization parameters that minimize average errors for the training data. We first extend methods from Chung et al (2011 SIAM J. Sci. Comput. 33 3132–52) to the general-form Tikhonov problem. Then we develop a learning approach for multi-parameter Tikhonov problems, for the case where all involved matrices are simultaneously diagonalizable. For problems where this is not the case, we describe an approach to compute near-optimal regularization parameters by using operator approximations for the original problem. Finally, we propose a new class of regularizing filters, where solutions correspond to multi-parameter Tikhonov solutions, that requires less data than previously proposed optimal error filters, avoids the generalized SVD, and allows flexibility and novelty in the choice of regularization matrices. Numerical results for 1D and 2D examples using different norms on the errors show the effectiveness of our methods. (paper)

Stochastic abstract policies: generalizing knowledge to improve reinforcement learning.

Science.gov (United States)

Koga, Marcelo L; Freire, Valdinei; Costa, Anna H R

2015-01-01

Reinforcement learning (RL) enables an agent to learn behavior by acquiring experience through trial-and-error interactions with a dynamic environment. However, knowledge is usually built from scratch and learning to behave may take a long time. Here, we improve the learning performance by leveraging prior knowledge; that is, the learner shows proper behavior from the beginning of a target task, using the knowledge from a set of known, previously solved, source tasks. In this paper, we argue that building stochastic abstract policies that generalize over past experiences is an effective way to provide such improvement and this generalization outperforms the current practice of using a library of policies. We achieve that contributing with a new algorithm, AbsProb-PI-multiple and a framework for transferring knowledge represented as a stochastic abstract policy in new RL tasks. Stochastic abstract policies offer an effective way to encode knowledge because the abstraction they provide not only generalizes solutions but also facilitates extracting the similarities among tasks. We perform experiments in a robotic navigation environment and analyze the agent's behavior throughout the learning process and also assess the transfer ratio for different amounts of source tasks. We compare our method with the transfer of a library of policies, and experiments show that the use of a generalized policy produces better results by more effectively guiding the agent when learning a target task.

Linear System Control Using Stochastic Learning Automata

Science.gov (United States)

Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.

1998-01-01

This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.

Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

KAUST Repository

Haji Ali, Abdul Lateef

2016-08-26

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

Stochastically Estimating Modular Criticality in Large-Scale Logic Circuits Using Sparsity Regularization and Compressive Sensing

Directory of Open Access Journals (Sweden)

Mohammed Alawad

2015-03-01

Full Text Available This paper considers the problem of how to efficiently measure a large and complex information field with optimally few observations. Specifically, we investigate how to stochastically estimate modular criticality values in a large-scale digital circuit with a very limited number of measurements in order to minimize the total measurement efforts and time. We prove that, through sparsity-promoting transform domain regularization and by strategically integrating compressive sensing with Bayesian learning, more than 98% of the overall measurement accuracy can be achieved with fewer than 10% of measurements as required in a conventional approach that uses exhaustive measurements. Furthermore, we illustrate that the obtained criticality results can be utilized to selectively fortify large-scale digital circuits for operation with narrow voltage headrooms and in the presence of soft-errors rising at near threshold voltage levels, without excessive hardware overheads. Our numerical simulation results have shown that, by optimally allocating only 10% circuit redundancy, for some large-scale benchmark circuits, we can achieve more than a three-times reduction in its overall error probability, whereas if randomly distributing such 10% hardware resource, less than 2% improvements in the target circuit’s overall robustness will be observed. Finally, we conjecture that our proposed approach can be readily applied to estimate other essential properties of digital circuits that are critical to designing and analyzing them, such as the observability measure in reliability analysis and the path delay estimation in stochastic timing analysis. The only key requirement of our proposed methodology is that these global information fields exhibit a certain degree of smoothness, which is universally true for almost any physical phenomenon.

Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

Science.gov (United States)

Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

2018-06-01

We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

Stochastic Online Learning in Dynamic Networks under Unknown Models

Science.gov (United States)

2016-08-02

The key is to develop online learning strategies at each individual node. Specifically, through local information exchange with its neighbors, each...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning...Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for

Learning Sparse Visual Representations with Leaky Capped Norm Regularizers

OpenAIRE

Wangni, Jianqiao; Lin, Dahua

2017-01-01

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this problem. Our contribution consists of three parts. First, we propose the leaky capped norm regularization (LCNR), which allows model weights below a certain threshold to be regularized more strongly as opposed to those above, therefore imposes strong sparsity and...

Comparing Exploration Strategies for Q-learning in Random Stochastic Mazes

NARCIS (Netherlands)

Tijsma, Arryon; Drugan, Madalina; Wiering, Marco

2016-01-01

Balancing the ratio between exploration and exploitation is an important problem in reinforcement learning. This paper evaluates four different exploration strategies combined with Q-learning using random stochastic mazes to investigate their performances. We will compare: UCB-1, softmax,

Learning stochastic reward distributions in a speeded pointing task.

Science.gov (United States)

Seydell, Anna; McCann, Brian C; Trommershäuser, Julia; Knill, David C

2008-04-23

Recent studies have shown that humans effectively take into account task variance caused by intrinsic motor noise when planning fast hand movements. However, previous evidence suggests that humans have greater difficulty accounting for arbitrary forms of stochasticity in their environment, both in economic decision making and sensorimotor tasks. We hypothesized that humans can learn to optimize movement strategies when environmental randomness can be experienced and thus implicitly learned over several trials, especially if it mimics the kinds of randomness for which subjects might have generative models. We tested the hypothesis using a task in which subjects had to rapidly point at a target region partly covered by three stochastic penalty regions introduced as "defenders." At movement completion, each defender jumped to a new position drawn randomly from fixed probability distributions. Subjects earned points when they hit the target, unblocked by a defender, and lost points otherwise. Results indicate that after approximately 600 trials, subjects approached optimal behavior. We further tested whether subjects simply learned a set of stimulus-contingent motor plans or the statistics of defenders' movements by training subjects with one penalty distribution and then testing them on a new penalty distribution. Subjects immediately changed their strategy to achieve the same average reward as subjects who had trained with the second penalty distribution. These results indicate that subjects learned the parameters of the defenders' jump distributions and used this knowledge to optimally plan their hand movements under conditions involving stochastic rewards and penalties.

Stochastic collusion and the power law of learning: a general reinforcement learning model of cooperation

NARCIS (Netherlands)

Flache, A.

2002-01-01

Concerns about models of cultural adaptation as analogs of genetic selection have led cognitive game theorists to explore learning-theoretic specifications. Two prominent examples, the Bush-Mosteller stochastic learning model and the Roth-Erev payoff-matching model, are aligned and integrated as

Manifold regularized multitask learning for semi-supervised multilabel image classification.

Science.gov (United States)

Luo, Yong; Tao, Dacheng; Geng, Bo; Xu, Chao; Maybank, Stephen J

2013-02-01

It is a significant challenge to classify images with multiple labels by using only a small number of labeled samples. One option is to learn a binary classifier for each label and use manifold regularization to improve the classification performance by exploring the underlying geometric structure of the data distribution. However, such an approach does not perform well in practice when images from multiple concepts are represented by high-dimensional visual features. Thus, manifold regularization is insufficient to control the model complexity. In this paper, we propose a manifold regularized multitask learning (MRMTL) algorithm. MRMTL learns a discriminative subspace shared by multiple classification tasks by exploiting the common structure of these tasks. It effectively controls the model complexity because different tasks limit one another's search volume, and the manifold regularization ensures that the functions in the shared hypothesis space are smooth along the data manifold. We conduct extensive experiments, on the PASCAL VOC'07 dataset with 20 classes and the MIR dataset with 38 classes, by comparing MRMTL with popular image classification algorithms. The results suggest that MRMTL is effective for image classification.

A Q-Learning Approach to Flocking With UAVs in a Stochastic Environment.

Science.gov (United States)

Hung, Shao-Ming; Givigi, Sidney N

2017-01-01

In the past two decades, unmanned aerial vehicles (UAVs) have demonstrated their efficacy in supporting both military and civilian applications, where tasks can be dull, dirty, dangerous, or simply too costly with conventional methods. Many of the applications contain tasks that can be executed in parallel, hence the natural progression is to deploy multiple UAVs working together as a force multiplier. However, to do so requires autonomous coordination among the UAVs, similar to swarming behaviors seen in animals and insects. This paper looks at flocking with small fixed-wing UAVs in the context of a model-free reinforcement learning problem. In particular, Peng's Q(λ) with a variable learning rate is employed by the followers to learn a control policy that facilitates flocking in a leader-follower topology. The problem is structured as a Markov decision process, where the agents are modeled as small fixed-wing UAVs that experience stochasticity due to disturbances such as winds and control noises, as well as weight and balance issues. Learned policies are compared to ones solved using stochastic optimal control (i.e., dynamic programming) by evaluating the average cost incurred during flight according to a cost function. Simulation results demonstrate the feasibility of the proposed learning approach at enabling agents to learn how to flock in a leader-follower topology, while operating in a nonstationary stochastic environment.

Reply : Collective Action and the Empirical Content of Stochastic Learning Models

NARCIS (Netherlands)

Macy, M.W.; Flache, A.

2007-01-01

We are grateful for the opportunity that Bendor, Diermeier, and Ting (hereafter BDT) have provided to address important questions about the empirical content of learning theoretic solutions to the collective action problem. They discuss two well-known classes of adaptive models— stochastic learning

Stochastic quantization and gauge invariance

International Nuclear Information System (INIS)

Viana, R.L.

1987-01-01

A survey of the fundamental ideas about Parisi-Wu's Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories, is done. In particular, the Analytic Stochastic Regularization Scheme is used to calculate the polarization tensor for Quantum Electrodynamics with Dirac bosons or Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested. (author)

Characterization and reconstruction of 3D stochastic microstructures via supervised learning.

Science.gov (United States)

Bostanabad, R; Chen, W; Apley, D W

2016-12-01

The need for computational characterization and reconstruction of volumetric maps of stochastic microstructures for understanding the role of material structure in the processing-structure-property chain has been highlighted in the literature. Recently, a promising characterization and reconstruction approach has been developed where the essential idea is to convert the digitized microstructure image into an appropriate training dataset to learn the stochastic nature of the morphology by fitting a supervised learning model to the dataset. This compact model can subsequently be used to efficiently reconstruct as many statistically equivalent microstructure samples as desired. The goal of this paper is to build upon the developed approach in three major directions by: (1) extending the approach to characterize 3D stochastic microstructures and efficiently reconstruct 3D samples, (2) improving the performance of the approach by incorporating user-defined predictors into the supervised learning model, and (3) addressing potential computational issues by introducing a reduced model which can perform as effectively as the full model. We test the extended approach on three examples and show that the spatial dependencies, as evaluated via various measures, are well preserved in the reconstructed samples. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Multi-task feature learning by using trace norm regularization

Directory of Open Access Journals (Sweden)

Jiangmei Zhang

2017-11-01

Full Text Available Multi-task learning can extract the correlation of multiple related machine learning problems to improve performance. This paper considers applying the multi-task learning method to learn a single task. We propose a new learning approach, which employs the mixture of expert model to divide a learning task into several related sub-tasks, and then uses the trace norm regularization to extract common feature representation of these sub-tasks. A nonlinear extension of this approach by using kernel is also provided. Experiments conducted on both simulated and real data sets demonstrate the advantage of the proposed approach.

Geometric continuum regularization of quantum field theory

International Nuclear Information System (INIS)

Halpern, M.B.

1989-01-01

An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

Stochastic quantization and gauge theories

International Nuclear Information System (INIS)

Kolck, U. van.

1987-01-01

Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt

Regular graph construction for semi-supervised learning

International Nuclear Information System (INIS)

Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang

2014-01-01

Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN

Learning-based stochastic object models for characterizing anatomical variations

Science.gov (United States)

Dolly, Steven R.; Lou, Yang; Anastasio, Mark A.; Li, Hua

2018-03-01

It is widely known that the optimization of imaging systems based on objective, task-based measures of image quality via computer-simulation requires the use of a stochastic object model (SOM). However, the development of computationally tractable SOMs that can accurately model the statistical variations in human anatomy within a specified ensemble of patients remains a challenging task. Previously reported numerical anatomic models lack the ability to accurately model inter-patient and inter-organ variations in human anatomy among a broad patient population, mainly because they are established on image data corresponding to a few of patients and individual anatomic organs. This may introduce phantom-specific bias into computer-simulation studies, where the study result is heavily dependent on which phantom is used. In certain applications, however, databases of high-quality volumetric images and organ contours are available that can facilitate this SOM development. In this work, a novel and tractable methodology for learning a SOM and generating numerical phantoms from a set of volumetric training images is developed. The proposed methodology learns geometric attribute distributions (GAD) of human anatomic organs from a broad patient population, which characterize both centroid relationships between neighboring organs and anatomic shape similarity of individual organs among patients. By randomly sampling the learned centroid and shape GADs with the constraints of the respective principal attribute variations learned from the training data, an ensemble of stochastic objects can be created. The randomness in organ shape and position reflects the learned variability of human anatomy. To demonstrate the methodology, a SOM of an adult male pelvis is computed and examples of corresponding numerical phantoms are created.

Visual Perceptual Echo Reflects Learning of Regularities in Rapid Luminance Sequences.

Science.gov (United States)

Chang, Acer Y-C; Schwartzman, David J; VanRullen, Rufin; Kanai, Ryota; Seth, Anil K

2017-08-30

A novel neural signature of active visual processing has recently been described in the form of the "perceptual echo", in which the cross-correlation between a sequence of randomly fluctuating luminance values and occipital electrophysiological signals exhibits a long-lasting periodic (∼100 ms cycle) reverberation of the input stimulus (VanRullen and Macdonald, 2012). As yet, however, the mechanisms underlying the perceptual echo and its function remain unknown. Reasoning that natural visual signals often contain temporally predictable, though nonperiodic features, we hypothesized that the perceptual echo may reflect a periodic process associated with regularity learning. To test this hypothesis, we presented subjects with successive repetitions of a rapid nonperiodic luminance sequence, and examined the effects on the perceptual echo, finding that echo amplitude linearly increased with the number of presentations of a given luminance sequence. These data suggest that the perceptual echo reflects a neural signature of regularity learning.Furthermore, when a set of repeated sequences was followed by a sequence with inverted luminance polarities, the echo amplitude decreased to the same level evoked by a novel stimulus sequence. Crucially, when the original stimulus sequence was re-presented, the echo amplitude returned to a level consistent with the number of presentations of this sequence, indicating that the visual system retained sequence-specific information, for many seconds, even in the presence of intervening visual input. Altogether, our results reveal a previously undiscovered regularity learning mechanism within the human visual system, reflected by the perceptual echo. SIGNIFICANCE STATEMENT How the brain encodes and learns fast-changing but nonperiodic visual input remains unknown, even though such visual input characterizes natural scenes. We investigated whether the phenomenon of "perceptual echo" might index such learning. The perceptual echo is a

An Analysis of Stochastic Game Theory for Multiagent Reinforcement Learning

National Research Council Canada - National Science Library

Bowling, Michael

2000-01-01

.... In this paper we contribute a comprehensive presentation of the relevant techniques for solving stochastic games from both the game theory community and reinforcement learning communities. We examine the assumptions and limitations of these algorithms, and identify similarities between these algorithms, single agent reinforcement learners, and basic game theory techniques.

Feature selection and multi-kernel learning for adaptive graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan

2014-09-20

Nonnegative matrix factorization (NMF), a popular part-based representation technique, does not capture the intrinsic local geometric structure of the data space. Graph regularized NMF (GNMF) was recently proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data set. However, GNMF has two main bottlenecks. First, using the original feature space directly to construct the graph is not necessarily optimal because of the noisy and irrelevant features and nonlinear distributions of data samples. Second, one possible way to handle the nonlinear distribution of data samples is by kernel embedding. However, it is often difficult to choose the most suitable kernel. To solve these bottlenecks, we propose two novel graph-regularized NMF methods, AGNMFFS and AGNMFMK, by introducing feature selection and multiple-kernel learning to the graph regularized NMF, respectively. Instead of using a fixed graph as in GNMF, the two proposed methods learn the nearest neighbor graph that is adaptive to the selected features and learned multiple kernels, respectively. For each method, we propose a unified objective function to conduct feature selection/multi-kernel learning, NMF and adaptive graph regularization simultaneously. We further develop two iterative algorithms to solve the two optimization problems. Experimental results on two challenging pattern classification tasks demonstrate that the proposed methods significantly outperform state-of-the-art data representation methods.

Substructural Regularization With Data-Sensitive Granularity for Sequence Transfer Learning.

Science.gov (United States)

Sun, Shichang; Liu, Hongbo; Meng, Jiana; Chen, C L Philip; Yang, Yu

2018-06-01

Sequence transfer learning is of interest in both academia and industry with the emergence of numerous new text domains from Twitter and other social media tools. In this paper, we put forward the data-sensitive granularity for transfer learning, and then, a novel substructural regularization transfer learning model (STLM) is proposed to preserve target domain features at substructural granularity in the light of the condition of labeled data set size. Our model is underpinned by hidden Markov model and regularization theory, where the substructural representation can be integrated as a penalty after measuring the dissimilarity of substructures between target domain and STLM with relative entropy. STLM can achieve the competing goals of preserving the target domain substructure and utilizing the observations from both the target and source domains simultaneously. The estimation of STLM is very efficient since an analytical solution can be derived as a necessary and sufficient condition. The relative usability of substructures to act as regularization parameters and the time complexity of STLM are also analyzed and discussed. Comprehensive experiments of part-of-speech tagging with both Brown and Twitter corpora fully justify that our model can make improvements on all the combinations of source and target domains.

L1-norm locally linear representation regularization multi-source adaptation learning.

Science.gov (United States)

Tao, Jianwen; Wen, Shiting; Hu, Wenjun

2015-09-01

In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this "small sample" regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object. Copyright © 2015 Elsevier Ltd. All rights reserved.

Manifold Regularized Experimental Design for Active Learning.

Science.gov (United States)

Zhang, Lining; Shum, Hubert P H; Shao, Ling

2016-12-02

Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.

ANALYSIS OF EFFECTIVENESS OF METHODOLOGICAL SYSTEM FOR PROBABILITY AND STOCHASTIC PROCESSES COMPUTER-BASED LEARNING FOR PRE-SERVICE ENGINEERS

Directory of Open Access Journals (Sweden)

E. Chumak

2015-04-01

Full Text Available The author substantiates that only methodological training systems of mathematical disciplines with implementation of information and communication technologies (ICT can meet the requirements of modern educational paradigm and make possible to increase the educational efficiency. Due to this fact, the necessity of developing the methodology of theory of probability and stochastic processes computer-based learning for pre-service engineers is underlined in the paper. The results of the experimental study for analysis of the efficiency of methodological system of theory of probability and stochastic processes computer-based learning for pre-service engineers are shown. The analysis includes three main stages: ascertaining, searching and forming. The key criteria of the efficiency of designed methodological system are the level of probabilistic and stochastic skills of students and their learning motivation. The effect of implementing the methodological system of probability theory and stochastic processes computer-based learning on the level of students’ IT literacy is shown in the paper. The expanding of the range of objectives of ICT applying by students is described by author. The level of formation of students’ learning motivation on the ascertaining and forming stages of the experiment is analyzed. The level of intrinsic learning motivation for pre-service engineers is defined on these stages of the experiment. For this purpose, the methodology of testing the students’ learning motivation in the chosen specialty is presented in the paper. The increasing of intrinsic learning motivation of the experimental group students (E group against the control group students (C group is demonstrated.

Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

International Nuclear Information System (INIS)

Jia, Ningning; Lam, Edmund Y

2010-01-01

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k 1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks

Error analysis of stochastic gradient descent ranking.

Science.gov (United States)

Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan

2013-06-01

Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.

Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance

NARCIS (Netherlands)

Schrager, D.F.; Pelsser, A.

2004-01-01

We derive general pricing formulas for Rate of Return Guarantees in Regular Premium Unit Linked Insurance under stochastic interest rates. Our main contribution focusses on the effect of stochastic interest rates. First, we show the effect of stochastic interest rates can be interpreted as, what is

Diagrammatic methods in phase-space regularization

International Nuclear Information System (INIS)

Bern, Z.; Halpern, M.B.; California Univ., Berkeley

1987-11-01

Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phase-space form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the nogrowth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization. (orig.)

Quantum learning of classical stochastic processes: The completely positive realization problem

International Nuclear Information System (INIS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Quantum learning of classical stochastic processes: The completely positive realization problem

Science.gov (United States)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Quantum learning of classical stochastic processes: The completely positive realization problem

Energy Technology Data Exchange (ETDEWEB)

Monràs, Alex [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Winter, Andreas [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys, 23, 08010 Barcelona (Spain)

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Redefining "Learning" in Statistical Learning: What Does an Online Measure Reveal About the Assimilation of Visual Regularities?

Science.gov (United States)

Siegelman, Noam; Bogaerts, Louisa; Kronenfeld, Ofer; Frost, Ram

2017-10-07

From a theoretical perspective, most discussions of statistical learning (SL) have focused on the possible "statistical" properties that are the object of learning. Much less attention has been given to defining what "learning" is in the context of "statistical learning." One major difficulty is that SL research has been monitoring participants' performance in laboratory settings with a strikingly narrow set of tasks, where learning is typically assessed offline, through a set of two-alternative-forced-choice questions, which follow a brief visual or auditory familiarization stream. Is that all there is to characterizing SL abilities? Here we adopt a novel perspective for investigating the processing of regularities in the visual modality. By tracking online performance in a self-paced SL paradigm, we focus on the trajectory of learning. In a set of three experiments we show that this paradigm provides a reliable and valid signature of SL performance, and it offers important insights for understanding how statistical regularities are perceived and assimilated in the visual modality. This demonstrates the promise of integrating different operational measures to our theory of SL. © 2017 Cognitive Science Society, Inc.

Full particle orbit effects in regular and stochastic magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France); Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); Castillo-Negrete, Diego del [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States); Dif-Pradalier, Guilhem; Garbet, Xavier [CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France)

2016-07-15

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the

Less is more: regularization perspectives on large scale machine learning

CERN Multimedia

CERN. Geneva

2017-01-01

Deep learning based techniques provide a possible solution at the expanse of theoretical guidance and, especially, of computational requirements. It is then a key challenge for large scale machine learning to devise approaches guaranteed to be accurate and yet computationally efficient. In this talk, we will consider a regularization perspectives on machine learning appealing to classical ideas in linear algebra and inverse problems to scale-up dramatically nonparametric methods such as kernel methods, often dismissed because of prohibitive costs. Our analysis derives optimal theoretical guarantees while providing experimental results at par or out-performing state of the art approaches.

Fixation and escape times in stochastic game learning

International Nuclear Information System (INIS)

Realpe-Gomez, John; Szczesny, Bartosz; Galla, Tobias; Dall’Asta, Luca

2012-01-01

Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2×2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed. (paper)

Stochastic synaptic plasticity with memristor crossbar arrays

KAUST Repository

Naous, Rawan

2016-11-01

Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.

Stochastic synaptic plasticity with memristor crossbar arrays

KAUST Repository

Naous, Rawan; Al-Shedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled N.

2016-01-01

Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

Science.gov (United States)

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Stochastic quantization for the axial model

International Nuclear Information System (INIS)

Farina, C.; Montani, H.; Albuquerque, L.C.

1991-01-01

We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process

Stochastic Analysis : A Series of Lectures

CERN Document Server

Dozzi, Marco; Flandoli, Franco; Russo, Francesco

2015-01-01

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...

Stochastic Learning of Multi-Instance Dictionary for Earth Mover's Distance based Histogram Comparison

OpenAIRE

Fan, Jihong; Liang, Ru-Ze

2016-01-01

Dictionary plays an important role in multi-instance data representation. It maps bags of instances to histograms. Earth mover's distance (EMD) is the most effective histogram distance metric for the application of multi-instance retrieval. However, up to now, there is no existing multi-instance dictionary learning methods designed for EMD based histogram comparison. To fill this gap, we develop the first EMD-optimal dictionary learning method using stochastic optimization method. In the stoc...

Regularized maximum correntropy machine

KAUST Repository

Wang, Jim Jing-Yan; Wang, Yunji; Jing, Bing-Yi; Gao, Xin

2015-01-01

In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.

Regularized maximum correntropy machine

KAUST Repository

Wang, Jim Jing-Yan

2015-02-12

In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.

Manifold regularized multitask feature learning for multimodality disease classification.

Science.gov (United States)

Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang

2015-02-01

Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis. © 2014 Wiley Periodicals, Inc.

A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting

Science.gov (United States)

Kim, T.; Joo, K.; Seo, J.; Heo, J. H.

2016-12-01

Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.

Infinite stochastic acceleration of charged particles from non-relativistic initial energies

International Nuclear Information System (INIS)

Buts, V.A.; Manujlenko, O.V.; Turkin, Yu.A.

1997-01-01

Stochastic charged particle acceleration by electro-magnetic field due to overlapping of non-linear cyclotron resonances is considered. It was shown that non-relativistic charged particles are involved in infinitive stochastic acceleration regime. This effect can be used for stochastic acceleration or for plasma heating by regular electro-magnetic fields

Symmetries of stochastic differential equations: A geometric approach

Energy Technology Data Exchange (ETDEWEB)

De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

2016-06-15

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

Collective stochastic coherence in recurrent neuronal networks

Science.gov (United States)

Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi

2016-09-01

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.

A regularized approach for geodesic-based semisupervised multimanifold learning.

Science.gov (United States)

Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun

2014-05-01

Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.

Multiple Learning Strategies Project. Building Maintenance & Engineering. Regular Vocational. [Vol. 2.

Science.gov (United States)

Smith, Dwight; And Others

This instructional package is one of two designed for regular vocational students in the vocational area of building maintenance and engineering. The fifty-three learning modules are organized into ten units: office cleaning; grounds; sanitation; boiler maintenance and operation; power and hand tools; cabinet construction; repair of damaged…

Stochastic optimal control in infinite dimension dynamic programming and HJB equations

CERN Document Server

Fabbri, Giorgio; Święch, Andrzej

2017-01-01

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...

Learning Errors by Radial Basis Function Neural Networks and Regularization Networks

Czech Academy of Sciences Publication Activity Database

Neruda, Roman; Vidnerová, Petra

2009-01-01

Roč. 1, č. 2 (2009), s. 49-57 ISSN 2005-4262 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : neural network * RBF networks * regularization * learning Subject RIV: IN - Informatics, Computer Science http://www.sersc.org/journals/IJGDC/vol2_no1/5.pdf

Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.

Science.gov (United States)

Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing

2018-03-01

In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.

The "Learning in Regular Classrooms" Initiative for Inclusive Education in China

Science.gov (United States)

Xu, Su Qiong; Cooper, Paul; Sin, Kenneth

2018-01-01

The purpose of this article is to understand the Learning in Regular Classrooms (LRC) initiative for inclusive education in China. First, the paper reviews the policy, legislation, and practice in relation to the LRC. It then goes on to explore the specific social-political context of the LRC, and compares the Chinese LRC with the Western…

Continuous strong Markov processes in dimension one a stochastic calculus approach

CERN Document Server

Assing, Sigurd

1998-01-01

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Effects of dopamine medication on sequence learning with stochastic feedback in Parkinson's disease

Directory of Open Access Journals (Sweden)

Moonsang Seo

2010-08-01

Full Text Available A growing body of evidence suggests that the midbrain dopamine system plays a key role in reinforcement learning and disruption of the midbrain dopamine system in Parkinson's disease (PD may lead to deficits on tasks that require learning from feedback. We examined how changes in dopamine levels (‘ON’ and ‘OFF’ their dopamine medication affect sequence learning from stochastic positive and negative feedback using Bayesian reinforcement learning models. We found deficits in sequence learning in patients with PD when they were ‘ON’ and ‘OFF’ medication relative to healthy controls, but smaller differences between patients ‘OFF’ and ‘ON’. The deficits were mainly due to decreased learning from positive feedback, although across all participant groups learning was more strongly associated with positive than negative feedback in our task. The learning in our task is likely mediated by the relatively depleted dorsal striatum and not the relatively intact ventral striatum. Therefore, the changes we see in our task may be due to a strong loss of phasic dopamine signals in the dorsal striatum in PD.

Effects of Dopamine Medication on Sequence Learning with Stochastic Feedback in Parkinson's Disease

Science.gov (United States)

Seo, Moonsang; Beigi, Mazda; Jahanshahi, Marjan; Averbeck, Bruno B.

2010-01-01

A growing body of evidence suggests that the midbrain dopamine system plays a key role in reinforcement learning and disruption of the midbrain dopamine system in Parkinson's disease (PD) may lead to deficits on tasks that require learning from feedback. We examined how changes in dopamine levels (“ON” and “OFF” their dopamine medication) affect sequence learning from stochastic positive and negative feedback using Bayesian reinforcement learning models. We found deficits in sequence learning in patients with PD when they were “ON” and “OFF” medication relative to healthy controls, but smaller differences between patients “OFF” and “ON”. The deficits were mainly due to decreased learning from positive feedback, although across all participant groups learning was more strongly associated with positive than negative feedback in our task. The learning in our task is likely mediated by the relatively depleted dorsal striatum and not the relatively intact ventral striatum. Therefore, the changes we see in our task may be due to a strong loss of phasic dopamine signals in the dorsal striatum in PD. PMID:20740077

On the relationships between generative encodings, regularity, and learning abilities when evolving plastic artificial neural networks.

Directory of Open Access Journals (Sweden)

Paul Tonelli

Full Text Available A major goal of bio-inspired artificial intelligence is to design artificial neural networks with abilities that resemble those of animal nervous systems. It is commonly believed that two keys for evolving nature-like artificial neural networks are (1 the developmental process that links genes to nervous systems, which enables the evolution of large, regular neural networks, and (2 synaptic plasticity, which allows neural networks to change during their lifetime. So far, these two topics have been mainly studied separately. The present paper shows that they are actually deeply connected. Using a simple operant conditioning task and a classic evolutionary algorithm, we compare three ways to encode plastic neural networks: a direct encoding, a developmental encoding inspired by computational neuroscience models, and a developmental encoding inspired by morphogen gradients (similar to HyperNEAT. Our results suggest that using a developmental encoding could improve the learning abilities of evolved, plastic neural networks. Complementary experiments reveal that this result is likely the consequence of the bias of developmental encodings towards regular structures: (1 in our experimental setup, encodings that tend to produce more regular networks yield networks with better general learning abilities; (2 whatever the encoding is, networks that are the more regular are statistically those that have the best learning abilities.

Does language help regularity learning? The influence of verbalizations on implicit sequential regularity learning and the emergence of explicit knowledge in children, younger and older adults.

Science.gov (United States)

Ferdinand, Nicola K; Kray, Jutta

2017-03-01

This study aimed at investigating the ability to learn regularities across the life span and examine whether this learning process can be supported or hampered by verbalizations. For this purpose, children (aged 8-10 years) and younger (aged 19-30 years) and older (aged 70-80 years) adults took part in a sequence learning experiment. We found that verbalizing sequence-congruent information during learning is a powerful tool to generate explicit knowledge and it is especially helpful for younger adults. Although recent research suggests that implicit learning can be influenced by directing the participants' attention to relevant aspects of the task, verbalizations had a much weaker influence on implicit than explicit learning. Our results show that verbalizing during learning slows down reaction times (RTs) but does not influence the amount of implicit learning. Especially older adults were not able to overcome the cost of the dual-task situation. Younger adults, in contrast, show an initial dual-tasking cost that, in the case of a helpful verbalization, is overcome with practice and turns into a RT and learning benefit. However, when the verbalization is omitted this benefit is lost, that is, better implicit learning seems to be confined to situations in which the supporting verbalization is maintained. Additionally, we did not find reliable age differences in implicit learning in the no verbalization groups, which speaks in favor of age-invariant models of implicit learning across the life span. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Implicit learning of non-linguistic and linguistic regularities in children with dyslexia.

Science.gov (United States)

Nigro, Luciana; Jiménez-Fernández, Gracia; Simpson, Ian C; Defior, Sylvia

2016-07-01

One of the hallmarks of dyslexia is the failure to automatise written patterns despite repeated exposure to print. Although many explanations have been proposed to explain this problem, researchers have recently begun to explore the possibility that an underlying implicit learning deficit may play a role in dyslexia. This hypothesis has been investigated through non-linguistic tasks exploring implicit learning in a general domain. In this study, we examined the abilities of children with dyslexia to implicitly acquire positional regularities embedded in both non-linguistic and linguistic stimuli. In experiment 1, 42 children (21 with dyslexia and 21 typically developing) were exposed to rule-governed shape sequences; whereas in experiment 2, a new group of 42 children were exposed to rule-governed letter strings. Implicit learning was assessed in both experiments via a forced-choice task. Experiments 1 and 2 showed a similar pattern of results. ANOVA analyses revealed no significant differences between the dyslexic and the typically developing group, indicating that children with dyslexia are not impaired in the acquisition of simple positional regularities, regardless of the nature of the stimuli. However, within group t-tests suggested that children from the dyslexic group could not transfer the underlying positional rules to novel instances as efficiently as typically developing children.

Gift from statistical learning: Visual statistical learning enhances memory for sequence elements and impairs memory for items that disrupt regularities.

Science.gov (United States)

Otsuka, Sachio; Saiki, Jun

2016-02-01

Prior studies have shown that visual statistical learning (VSL) enhances familiarity (a type of memory) of sequences. How do statistical regularities influence the processing of each triplet element and inserted distractors that disrupt the regularity? Given that increased attention to triplets induced by VSL and inhibition of unattended triplets, we predicted that VSL would promote memory for each triplet constituent, and degrade memory for inserted stimuli. Across the first two experiments, we found that objects from structured sequences were more likely to be remembered than objects from random sequences, and that letters (Experiment 1) or objects (Experiment 2) inserted into structured sequences were less likely to be remembered than those inserted into random sequences. In the subsequent two experiments, we examined an alternative account for our results, whereby the difference in memory for inserted items between structured and random conditions is due to individuation of items within random sequences. Our findings replicated even when control letters (Experiment 3A) or objects (Experiment 3B) were presented before or after, rather than inserted into, random sequences. Our findings suggest that statistical learning enhances memory for each item in a regular set and impairs memory for items that disrupt the regularity. Copyright © 2015 Elsevier B.V. All rights reserved.

Semi-supervised learning via regularized boosting working on multiple semi-supervised assumptions.

Science.gov (United States)

Chen, Ke; Wang, Shihai

2011-01-01

Semi-supervised learning concerns the problem of learning in the presence of labeled and unlabeled data. Several boosting algorithms have been extended to semi-supervised learning with various strategies. To our knowledge, however, none of them takes all three semi-supervised assumptions, i.e., smoothness, cluster, and manifold assumptions, together into account during boosting learning. In this paper, we propose a novel cost functional consisting of the margin cost on labeled data and the regularization penalty on unlabeled data based on three fundamental semi-supervised assumptions. Thus, minimizing our proposed cost functional with a greedy yet stagewise functional optimization procedure leads to a generic boosting framework for semi-supervised learning. Extensive experiments demonstrate that our algorithm yields favorite results for benchmark and real-world classification tasks in comparison to state-of-the-art semi-supervised learning algorithms, including newly developed boosting algorithms. Finally, we discuss relevant issues and relate our algorithm to the previous work.

Multiple Learning Strategies Project. Small Engine Repair Service. Regular Vocational. [Vol. 1.

Science.gov (United States)

Pitts, Jim; And Others

This instructional package is one of two designed for use by regular vocational students in the vocational area of small engine repair service. Contained in this document are forty-four learning modules organized into ten units: engine block; air cleaner; starters; fuel tanks; lines, filters, and pumps; carburetors; electrical; magneto systems;…

Doubly stochastic Poisson processes in artificial neural learning.

Science.gov (United States)

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Magnetic Tunnel Junction Based Long-Term Short-Term Stochastic Synapse for a Spiking Neural Network with On-Chip STDP Learning

Science.gov (United States)

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-01

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.

Basis Expansion Approaches for Regularized Sequential Dictionary Learning Algorithms With Enforced Sparsity for fMRI Data Analysis.

Science.gov (United States)

Seghouane, Abd-Krim; Iqbal, Asif

2017-09-01

Sequential dictionary learning algorithms have been successfully applied to functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are, however, structured data matrices with the notions of temporal smoothness in the column direction. This prior information, which can be converted into a constraint of smoothness on the learned dictionary atoms, has seldomly been included in classical dictionary learning algorithms when applied to fMRI data analysis. In this paper, we tackle this problem by proposing two new sequential dictionary learning algorithms dedicated to fMRI data analysis by accounting for this prior information. These algorithms differ from the existing ones in their dictionary update stage. The steps of this stage are derived as a variant of the power method for computing the SVD. The proposed algorithms generate regularized dictionary atoms via the solution of a left regularized rank-one matrix approximation problem where temporal smoothness is enforced via regularization through basis expansion and sparse basis expansion in the dictionary update stage. Applications on synthetic data experiments and real fMRI data sets illustrating the performance of the proposed algorithms are provided.

Learning SAS’s Perl Regular Expression Matching the Easy Way: By Doing

Science.gov (United States)

2015-01-12

Doing 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Paul Genovesi 5d. PROJECT NUMBER 5e. TASK NUMBER 5f...regex_learning_tool allows both beginner and expert to efficiently practice PRX matching by selecting and processing only the match records that the user is interested...perl regular expression and/or source string. The regex_learning_tool allows both beginner and expert to efficiently practice PRX matching by

Bayesian nonparametric dictionary learning for compressed sensing MRI.

Science.gov (United States)

Huang, Yue; Paisley, John; Lin, Qin; Ding, Xinghao; Fu, Xueyang; Zhang, Xiao-Ping

2014-12-01

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.

Stochastic Averaging for Constrained Optimization With Application to Online Resource Allocation

Science.gov (United States)

Chen, Tianyi; Mokhtari, Aryan; Wang, Xin; Ribeiro, Alejandro; Giannakis, Georgios B.

2017-06-01

Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.

A Large-Scale Multi-Hop Localization Algorithm Based on Regularized Extreme Learning for Wireless Networks.

Science.gov (United States)

Zheng, Wei; Yan, Xiaoyong; Zhao, Wei; Qian, Chengshan

2017-12-20

A novel large-scale multi-hop localization algorithm based on regularized extreme learning is proposed in this paper. The large-scale multi-hop localization problem is formulated as a learning problem. Unlike other similar localization algorithms, the proposed algorithm overcomes the shortcoming of the traditional algorithms which are only applicable to an isotropic network, therefore has a strong adaptability to the complex deployment environment. The proposed algorithm is composed of three stages: data acquisition, modeling and location estimation. In data acquisition stage, the training information between nodes of the given network is collected. In modeling stage, the model among the hop-counts and the physical distances between nodes is constructed using regularized extreme learning. In location estimation stage, each node finds its specific location in a distributed manner. Theoretical analysis and several experiments show that the proposed algorithm can adapt to the different topological environments with low computational cost. Furthermore, high accuracy can be achieved by this method without setting complex parameters.

Quantum stochastics

CERN Document Server

Chang, Mou-Hsiung

2015-01-01

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...

Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer.

Science.gov (United States)

Li, Zhenni; Ding, Shuxue; Li, Yujie; Yang, Zuyuan; Xie, Shengli; Chen, Wuhui

2018-02-01

Recently there has been increasing attention towards analysis dictionary learning. In analysis dictionary learning, it is an open problem to obtain the strong sparsity-promoting solutions efficiently while simultaneously avoiding the trivial solutions of the dictionary. In this paper, to obtain the strong sparsity-promoting solutions, we employ the ℓ 1∕2 norm as a regularizer. The very recent study on ℓ 1∕2 norm regularization theory in compressive sensing shows that its solutions can give sparser results than using the ℓ 1 norm. We transform a complex nonconvex optimization into a number of one-dimensional minimization problems. Then the closed-form solutions can be obtained efficiently. To avoid trivial solutions, we apply manifold optimization to update the dictionary directly on the manifold satisfying the orthonormality constraint, so that the dictionary can avoid the trivial solutions well while simultaneously capturing the intrinsic properties of the dictionary. The experiments with synthetic and real-world data verify that the proposed algorithm for analysis dictionary learning can not only obtain strong sparsity-promoting solutions efficiently, but also learn more accurate dictionary in terms of dictionary recovery and image processing than the state-of-the-art algorithms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition

KAUST Repository

Bessaih, Hakima

2015-11-02

The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.

Online co-regularized algorithms

NARCIS (Netherlands)

Ruijter, T. de; Tsivtsivadze, E.; Heskes, T.

2012-01-01

We propose an online co-regularized learning algorithm for classification and regression tasks. We demonstrate that by sequentially co-regularizing prediction functions on unlabeled data points, our algorithm provides improved performance in comparison to supervised methods on several UCI benchmarks

Multiple Kernel Learning for adaptive graph regularized nonnegative matrix factorization

KAUST Repository

Wang, Jim Jing-Yan; AbdulJabbar, Mustafa Abdulmajeed

2012-01-01

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of non-negative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation, which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.

Statistical inference and comparison of stochastic models for the hydraulic conductivity at the Finnsjoen-site

International Nuclear Information System (INIS)

Norman, S.

1992-04-01

The origin of this study was to find a good, or even the best, stochastic model for the hydraulic conductivity field at the Finnsjoe site. The conductivity field in question are regularized, that is upscaled. The reason for performing regularization of measurement data is primarily the need for long correlation scales. This is needed in order to model reasonably large domains that can be used when describing regional groundwater flow accurately. A theory of regularization is discussed in this report. In order to find the best model, jacknifing is employed to compare different stochastic models. The theory for this method is described. In the act of doing so we also take a look at linear predictor theory, so called kriging, and include a general discussion of stochastic functions and intrinsic random functions. The statistical inference methods for finding the models are also described, in particular regression, iterative generalized regression (IGLSE) and non-parametric variogram estimators. A large amount of results is presented for a regularization scale of 36 metre. (30 refs.) (au)

Semi-supervised manifold learning with affinity regularization for Alzheimer's disease identification using positron emission tomography imaging.

Science.gov (United States)

Lu, Shen; Xia, Yong; Cai, Tom Weidong; Feng, David Dagan

2015-01-01

Dementia, Alzheimer's disease (AD) in particular is a global problem and big threat to the aging population. An image based computer-aided dementia diagnosis method is needed to providing doctors help during medical image examination. Many machine learning based dementia classification methods using medical imaging have been proposed and most of them achieve accurate results. However, most of these methods make use of supervised learning requiring fully labeled image dataset, which usually is not practical in real clinical environment. Using large amount of unlabeled images can improve the dementia classification performance. In this study we propose a new semi-supervised dementia classification method based on random manifold learning with affinity regularization. Three groups of spatial features are extracted from positron emission tomography (PET) images to construct an unsupervised random forest which is then used to regularize the manifold learning objective function. The proposed method, stat-of-the-art Laplacian support vector machine (LapSVM) and supervised SVM are applied to classify AD and normal controls (NC). The experiment results show that learning with unlabeled images indeed improves the classification performance. And our method outperforms LapSVM on the same dataset.

Measuring time series regularity using nonlinear similarity-based sample entropy

International Nuclear Information System (INIS)

Xie Hongbo; He Weixing; Liu Hui

2008-01-01

Sampe Entropy (SampEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors is based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of SampEn. Sigmoid function is a smoothed and continuous version of Heaviside function. To overcome the problems SampEn encountered, a modified SampEn (mSampEn) based on nonlinear Sigmoid function was proposed. The performance of mSampEn was tested on the independent identically distributed (i.i.d.) uniform random numbers, the MIX stochastic model, the Rossler map, and the Hennon map. The results showed that mSampEn was superior to SampEn in several aspects, including giving entropy definition in case of small parameters, better relative consistency, robust to noise, and more independence on record length when characterizing time series generated from either deterministic or stochastic system with different regularities

Comparison between stochastic and machine learning methods for hydrological multi-step ahead forecasting: All forecasts are wrong!

Science.gov (United States)

Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

2017-04-01

Machine learning (ML) is considered to be a promising approach to hydrological processes forecasting. We conduct a comparison between several stochastic and ML point estimation methods by performing large-scale computational experiments based on simulations. The purpose is to provide generalized results, while the respective comparisons in the literature are usually based on case studies. The stochastic methods used include simple methods, models from the frequently used families of Autoregressive Moving Average (ARMA), Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Exponential Smoothing models. The ML methods used are Random Forests (RF), Support Vector Machines (SVM) and Neural Networks (NN). The comparison refers to the multi-step ahead forecasting properties of the methods. A total of 20 methods are used, among which 9 are the ML methods. 12 simulation experiments are performed, while each of them uses 2 000 simulated time series of 310 observations. The time series are simulated using stochastic processes from the families of ARMA and ARFIMA models. Each time series is split into a fitting (first 300 observations) and a testing set (last 10 observations). The comparative assessment of the methods is based on 18 metrics, that quantify the methods' performance according to several criteria related to the accurate forecasting of the testing set, the capturing of its variation and the correlation between the testing and forecasted values. The most important outcome of this study is that there is not a uniformly better or worse method. However, there are methods that are regularly better or worse than others with respect to specific metrics. It appears that, although a general ranking of the methods is not possible, their classification based on their similar or contrasting performance in the various metrics is possible to some extent. Another important conclusion is that more sophisticated methods do not necessarily provide better forecasts

Memristors Empower Spiking Neurons With Stochasticity

KAUST Repository

Al-Shedivat, Maruan

2015-06-01

Recent theoretical studies have shown that probabilistic spiking can be interpreted as learning and inference in cortical microcircuits. This interpretation creates new opportunities for building neuromorphic systems driven by probabilistic learning algorithms. However, such systems must have two crucial features: 1) the neurons should follow a specific behavioral model, and 2) stochastic spiking should be implemented efficiently for it to be scalable. This paper proposes a memristor-based stochastically spiking neuron that fulfills these requirements. First, the analytical model of the memristor is enhanced so it can capture the behavioral stochasticity consistent with experimentally observed phenomena. The switching behavior of the memristor model is demonstrated to be akin to the firing of the stochastic spike response neuron model, the primary building block for probabilistic algorithms in spiking neural networks. Furthermore, the paper proposes a neural soma circuit that utilizes the intrinsic nondeterminism of memristive switching for efficient spike generation. The simulations and analysis of the behavior of a single stochastic neuron and a winner-take-all network built of such neurons and trained on handwritten digits confirm that the circuit can be used for building probabilistic sampling and pattern adaptation machinery in spiking networks. The findings constitute an important step towards scalable and efficient probabilistic neuromorphic platforms. © 2011 IEEE.

Estimation of Stochastic Volatility Models by Nonparametric Filtering

DEFF Research Database (Denmark)

Kanaya, Shin; Kristensen, Dennis

2016-01-01

/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...

Manifold Regularized Correlation Object Tracking.

Science.gov (United States)

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2018-05-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.

Sequence Learning with Stochastic Feedback in a Cross-Cultural Sample of Boys in the Autistic Spectrum

Science.gov (United States)

Hentschel, Maren; Lange-Kuttner, Christiane; Averbeck, Bruno B.

2016-01-01

The study investigated sequence learning from stochastic feedback in boys with Autistic Spectrum Disorder (ASD) and typically developed (TD) boys. We asked boys with ASD from Nigeria and the UK as well as age- and gender-matched controls (also males only) to deduce a sequence of four left and right button presses, LLRR, RRLL, LRLR, RLRL, LRRL and…

Manifold regularized matrix completion for multi-label learning with ADMM.

Science.gov (United States)

Liu, Bin; Li, Yingming; Xu, Zenglin

2018-05-01

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach. Copyright © 2018 Elsevier Ltd. All rights reserved.

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan; Sun, Yijun; Gao, Xin

2014-01-01

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan

2014-04-17

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse structure, we assume that each multimedia object could be represented as a sparse linear combination of all other objects, and combination coefficients are regarded as a similarity measure between objects and used to regularize their ranking scores. Moreover, we propose to learn the sparse combination coefficients and the ranking scores simultaneously. A unified objective function is constructed with regard to both the combination coefficients and the ranking scores, and is optimized by an iterative algorithm. Experiments on two multimedia database retrieval data sets demonstrate the significant improvements of the propose algorithm over state-of-the-art ranking score learning algorithms.

Travel time tomography with local image regularization by sparsity constrained dictionary learning

Science.gov (United States)

Bianco, M.; Gerstoft, P.

2017-12-01

We propose a regularization approach for 2D seismic travel time tomography which models small rectangular groups of slowness pixels, within an overall or `global' slowness image, as sparse linear combinations of atoms from a dictionary. The groups of slowness pixels are referred to as patches and a dictionary corresponds to a collection of functions or `atoms' describing the slowness in each patch. These functions could for example be wavelets.The patch regularization is incorporated into the global slowness image. The global image models the broad features, while the local patch images incorporate prior information from the dictionary. Further, high resolution slowness within patches is permitted if the travel times from the global estimates support it. The proposed approach is formulated as an algorithm, which is repeated until convergence is achieved: 1) From travel times, find the global slowness image with a minimum energy constraint on the pixel variance relative to a reference. 2) Find the patch level solutions to fit the global estimate as a sparse linear combination of dictionary atoms.3) Update the reference as the weighted average of the patch level solutions.This approach relies on the redundancy of the patches in the seismic image. Redundancy means that the patches are repetitions of a finite number of patterns, which are described by the dictionary atoms. Redundancy in the earth's structure was demonstrated in previous works in seismics where dictionaries of wavelet functions regularized inversion. We further exploit redundancy of the patches by using dictionary learning algorithms, a form of unsupervised machine learning, to estimate optimal dictionaries from the data in parallel with the inversion. We demonstrate our approach on densely, but irregularly sampled synthetic seismic images.

Ray and wave optics of integrable and stochastic systems

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1979-07-01

The generalization of WKB methods to more than one dimension is discussed in terms of the integrability or non-integrability of the geometrical optics (ray Hamiltonian) system derived in the short-wave approximation. In the two-dimensional case the ray trajectories are either regular or stochastic, and the qualitative differences between these types of motion are manifested in the characteristics of the spectra and eigenfunctions. These are examined for a model system which may be integrable or stochastic, depending on a single parameter

STOCHASTIC GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION

Directory of Open Access Journals (Sweden)

Nataša Krejić

2014-12-01

Full Text Available This papers presents an overview of gradient based methods for minimization of noisy functions. It is assumed that the objective functions is either given with error terms of stochastic nature or given as the mathematical expectation. Such problems arise in the context of simulation based optimization. The focus of this presentation is on the gradient based Stochastic Approximation and Sample Average Approximation methods. The concept of stochastic gradient approximation of the true gradient can be successfully extended to deterministic problems. Methods of this kind are presented for the data fitting and machine learning problems.

Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.

Science.gov (United States)

Borgogno, Fabio; D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

2012-01-21

Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers. Copyright © 2011 Elsevier Ltd. All rights reserved.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

Science.gov (United States)

Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

A stochastic cloud model for cloud and ozone retrievals from UV measurements

International Nuclear Information System (INIS)

Efremenko, Dmitry S.; Schüssler, Olena; Doicu, Adrian; Loyola, Diego

2016-01-01

The new generation of satellite instruments provides measurements in and around the Oxygen A-band on a global basis and with a relatively high spatial resolution. These data are commonly used for the determination of cloud properties. A stochastic model and radiative transfer model, previously developed by the authors, is used as the forward model component in retrievals of cloud parameters and ozone total and partial columns. The cloud retrieval algorithm combines local and global optimization routines, and yields a retrieval accuracy of about 1% and a fast computational time. Retrieved parameters are the cloud optical thickness and the cloud-top height. It was found that the use of the independent pixel approximation instead of the stochastic cloud model leads to large errors in the retrieved cloud parameters, as well as, in the retrieved ozone height resolved partial columns. The latter can be reduced by using the stochastic cloud model to compute the optimal value of the regularization parameter in the framework of Tikhonov regularization. - Highlights: • A stochastic radiative transfer model for retrieving clouds/ozone is designed. • Errors of independent pixel approximation (IPA) for O3 total column are small. • The error of IPA for ozone profile retrieval may become large. • The use of stochastic model reduces the error of ozone profile retrieval.

Sparse learning of stochastic dynamical equations

Science.gov (United States)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

Stochastic volatility and stochastic leverage

DEFF Research Database (Denmark)

Veraart, Almut; Veraart, Luitgard A. M.

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

Impact of wave phase jumps on stochastic heating

International Nuclear Information System (INIS)

Zasenko, V.I.; Zagorodny, A.G.; Cherniak, O.M.

2016-01-01

Interaction of charged particles with fields of random waves brings about known effects of stochastic acceleration and heating. Jumps of wave phases can increase the intensity of these processes substantially. Numerical simulation of particle heating and acceleration by waves with regular phases, waves with jumping phase and stochastic electric field impulses is performed. Comparison of the results shows that to some extent an impact of phase jumps is similar to the action of separate field impulses. Jumps of phase not only increase the intensity of resonant particle heating but involves in this process non-resonant particles from a wide range of initial velocities

Cross-Modality Image Synthesis via Weakly Coupled and Geometry Co-Regularized Joint Dictionary Learning.

Science.gov (United States)

Huang, Yawen; Shao, Ling; Frangi, Alejandro F

2018-03-01

Multi-modality medical imaging is increasingly used for comprehensive assessment of complex diseases in either diagnostic examinations or as part of medical research trials. Different imaging modalities provide complementary information about living tissues. However, multi-modal examinations are not always possible due to adversary factors, such as patient discomfort, increased cost, prolonged scanning time, and scanner unavailability. In additionally, in large imaging studies, incomplete records are not uncommon owing to image artifacts, data corruption or data loss, which compromise the potential of multi-modal acquisitions. In this paper, we propose a weakly coupled and geometry co-regularized joint dictionary learning method to address the problem of cross-modality synthesis while considering the fact that collecting the large amounts of training data is often impractical. Our learning stage requires only a few registered multi-modality image pairs as training data. To employ both paired images and a large set of unpaired data, a cross-modality image matching criterion is proposed. Then, we propose a unified model by integrating such a criterion into the joint dictionary learning and the observed common feature space for associating cross-modality data for the purpose of synthesis. Furthermore, two regularization terms are added to construct robust sparse representations. Our experimental results demonstrate superior performance of the proposed model over state-of-the-art methods.

Learning About Time Within the Spinal Cord II: Evidence that Temporal Regularity is Encoded by a Spinal Oscillator

Directory of Open Access Journals (Sweden)

Kuan Hsien Lee

2016-02-01

Full Text Available How a stimulus impacts spinal cord function depends upon temporal relations. When intermittent noxious stimulation (shock is applied and the interval between shock pulses is varied (unpredictable, it induces a lasting alteration that inhibits adaptive learning. If the same stimulus is applied in a temporally regular (predictable manner, the capacity to learn is preserved and a protective/restorative effect is engaged that counters the adverse effect of variable stimulation. Sensitivity to temporal relations implies a capacity to encode time. This study explores how spinal neurons discriminate variable and fixed spaced stimulation. Communication with the brain was blocked by means of a spinal transection and adaptive capacity was tested using an instrumental learning task. In this task, subjects must learn to maintain a hind limb in a flexed position to minimize shock exposure. To evaluate the possibility that a distinct class of afferent fibers provide a sensory cue for regularity, we manipulated the temporal relation between shocks given to two dermatomes (leg and tail. Evidence for timing emerged when the stimuli were applied in a coherent manner across dermatomes, implying that a central (spinal process detects regularity. Next, we show that fixed spaced stimulation has a restorative effect when half the physical stimuli are randomly omitted, as long as the stimuli remain in phase, suggesting that stimulus regularity is encoded by an internal oscillator Research suggests that the oscillator that drives the tempo of stepping depends upon neurons within the rostral lumbar (L1-L2 region. Disrupting communication with the L1-L2 tissue by means of a L3 transection eliminated the restorative effect of fixed spaced stimulation. Implications of the results for step training and rehabilitation after injury are discussed.

Representing and computing regular languages on massively parallel networks

Energy Technology Data Exchange (ETDEWEB)

Miller, M.I.; O' Sullivan, J.A. (Electronic Systems and Research Lab., of Electrical Engineering, Washington Univ., St. Louis, MO (US)); Boysam, B. (Dept. of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Inst., Troy, NY (US)); Smith, K.R. (Dept. of Electrical Engineering, Southern Illinois Univ., Edwardsville, IL (US))

1991-01-01

This paper proposes a general method for incorporating rule-based constraints corresponding to regular languages into stochastic inference problems, thereby allowing for a unified representation of stochastic and syntactic pattern constraints. The authors' approach first established the formal connection of rules to Chomsky grammars, and generalizes the original work of Shannon on the encoding of rule-based channel sequences to Markov chains of maximum entropy. This maximum entropy probabilistic view leads to Gibb's representations with potentials which have their number of minima growing at precisely the exponential rate that the language of deterministically constrained sequences grow. These representations are coupled to stochastic diffusion algorithms, which sample the language-constrained sequences by visiting the energy minima according to the underlying Gibbs' probability law. The coupling to stochastic search methods yields the all-important practical result that fully parallel stochastic cellular automata may be derived to generate samples from the rule-based constraint sets. The production rules and neighborhood state structure of the language of sequences directly determines the necessary connection structures of the required parallel computing surface. Representations of this type have been mapped to the DAP-510 massively-parallel processor consisting of 1024 mesh-connected bit-serial processing elements for performing automated segmentation of electron-micrograph images.

Memristor-based neural networks: Synaptic versus neuronal stochasticity

KAUST Repository

Naous, Rawan

2016-11-02

In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.

Land Cover Segmentation of Airborne LiDAR Data Using Stochastic Atrous Network

Directory of Open Access Journals (Sweden)

Hasan Asy’ari Arief

2018-06-01

Full Text Available Inspired by the success of deep learning techniques in dense-label prediction and the increasing availability of high precision airborne light detection and ranging (LiDAR data, we present a research process that compares a collection of well-proven semantic segmentation architectures based on the deep learning approach. Our investigation concludes with the proposition of some novel deep learning architectures for generating detailed land resource maps by employing a semantic segmentation approach. The contribution of our work is threefold. (1 First, we implement the multiclass version of the intersection-over-union (IoU loss function that contributes to handling highly imbalanced datasets and preventing overfitting. (2 Thereafter, we propose a novel deep learning architecture integrating the deep atrous network architecture with the stochastic depth approach for speeding up the learning process, and impose a regularization effect. (3 Finally, we introduce an early fusion deep layer that combines image-based and LiDAR-derived features. In a benchmark study carried out using the Follo 2014 LiDAR data and the NIBIO AR5 land resources dataset, we compare our proposals to other deep learning architectures. A quantitative comparison shows that our best proposal provides more than 5% relative improvement in terms of mean intersection-over-union over the atrous network, providing a basis for a more frequent and improved use of LiDAR data for automatic land cover segmentation.

Detecting change in stochastic sound sequences.

Directory of Open Access Journals (Sweden)

Benjamin Skerritt-Davis

2018-05-01

Full Text Available Our ability to parse our acoustic environment relies on the brain's capacity to extract statistical regularities from surrounding sounds. Previous work in regularity extraction has predominantly focused on the brain's sensitivity to predictable patterns in sound sequences. However, natural sound environments are rarely completely predictable, often containing some level of randomness, yet the brain is able to effectively interpret its surroundings by extracting useful information from stochastic sounds. It has been previously shown that the brain is sensitive to the marginal lower-order statistics of sound sequences (i.e., mean and variance. In this work, we investigate the brain's sensitivity to higher-order statistics describing temporal dependencies between sound events through a series of change detection experiments, where listeners are asked to detect changes in randomness in the pitch of tone sequences. Behavioral data indicate listeners collect statistical estimates to process incoming sounds, and a perceptual model based on Bayesian inference shows a capacity in the brain to track higher-order statistics. Further analysis of individual subjects' behavior indicates an important role of perceptual constraints in listeners' ability to track these sensory statistics with high fidelity. In addition, the inference model facilitates analysis of neural electroencephalography (EEG responses, anchoring the analysis relative to the statistics of each stochastic stimulus. This reveals both a deviance response and a change-related disruption in phase of the stimulus-locked response that follow the higher-order statistics. These results shed light on the brain's ability to process stochastic sound sequences.

Time-ordered product expansions for computational stochastic system biology

International Nuclear Information System (INIS)

Mjolsness, Eric

2013-01-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)

Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.

Science.gov (United States)

Cheng, Jian; Jiang, Tianzi; Deriche, Rachid; Shen, Dinggang; Yap, Pew-Thian

2013-01-01

Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces

Machine learning properties of materials and molecules with entropy-regularized kernels

Science.gov (United States)

Ceriotti, Michele; Bartók, Albert; CsáNyi, GáBor; de, Sandip

Application of machine-learning methods to physics, chemistry and materials science is gaining traction as a strategy to obtain accurate predictions of the properties of matter at a fraction of the typical cost of quantum mechanical electronic structure calculations. In this endeavor, one can leverage general-purpose frameworks for supervised-learning. It is however very important that the input data - for instance the positions of atoms in a molecule or solid - is processed into a form that reflects all the underlying physical symmetries of the problem, and that possesses the regularity properties that are required by machine-learning algorithms. Here we introduce a general strategy to build a representation of this kind. We will start from existing approaches to compare local environments (basically, groups of atoms), and combine them using techniques borrowed from optimal transport theory, discussing the relation between this idea and additive energy decompositions. We will present a few examples demonstrating the potential of this approach as a tool to predict molecular and materials' properties with an accuracy on par with state-of-the-art electronic structure methods. MARVEL NCCR (Swiss National Science Foundation) and ERC StG HBMAP (European Research Council, G.A. 677013).

Stochastic integration by parts and functional Itô calculus

CERN Document Server

Vives, Josep

2016-01-01

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...

Solution path for manifold regularized semisupervised classification.

Science.gov (United States)

Wang, Gang; Wang, Fei; Chen, Tao; Yeung, Dit-Yan; Lochovsky, Frederick H

2012-04-01

Traditional learning algorithms use only labeled data for training. However, labeled examples are often difficult or time consuming to obtain since they require substantial human labeling efforts. On the other hand, unlabeled data are often relatively easy to collect. Semisupervised learning addresses this problem by using large quantities of unlabeled data with labeled data to build better learning algorithms. In this paper, we use the manifold regularization approach to formulate the semisupervised learning problem where a regularization framework which balances a tradeoff between loss and penalty is established. We investigate different implementations of the loss function and identify the methods which have the least computational expense. The regularization hyperparameter, which determines the balance between loss and penalty, is crucial to model selection. Accordingly, we derive an algorithm that can fit the entire path of solutions for every value of the hyperparameter. Its computational complexity after preprocessing is quadratic only in the number of labeled examples rather than the total number of labeled and unlabeled examples.

Stochastic methods of data modeling: application to the reconstruction of non-regular data

International Nuclear Information System (INIS)

Buslig, Leticia

2014-01-01

This research thesis addresses two issues or applications related to IRSN studies. The first one deals with the mapping of measurement data (the IRSN must regularly control the radioactivity level in France and, for this purpose, uses a network of sensors distributed among the French territory). The objective is then to predict, by means of reconstruction model which used observations, maps which will be used to inform the population. The second application deals with the taking of uncertainties into account in complex computation codes (the IRSN must perform safety studies to assess the risks of loss of integrity of a nuclear reactor in case of hypothetical accidents, and for this purpose, codes are used which simulate physical phenomena occurring within an installation). Some input parameters are not precisely known, and the author therefore tries to assess the impact of some uncertainties on simulated values. She notably aims at seeing whether variations of input parameters may push the system towards a behaviour which is very different from that obtained with parameters having a reference value, or even towards a state in which safety conditions are not met. The precise objective of this second part is then to a reconstruction model which is not costly (in terms of computation time) and to perform simulation in relevant areas (strong gradient areas, threshold overrun areas, so on). Two issues are then important: the choice of the approximation model and the construction of the experiment plan. The model is based on a kriging-type stochastic approach, and an important part of the work addresses the development of new numerical techniques of experiment planning. The first part proposes a generic criterion of adaptive planning, and reports its analysis and implementation. In the second part, an alternative to error variance addition is developed. Methodological developments are tested on analytic functions, and then applied to the cases of measurement mapping and

Brain-inspired Stochastic Models and Implementations

KAUST Repository

Al-Shedivat, Maruan

2015-05-12

One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.

Chord length distributions between hard disks and spheres in regular, semi-regular, and quasi-random structures

International Nuclear Information System (INIS)

Olson, Gordon L.

2008-01-01

In binary stochastic media in two- and three-dimensions consisting of randomly placed impenetrable disks or spheres, the chord lengths in the background material between disks and spheres closely follow exponential distributions if the disks and spheres occupy less than 10% of the medium. This work demonstrates that for regular spatial structures of disks and spheres, the tails of the chord length distributions (CLDs) follow power laws rather than exponentials. In dilute media, when the disks and spheres are widely spaced, the slope of the power law seems to be independent of the details of the structure. When approaching a close-packed arrangement, the exact placement of the spheres can make a significant difference. When regular structures are perturbed by small random displacements, the CLDs become power laws with steeper slopes. An example CLD from a quasi-random distribution of spheres in clusters shows a modified exponential distribution

Chord length distributions between hard disks and spheres in regular, semi-regular, and quasi-random structures

Energy Technology Data Exchange (ETDEWEB)

Olson, Gordon L. [Computer and Computational Sciences Division (CCS-2), Los Alamos National Laboratory, 5 Foxglove Circle, Madison, WI 53717 (United States)], E-mail: olson99@tds.net

2008-11-15

In binary stochastic media in two- and three-dimensions consisting of randomly placed impenetrable disks or spheres, the chord lengths in the background material between disks and spheres closely follow exponential distributions if the disks and spheres occupy less than 10% of the medium. This work demonstrates that for regular spatial structures of disks and spheres, the tails of the chord length distributions (CLDs) follow power laws rather than exponentials. In dilute media, when the disks and spheres are widely spaced, the slope of the power law seems to be independent of the details of the structure. When approaching a close-packed arrangement, the exact placement of the spheres can make a significant difference. When regular structures are perturbed by small random displacements, the CLDs become power laws with steeper slopes. An example CLD from a quasi-random distribution of spheres in clusters shows a modified exponential distribution.

Expanding the boundaries of evaluative learning research: How intersecting regularities shape our likes and dislikes.

Science.gov (United States)

Hughes, Sean; De Houwer, Jan; Perugini, Marco

2016-06-01

Over the last 30 years, researchers have identified several types of procedures through which novel preferences may be formed and existing ones altered. For instance, regularities in the presence of a single stimulus (as in the case of mere exposure) or 2 or more stimuli (as in the case of evaluative conditioning) have been shown to influence liking. We propose that intersections between regularities represent a previously unrecognized class of procedures for changing liking. Across 4 related studies, we found strong support for the hypothesis that when environmental regularities intersect with one another (i.e., share elements or have elements that share relations with other elements), the evaluative properties of the elements of those regularities can change. These changes in liking were observed across a range of stimuli and procedures and were evident when self-report measures, implicit measures, and behavioral choice measures of liking were employed. Functional and mental explanations of this phenomenon are offered followed by a discussion of how this new type of evaluative learning effect can accelerate theoretical, methodological, and empirical development in attitude research. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

KAUST Repository

Malenova, G.

2016-09-08

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.

A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

KAUST Repository

Malenova, G.; Motamed, M.; Runborg, O.; Tempone, Raul

2016-01-01

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.

Faculty Perceptions of the National Undergraduate Teaching and Learning Evaluation at Regular Higher Education Institutions from 2003 to 2008 in China

Science.gov (United States)

An, Jumei

2012-01-01

This study explored how faculty members at regular higher education institutions in China perceived the National Undergraduate Teaching and Learning Evaluation (NUTLE). Specifically, this study examined how the NUTLE influenced faculty teaching and research and how the NUTLE influenced student learning outcomes. Primarily descriptive and…

Neuro-Inspired Computing with Stochastic Electronics

KAUST Repository

Naous, Rawan

2016-01-06

The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-03-28

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Stochastic inflation: Quantum phase-space approach

International Nuclear Information System (INIS)

Habib, S.

1992-01-01

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence

Stochastic Blind Motion Deblurring

KAUST Repository

Xiao, Lei

2015-05-13

Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.

Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications

Science.gov (United States)

Chaki, Sagar; Gurfinkel, Arie

2010-01-01

We develop a learning-based automated Assume-Guarantee (AG) reasoning framework for verifying omega-regular properties of concurrent systems. We study the applicability of non-circular (AGNC) and circular (AG-C) AG proof rules in the context of systems with infinite behaviors. In particular, we show that AG-NC is incomplete when assumptions are restricted to strictly infinite behaviors, while AG-C remains complete. We present a general formalization, called LAG, of the learning based automated AG paradigm. We show how existing approaches for automated AG reasoning are special instances of LAG.We develop two learning algorithms for a class of systems, called infinite regular systems, that combine finite and infinite behaviors. We show that for infinity-regular systems, both AG-NC and AG-C are sound and complete. Finally, we show how to instantiate LAG to do automated AG reasoning for infinite regular, and omega-regular, systems using both AG-NC and AG-C as proof rules

Multimodal manifold-regularized transfer learning for MCI conversion prediction.

Science.gov (United States)

Cheng, Bo; Liu, Mingxia; Suk, Heung-Il; Shen, Dinggang; Zhang, Daoqiang

2015-12-01

As the early stage of Alzheimer's disease (AD), mild cognitive impairment (MCI) has high chance to convert to AD. Effective prediction of such conversion from MCI to AD is of great importance for early diagnosis of AD and also for evaluating AD risk pre-symptomatically. Unlike most previous methods that used only the samples from a target domain to train a classifier, in this paper, we propose a novel multimodal manifold-regularized transfer learning (M2TL) method that jointly utilizes samples from another domain (e.g., AD vs. normal controls (NC)) as well as unlabeled samples to boost the performance of the MCI conversion prediction. Specifically, the proposed M2TL method includes two key components. The first one is a kernel-based maximum mean discrepancy criterion, which helps eliminate the potential negative effect induced by the distributional difference between the auxiliary domain (i.e., AD and NC) and the target domain (i.e., MCI converters (MCI-C) and MCI non-converters (MCI-NC)). The second one is a semi-supervised multimodal manifold-regularized least squares classification method, where the target-domain samples, the auxiliary-domain samples, and the unlabeled samples can be jointly used for training our classifier. Furthermore, with the integration of a group sparsity constraint into our objective function, the proposed M2TL has a capability of selecting the informative samples to build a robust classifier. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database validate the effectiveness of the proposed method by significantly improving the classification accuracy of 80.1 % for MCI conversion prediction, and also outperforming the state-of-the-art methods.

On the Stochastic Wave Equation with Nonlinear Damping

International Nuclear Information System (INIS)

Kim, Jong Uhn

2008-01-01

We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

Stochastic Averaging and Stochastic Extremum Seeking

CERN Document Server

Liu, Shu-Jun

2012-01-01

Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

Maximum mutual information regularized classification

KAUST Repository

Wang, Jim Jing-Yan

2014-09-07

In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.

Maximum mutual information regularized classification

KAUST Repository

Wang, Jim Jing-Yan; Wang, Yi; Zhao, Shiguang; Gao, Xin

2014-01-01

In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.

Manifold Regularized Correlation Object Tracking

OpenAIRE

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2017-01-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...

HYDRASTAR - a code for stochastic simulation of groundwater flow

International Nuclear Information System (INIS)

Norman, S.

1992-05-01

The computer code HYDRASTAR was developed as a tool for groundwater flow and transport simulations in the SKB 91 safety analysis project. Its conceptual ideas can be traced back to a report by Shlomo Neuman in 1988, see the reference section. The main idea of the code is the treatment of the rock as a stochastic continuum which separates it from the deterministic methods previously employed by SKB and also from the discrete fracture models. The current report is a comprehensive description of HYDRASTAR including such topics as regularization or upscaling of a hydraulic conductivity field, unconditional and conditional simulation of stochastic processes, numerical solvers for the hydrology and streamline equations and finally some proposals for future developments

Extreme values, regular variation and point processes

CERN Document Server

Resnick, Sidney I

1987-01-01

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records It emphasizes the core primacy of three topics necessary for understanding extremes the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enj...

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

Science.gov (United States)

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

Generalization Performance of Regularized Ranking With Multiscale Kernels.

Science.gov (United States)

Zhou, Yicong; Chen, Hong; Lan, Rushi; Pan, Zhibin

2016-05-01

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

Inherently stochastic spiking neurons for probabilistic neural computation

KAUST Repository

Al-Shedivat, Maruan

2015-04-01

Neuromorphic engineering aims to design hardware that efficiently mimics neural circuitry and provides the means for emulating and studying neural systems. In this paper, we propose a new memristor-based neuron circuit that uniquely complements the scope of neuron implementations and follows the stochastic spike response model (SRM), which plays a cornerstone role in spike-based probabilistic algorithms. We demonstrate that the switching of the memristor is akin to the stochastic firing of the SRM. Our analysis and simulations show that the proposed neuron circuit satisfies a neural computability condition that enables probabilistic neural sampling and spike-based Bayesian learning and inference. Our findings constitute an important step towards memristive, scalable and efficient stochastic neuromorphic platforms. © 2015 IEEE.

Correction of engineering servicing regularity of transporttechnological machines in operational process

Science.gov (United States)

Makarova, A. N.; Makarov, E. I.; Zakharov, N. S.

2018-03-01

In the article, the issue of correcting engineering servicing regularity on the basis of actual dependability data of cars in operation is considered. The purpose of the conducted research is to increase dependability of transport-technological machines by correcting engineering servicing regularity. The subject of the research is the mechanism of engineering servicing regularity influence on reliability measure. On the basis of the analysis of researches carried out before, a method of nonparametric estimation of car failure measure according to actual time-to-failure data was chosen. A possibility of describing the failure measure dependence on engineering servicing regularity by various mathematical models is considered. It is proven that the exponential model is the most appropriate for that purpose. The obtained results can be used as a separate method of engineering servicing regularity correction with certain operational conditions taken into account, as well as for the technical-economical and economical-stochastic methods improvement. Thus, on the basis of the conducted researches, a method of engineering servicing regularity correction of transport-technological machines in the operational process was developed. The use of that method will allow decreasing the number of failures.

The construction of semantic memory: grammar based representations learned from relational episodic information

Directory of Open Access Journals (Sweden)

Francesco P Battaglia

2011-08-01

Full Text Available After acquisition, memories underlie a process of consolidation, making them more resistant to interference and brain injury. Memory consolidation involves systems-level interactions, most importantly between the hippocampus and associated structures, which takes part in the initial encoding of memory, and the neocortex, which supports long-term storage. This dichotomy parallels the contrast between episodic memory (tied to the hippocampal formation, collecting an autobiographical stream of experiences, and semantic memory, a repertoire of facts and statistical regularities about the world, involving the neocortex at large. Experimental evidence points to a gradual transformation of memories, following encoding, from an episodic to a semantic character. This may require an exchange of information between different memory modules during inactive periods. We propose a theory for such interactions and for the formation of semantic memory, in which episodic memory is encoded as relational data. Semantic memory is modeled as a modified stochastic grammar, which learns to parse episodic configurations expressed as an association matrix. The grammar produces tree-like representations of episodes, describing the relationships between its main constituents at multiple levels of categorization, based on its current knowledge of world regularities. These regularities are learned by the grammar from episodic memory information, through an expectation-maximization procedure, analogous to the inside-outside algorithm for stochastic context-free grammars. We propose that a Monte-Carlo sampling version of this algorithm can be mapped on the dynamics of ``sleep replay'' of previously acquired information in the hippocampus and neocortex. We propose that the model can reproduce several properties of semantic memory such as decontextualization, top-down processing, and creation of schemata.

The Construction of Semantic Memory: Grammar-Based Representations Learned from Relational Episodic Information

Science.gov (United States)

Battaglia, Francesco P.; Pennartz, Cyriel M. A.

2011-01-01

After acquisition, memories underlie a process of consolidation, making them more resistant to interference and brain injury. Memory consolidation involves systems-level interactions, most importantly between the hippocampus and associated structures, which takes part in the initial encoding of memory, and the neocortex, which supports long-term storage. This dichotomy parallels the contrast between episodic memory (tied to the hippocampal formation), collecting an autobiographical stream of experiences, and semantic memory, a repertoire of facts and statistical regularities about the world, involving the neocortex at large. Experimental evidence points to a gradual transformation of memories, following encoding, from an episodic to a semantic character. This may require an exchange of information between different memory modules during inactive periods. We propose a theory for such interactions and for the formation of semantic memory, in which episodic memory is encoded as relational data. Semantic memory is modeled as a modified stochastic grammar, which learns to parse episodic configurations expressed as an association matrix. The grammar produces tree-like representations of episodes, describing the relationships between its main constituents at multiple levels of categorization, based on its current knowledge of world regularities. These regularities are learned by the grammar from episodic memory information, through an expectation-maximization procedure, analogous to the inside–outside algorithm for stochastic context-free grammars. We propose that a Monte-Carlo sampling version of this algorithm can be mapped on the dynamics of “sleep replay” of previously acquired information in the hippocampus and neocortex. We propose that the model can reproduce several properties of semantic memory such as decontextualization, top-down processing, and creation of schemata. PMID:21887143

Intrinsic periodic and aperiodic stochastic resonance in an electrochemical cell

Science.gov (United States)

Tiwari, Ishant; Phogat, Richa; Parmananda, P.; Ocampo-Espindola, J. L.; Rivera, M.

2016-08-01

In this paper we show the interaction of a composite of a periodic or aperiodic signal and intrinsic electrochemical noise with the nonlinear dynamics of an electrochemical cell configured to study the corrosion of iron in an acidic media. The anodic voltage setpoint (V0) in the cell is chosen such that the anodic current (I ) exhibits excitable fixed point behavior in the absence of noise. The subthreshold periodic (aperiodic) signal consists of a train of rectangular pulses with a fixed amplitude and width, separated by regular (irregular) time intervals. The irregular time intervals chosen are of deterministic and stochastic origins. The amplitude of the intrinsic internal noise, regulated by the concentration of chloride ions, is then monotonically increased, and the provoked dynamics are analyzed. The signal to noise ratio and the cross-correlation coefficient versus the chloride ions' concentration curves have a unimodal shape indicating the emergence of an intrinsic periodic or aperiodic stochastic resonance. The abscissa for the maxima of these unimodal curves correspond to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed. In the particular case of the intrinsic periodic stochastic resonance, the scanning electron microscope images for the electrode metal surfaces are shown for certain values of chloride ions' concentrations. These images, qualitatively, corroborate the emergence of order as a result of the interaction between the nonlinear dynamics and the composite signal.

Stochastic foundations of undulatory transport phenomena: generalized Poisson–Kac processes—part I basic theory

International Nuclear Information System (INIS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-01-01

This article introduces the notion of generalized Poisson–Kac (GPK) processes which generalize the class of ‘telegrapher’s noise dynamics’ introduced by Kac (1974 Rocky Mount. J. Math . 4 497) in 1974, using Poissonian stochastic perturbations. In GPK processes the stochastic perturbation acts as a switching amongst a set of stochastic velocity vectors controlled by a Markov-chain dynamics. GPK processes possess trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the convergence towards Brownian motion (and to stochastic dynamics driven by Wiener perturbations), which characterizes also the long-term/long-distance properties of these processes. In this article we introduce the structural properties of GPK processes, leaving all the physical implications to part II and part III (Giona et al 2016a J. Phys. A: Math. Theor ., 2016b J. Phys. A: Math. Theor .). (paper)

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

Science.gov (United States)

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

A Stochastic Maximum Principle for General Mean-Field Systems

International Nuclear Information System (INIS)

Buckdahn, Rainer; Li, Juan; Ma, Jin

2016-01-01

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.

A Stochastic Maximum Principle for General Mean-Field Systems

Energy Technology Data Exchange (ETDEWEB)

Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)

2016-12-15

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.

Gene selection for microarray data classification via subspace learning and manifold regularization.

Science.gov (United States)

Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui

2017-12-19

With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.

Stochastic model of energetic nuclear reactor

International Nuclear Information System (INIS)

Bojko, R.V.; Ryazanov, V.V.

2002-01-01

Behaviour of nuclear reactor was treated using the theory of branching processes. As mathematical model descriptive the neutron number in time the Markov occasional process is proposed. Application of branching occasional processes with variable regime to the description of neutron behaviour in the reactor makes possible conducting strong description of critical operation regime and demonstrates the severity of the process. Three regimes of the critical behaviour depending on the sign of manipulated variables and feedbacks were discovered. Probability regularities peculiar to the behaviour of the reactor are embodied to the suggested stochastic model [ru

Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-01-06

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Derivation of the Schroedinger equation from stochastic mechanics

International Nuclear Information System (INIS)

Wallstrom, T.C.

1988-01-01

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schroedinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time-integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p t (x,y) > cp(y), and this result is applied to show that the set of spin-1/2 diffusions is uniformly ergodic. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp-Haag-Dankel diffusions onto IR 3 converge to a Markovian limit process. This conjecture is proved for the spin-1/2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schroedinger equation

Applied stochastic modelling

CERN Document Server

Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P

2008-01-01

Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...

Interactions of Chemistry Teachers with Gifted Students in a Regular High-School Chemistry Classroom

Science.gov (United States)

Benny, Naama; Blonder, Ron

2018-01-01

Regular high-school chemistry teachers view gifted students as one of several types of students in a regular (mixed-ability) classroom. Gifted students have a range of unique abilities that characterize their learning process: mostly they differ in three key learning aspects: their faster learning pace, increased depth of understanding, and…

Regularization theory for ill-posed problems selected topics

CERN Document Server

Lu, Shuai

2013-01-01

Thismonograph is a valuable contribution to thehighly topical and extremly productive field ofregularisationmethods for inverse and ill-posed problems. The author is an internationally outstanding and acceptedmathematicianin this field. In his book he offers a well-balanced mixtureof basic and innovative aspects.He demonstrates new,differentiatedviewpoints, and important examples for applications. The bookdemontrates thecurrent developments inthe field of regularization theory,such as multiparameter regularization and regularization in learning theory. The book is written for graduate and PhDs

Learning automata an introduction

CERN Document Server

Narendra, Kumpati S

2012-01-01

This self-contained introductory text on the behavior of learning automata focuses on how a sequential decision-maker with a finite number of choices responds in a random environment. Topics include fixed structure automata, variable structure stochastic automata, convergence, 0 and S models, nonstationary environments, interconnected automata and games, and applications of learning automata. A must for all students of stochastic algorithms, this treatment is the work of two well-known scientists and is suitable for a one-semester graduate course in automata theory and stochastic algorithms.

Implicit learning out of the lab: the case of orthographic regularities.

Science.gov (United States)

Pacton, S; Perruchet, P; Fayol, M; Cleeremans, A

2001-09-01

Children's (Grades 1 to 5) implicit learning of French orthographic regularities was investigated through nonword judgment (Experiments 1 and 2) and completion (Experiments 3a and 3b) tasks. Children were increasingly sensitive to (a) the frequency of double consonants (Experiments 1, 2, and 3a), (b) the fact that vowels can never be doubled (Experiment 2), and (c) the legal position of double consonants (Experiments 2 and 3b). The latter effect transferred to never doubled consonants but with a decrement in performance. Moreover, this decrement persisted without any trend toward fading, even after the massive amounts of experience provided by years of practice. This result runs against the idea that transfer to novel material is indicative of abstract rule-based knowledge and suggests instead the action of mechanisms sensitive to the statistical properties of the material. A connectionist model is proposed as an instantiation of such mechanisms.

Transient Response Analysis of Metropolis Learning in Games

KAUST Repository

Jaleel, Hassan

2017-10-19

The objective of this work is to provide a qualitative description of the transient properties of stochastic learning dynamics like adaptive play, log-linear learning, and Metropolis learning. The solution concept used in these learning dynamics for potential games is that of stochastic stability, which is based on the stationary distribution of the reversible Markov chain representing the learning process. However, time to converge to a stochastically stable state is exponential in the inverse of noise, which limits the use of stochastic stability as an effective solution concept for these dynamics. We propose a complete solution concept that qualitatively describes the state of the system at all times. The proposed concept is prevalent in control systems literature where a solution to a linear or a non-linear system has two parts, transient response and steady state response. Stochastic stability provides the steady state response of stochastic learning rules. In this work, we study its transient properties. Starting from an initial condition, we identify the subsets of the state space called cycles that have small hitting times and long exit times. Over the long time scales, we provide a description of how the distributions over joint action profiles transition from one cycle to another till it reaches the globally optimal state.

Transient Response Analysis of Metropolis Learning in Games

KAUST Repository

Jaleel, Hassan; Shamma, Jeff S.

2017-01-01

The objective of this work is to provide a qualitative description of the transient properties of stochastic learning dynamics like adaptive play, log-linear learning, and Metropolis learning. The solution concept used in these learning dynamics for potential games is that of stochastic stability, which is based on the stationary distribution of the reversible Markov chain representing the learning process. However, time to converge to a stochastically stable state is exponential in the inverse of noise, which limits the use of stochastic stability as an effective solution concept for these dynamics. We propose a complete solution concept that qualitatively describes the state of the system at all times. The proposed concept is prevalent in control systems literature where a solution to a linear or a non-linear system has two parts, transient response and steady state response. Stochastic stability provides the steady state response of stochastic learning rules. In this work, we study its transient properties. Starting from an initial condition, we identify the subsets of the state space called cycles that have small hitting times and long exit times. Over the long time scales, we provide a description of how the distributions over joint action profiles transition from one cycle to another till it reaches the globally optimal state.

Doubly stochastic coherence in complex neuronal networks

Science.gov (United States)

Gao, Yang; Wang, Jianjun

2012-11-01

A system composed of coupled FitzHugh-Nagumo neurons with various topological structures is investigated under the co-presence of two independently additive and multiplicative Gaussian white noises, in which particular attention is paid to the neuronal networks spiking regularity. As the additive noise intensity and the multiplicative noise intensity are simultaneously adjusted to optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of doubly stochastic coherence. The network topology randomness exerts different influences on the temporal coherence of the spiking oscillation for dissimilar coupling strength regimes. At a small coupling strength, the spiking regularity shows nearly no difference in the regular, small-world, and completely random networks. At an intermediate coupling strength, the temporal periodicity in a small-world neuronal network can be improved slightly by adding a small fraction of long-range connections. At a large coupling strength, the dynamical behavior of the neurons completely loses the resonance property with regard to the additive noise intensity or the multiplicative noise intensity, and the spiking regularity decreases considerably with the increase of the network topology randomness. The network topology randomness plays more of a depressed role than a favorable role in improving the temporal coherence of the spiking oscillation in the neuronal network research study.

A 2-transistor/1-resistor artificial synapse capable of communication and stochastic learning in neuromorphic systems.

Science.gov (United States)

Wang, Zhongqiang; Ambrogio, Stefano; Balatti, Simone; Ielmini, Daniele

2014-01-01

Resistive (or memristive) switching devices based on metal oxides find applications in memory, logic and neuromorphic computing systems. Their small area, low power operation, and high functionality meet the challenges of brain-inspired computing aiming at achieving a huge density of active connections (synapses) with low operation power. This work presents a new artificial synapse scheme, consisting of a memristive switch connected to 2 transistors responsible for gating the communication and learning operations. Spike timing dependent plasticity (STDP) is achieved through appropriate shaping of the pre-synaptic and the post synaptic spikes. Experiments with integrated artificial synapses demonstrate STDP with stochastic behavior due to (i) the natural variability of set/reset processes in the nanoscale switch, and (ii) the different response of the switch to a given stimulus depending on the initial state. Experimental results are confirmed by model-based simulations of the memristive switching. Finally, system-level simulations of a 2-layer neural network and a simplified STDP model show random learning and recognition of patterns.

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

International Nuclear Information System (INIS)

Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

2013-01-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

Stochastic subset selection for learning with kernel machines.

Science.gov (United States)

Rhinelander, Jason; Liu, Xiaoping P

2012-06-01

Kernel machines have gained much popularity in applications of machine learning. Support vector machines (SVMs) are a subset of kernel machines and generalize well for classification, regression, and anomaly detection tasks. The training procedure for traditional SVMs involves solving a quadratic programming (QP) problem. The QP problem scales super linearly in computational effort with the number of training samples and is often used for the offline batch processing of data. Kernel machines operate by retaining a subset of observed data during training. The data vectors contained within this subset are referred to as support vectors (SVs). The work presented in this paper introduces a subset selection method for the use of kernel machines in online, changing environments. Our algorithm works by using a stochastic indexing technique when selecting a subset of SVs when computing the kernel expansion. The work described here is novel because it separates the selection of kernel basis functions from the training algorithm used. The subset selection algorithm presented here can be used in conjunction with any online training technique. It is important for online kernel machines to be computationally efficient due to the real-time requirements of online environments. Our algorithm is an important contribution because it scales linearly with the number of training samples and is compatible with current training techniques. Our algorithm outperforms standard techniques in terms of computational efficiency and provides increased recognition accuracy in our experiments. We provide results from experiments using both simulated and real-world data sets to verify our algorithm.

Stochastic weather inputs for improved urban water demand forecasting: application of nonlinear input variable selection and machine learning methods

Science.gov (United States)

Quilty, J.; Adamowski, J. F.

2015-12-01

Urban water supply systems are often stressed during seasonal outdoor water use as water demands related to the climate are variable in nature making it difficult to optimize the operation of the water supply system. Urban water demand forecasts (UWD) failing to include meteorological conditions as inputs to the forecast model may produce poor forecasts as they cannot account for the increase/decrease in demand related to meteorological conditions. Meteorological records stochastically simulated into the future can be used as inputs to data-driven UWD forecasts generally resulting in improved forecast accuracy. This study aims to produce data-driven UWD forecasts for two different Canadian water utilities (Montreal and Victoria) using machine learning methods by first selecting historical UWD and meteorological records derived from a stochastic weather generator using nonlinear input variable selection. The nonlinear input variable selection methods considered in this work are derived from the concept of conditional mutual information, a nonlinear dependency measure based on (multivariate) probability density functions and accounts for relevancy, conditional relevancy, and redundancy from a potential set of input variables. The results of our study indicate that stochastic weather inputs can improve UWD forecast accuracy for the two sites considered in this work. Nonlinear input variable selection is suggested as a means to identify which meteorological conditions should be utilized in the forecast.

Essentials of stochastic processes

CERN Document Server

Durrett, Richard

2016-01-01

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...

Stochastic Analysis 2010

CERN Document Server

Crisan, Dan

2011-01-01

"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa

Stochastic Spectral Descent for Discrete Graphical Models

International Nuclear Information System (INIS)

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan

2015-01-01

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.

Applications of Stochastic Analyses for Collaborative Learning and Cognitive Assessment

National Research Council Canada - National Science Library

Soller, Amy; Stevens, Ron

2007-01-01

.... Examples ranging from fields as diverse as defense analysis, cognitive science, and instruction are illustrated throughout to demonstrate the variety of applications that benefit from such stochastic...

Multi-agent machine learning a reinforcement approach

CERN Document Server

Schwartz, H M

2014-01-01

The book begins with a chapter on traditional methods of supervised learning, covering recursive least squares learning, mean square error methods, and stochastic approximation. Chapter 2 covers single agent reinforcement learning. Topics include learning value functions, Markov games, and TD learning with eligibility traces. Chapter 3 discusses two player games including two player matrix games with both pure and mixed strategies. Numerous algorithms and examples are presented. Chapter 4 covers learning in multi-player games, stochastic games, and Markov games, focusing on learning multi-pla

Introducing regular formative assessment to enhance learning among dental students at Islamic International Dental College.

Science.gov (United States)

Riaz, Fatima; Yasmin, Shahina; Yasmin, Raheela

2015-12-01

To evaluate the effectiveness of Formative Assessment in enhancing learning among dental students, and to interpret the assessment from students' perspective in this regard. The experimental non-randomised controlled study was conducted from January to June 2013 at Islamic International Dental College, Islamabad, and comprised first year Bachelor of Dental Surgery students attending regular physiology lectures and tutorials. Summative assessments conducted at the end of each unit were included as pre-intervention tests. After one month's planning, central nervous system unit was delivered in a month's trial with four formative assessment and feedback sessions (one per week). Likert scale-based student feedback questionnaire was administered. Post-intervention summative assessment was done by Multiple Choice and Short Essay Questions. Data was analysed using SPSS 17. Out of 68 students, 64(94.1%) agreed that a conducive environment was maintained and 62(90%) agreed that such sessions should be continued throughout the year; 59(87%) reflected that the feedback provided by the teacher was timely and positive and ensured equitable participation; 56(82%)agreed that it enhanced their interest in the subject; 56(68%) agreed that they were now more focussed; and43(63%)were of the opinion that they have progressed in the subject through these sessions. There was highly significant improvement in the monthly post-intervention test scores compared to pre-intervention test (p=0.000). Formative assessment sessions enhanced motivation and learning in first year dental students. Organised regular sessions with students' feedback may contribute to the development of pedagogic practice.

Simple method to generate and fabricate stochastic porous scaffolds

Energy Technology Data Exchange (ETDEWEB)

Yang, Nan, E-mail: y79nzw@163.com; Gao, Lilan; Zhou, Kuntao

2015-11-01

Considerable effort has been made to generate regular porous structures (RPSs) using function-based methods, although little effort has been made for constructing stochastic porous structures (SPSs) using the same methods. In this short communication, we propose a straightforward method for SPS construction that is simple in terms of methodology and the operations used. Using our method, we can obtain a SPS with functionally graded, heterogeneous and interconnected pores, target pore size and porosity distributions, which are useful for applications in tissue engineering. The resulting SPS models can be directly fabricated using additive manufacturing (AM) techniques. - Highlights: • Random porous structures are constructed based on their regular counterparts. • Functionally graded random pores can be constructed easily. • The scaffolds can be directly fabricated using additive manufacturing techniques.

Stochastic and non-stochastic effects - a conceptual analysis

International Nuclear Information System (INIS)

Karhausen, L.R.

1980-01-01

The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)

Perception of stochastically undersampled sound waveforms: A model of auditory deafferentation

Directory of Open Access Journals (Sweden)

Enrique A Lopez-Poveda

2013-07-01

Full Text Available Auditory deafferentation, or permanent loss of auditory nerve afferent terminals, occurs after noise overexposure and aging and may accompany many forms of hearing loss. It could cause significant auditory impairment but is undetected by regular clinical tests and so its effects on perception are poorly understood. Here, we hypothesize and test a neural mechanism by which deafferentation could deteriorate perception. The basic idea is that the spike train produced by each auditory afferent resembles a stochastically digitized version of the sound waveform and that the quality of the waveform representation in the whole nerve depends on the number of aggregated spike trains or auditory afferents. We reason that because spikes occur stochastically in time with a higher probability for high- than for low-intensity sounds, more afferents would be required for the nerve to faithfully encode high-frequency or low-intensity waveform features than low-frequency or high-intensity features. Deafferentation would thus degrade the encoding of these features. We further reason that due to the stochastic nature of nerve firing, the degradation would be greater in noise than in quiet. This hypothesis is tested using a vocoder. Sounds were filtered through ten adjacent frequency bands. For the signal in each band, multiple stochastically subsampled copies were obtained to roughly mimic different stochastic representations of that signal conveyed by different auditory afferents innervating a given cochlear region. These copies were then aggregated to obtain an acoustic stimulus. Tone detection and speech identification tests were performed by young, normal-hearing listeners using different numbers of stochastic samplers per frequency band in the vocoder. Results support the hypothesis that stochastic undersampling of the sound waveform, inspired by deafferentation, impairs speech perception in noise more than in quiet, consistent with auditory aging effects.

Perception of stochastically undersampled sound waveforms: a model of auditory deafferentation

Science.gov (United States)

Lopez-Poveda, Enrique A.; Barrios, Pablo

2013-01-01

Auditory deafferentation, or permanent loss of auditory nerve afferent terminals, occurs after noise overexposure and aging and may accompany many forms of hearing loss. It could cause significant auditory impairment but is undetected by regular clinical tests and so its effects on perception are poorly understood. Here, we hypothesize and test a neural mechanism by which deafferentation could deteriorate perception. The basic idea is that the spike train produced by each auditory afferent resembles a stochastically digitized version of the sound waveform and that the quality of the waveform representation in the whole nerve depends on the number of aggregated spike trains or auditory afferents. We reason that because spikes occur stochastically in time with a higher probability for high- than for low-intensity sounds, more afferents would be required for the nerve to faithfully encode high-frequency or low-intensity waveform features than low-frequency or high-intensity features. Deafferentation would thus degrade the encoding of these features. We further reason that due to the stochastic nature of nerve firing, the degradation would be greater in noise than in quiet. This hypothesis is tested using a vocoder. Sounds were filtered through ten adjacent frequency bands. For the signal in each band, multiple stochastically subsampled copies were obtained to roughly mimic different stochastic representations of that signal conveyed by different auditory afferents innervating a given cochlear region. These copies were then aggregated to obtain an acoustic stimulus. Tone detection and speech identification tests were performed by young, normal-hearing listeners using different numbers of stochastic samplers per frequency band in the vocoder. Results support the hypothesis that stochastic undersampling of the sound waveform, inspired by deafferentation, impairs speech perception in noise more than in quiet, consistent with auditory aging effects. PMID:23882176

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

Energy Technology Data Exchange (ETDEWEB)

Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)

2016-12-10

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

International Nuclear Information System (INIS)

Johnson, Michael D.

2016-01-01

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

Multiple graph regularized protein domain ranking.

Science.gov (United States)

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-11-19

Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

Science.gov (United States)

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression.

Science.gov (United States)

Zhen, Xiantong; Yu, Mengyang; Islam, Ali; Bhaduri, Mousumi; Chan, Ian; Li, Shuo

2017-09-01

Multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis. However, due to the huge image variability and ambiguity, it is fundamentally challenging to handle the highly complex input-target relationship of multioutput regression, especially with indiscriminate high-dimensional representations. In this paper, we propose a novel supervised descriptor learning (SDL) algorithm for multioutput regression, which can establish discriminative and compact feature representations to improve the multivariate estimation performance. The SDL is formulated as generalized low-rank approximations of matrices with a supervised manifold regularization. The SDL is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low-dimensional space aligned to targets. The achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression, which enables more accurate and efficient multivariate estimation. We conduct extensive evaluation of the proposed SDL on both synthetic data and real-world multioutput regression tasks for both computer vision and medical image analysis. Experimental results have shown that the proposed SDL can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts. Our method establishes a novel SDL framework for multioutput regression, which can be widely used to boost the performance in different applications.

Regularizing portfolio optimization

International Nuclear Information System (INIS)

Still, Susanne; Kondor, Imre

2010-01-01

The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.

Regularizing portfolio optimization

Science.gov (United States)

Still, Susanne; Kondor, Imre

2010-07-01

The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.

Stochastic Frontier Estimation of Efficient Learning in Video Games

Science.gov (United States)

Hamlen, Karla R.

2012-01-01

Stochastic Frontier Regression Analysis was used to investigate strategies and skills that are associated with the minimization of time required to achieve proficiency in video games among students in grades four and five. Students self-reported their video game play habits, including strategies and skills used to become good at the video games…

UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA

Directory of Open Access Journals (Sweden)

IONIŢĂ Elena

2015-06-01

Full Text Available This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. Semi-regular polyhedra are convex polyhedra with regular polygon faces, several types and equal solid angles of the same type. A net of a polyhedron is a collection of edges in the plane which are the unfolded edges of the solid. Modeling and unfolding Platonic and Arhimediene polyhedra will be using 3dsMAX program. This paper is intended as an example of descriptive geometry applications.

Graph Regularized Auto-Encoders for Image Representation.

Science.gov (United States)

Yiyi Liao; Yue Wang; Yong Liu

2017-06-01

Image representation has been intensively explored in the domain of computer vision for its significant influence on the relative tasks such as image clustering and classification. It is valuable to learn a low-dimensional representation of an image which preserves its inherent information from the original image space. At the perspective of manifold learning, this is implemented with the local invariant idea to capture the intrinsic low-dimensional manifold embedded in the high-dimensional input space. Inspired by the recent successes of deep architectures, we propose a local invariant deep nonlinear mapping algorithm, called graph regularized auto-encoder (GAE). With the graph regularization, the proposed method preserves the local connectivity from the original image space to the representation space, while the stacked auto-encoders provide explicit encoding model for fast inference and powerful expressive capacity for complex modeling. Theoretical analysis shows that the graph regularizer penalizes the weighted Frobenius norm of the Jacobian matrix of the encoder mapping, where the weight matrix captures the local property in the input space. Furthermore, the underlying effects on the hidden representation space are revealed, providing insightful explanation to the advantage of the proposed method. Finally, the experimental results on both clustering and classification tasks demonstrate the effectiveness of our GAE as well as the correctness of the proposed theoretical analysis, and it also suggests that GAE is a superior solution to the current deep representation learning techniques comparing with variant auto-encoders and existing local invariant methods.

Energy consumption and entropy production in a stochastic formulation of BCM learning

International Nuclear Information System (INIS)

De Oliveira, L R; Castellani, G; Turchetti, G

2013-01-01

Biochemical processes in living cells are open systems, therefore they exchange materials with their environment and they consume chemical energy. These processes are molecular-based and for that reason the role of fluctuations can not be ignored and the stochastic description is the most appropriate one. The chemical master equation describes in exact way the probabilistic dynamics of a given discrete set of states and helps us to understand and clarify the differences between closed and open systems. A closed system is related to a condition of detailed balance (DB), i.e. an equilibrium state. After a sufficiently long period, an open system will reach a non-equilibrium steady state (NESS) that is sustained by a flux of external energy. We demonstrate that two implementations of the BCM learning rule (BCM82) and (BCM92) are, respectively, always in DB, and never in DB. We define a one parameter parametrization of the BCM learning rule that interpolates between these two extremes. We compute thermodynamical quantities such as internal energy, free energy (both Helmholtz and Gibbs) and entropy. The entropy variation in the case of open systems (i.e. when DB does not hold) can be divided into internal entropy production and entropy exchanged with surroundings. We show how the entropy variation can be used to find the optimal value (corresponding to increased robustness and stability) for the parameter used in the BCM parametrization. Finally, we use the calculation of the work to drive the system from an initial state to the steady state as the parameter of the plasticity of the system

Teacher Effectiveness in Adapting Instruction to the Needs of Pupils With Learning Difficulties in Regular Primary Schools in Ghana

Directory of Open Access Journals (Sweden)

Abdul-Razak Kuyini Alhassan

2014-01-01

Full Text Available Ghana education system has failed to effectively address the needs of pupils with learning difficulties (LDs in regular classrooms. Underachievement, school dropout, streetism, and antisocial behaviors are the consequences. Teachers’ lack of adequate competence in adaptive instruction is one of the fundamental reasons responsible for this anomaly. This study aims to examine teachers’ competence in adapting instructions to teach pupils with LDs in the regular classroom in Ghana. The data were gathered from 387 sampled teachers in a cross-sectional survey using questionnaires and structured observation methods. We analyzed the data using descriptive statistic, chi-square test, correlation, t test, and ANOVA. The results show that (a teachers have limited to moderate competence in adaptive instruction, (b adaptive teaching is strongly associated with teachers’ competence in teaching pupils with LDs in the regular classroom, and (c apart from gender and class size, teachers’ background variables such as school location and teaching experience differ significantly. The study has serious implications for Ghana’s inclusive education policy and teaching practice.

Supervised scale-regularized linear convolutionary filters

DEFF Research Database (Denmark)

Loog, Marco; Lauze, Francois Bernard

2017-01-01

also be solved relatively efficient. All in all, the idea is to properly control the scale of a trained filter, which we solve by introducing a specific regularization term into the overall objective function. We demonstrate, on an artificial filter learning problem, the capabil- ities of our basic...

Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise

Science.gov (United States)

Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.

2012-07-01

The primitive equations (PEs) are a basic model in the study of large scale oceanic and atmospheric dynamics. These systems form the analytical core of the most advanced general circulation models. For this reason and due to their challenging nonlinear and anisotropic structure, the PEs have recently received considerable attention from the mathematical community. On the other hand, in view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the PEs and more generally. In this work we study a stochastic version of the PEs. We establish the global existence and uniqueness of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, L^{p}_{t}L^{q}_{x} estimates on the pressure and stopping time arguments.

Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise

International Nuclear Information System (INIS)

Debussche, A; Glatt-Holtz, N; Temam, R; Ziane, M

2012-01-01

The primitive equations (PEs) are a basic model in the study of large scale oceanic and atmospheric dynamics. These systems form the analytical core of the most advanced general circulation models. For this reason and due to their challenging nonlinear and anisotropic structure, the PEs have recently received considerable attention from the mathematical community. On the other hand, in view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the PEs and more generally. In this work we study a stochastic version of the PEs. We establish the global existence and uniqueness of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, L p t L q x estimates on the pressure and stopping time arguments

Multi-label learning with fuzzy hypergraph regularization for protein subcellular location prediction.

Science.gov (United States)

Chen, Jing; Tang, Yuan Yan; Chen, C L Philip; Fang, Bin; Lin, Yuewei; Shang, Zhaowei

2014-12-01

Protein subcellular location prediction aims to predict the location where a protein resides within a cell using computational methods. Considering the main limitations of the existing methods, we propose a hierarchical multi-label learning model FHML for both single-location proteins and multi-location proteins. The latent concepts are extracted through feature space decomposition and label space decomposition under the nonnegative data factorization framework. The extracted latent concepts are used as the codebook to indirectly connect the protein features to their annotations. We construct dual fuzzy hypergraphs to capture the intrinsic high-order relations embedded in not only feature space, but also label space. Finally, the subcellular location annotation information is propagated from the labeled proteins to the unlabeled proteins by performing dual fuzzy hypergraph Laplacian regularization. The experimental results on the six protein benchmark datasets demonstrate the superiority of our proposed method by comparing it with the state-of-the-art methods, and illustrate the benefit of exploiting both feature correlations and label correlations.

Ensemble manifold regularization.

Science.gov (United States)

Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng

2012-06-01

We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan

2012-11-19

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

KAUST Repository

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2012-01-01

Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

Multiple graph regularized protein domain ranking

Directory of Open Access Journals (Sweden)

Wang Jim

2012-11-01

Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

A probabilistic graphical model based stochastic input model construction

International Nuclear Information System (INIS)

Wan, Jiang; Zabaras, Nicholas

2014-01-01

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media

Machine-Learning Research

OpenAIRE

Dietterich, Thomas G.

1997-01-01

Machine-learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (1) the improvement of classification accuracy by learning ensembles of classifiers, (2) methods for scaling up supervised learning algorithms, (3) reinforcement learning, and (4) the learning of complex stochastic models.

Least square regularized regression in sum space.

Science.gov (United States)

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Infants Learn Phonotactic Regularities from Brief Auditory Experience.

Science.gov (United States)

Chambers, Kyle E.; Onishi, Kristine H.; Fisher, Cynthia

2003-01-01

Two experiments investigated whether novel phonotactic regularities, not present in English, could be acquired by 16.5-month-olds from brief auditory experience. Subjects listened to consonant-vowel-consonant syllables in which particular consonants were artificially restricted to either initial or final position. Findings in a subsequent…

Bayesian Estimation and Inference using Stochastic Hardware

Directory of Open Access Journals (Sweden)

Chetan Singh Thakur

2016-03-01

Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

Bayesian Estimation and Inference Using Stochastic Electronics.

Science.gov (United States)

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

OpenAIRE

Kim, Hyun-Jung; Lototsky, Sergey V

2017-01-01

Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the stochastic heat equation with space-only Gaussian white noise on a bounded interval. The main result is that the space-time regularity of the solution is the same for additive noise and for multiplicative noise in the Wick-It\\^o-Skorokhod interpretation.

Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1

Directory of Open Access Journals (Sweden)

Henri Schurz

2010-09-01

Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.

Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks

Science.gov (United States)

Yulmetyev, Renat; Emelyanova, Natalya; Demin, Sergey; Gafarov, Fail; Hänggi, Peter; Yulmetyeva, Dinara

2003-05-01

For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long-time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long-range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non-Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks with a view to time discreteness and effects of statistical memory.

Online learning in repeated auctions

OpenAIRE

Weed, Jonathan; Perchet, Vianney; Rigollet, Philippe

2015-01-01

Motivated by online advertising auctions, we consider repeated Vickrey auctions where goods of unknown value are sold sequentially and bidders only learn (potentially noisy) information about a good's value once it is purchased. We adopt an online learning approach with bandit feedback to model this problem and derive bidding strategies for two models: stochastic and adversarial. In the stochastic model, the observed values of the goods are random variables centered around the true value of t...

Discharge regularity in the turtle posterior crista: comparisons between experiment and theory.

Science.gov (United States)

Goldberg, Jay M; Holt, Joseph C

2013-12-01

Intra-axonal recordings were made from bouton fibers near their termination in the turtle posterior crista. Spike discharge, miniature excitatory postsynaptic potentials (mEPSPs), and afterhyperpolarizations (AHPs) were monitored during resting activity in both regularly and irregularly discharging units. Quantal size (qsize) and quantal rate (qrate) were estimated by shot-noise theory. Theoretically, the ratio, σV/(dμV/dt), between synaptic noise (σV) and the slope of the mean voltage trajectory (dμV/dt) near threshold crossing should determine discharge regularity. AHPs are deeper and more prolonged in regular units; as a result, dμV/dt is larger, the more regular the discharge. The qsize is larger and qrate smaller in irregular units; these oppositely directed trends lead to little variation in σV with discharge regularity. Of the two variables, dμV/dt is much more influential than the nearly constant σV in determining regularity. Sinusoidal canal-duct indentations at 0.3 Hz led to modulations in spike discharge and synaptic voltage. Gain, the ratio between the amplitudes of the two modulations, and phase leads re indentation of both modulations are larger in irregular units. Gain variations parallel the sensitivity of the postsynaptic spike encoder, the set of conductances that converts synaptic input into spike discharge. Phase variations reflect both synaptic inputs to the encoder and postsynaptic processes. Experimental data were interpreted using a stochastic integrate-and-fire model. Advantages of an irregular discharge include an enhanced encoder gain and the prevention of nonlinear phase locking. Regular and irregular units are more efficient, respectively, in the encoding of low- and high-frequency head rotations, respectively.

Stochastic Bus Dispatching Model untuk Optimalisasi Jumlah Bus Transjakarta Koridor 3

Directory of Open Access Journals (Sweden)

Zahedi Zahedi

2011-12-01

Full Text Available The increasing number of road user causing traffic jam finds out a way, busway. However, in its implementation, the number of fleet available does not enough to take the passengers. It results in the an amassed of passengers at several bus stops. This leads to passenger dissatisfaction satisfaction which eventually causes Transjakarta users to reuse private cars. Definitely this situation may builds up traffic jams. Stochastic Bus Dispatching Model is used to simulate public transportation that operates regularly. 

Deterministic and stochastic control of chimera states in delayed feedback oscillator

Energy Technology Data Exchange (ETDEWEB)

Semenov, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Maistrenko, Y. [Institute of Mathematics and Center for Medical and Biotechnical Research, NAS of Ukraine, Tereschenkivska Str. 3, 01601 Kyiv (Ukraine)

2016-06-08

Chimera states, characterized by the coexistence of regular and chaotic dynamics, are found in a nonlinear oscillator model with negative time-delayed feedback. The control of these chimera states by external periodic forcing is demonstrated by numerical simulations. Both deterministic and stochastic external periodic forcing are considered. It is shown that multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. The constructive role of noise in the formation of a chimera states is shown.

STOCHASTIC FLOWS OF MAPPINGS

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

Regularity and chaos in Vlasov evolution of nuclear matter

Energy Technology Data Exchange (ETDEWEB)

Jacquot, B.; Guarnera, A.; Chomaz, Ph.; Colonna, M.

1995-12-31

A careful analysis of the mean-field dynamics inside the spinodal instability region is performed. It is shown that, conversely to some recently published results the mean-field evolution appears mostly regular over a long time scale, while some disorder is observed only very late, when fragments are already formed This onset of chaos can be related to the fragment interaction which induces some coalescence effects. Moreover it is shown that the time scale over which the chaos start to develop are very sensitive to the range of the considered force. All the presented results support the various analyses of spinodal instabilities obtained using stochastic mean field approaches. (author). 16 refs. Submitted to Physical Review, C (US).

Stochastic Variational Learning in Recurrent Spiking Networks

Directory of Open Access Journals (Sweden)

Danilo eJimenez Rezende

2014-04-01

Full Text Available The ability to learn and perform statistical inference with biologically plausible recurrent network of spiking neurons is an important step towards understanding perception and reasoning. Here we derive and investigate a new learning rule for recurrent spiking networks with hidden neurons, combining principles from variational learning and reinforcement learning. Our network defines a generative model over spike train histories and the derived learning rule has the form of a local Spike Timing Dependent Plasticity rule modulated by global factors (neuromodulators conveying information about ``novelty on a statistically rigorous ground.Simulations show that our model is able to learn bothstationary and non-stationary patterns of spike trains.We also propose one experiment that could potentially be performed with animals in order to test the dynamics of the predicted novelty signal.

Stochastic variational learning in recurrent spiking networks.

Science.gov (United States)

Jimenez Rezende, Danilo; Gerstner, Wulfram

2014-01-01

The ability to learn and perform statistical inference with biologically plausible recurrent networks of spiking neurons is an important step toward understanding perception and reasoning. Here we derive and investigate a new learning rule for recurrent spiking networks with hidden neurons, combining principles from variational learning and reinforcement learning. Our network defines a generative model over spike train histories and the derived learning rule has the form of a local Spike Timing Dependent Plasticity rule modulated by global factors (neuromodulators) conveying information about "novelty" on a statistically rigorous ground. Simulations show that our model is able to learn both stationary and non-stationary patterns of spike trains. We also propose one experiment that could potentially be performed with animals in order to test the dynamics of the predicted novelty signal.

Information operator approach and iterative regularization methods for atmospheric remote sensing

International Nuclear Information System (INIS)

Doicu, A.; Hilgers, S.; Bargen, A. von; Rozanov, A.; Eichmann, K.-U.; Savigny, C. von; Burrows, J.P.

2007-01-01

In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO 2 retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen

An Improved Multispectral Palmprint Recognition System Using Autoencoder with Regularized Extreme Learning Machine

Directory of Open Access Journals (Sweden)

Abdu Gumaei

2018-01-01

Full Text Available Multispectral palmprint recognition system (MPRS is an essential technology for effective human identification and verification tasks. To improve the accuracy and performance of MPRS, a novel approach based on autoencoder (AE and regularized extreme learning machine (RELM is proposed in this paper. The proposed approach is intended to make the recognition faster by reducing the number of palmprint features without degrading the accuracy of classifier. To achieve this objective, first, the region of interest (ROI from palmprint images is extracted by David Zhang’s method. Second, an efficient normalized Gist (NGist descriptor is used for palmprint feature extraction. Then, the dimensionality of extracted features is reduced using optimized AE. Finally, the reduced features are fed to the RELM for classification. A comprehensive set of experiments are conducted on the benchmark MS-PolyU dataset. The results were significantly high compared to the state-of-the-art approaches, and the robustness and efficiency of the proposed approach are revealed.

Stochastic processes

CERN Document Server

Parzen, Emanuel

1962-01-01

Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine

Algorithmic detectability threshold of the stochastic block model

Science.gov (United States)

Kawamoto, Tatsuro

2018-03-01

The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.

Verification of HYDRASTAR - A code for stochastic continuum simulation of groundwater flow

International Nuclear Information System (INIS)

Norman, S.

1991-07-01

HYDRASTAR is a code developed at Starprog AB for use in the SKB 91 performance assessment project with the following principal function: - Reads the actual conductivity measurements from a file created from the data base GEOTAB. - Regularizes the measurements to a user chosen calculation scale. - Generates three dimensional unconditional realizations of the conductivity field by using a supplied model of the conductivity field as a stochastic function. - Conditions the simulated conductivity field on the actual regularized measurements. - Reads the boundary conditions from a regional deterministic NAMMU computation. - Calculates the hydraulic head field, Darcy velocity field, stream lines and water travel times by solving the stationary hydrology equation and the streamline equation obtained with the velocities calculated from Darcy's law. - Generates visualizations of the realizations if desired. - Calculates statistics such as semivariograms and expectation values of the output fields by repeating the above procedure by iterations of the Monte Carlo type. When using computer codes for safety assessment purpose validation and verification of the codes are important. Thus this report describes a work performed with the goal of verifying parts of HYDRASTAR. The verification described in this report uses comparisons with two other solutions of related examples: A. Comparison with a so called perturbation solution of the stochastical stationary hydrology equation. This as an analytical approximation of the stochastical stationary hydrology equation valid in the case of small variability of the unconditional random conductivity field. B. Comparison with the (Hydrocoin, 1988), case 2. This is a classical example of a hydrology problem with a deterministic conductivity field. The principal feature of the problem is the presence of narrow fracture zones with high conductivity. the compared output are the hydraulic head field and a number of stream lines originating from a

Simplified reactive power management strategy for complex power grids under stochastic operation and incomplete information

DEFF Research Database (Denmark)

Vlachogiannis, Ioannis (John)

2009-01-01

grids is a major issue for system operators. Under these circumstances an online reactive power management strategy with minimum risk concerning all uncertain and stochastic parameters is proposed. Therefore, new concepts such as reactive power-weighted node-to-node linking and reactive power control......In the current released energy market, the large-scale complex transmission networks and the distribution ones with dispersed energy sources and "intelligent" components operate under uncertainties, stochastic and prior incomplete information. A safe and reliable operation of such complex power...... capability are introduced. A distributed and interconnected stochastic learning automata system is implemented to manage, in a unified and unique way, the reactive power in complex power grids with stochastic reactive power demand and detect the vulnerable part. The proposed simplified strategy can also...

The Regular Education Initiative: A Deja Vu Remembered with Sadness and Concern.

Science.gov (United States)

Silver, Larry B.

1991-01-01

This article compares the ideals of the regular education initiative to provide services for learning-disabled students within the regular classroom to the ideals and resulting negative effects (e.g., homelessness) of the deinstitutionalization of the mentally ill during the 1960s. Resistance to efforts to decrease or eliminate special education…

A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis.

Science.gov (United States)

Liu, Zitao; Hauskrecht, Milos

2015-01-01

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.

Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes

Science.gov (United States)

Liyanagedera, Chamika M.; Sengupta, Abhronil; Jaiswal, Akhilesh; Roy, Kaushik

2017-12-01

Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway to achieving "brainlike" compact and energy-efficient cognitive intelligence. The computational model attempt to exploit the intrinsic device stochasticity of nanoelectronic synaptic or neural components to perform learning or inference. However, there has been limited analysis on the scaling effect of stochastic spin devices and its impact on the operation of such stochastic networks at the system level. This work attempts to explore the design space and analyze the performance of nanomagnet-based stochastic neuromorphic computing architectures for magnets with different barrier heights. We illustrate how the underlying network architecture must be modified to account for the random telegraphic switching behavior displayed by magnets with low barrier heights as they are scaled into the superparamagnetic regime. We perform a device-to-system-level analysis on a deep neural-network architecture for a digit-recognition problem on the MNIST data set.

Simplified reactive power management strategy for complex power grids under stochastic operation and incomplete information

International Nuclear Information System (INIS)

Vlachogiannis, John G.

2009-01-01

In the current released energy market, the large-scale complex transmission networks and the distribution ones with dispersed energy sources and 'intelligent' components operate under uncertainties, stochastic and prior incomplete information. A safe and reliable operation of such complex power grids is a major issue for system operators. Under these circumstances an online reactive power management strategy with minimum risk concerning all uncertain and stochastic parameters is proposed. Therefore, new concepts such as reactive power-weighted node-to-node linking and reactive power control capability are introduced. A distributed and interconnected stochastic learning automata system is implemented to manage, in a unified and unique way, the reactive power in complex power grids with stochastic reactive power demand and detect the vulnerable part. The proposed simplified strategy can also consider more stochastic aspects such as variable grid's topology. Results of the proposed strategy obtained on the networks of IEEE 30-bus and IEEE 118-bus systems demonstrate the effectiveness of the proposed strategy.

Effects of noise on convergent game-learning dynamics

International Nuclear Information System (INIS)

Sanders, James B T; Galla, Tobias; Shapiro, Jonathan L

2012-01-01

We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is stochastic when players only have limited information about their opponents’ strategic propensities. The effects of this noise are studied analytically in the case where it is small but finite, and we show that the statistics and correlation properties of fluctuations can be computed to a high accuracy. We find that the system can exhibit quasicycles, driven by intrinsic noise. If players are asymmetric and use different parameters for their learning, a net payoff advantage can be achieved due to these stochastic oscillations around the deterministic equilibrium. (paper)

Listening to their voices: The essence of the experience of special and regular education students as they learn monarch, Danaus plexippus, biology and ecology

Science.gov (United States)

Koomen, Michele Jean Hollingsworth

This dissertation reports on a phenomenological study of nine regular and special education students as they studied insect biology and ecology in their inclusive seventh grade life science class. Three fundamental data collection methods of interpretive research (student observations, interviews and artifact analysis) framed the data collection of this study. Hermeneutic phenomenological analysis and a seven-step framework, beginning with establishment of the unit of analysis and ending in theory generation, were used to systematically analyze the data resulting in the emergence of four main themes. The essence of the lived experience of the study participants reveal a variety of ways working with others in groups supported their learning. Students reported that it was easier to share ideas, ask questions and complete their work when they worked together with other classmates. A second finding of this study, It's kind of hard in learning science, exposes some of the anxiety and the challenges that are part of the experiences of both regular and special education students in learning science. A third finding reveals that for the students in this study the practice of inquiry learning in science is fragile. Despite daily opportunities in inquiry activities, many students are fixated in finding the "right" answers and just getting their "work done." The practice of inquiry is also fragile because of the perceptions of how we go about doing and learning science. The perception of practicing science for the special education students was moderated and limited by their viewpoint that science is coupled with language arts. The last major theme describes the manner in which both student groups navigate through science learning using various strategies that contribute to their learning or engaging in behaviors that seem to conceal their learning differences. The results of this research have implication for inclusive classroom teachers, special educators, teacher educators

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

NARCIS (Netherlands)

van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.

2009-01-01

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of

A stochastic context free grammar based framework for analysis of protein sequences

Directory of Open Access Journals (Sweden)

Nebel Jean-Christophe

2009-10-01

Full Text Available Abstract Background In the last decade, there have been many applications of formal language theory in bioinformatics such as RNA structure prediction and detection of patterns in DNA. However, in the field of proteomics, the size of the protein alphabet and the complexity of relationship between amino acids have mainly limited the application of formal language theory to the production of grammars whose expressive power is not higher than stochastic regular grammars. However, these grammars, like other state of the art methods, cannot cover any higher-order dependencies such as nested and crossing relationships that are common in proteins. In order to overcome some of these limitations, we propose a Stochastic Context Free Grammar based framework for the analysis of protein sequences where grammars are induced using a genetic algorithm. Results This framework was implemented in a system aiming at the production of binding site descriptors. These descriptors not only allow detection of protein regions that are involved in these sites, but also provide insight in their structure. Grammars were induced using quantitative properties of amino acids to deal with the size of the protein alphabet. Moreover, we imposed some structural constraints on grammars to reduce the extent of the rule search space. Finally, grammars based on different properties were combined to convey as much information as possible. Evaluation was performed on sites of various sizes and complexity described either by PROSITE patterns, domain profiles or a set of patterns. Results show the produced binding site descriptors are human-readable and, hence, highlight biologically meaningful features. Moreover, they achieve good accuracy in both annotation and detection. In addition, findings suggest that, unlike current state-of-the-art methods, our system may be particularly suited to deal with patterns shared by non-homologous proteins. Conclusion A new Stochastic Context Free

The interpolation method of stochastic functions and the stochastic variational principle

International Nuclear Information System (INIS)

Liu Xianbin; Chen Qiu

1993-01-01

Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second

Variational inference & deep learning: A new synthesis

OpenAIRE

Kingma, D.P.

2017-01-01

In this thesis, Variational Inference and Deep Learning: A New Synthesis, we propose novel solutions to the problems of variational (Bayesian) inference, generative modeling, representation learning, semi-supervised learning, and stochastic optimization.

Variational inference & deep learning : A new synthesis

NARCIS (Netherlands)

Kingma, D.P.

2017-01-01

In this thesis, Variational Inference and Deep Learning: A New Synthesis, we propose novel solutions to the problems of variational (Bayesian) inference, generative modeling, representation learning, semi-supervised learning, and stochastic optimization.

Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods

CERN Document Server

Bhatnagar, S; Prashanth, L A

2013-01-01

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...

Adaptive Control Using Fully Online Sequential-Extreme Learning Machine and a Case Study on Engine Air-Fuel Ratio Regulation

Directory of Open Access Journals (Sweden)

Pak Kin Wong

2014-01-01

Full Text Available Most adaptive neural control schemes are based on stochastic gradient-descent backpropagation (SGBP, which suffers from local minima problem. Although the recently proposed regularized online sequential-extreme learning machine (ReOS-ELM can overcome this issue, it requires a batch of representative initial training data to construct a base model before online learning. The initial data is usually difficult to collect in adaptive control applications. Therefore, this paper proposes an improved version of ReOS-ELM, entitled fully online sequential-extreme learning machine (FOS-ELM. While retaining the advantages of ReOS-ELM, FOS-ELM discards the initial training phase, and hence becomes suitable for adaptive control applications. To demonstrate its effectiveness, FOS-ELM was applied to the adaptive control of engine air-fuel ratio based on a simulated engine model. Besides, controller parameters were also analyzed, in which it is found that large hidden node number with small regularization parameter leads to the best performance. A comparison among FOS-ELM and SGBP was also conducted. The result indicates that FOS-ELM achieves better tracking and convergence performance than SGBP, since FOS-ELM tends to learn the unknown engine model globally whereas SGBP tends to “forget” what it has learnt. This implies that FOS-ELM is more preferable for adaptive control applications.

K--12 science educator perception of instructing students with learning disabilities in the regular classroom

Science.gov (United States)

Holliday-Cashwell, Janet Rose

2000-10-01

Selected K--12 public school science educators in 14 eastern North Carolina counties were surveyed to examine their perceptions of their undergraduate preparation programs with regard to instructing students with learning disabilities in the regular classroom. A quantitative study, this research examined science educator preparedness in instructing students with learning disabilities by evaluating educator perception in regard to mainstrearned and inclusive educational settings. Specifically, two null hypotheses were tested. Null hypothesis I stated a significant difference does not exist between selected North Carolina K--12 science educators' perceptions of their undergraduate teacher education preparation programs and their perceptions of their abilities to instruct students needing accommodations on behalf of their learning disabilities in mainstrearned or inclusive settings. Participants' responses to perception as well as value statements regarding opinions, adaptations, and undergraduate training with respect to mainstreaming and inclusion were evaluated through t-test analyses of 22 Likert-scale items. Null hypothesis 1 was not accepted because a statistically significant difference did exist between the educators' perceptions of their undergraduate training and their perceived abilities to instruct students with learning disabilities in mainstreamed or inclusive settings. Null hypothesis 2 stated a significant difference does not exist between selected North Carolina K--12 science educators' attained educational level; grade level currently taught, supervised or chaired; and years of experience in teaching science, supervising science education, and/or chairing science departments in selected North Carolina public schools and their opinions of their undergraduate teacher education program with regard to instructing students with learning disabilities in mainstreamed or inclusive educational settings. Null hypothesis 2 was evaluated through an analysis of

Stochastic thermodynamics

Science.gov (United States)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response

Diverse Regular Employees and Non-regular Employment (Japanese)

OpenAIRE

MORISHIMA Motohiro

2011-01-01

Currently there are high expectations for the introduction of policies related to diverse regular employees. These policies are a response to the problem of disparities between regular and non-regular employees (part-time, temporary, contract and other non-regular employees) and will make it more likely that workers can balance work and their private lives while companies benefit from the advantages of regular employment. In this paper, I look at two issues that underlie this discussion. The ...

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

Science.gov (United States)

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Regularized Label Relaxation Linear Regression.

Science.gov (United States)

Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung; Fang, Bingwu

2018-04-01

Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on -norm and -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time.

Enhanced manifold regularization for semi-supervised classification.

Science.gov (United States)

Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong

2016-06-01

Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.

Generalized bounds for convex multistage stochastic programs

CERN Document Server

Künzi, H; Fandel, G; Trockel, W; Basile, A; Drexl, A; Dawid, H; Inderfurth, K; Kürsten, W; Schittko, U

2005-01-01

This work was completed during my tenure as a scientific assistant and d- toral student at the Institute for Operations Research at the University of St. Gallen. During that time, I was involved in several industry projects in the field of power management, on the occasion of which I was repeatedly c- fronted with complex decision problems under uncertainty. Although usually hard to solve, I quickly learned to appreciate the benefit of stochastic progr- ming models and developed a strong interest in their theoretical properties. Motivated both by practical questions and theoretical concerns, I became p- ticularly interested in the art of finding tight bounds on the optimal value of a given model. The present work attempts to make a contribution to this important branch of stochastic optimization theory. In particular, it aims at extending some classical bounding methods to broader problem classes of practical relevance. This book was accepted as a doctoral thesis by the University of St. Gallen in June 2004.1...

An efficient scenario-based stochastic programming framework for multi-objective optimal micro-grid operation

International Nuclear Information System (INIS)

Niknam, Taher; Azizipanah-Abarghooee, Rasoul; Narimani, Mohammad Rasoul

2012-01-01

Highlights: ► Proposes a stochastic model for optimal energy management. ► Consider uncertainties related to the forecasted values for load demand. ► Consider uncertainties of forecasted values of output power of wind and photovoltaic units. ► Consider uncertainties of forecasted values of market price. ► Present an improved multi-objective teaching–learning-based optimization. -- Abstract: This paper proposes a stochastic model for optimal energy management with the goal of cost and emission minimization. In this model, the uncertainties related to the forecasted values for load demand, available output power of wind and photovoltaic units and market price are modeled by a scenario-based stochastic programming. In the presented method, scenarios are generated by a roulette wheel mechanism based on probability distribution functions of the input random variables. Through this method, the inherent stochastic nature of the proposed problem is released and the problem is decomposed into a deterministic problem. An improved multi-objective teaching–learning-based optimization is implemented to yield the best expected Pareto optimal front. In the proposed stochastic optimization method, a novel self adaptive probabilistic modification strategy is offered to improve the performance of the presented algorithm. Also, a set of non-dominated solutions are stored in a repository during the simulation process. Meanwhile, the size of the repository is controlled by usage of a fuzzy-based clustering technique. The best expected compromise solution stored in the repository is selected via the niching mechanism in a way that solutions are encouraged to seek the lesser explored regions. The proposed framework is applied in a typical grid-connected micro grid in order to verify its efficiency and feasibility.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Stochastic neuron models

CERN Document Server

Greenwood, Priscilla E

2016-01-01

This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...

Stochastic differential equations for quantum dynamics of spin-boson networks

International Nuclear Information System (INIS)

Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E

2015-01-01

A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)

Stochastic Processes in Finance and Behavioral Finance

OpenAIRE

Steinbacher, Matjaz

2008-01-01

In the paper, we put some foundations for studying asset pricing and finance as a stochastic and behavioral process. In such process, preferences and psychology of agents represent the most important factor in the decision-making of people. Individuals have their own ways of acquiring the information they need, how to deal with them and how to make predictions and decisions. People usually also do not behave consistent in time, but learn. Therefore, in order to understand the behavior on the ...

Weak-noise limit of a piecewise-smooth stochastic differential equation.

Science.gov (United States)

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Cycles of cooperation and defection in imperfect learning

International Nuclear Information System (INIS)

Galla, Tobias

2011-01-01

We investigate a model of learning the iterated prisoner's dilemma game. Players have the choice between three strategies: always defect (ALLD), always cooperate (ALLC) and tit-for-tat (TFT). The only strict Nash equilibrium in this situation is ALLD. When players learn to play this game convergence to the equilibrium is not guaranteed, for example we find cooperative behaviour if players discount observations in the distant past. When agents use small samples of observed moves to estimate their opponent's strategy the learning process is stochastic, and sustained oscillations between cooperation and defection can emerge. These cycles are similar to those found in stochastic evolutionary processes, but the origin of the noise sustaining the oscillations is different and lies in the imperfect sampling of the opponent's strategy. Based on a systematic expansion technique, we are able to predict the properties of these learning cycles, providing an analytical tool with which the outcome of more general stochastic adaptation processes can be characterised

Stochastic tools in turbulence

CERN Document Server

Lumey, John L

2012-01-01

Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

Discriminative Elastic-Net Regularized Linear Regression.

Science.gov (United States)

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Spike-based decision learning of Nash equilibria in two-player games.

Directory of Open Access Journals (Sweden)

Johannes Friedrich

Full Text Available Humans and animals face decision tasks in an uncertain multi-agent environment where an agent's strategy may change in time due to the co-adaptation of others strategies. The neuronal substrate and the computational algorithms underlying such adaptive decision making, however, is largely unknown. We propose a population coding model of spiking neurons with a policy gradient procedure that successfully acquires optimal strategies for classical game-theoretical tasks. The suggested population reinforcement learning reproduces data from human behavioral experiments for the blackjack and the inspector game. It performs optimally according to a pure (deterministic and mixed (stochastic Nash equilibrium, respectively. In contrast, temporal-difference(TD-learning, covariance-learning, and basic reinforcement learning fail to perform optimally for the stochastic strategy. Spike-based population reinforcement learning, shown to follow the stochastic reward gradient, is therefore a viable candidate to explain automated decision learning of a Nash equilibrium in two-player games.

Stochastic pump effect and geometric phases in dissipative and stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Supporting primary school teachers in differentiating in the regular classroom

NARCIS (Netherlands)

Eysink, Tessa H.S.; Hulsbeek, Manon; Gijlers, Hannie

Many primary school teachers experience difficulties in effectively differentiating in the regular classroom. This study investigated the effect of the STIP-approach on teachers' differentiation activities and self-efficacy, and children's learning outcomes and instructional value. Teachers using

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

International Nuclear Information System (INIS)

Bouard, Anne de; Debussche, Arnaud

2006-01-01

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

Sequential stochastic optimization

CERN Document Server

Cairoli, Renzo

1996-01-01

Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet

Laplacian embedded regression for scalable manifold regularization.

Science.gov (United States)

Chen, Lin; Tsang, Ivor W; Xu, Dong

2012-06-01

Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real

Coordinate-invariant regularization

International Nuclear Information System (INIS)

Halpern, M.B.

1987-01-01

A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc

Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power

DEFF Research Database (Denmark)

Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

International Nuclear Information System (INIS)

Branicki, M.; Majda, A.J.

2013-01-01

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum

Stochastic models with power-law tails the equation X = AX + B

CERN Document Server

Buraczewski, Dariusz; Mikosch, Thomas

2016-01-01

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...

xSPDE: Extensible software for stochastic equations

Directory of Open Access Journals (Sweden)

Simon Kiesewetter

2016-01-01

Full Text Available We introduce an extensible software toolbox, xSPDE, for solving ordinary and partial stochastic differential equations. The toolbox makes extensive use of vector and parallel methods. Inputs are exceptionally simple, to reduce the learning curve, with default options for all of the many input parameters. The code calculates functional means, correlations and spectra, checks for errors in both time-step and sampling, and provides several choices of algorithm. Most aspects of the code, including the numerical algorithm, have a modular functional design to allow user modifications.

Effects of regular aerobic exercise on visual perceptual learning.

Science.gov (United States)

Connell, Charlotte J W; Thompson, Benjamin; Green, Hayden; Sullivan, Rachel K; Gant, Nicholas

2017-12-02

This study investigated the influence of five days of moderate intensity aerobic exercise on the acquisition and consolidation of visual perceptual learning using a motion direction discrimination (MDD) task. The timing of exercise relative to learning was manipulated by administering exercise either before or after perceptual training. Within a matched-subjects design, twenty-seven healthy participants (n = 9 per group) completed five consecutive days of perceptual training on a MDD task under one of three interventions: no exercise, exercise before the MDD task, or exercise after the MDD task. MDD task accuracy improved in all groups over the five-day period, but there was a trend for impaired learning when exercise was performed before visual perceptual training. MDD task accuracy (mean ± SD) increased in exercise before by 4.5 ± 6.5%; exercise after by 11.8 ± 6.4%; and no exercise by 11.3 ± 7.2%. All intervention groups displayed similar MDD threshold reductions for the trained and untrained motion axes after training. These findings suggest that moderate daily exercise does not enhance the rate of visual perceptual learning for an MDD task or the transfer of learning to an untrained motion axis. Furthermore, exercise performed immediately prior to a visual perceptual learning task may impair learning. Further research with larger groups is required in order to better understand these effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stability and synchronization control of stochastic neural networks

CERN Document Server

Zhou, Wuneng; Zhou, Liuwei; Tong, Dongbing

2016-01-01

This book reports on the latest findings in the study of Stochastic Neural Networks (SNN). The book collects the novel model of the disturbance driven by Levy process, the research method of M-matrix, and the adaptive control method of the SNN in the context of stability and synchronization control. The book will be of interest to university researchers, graduate students in control science and engineering and neural networks who wish to learn the core principles, methods, algorithms and applications of SNN.

The Evolution of Frequency Distributions: Relating Regularization to Inductive Biases through Iterated Learning

Science.gov (United States)

Reali, Florencia; Griffiths, Thomas L.

2009-01-01

The regularization of linguistic structures by learners has played a key role in arguments for strong innate constraints on language acquisition, and has important implications for language evolution. However, relating the inductive biases of learners to regularization behavior in laboratory tasks can be challenging without a formal model. In this…

Multiview Hessian regularization for image annotation.

Science.gov (United States)

Liu, Weifeng; Tao, Dacheng

2013-07-01

The rapid development of computer hardware and Internet technology makes large scale data dependent models computationally tractable, and opens a bright avenue for annotating images through innovative machine learning algorithms. Semisupervised learning (SSL) therefore received intensive attention in recent years and was successfully deployed in image annotation. One representative work in SSL is Laplacian regularization (LR), which smoothes the conditional distribution for classification along the manifold encoded in the graph Laplacian, however, it is observed that LR biases the classification function toward a constant function that possibly results in poor generalization. In addition, LR is developed to handle uniformly distributed data (or single-view data), although instances or objects, such as images and videos, are usually represented by multiview features, such as color, shape, and texture. In this paper, we present multiview Hessian regularization (mHR) to address the above two problems in LR-based image annotation. In particular, mHR optimally combines multiple HR, each of which is obtained from a particular view of instances, and steers the classification function that varies linearly along the data manifold. We apply mHR to kernel least squares and support vector machines as two examples for image annotation. Extensive experiments on the PASCAL VOC'07 dataset validate the effectiveness of mHR by comparing it with baseline algorithms, including LR and HR.

Manifold Based Low-rank Regularization for Image Restoration and Semi-supervised Learning

OpenAIRE

Lai, Rongjie; Li, Jia

2017-01-01

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold structure has been considered in many data processing problems. Inspired by this concept, we consider a manifold based low-rank regularization as a linear approximation of manifold dimension. This regularization is less restricted than the global low-rank regu...

Regular classroom assessment as a means of enhancing Teacher ...

African Journals Online (AJOL)

This study was an action research which employed regular classroom tests to help students learn and understand some concepts in electricity and magnetism. The participants of the study were 35 Level 200 B.Ed. (Basic Education, JSS Option) pre-service science teachers of the University of Education, Winneba in the ...

Who Learns More? Cultural Differences in Implicit Sequence Learning

Science.gov (United States)

Fu, Qiufang; Dienes, Zoltan; Shang, Junchen; Fu, Xiaolan

2013-01-01

Background It is well documented that East Asians differ from Westerners in conscious perception and attention. However, few studies have explored cultural differences in unconscious processes such as implicit learning. Methodology/Principal Findings The global-local Navon letters were adopted in the serial reaction time (SRT) task, during which Chinese and British participants were instructed to respond to global or local letters, to investigate whether culture influences what people acquire in implicit sequence learning. Our results showed that from the beginning British expressed a greater local bias in perception than Chinese, confirming a cultural difference in perception. Further, over extended exposure, the Chinese learned the target regularity better than the British when the targets were global, indicating a global advantage for Chinese in implicit learning. Moreover, Chinese participants acquired greater unconscious knowledge of an irrelevant regularity than British participants, indicating that the Chinese were more sensitive to contextual regularities than the British. Conclusions/Significance The results suggest that cultural biases can profoundly influence both what people consciously perceive and unconsciously learn. PMID:23940773

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on genera...

Functional Abstraction of Stochastic Hybrid Systems

NARCIS (Netherlands)

Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.

2006-01-01

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways

Stochastic quantisation: theme and variation

International Nuclear Information System (INIS)

Klauder, J.R.; Kyoto Univ.

1987-01-01

The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)

Binary Stochastic Representations for Large Multi-class Classification

KAUST Repository

Gerald, Thomas

2017-10-23

Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top performance in this context, these approaches suffer of a high inference complexity, linear w.r.t. the number of categories. Different models based on the notion of binary codes have been proposed to overcome this limitation, achieving in a sublinear inference complexity. But they a priori need to decide which binary code to associate to which category before learning using more or less complex heuristics. We propose a new end-to-end model which aims at simultaneously learning to associate binary codes with categories, but also learning to map inputs to binary codes. This approach called Deep Stochastic Neural Codes (DSNC) keeps the sublinear inference complexity but do not need any a priori tuning. Experimental results on different datasets show the effectiveness of the approach w.r.t. baseline methods.

Selection of regularization parameter for l1-regularized damage detection

Science.gov (United States)

Hou, Rongrong; Xia, Yong; Bao, Yuequan; Zhou, Xiaoqing

2018-06-01

The l1 regularization technique has been developed for structural health monitoring and damage detection through employing the sparsity condition of structural damage. The regularization parameter, which controls the trade-off between data fidelity and solution size of the regularization problem, exerts a crucial effect on the solution. However, the l1 regularization problem has no closed-form solution, and the regularization parameter is usually selected by experience. This study proposes two strategies of selecting the regularization parameter for the l1-regularized damage detection problem. The first method utilizes the residual and solution norms of the optimization problem and ensures that they are both small. The other method is based on the discrepancy principle, which requires that the variance of the discrepancy between the calculated and measured responses is close to the variance of the measurement noise. The two methods are applied to a cantilever beam and a three-story frame. A range of the regularization parameter, rather than one single value, can be determined. When the regularization parameter in this range is selected, the damage can be accurately identified even for multiple damage scenarios. This range also indicates the sensitivity degree of the damage identification problem to the regularization parameter.

STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...

African Journals Online (AJOL)

eobe

STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.

Application of regularization technique in image super-resolution algorithm via sparse representation

Science.gov (United States)

Huang, De-tian; Huang, Wei-qin; Huang, Hui; Zheng, Li-xin

2017-11-01

To make use of the prior knowledge of the image more effectively and restore more details of the edges and structures, a novel sparse coding objective function is proposed by applying the principle of the non-local similarity and manifold learning on the basis of super-resolution algorithm via sparse representation. Firstly, the non-local similarity regularization term is constructed by using the similar image patches to preserve the edge information. Then, the manifold learning regularization term is constructed by utilizing the locally linear embedding approach to enhance the structural information. The experimental results validate that the proposed algorithm has a significant improvement compared with several super-resolution algorithms in terms of the subjective visual effect and objective evaluation indices.

Stochastic quantization and gravity

International Nuclear Information System (INIS)

Rumpf, H.

1984-01-01

We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)

Stochastic climate theory

NARCIS (Netherlands)

Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.

2017-01-01

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of

2–stage stochastic Runge–Kutta for stochastic delay differential equations

Energy Technology Data Exchange (ETDEWEB)

Rosli, Norhayati; Jusoh Awang, Rahimah [Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia); Bahar, Arifah; Yeak, S. H. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Learning Spaces

CERN Document Server

Falmagne, Jean-Claude

2011-01-01

Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of A

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

Science.gov (United States)

Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

2015-12-01

Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.

Space-time-modulated stochastic processes

Science.gov (United States)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Do basal Ganglia amplify willed action by stochastic resonance? A model.

Directory of Open Access Journals (Sweden)

V Srinivasa Chakravarthy

Full Text Available Basal ganglia are usually attributed a role in facilitating willed action, which is found to be impaired in Parkinson's disease, a pathology of basal ganglia. We hypothesize that basal ganglia possess the machinery to amplify will signals, presumably weak, by stochastic resonance. Recently we proposed a computational model of Parkinsonian reaching, in which the contributions from basal ganglia aid the motor cortex in learning to reach. The model was cast in reinforcement learning framework. We now show that the above basal ganglia computational model has all the ingredients of stochastic resonance process. In the proposed computational model, we consider the problem of moving an arm from a rest position to a target position: the two positions correspond to two extrema of the value function. A single kick (a half-wave of sinusoid, of sufficiently low amplitude given to the system in resting position, succeeds in taking the system to the target position, with high probability, only at a critical noise level. But for suboptimal noise levels, the model arm's movements resemble Parkinsonian movement symptoms like akinetic rigidity (low noise and dyskinesias (high noise.

Selecting protein families for environmental features based on manifold regularization.

Science.gov (United States)

Jiang, Xingpeng; Xu, Weiwei; Park, E K; Li, Guangrong

2014-06-01

Recently, statistics and machine learning have been developed to identify functional or taxonomic features of environmental features or physiological status. Important proteins (or other functional and taxonomic entities) to environmental features can be potentially used as biosensors. A major challenge is how the distribution of protein and gene functions embodies the adaption of microbial communities across environments and host habitats. In this paper, we propose a novel regularization method for linear regression to adapt the challenge. The approach is inspired by local linear embedding (LLE) and we call it a manifold-constrained regularization for linear regression (McRe). The novel regularization procedure also has potential to be used in solving other linear systems. We demonstrate the efficiency and the performance of the approach in both simulation and real data.

Elitism and Stochastic Dominance

OpenAIRE

Bazen, Stephen; Moyes, Patrick

2011-01-01

Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...

On Stochastic Dependence

Science.gov (United States)

Meyer, Joerg M.

2018-01-01

The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

Stochastic massless fields I: Integer spin

International Nuclear Information System (INIS)

Lim, S.C.

1981-04-01

Nelson's stochastic quantization scheme is applied to classical massless tensor potential in ''Coulomb'' gauge. The relationship between stochastic potential field in various gauges is discussed using the case of vector potential as an illustration. It is possible to identify the Euclidean tensor potential with the corresponding stochastic field in physical Minkowski space-time. Stochastic quantization of massless fields can also be carried out in terms of field strength tensors. An example of linearized stochastic gravitational field in vacuum is given. (author)

Stochastic processes inference theory

CERN Document Server

Rao, Malempati M

2014-01-01

This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.

Stochastic cooling

International Nuclear Information System (INIS)

Bisognano, J.; Leemann, C.

1982-03-01

Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Enhancement of ELM by Clustering Discrimination Manifold Regularization and Multiobjective FOA for Semisupervised Classification

OpenAIRE

Qing Ye; Hao Pan; Changhua Liu

2015-01-01

A novel semisupervised extreme learning machine (ELM) with clustering discrimination manifold regularization (CDMR) framework named CDMR-ELM is proposed for semisupervised classification. By using unsupervised fuzzy clustering method, CDMR framework integrates clustering discrimination of both labeled and unlabeled data with twinning constraints regularization. Aiming at further improving the classification accuracy and efficiency, a new multiobjective fruit fly optimization algorithm (MOFOA)...

Stochastic Analysis with Financial Applications

CERN Document Server

Kohatsu-Higa, Arturo; Sheu, Shuenn-Jyi

2011-01-01

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. This book also covers the areas of backward stochastic differential equations via the (non-li

Parameter discovery in stochastic biological models using simulated annealing and statistical model checking.

Science.gov (United States)

Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J

2014-01-01

Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.

Geometrical methods in learning theory

International Nuclear Information System (INIS)

Burdet, G.; Combe, Ph.; Nencka, H.

2001-01-01

The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

Energy Technology Data Exchange (ETDEWEB)

Yilmaz, Ergin, E-mail: erginyilmaz@yahoo.com [Department of Biomedical Engineering, Engineering Faculty, Bülent Ecevit University, 67100 Zonguldak (Turkey); Ozer, Mahmut [Department of Electrical and Electronics Engineering, Engineering Faculty, Bülent Ecevit University, 67100 Zonguldak (Turkey)

2013-08-01

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.

Stochastic Reachability Analysis of Hybrid Systems

CERN Document Server

Bujorianu, Luminita Manuela

2012-01-01

Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...

On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate

Directory of Open Access Journals (Sweden)

Jin Liang

2017-10-01

Full Text Available In this paper we study a corporate bond-pricing model with credit rating migration and astochastic interest rate. The volatility of bond price in the model strongly depends on potential creditrating migration and stochastic change of the interest rate. This new model improves the previousexisting models in which the interest rate is considered to be a constant. The existence, uniquenessand regularity of the solution for the model are established. Moreover, some properties includingthe smoothness of the free boundary are obtained. Furthermore, some numerical computations arepresented to illustrate the theoretical results.

Stochastic models of cellular circadian rhythms in plants help to understand the impact of noise on robustness and clock structure

Directory of Open Access Journals (Sweden)

Maria Luisa eGuerriero

2014-10-01

Full Text Available Rhythmic behavior is essential for plants; for example, daily (circadian rhythms control photosynthesis and seasonal rhythms regulate their life cycle. The core of the circadian clock is a genetic network that coordinates the expression of specific clock genes in a circadian rhythm reflecting the 24-hour day/night cycle.Circadian clocks exhibit stochastic noise due to the low copy numbers of clock genes and the consequent cell-to-cell variation: this intrinsic noise plays a major role in circadian clocks by inducing more robust oscillatory behavior. Another source of noise is the environment, which causes variation in temperature and light intensity: this extrinsic noise is part of the requirement for the structural complexity of clock networks.Advances in experimental techniques now permit single-cell measurements and the development of single-cell models. Here we present some modeling studies showing the importance of considering both types of noise in understanding how plants adapt to regular and irregular light variations. Stochastic models have proven useful for understanding the effect of regular variations. By contrast, the impact of irregular variations and the interaction of different noise sources are less studied.

C1,1 regularity for degenerate elliptic obstacle problems

Science.gov (United States)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

Regularization of the big bang singularity with random perturbations

Science.gov (United States)

Belbruno, Edward; Xue, BingKan

2018-03-01

We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.

Stochastic Estimation via Polynomial Chaos

Science.gov (United States)

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Rule-based learning of regular past tense in children with specific language impairment.

Science.gov (United States)

Smith-Lock, Karen M

2015-01-01

The treatment of children with specific language impairment was used as a means to investigate whether a single- or dual-mechanism theory best conceptualizes the acquisition of English past tense. The dual-mechanism theory proposes that regular English past-tense forms are produced via a rule-based process whereas past-tense forms of irregular verbs are stored in the lexicon. Single-mechanism theories propose that both regular and irregular past-tense verbs are stored in the lexicon. Five 5-year-olds with specific language impairment received treatment for regular past tense. The children were tested on regular past-tense production and third-person singular "s" twice before treatment and once after treatment, at eight-week intervals. Treatment consisted of one-hour play-based sessions, once weekly, for eight weeks. Crucially, treatment focused on different lexical items from those in the test. Each child demonstrated significant improvement on the untreated past-tense test items after treatment, but no improvement on the untreated third-person singular "s". Generalization to untreated past-tense verbs could not be attributed to a frequency effect or to phonological similarity of trained and tested items. It is argued that the results are consistent with a dual-mechanism theory of past-tense inflection.

Remarks on stochastic acceleration

International Nuclear Information System (INIS)

Graeff, P.

1982-12-01

Stochastic acceleration and turbulent diffusion are strong turbulence problems since no expansion parameter exists. Hence the problem of finding rigorous results is of major interest both for checking approximations and for reference models. Since we have found a way of constructing such models in the turbulent diffusion case the question of the extension to stochastic acceleration now arises. The paper offers some possibilities illustrated by the case of 'stochastic free fall' which may be particularly interesting in the context of linear response theory. (orig.)

Synthetic Computation: Chaos Computing, Logical Stochastic Resonance, and Adaptive Computing

Science.gov (United States)

Kia, Behnam; Murali, K.; Jahed Motlagh, Mohammad-Reza; Sinha, Sudeshna; Ditto, William L.

Nonlinearity and chaos can illustrate numerous behaviors and patterns, and one can select different patterns from this rich library of patterns. In this paper we focus on synthetic computing, a field that engineers and synthesizes nonlinear systems to obtain computation. We explain the importance of nonlinearity, and describe how nonlinear systems can be engineered to perform computation. More specifically, we provide an overview of chaos computing, a field that manually programs chaotic systems to build different types of digital functions. Also we briefly describe logical stochastic resonance (LSR), and then extend the approach of LSR to realize combinational digital logic systems via suitable concatenation of existing logical stochastic resonance blocks. Finally we demonstrate how a chaotic system can be engineered and mated with different machine learning techniques, such as artificial neural networks, random searching, and genetic algorithm, to design different autonomous systems that can adapt and respond to environmental conditions.

Stochastic parameterizing manifolds and non-Markovian reduced equations stochastic manifolds for nonlinear SPDEs II

CERN Document Server

Chekroun, Mickaël D; Wang, Shouhong

2015-01-01

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

Stochastic spin-one massive field

International Nuclear Information System (INIS)

Lim, S.C.

1984-01-01

Stochastic quantization schemes of Nelson and Parisi and Wu are applied to a spin-one massive field. Unlike the scalar case Nelson's stochastic spin-one massive field cannot be identified with the corresponding euclidean field even if the fourth component of the euclidean coordinate is taken as equal to the real physical time. In the Parisi-Wu quantization scheme the stochastic Proca vector field has a similar property as the scalar field; which has an asymptotically stationary part and a transient part. The large equal-time limit of the expectation values of the stochastic Proca field are equal to the expectation values of the corresponding euclidean field. In the Stueckelberg formalism the Parisi-Wu scheme gives rise to a stochastic vector field which differs from the massless gauge field in that the gauge cannot be fixed by the choice of boundary condition. (orig.)

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)

2012-12-15

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

International Nuclear Information System (INIS)

Hosking, John Joseph Absalom

2012-01-01

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

The Role of Personality in a Regular Cognitive Monitoring Program.

Science.gov (United States)

Sadeq, Nasreen A; Valdes, Elise G; Harrison Bush, Aryn L; Andel, Ross

2018-02-20

This study examines the role of personality in cognitive performance, adherence, and satisfaction with regular cognitive self-monitoring. One hundred fifty-seven cognitively healthy older adults, age 55+, completed the 44-item Big-Five Inventory and were subsequently engaged in online monthly cognitive monitoring using the Cogstate Brief Battery for up to 35 months (M=14 mo, SD=7 mo). The test measures speed and accuracy in reaction time, visual learning, and working memory tasks. Neuroticism, although not related to cognitive performance overall (P>0.05), was related to a greater increase in accuracy (estimate=0.07, P=0.04) and speed (estimate=-0.09, P=0.03) on One Card Learning. Greater conscientiousness was related to faster overall speed on Detection (estimate=-1.62, P=0.02) and a significant rate of improvement in speed on One Card Learning (estimate=-0.10, Pconscientiousness were observed. Participants volunteering for regular cognitive monitoring may be quite uniform in terms of personality traits, with personality traits playing a relatively minor role in adherence and satisfaction. The more neurotic may exhibit better accuracy and improve in speed with time, whereas the more conscientious may perform faster overall and improve in speed on some tasks, but the effects appear small.

Stochastic TDHF and the Boltzman-Langevin equation

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations

Sparsity-regularized HMAX for visual recognition.

Directory of Open Access Journals (Sweden)

Xiaolin Hu

Full Text Available About ten years ago, HMAX was proposed as a simple and biologically feasible model for object recognition, based on how the visual cortex processes information. However, the model does not encompass sparse firing, which is a hallmark of neurons at all stages of the visual pathway. The current paper presents an improved model, called sparse HMAX, which integrates sparse firing. This model is able to learn higher-level features of objects on unlabeled training images. Unlike most other deep learning models that explicitly address global structure of images in every layer, sparse HMAX addresses local to global structure gradually along the hierarchy by applying patch-based learning to the output of the previous layer. As a consequence, the learning method can be standard sparse coding (SSC or independent component analysis (ICA, two techniques deeply rooted in neuroscience. What makes SSC and ICA applicable at higher levels is the introduction of linear higher-order statistical regularities by max pooling. After training, high-level units display sparse, invariant selectivity for particular individuals or for image categories like those observed in human inferior temporal cortex (ITC and medial temporal lobe (MTL. Finally, on an image classification benchmark, sparse HMAX outperforms the original HMAX by a large margin, suggesting its great potential for computer vision.

Adaptive Urban Stormwater Management Using a Two-stage Stochastic Optimization Model

Science.gov (United States)

Hung, F.; Hobbs, B. F.; McGarity, A. E.

2014-12-01

In many older cities, stormwater results in combined sewer overflows (CSOs) and consequent water quality impairments. Because of the expense of traditional approaches for controlling CSOs, cities are considering the use of green infrastructure (GI) to reduce runoff and pollutants. Examples of GI include tree trenches, rain gardens, green roofs, and rain barrels. However, the cost and effectiveness of GI are uncertain, especially at the watershed scale. We present a two-stage stochastic extension of the Stormwater Investment Strategy Evaluation (StormWISE) model (A. McGarity, JWRPM, 2012, 111-24) to explicitly model and optimize these uncertainties in an adaptive management framework. A two-stage model represents the immediate commitment of resources ("here & now") followed by later investment and adaptation decisions ("wait & see"). A case study is presented for Philadelphia, which intends to extensively deploy GI over the next two decades (PWD, "Green City, Clean Water - Implementation and Adaptive Management Plan," 2011). After first-stage decisions are made, the model updates the stochastic objective and constraints (learning). We model two types of "learning" about GI cost and performance. One assumes that learning occurs over time, is automatic, and does not depend on what has been done in stage one (basic model). The other considers learning resulting from active experimentation and learning-by-doing (advanced model). Both require expert probability elicitations, and learning from research and monitoring is modelled by Bayesian updating (as in S. Jacobi et al., JWRPM, 2013, 534-43). The model allocates limited financial resources to GI investments over time to achieve multiple objectives with a given reliability. Objectives include minimizing construction and O&M costs; achieving nutrient, sediment, and runoff volume targets; and community concerns, such as aesthetics, CO2 emissions, heat islands, and recreational values. CVaR (Conditional Value at Risk) and

Stochastic resonance in a stochastic bistable system with additive noises and square–wave signal

International Nuclear Information System (INIS)

Feng, Guo; Xiang-Dong, Luo; Shao-Fu, Li; Yu-Rong, Zhou

2010-01-01

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated. (general)

On the MSE Performance and Optimization of Regularized Problems

KAUST Repository

Alrashdi, Ayed

2016-11-01

The amount of data that has been measured, transmitted/received, and stored in the recent years has dramatically increased. So, today, we are in the world of big data. Fortunately, in many applications, we can take advantages of possible structures and patterns in the data to overcome the curse of dimensionality. The most well known structures include sparsity, low-rankness, block sparsity. This includes a wide range of applications such as machine learning, medical imaging, signal processing, social networks and computer vision. This also led to a specific interest in recovering signals from noisy compressed measurements (Compressed Sensing (CS) problem). Such problems are generally ill-posed unless the signal is structured. The structure can be captured by a regularizer function. This gives rise to a potential interest in regularized inverse problems, where the process of reconstructing the structured signal can be modeled as a regularized problem. This thesis particularly focuses on finding the optimal regularization parameter for such problems, such as ridge regression, LASSO, square-root LASSO and low-rank Generalized LASSO. Our goal is to optimally tune the regularizer to minimize the mean-squared error (MSE) of the solution when the noise variance or structure parameters are unknown. The analysis is based on the framework of the Convex Gaussian Min-max Theorem (CGMT) that has been used recently to precisely predict performance errors.

Stochastic quantization of Proca field

International Nuclear Information System (INIS)

Lim, S.C.

1981-03-01

We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)

Stochastic optimization methods

CERN Document Server

Marti, Kurt

2005-01-01

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.

Bayesian estimation of regularization and atlas building in diffeomorphic image registration.

Science.gov (United States)

Zhang, Miaomiao; Singh, Nikhil; Fletcher, P Thomas

2013-01-01

This paper presents a generative Bayesian model for diffeomorphic image registration and atlas building. We develop an atlas estimation procedure that simultaneously estimates the parameters controlling the smoothness of the diffeomorphic transformations. To achieve this, we introduce a Monte Carlo Expectation Maximization algorithm, where the expectation step is approximated via Hamiltonian Monte Carlo sampling on the manifold of diffeomorphisms. An added benefit of this stochastic approach is that it can successfully solve difficult registration problems involving large deformations, where direct geodesic optimization fails. Using synthetic data generated from the forward model with known parameters, we demonstrate the ability of our model to successfully recover the atlas and regularization parameters. We also demonstrate the effectiveness of the proposed method in the atlas estimation problem for 3D brain images.

Phenomenology of stochastic exponential growth

Science.gov (United States)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Characteristic effects of stochastic oscillatory forcing on neural firing: analytical theory and comparison to paddlefish electroreceptor data.

Science.gov (United States)

Bauermeister, Christoph; Schwalger, Tilo; Russell, David F; Neiman, Alexander B; Lindner, Benjamin

2013-01-01

Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this report. We consider a perfect integrate-and-fire neuron that is stimulated by a constant base current (to drive regular spontaneous firing), along with Gaussian narrow-band noise (a simple example of stochastic oscillations), and a broadband noise. We derive expressions for the nth-order interval distribution, its variance, and the serial correlation coefficients of the interspike intervals (ISIs) and confirm these analytical results by computer simulations. The theory is then applied to experimental data from electroreceptors of paddlefish, which have two distinct types of internal noisy oscillators, one forcing the other. The theory provides an analytical description of their afferent spiking statistics during spontaneous firing, and replicates a pronounced dependence of ISI serial correlation coefficients on the relative frequency of the driving oscillations, and furthermore allows extraction of certain parameters of the intrinsic oscillators embedded in these electroreceptors.

Thermodynamic efficiency of learning a rule in neural networks

Science.gov (United States)

Goldt, Sebastian; Seifert, Udo

2017-11-01

Biological systems have to build models from their sensory input data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a binary classification rule for these inputs from examples provided by a teacher. We analyse the ability of the network to apply the rule to new inputs, that is to generalise from past experience. Using stochastic thermodynamics, we show that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning. This allows us to introduce a thermodynamic efficiency of learning. We analytically compute the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit. In particular, we analyse three popular learning algorithms, namely Hebbian, Perceptron and AdaTron learning. Our work extends the methods of stochastic thermodynamics to a new type of learning problem and might form a suitable basis for investigating the thermodynamics of decision-making.

Learning and anticipation in online dynamic optimization with evolutionary algorithms: The stochastic case

NARCIS (Netherlands)

P.A.N. Bosman (Peter); J.A. La Poutré (Han); D. Thierens (Dirk)

2007-01-01

htmlabstractThe focus of this paper is on how to design evolutionary algorithms (EAs) for solving stochastic dynamic optimization problems online, i.e. as time goes by. For a proper design, the EA must not only be capable of tracking shifting optima, it must also take into account the future

Optimal Control for Stochastic Delay Evolution Equations

Energy Technology Data Exchange (ETDEWEB)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

Total variation regularization for fMRI-based prediction of behavior

Science.gov (United States)

Michel, Vincent; Gramfort, Alexandre; Varoquaux, Gaël; Eger, Evelyn; Thirion, Bertrand

2011-01-01

While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or spontaneous neuronal activity, are classically analyzed in a mass-univariate procedure yielding statistical parametric maps. This analysis framework disregards some important principles of brain organization: population coding, distributed and overlapping representations. Multivariate pattern analysis, i.e., the prediction of behavioural variables from brain activation patterns better captures this structure. To cope with the high dimensionality of the data, the learning method has to be regularized. However, the spatial structure of the image is not taken into account in standard regularization methods, so that the extracted features are often hard to interpret. More informative and interpretable results can be obtained with the ℓ1 norm of the image gradient, a.k.a. its Total Variation (TV), as regularization. We apply for the first time this method to fMRI data, and show that TV regularization is well suited to the purpose of brain mapping while being a powerful tool for brain decoding. Moreover, this article presents the first use of TV regularization for classification. PMID:21317080

Learning Orthographic Structure With Sequential Generative Neural Networks.

Science.gov (United States)

Testolin, Alberto; Stoianov, Ivilin; Sperduti, Alessandro; Zorzi, Marco

2016-04-01

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine (RBM), a stochastic recurrent neural network that extracts high-order structure from sensory data through unsupervised generative learning and can encode contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high-quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non-connectionist probabilistic models (n-grams and hidden Markov models). We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain. Copyright © 2015 Cognitive Science Society, Inc.

Fast distributed strategic learning for global optima in queueing access games

KAUST Repository

Tembine, Hamidou

2014-08-24

In this paper we examine combined fully distributed payoff and strategy learning (CODIPAS) in a queue-aware access game over a graph. The classical strategic learning analysis relies on vanishing or small learning rate and uses stochastic approximation tool to derive steady states and invariant sets of the underlying learning process. Here, the stochastic approximation framework does not apply due to non-vanishing learning rate. We propose a direct proof of convergence of the process. Interestingly, the convergence time to one of the global optima is almost surely finite and we explicitly characterize the convergence time. We show that pursuit-based CODIPAS learning is much faster than the classical learning algorithms in games. We extend the methodology to coalitional learning and proves a very fast formation of coalitions for queue-aware access games where the action space is dynamically changing depending on the location of the user over a graph.

Introduction to stochastic calculus

CERN Document Server

Karandikar, Rajeeva L

2018-01-01

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models

International Nuclear Information System (INIS)

Eyink, Gregory L.

2009-01-01

We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.

Brownian motion and stochastic calculus

CERN Document Server

Karatzas, Ioannis

1998-01-01

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

Variance decomposition in stochastic simulators.

Science.gov (United States)

Le Maître, O P; Knio, O M; Moraes, A

2015-06-28

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Variance decomposition in stochastic simulators

Science.gov (United States)

Le Maître, O. P.; Knio, O. M.; Moraes, A.

2015-06-01

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Variance decomposition in stochastic simulators

Energy Technology Data Exchange (ETDEWEB)

Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

2015-06-28

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Variance decomposition in stochastic simulators

KAUST Repository

Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro

2015-01-01

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Analytic continuation of quantum Monte Carlo data. Stochastic sampling method

Energy Technology Data Exchange (ETDEWEB)

Ghanem, Khaldoon; Koch, Erik [Institute for Advanced Simulation, Forschungszentrum Juelich, 52425 Juelich (Germany)

2016-07-01

We apply Bayesian inference to the analytic continuation of quantum Monte Carlo (QMC) data from the imaginary axis to the real axis. Demanding a proper functional Bayesian formulation of any analytic continuation method leads naturally to the stochastic sampling method (StochS) as the Bayesian method with the simplest prior, while it excludes the maximum entropy method and Tikhonov regularization. We present a new efficient algorithm for performing StochS that reduces computational times by orders of magnitude in comparison to earlier StochS methods. We apply the new algorithm to a wide variety of typical test cases: spectral functions and susceptibilities from DMFT and lattice QMC calculations. Results show that StochS performs well and is able to resolve sharp features in the spectrum.

Sleep Spindles in the Right Hemisphere Support Awareness of Regularities and Reflect Pre-Sleep Activations.

Science.gov (United States)

Yordanova, Juliana; Kolev, Vasil; Bruns, Eike; Kirov, Roumen; Verleger, Rolf

2017-11-01

The present study explored the sleep mechanisms which may support awareness of hidden regularities. Before sleep, 53 participants learned implicitly a lateralized variant of the serial response-time task in order to localize sensorimotor encoding either in the left or right hemisphere and induce implicit regularity representations. Electroencephalographic (EEG) activity was recorded at multiple electrodes during both task performance and sleep, searching for lateralized traces of the preceding activity during learning. Sleep EEG analysis focused on region-specific slow (9-12 Hz) and fast (13-16 Hz) sleep spindles during nonrapid eye movement sleep. Fast spindle activity at those motor regions that were activated during learning increased with the amount of postsleep awareness. Independently of side of learning, spindle activity at right frontal and fronto-central regions was involved: there, fast spindles increased with the transformation of sequence knowledge from implicit before sleep to explicit after sleep, and slow spindles correlated with individual abilities of gaining awareness. These local modulations of sleep spindles corresponded to regions with greater presleep activation in participants with postsleep explicit knowledge. Sleep spindle mechanisms are related to explicit awareness (1) by tracing the activation of motor cortical and right-hemisphere regions which had stronger involvement already during learning and (2) by recruitment of individually consolidated processing modules in the right hemisphere. The integration of different sleep spindle mechanisms with functional states during wake collectively supports the gain of awareness of previously experienced regularities, with a special role for the right hemisphere. © Sleep Research Society 2017. Published by Oxford University Press [on behalf of the Sleep Research Society].

Fast distributed strategic learning for global optima in queueing access games

KAUST Repository

Tembine, Hamidou

2014-01-01

In this paper we examine combined fully distributed payoff and strategy learning (CODIPAS) in a queue-aware access game over a graph. The classical strategic learning analysis relies on vanishing or small learning rate and uses stochastic

An introduction to probability and stochastic processes

CERN Document Server

Melsa, James L

2013-01-01

Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

Research on nonlinear stochastic dynamical price model

International Nuclear Information System (INIS)

Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

2008-01-01

In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

Stochastic Systems Uncertainty Quantification and Propagation

CERN Document Server

Grigoriu, Mircea

2012-01-01

Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables an...

Stochastic-field cavitation model

International Nuclear Information System (INIS)

Dumond, J.; Magagnato, F.; Class, A.

2013-01-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations

Stochastic-field cavitation model

Science.gov (United States)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

Energy Technology Data Exchange (ETDEWEB)

Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

Convex nonnegative matrix factorization with manifold regularization.

Science.gov (United States)

Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong

2015-03-01

Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Learning and coding in biological neural networks

Science.gov (United States)

Fiete, Ila Rani

How can large groups of neurons that locally modify their activities learn to collectively perform a desired task? Do studies of learning in small networks tell us anything about learning in the fantastically large collection of neurons that make up a vertebrate brain? What factors do neurons optimize by encoding sensory inputs or motor commands in the way they do? In this thesis I present a collection of four theoretical works: each of the projects was motivated by specific constraints and complexities of biological neural networks, as revealed by experimental studies; together, they aim to partially address some of the central questions of neuroscience posed above. We first study the role of sparse neural activity, as seen in the coding of sequential commands in a premotor area responsible for birdsong. We show that the sparse coding of temporal sequences in the songbird brain can, in a network where the feedforward plastic weights must translate the sparse sequential code into a time-varying muscle code, facilitate learning by minimizing synaptic interference. Next, we propose a biologically plausible synaptic plasticity rule that can perform goal-directed learning in recurrent networks of voltage-based spiking neurons that interact through conductances. Learning is based on the correlation of noisy local activity with a global reward signal; we prove that this rule performs stochastic gradient ascent on the reward. Thus, if the reward signal quantifies network performance on some desired task, the plasticity rule provably drives goal-directed learning in the network. To assess the convergence properties of the learning rule, we compare it with a known example of learning in the brain. Song-learning in finches is a clear example of a learned behavior, with detailed available neurophysiological data. With our learning rule, we train an anatomically accurate model birdsong network that drives a sound source to mimic an actual zebrafinch song. Simulation and

A non-linear dimension reduction methodology for generating data-driven stochastic input models

Science.gov (United States)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low

A non-linear dimension reduction methodology for generating data-driven stochastic input models

International Nuclear Information System (INIS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-01-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.

Learning Perl Student Workbook

CERN Document Server

foy, brian

2012-01-01

This is an ebook-only workbook to accompany the 6th Edition of Learning Perl ("the Llama"). If you're just getting started with Perl, this is the book you want-whether you're a programmer, system administrator, or web hacker. This 6th edition of Learning Perl covers recent changes to the language up to version 5.14. Exercises are presented in the first half of the workbook, with the answers in the second. Topics include: Scalar DataLists and ArraysSubroutinesInput and OutputHashesIn the World of Regular ExpressionsMatching with Regular ExpressionsProcessing Text with Regular Expressions10.

Stochastic volatility of volatility in continuous time

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Veraart, Almut

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility...... of volatility can be defined both non-parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated...

Quantum stochastic calculus associated with quadratic quantum noises

International Nuclear Information System (INIS)

Ji, Un Cig; Sinha, Kalyan B.

2016-01-01

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus

Quantum stochastic calculus associated with quadratic quantum noises

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

Set-Valued Stochastic Lebesque Integral and Representation Theorems

Directory of Open Access Journals (Sweden)

Jungang Li

2008-06-01

Full Text Available In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued stochastic process with respect to the time t . Finally we shall prove the presentation theorem of set-valued stochastic integral and dis- cuss further properties that will be useful to study set-valued stochastic differential equations with their applications.

Instantaneous stochastic perturbation theory

International Nuclear Information System (INIS)

Lüscher, Martin

2015-01-01

A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

A retrodictive stochastic simulation algorithm

International Nuclear Information System (INIS)

Vaughan, T.G.; Drummond, P.D.; Drummond, A.J.

2010-01-01

In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.

Stochastic processes and quantum theory

International Nuclear Information System (INIS)

Klauder, J.R.

1975-01-01

The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)

Stochastic Still Water Response Model

DEFF Research Database (Denmark)

Friis-Hansen, Peter; Ditlevsen, Ove Dalager

2002-01-01

In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

Stochastic quantization and topological theories

International Nuclear Information System (INIS)

Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.

1992-01-01

In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones

Stochastic quantization of Einstein gravity

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''

Momentum Maps and Stochastic Clebsch Action Principles

Science.gov (United States)

Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

2018-01-01

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

A data driven nonlinear stochastic model for blood glucose dynamics.

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Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Stochastic Gabor reflectivity and acoustic impedance inversion

Science.gov (United States)

Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

2018-02-01

, obtaining bias could help the method to estimate reliable AI. To justify the effect of random noise on deterministic and stochastic inversion results, a stationary noisy trace with signal-to-noise ratio equal to 2 was used. The results highlight the inability of deterministic inversion in dealing with a noisy data set even using a high number of regularization parameters. Also, despite the low level of signal, stochastic Gabor inversion not only can estimate correctly the wavelet’s properties but also, because of bias from well logs, the inversion result is very close to the real AI. Comparing deterministic and introduced inversion results on a real data set shows that low resolution results, especially in the deeper parts of seismic sections using deterministic inversion, creates significant reliability problems for seismic prospects, but this pitfall is solved completely using stochastic Gabor inversion. The estimated AI using Gabor inversion in the time domain is much better and faster than general Gabor inversion in the frequency domain. This is due to the extra number of windows required to analyze the time-frequency information and also the amount of temporal increment between windows. In contrast, stochastic Gabor inversion can estimate trustable physical properties close to the real characteristics. Applying to a real data set could give an ability to detect the direction of volcanic intrusion and the ability of lithology distribution delineation along the fan. Comparing the inversion results highlights the efficiency of stochastic Gabor inversion to delineate lateral lithology changes because of the improved frequency content and zero phasing of the final inversion volume.

Comments on the use of stochastic processes in the field of the ionizing radiations

International Nuclear Information System (INIS)

Alvarez Romero, Jose T.

2008-01-01

. Although models exist for the former one with stochastic processes such as birth-death, Poisson, two state or mixed states methods (Tan 1991), the conventional literature in radiobiology does not go beyond traditional target models of the Poisson or exponential type. Such approaches are dealt with by Rossi, Zaider, Goodhead, etc. in microdosimetry and radiobiology. Finally, in radiation protection the dose-effect projection models which back-up the recommendations of ICRP or from BEIR, probability functions, projection of regression time dependent models appear, buy very little, if any, is mentioned about their properties from the point of view of stochastic processes. Summing up, very little has been said about the nature of the stochastic background describing physical, chemical, biological and risk phenomena which are present in the field of ionizing radiations. In short, it would be nice to learn if there are processes such as: Gauss, Markov, branching, birth-death, Weiner, Poisson, stationary state methods or other ones to deal with these questions and further, to clarify the mathematical conditions they satisfy together with their significance and phenomenological consequences. (author)

Stochastic biomathematical models with applications to neuronal modeling

CERN Document Server

Batzel, Jerry; Ditlevsen, Susanne

2013-01-01

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

Distance-regular graphs

NARCIS (Netherlands)

van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

2016-01-01

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

Introduction to stochastic dynamic programming

CERN Document Server

Ross, Sheldon M; Lukacs, E

1983-01-01

Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

BRST stochastic quantization

International Nuclear Information System (INIS)

Hueffel, H.

1990-01-01

After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)

Stochastic quantum gravity

International Nuclear Information System (INIS)

Rumpf, H.

1987-01-01

We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)

Stochastic models, estimation, and control

CERN Document Server

Maybeck, Peter S

1982-01-01

This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

Model reduction method using variable-separation for stochastic saddle point problems

Science.gov (United States)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.

Regular expressions cookbook

CERN Document Server

Goyvaerts, Jan

2009-01-01

This cookbook provides more than 100 recipes to help you crunch data and manipulate text with regular expressions. Every programmer can find uses for regular expressions, but their power doesn't come worry-free. Even seasoned users often suffer from poor performance, false positives, false negatives, or perplexing bugs. Regular Expressions Cookbook offers step-by-step instructions for some of the most common tasks involving this tool, with recipes for C#, Java, JavaScript, Perl, PHP, Python, Ruby, and VB.NET. With this book, you will: Understand the basics of regular expressions through a

Perbedaan Motivasi Belajar, Mutu Keterampilan Belajar, dan Self Regulated Learning Siswa Kelas Diklat dan Siswa Kelas Reguler

Directory of Open Access Journals (Sweden)

Hafiz Hidayat

2016-03-01

Full Text Available This research was conducted as there was a difference between learning achievement of the students in regular class and in training class. Learning motivation, learning skill quality and self regulated learning are factors assumed to affect the students’ learning achievement. This research was intended to: (1 reveal the difference between learning motivation of the students in regular class and in training class, (2 the difference between learning skill quality of the students in regular class and in training class, and (3 self regulated learning of the students in regular class and in training class.This research applied descriptive comparative method. The population of the research was 312 students in class XI of SMA N 5 Padang. By using purposive sampling technique and simple random sampling technique, 65 students were chosen as the sample. The instrument of the research were learning motivation questionnaire (the reliability was 0.950, self regulated learning questionnaire (the reliability was 0.817, and AUM PTSDL Format SLTA (the reliability was 0.76. The data gathered then were analyzed by using Multivariate Analysis of Variance (MANOVA.The research findings indicated that: (1 learning motivation of the students both in training class and in regular class at SMA N 5 Padang was in high category, (2 in which significant difference learning motivation of the students in regular class was higher than that of students in training class, (3 the quality of students' learning skills training classes as very bad and regular classroom students classified as not good at SMA N 5 Padang, (4 there was a significant difference between learning skill quality of the students in regular class and in training class in which learning skill quality of the regular class was higher than that of the students in training class, and (5 students self regulated learning training class and regular class in high at SMA N 5 Padang is category good, (6 there were no

Stochastic theories of quantum mechanics

International Nuclear Information System (INIS)

De la Pena, L.; Cetto, A.M.

1991-01-01

The material of this article is organized into five sections. In Sect. I the basic characteristics of quantum systems are briefly discussed, with emphasis on their stochastic properties. In Sect. II a version of stochastic quantum mechanics is presented, to conclude that the quantum formalism admits an interpretation in terms of stochastic processes. In Sect. III the elements of stochastic electrodynamics are described, and its possibilities and limitations as a fundamental theory of quantum systems are discussed. Section IV contains a recent reformulation that overcomes the limitations of the theory discussed in the foregoing section. Finally, in Sect. V the theorems of EPR, Von Neumann and Bell are discussed briefly. The material is pedagogically presented and includes an ample list of references, but the details of the derivations are generally omitted. (Author)

Amygdala and ventral striatum make distinct contributions to reinforcement learning

Science.gov (United States)

Costa, Vincent D.; Monte, Olga Dal; Lucas, Daniel R.; Murray, Elisabeth A.; Averbeck, Bruno B.

2016-01-01

Summary Reinforcement learning (RL) theories posit that dopaminergic signals are integrated within the striatum to associate choices with outcomes. Often overlooked is that the amygdala also receives dopaminergic input and is involved in Pavlovian processes that influence choice behavior. To determine the relative contributions of the ventral striatum (VS) and amygdala to appetitive RL we tested rhesus macaques with VS or amygdala lesions on deterministic and stochastic versions of a two-arm bandit reversal learning task. When learning was characterized with a RL model relative to controls, amygdala lesions caused general decreases in learning from positive feedback and choice consistency. By comparison, VS lesions only affected learning in the stochastic task. Moreover, the VS lesions hastened the monkeys’ choice reaction times, which emphasized a speed-accuracy tradeoff that accounted for errors in deterministic learning. These results update standard accounts of RL by emphasizing distinct contributions of the amygdala and VS to RL. PMID:27720488

A heterogeneous stochastic FEM framework for elliptic PDEs

International Nuclear Information System (INIS)

Hou, Thomas Y.; Liu, Pengfei

2015-01-01

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Identification of a Discontinuous Parameter in Stochastic Parabolic Systems

International Nuclear Information System (INIS)

Aihara, S. I.

1998-01-01

The purpose of this paper is to study the identification problem for a spatially varying discontinuous parameter in stochastic diffusion equations. The consistency property of the maximum likelihood estimate (M.L.E.) and a generating algorithm for M.L.E. have been explored under the condition that the unknown parameter is in a sufficiently regular space with respect to spatial variables. In order to prove the consistency property of the M.L.E. for a discontinuous diffusion coefficient, we use the method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions. An iterative algorithm for generating the M.L.E. is also proposed with two numerical examples

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-01-01

to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

Dynamical and hamiltonian dilations of stochastic processes

International Nuclear Information System (INIS)

Baumgartner, B.; Gruemm, H.-R.

1982-01-01

This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)

LL-regular grammars

NARCIS (Netherlands)

Nijholt, Antinus

1980-01-01

Culik II and Cogen introduced the class of LR-regular grammars, an extension of the LR(k) grammars. In this paper we consider an analogous extension of the LL(k) grammars called the LL-regular grammars. The relation of this class of grammars to other classes of grammars will be shown. Any LL-regular

Professional Learning through Everyday Work: How Finance Professionals Self-Regulate Their Learning

Science.gov (United States)

Littlejohn, Allison; Milligan, Colin; Fontana, Rosa Pia; Margaryan, Anoush

2016-01-01

Professional learning is a critical component of ongoing improvement and innovation and the adoption of new practices in the workplace. Professional learning is often achieved through learning embedded in everyday work tasks. However, little is known about how professionals self-regulate their learning through regular work activities. This paper…

A multispin algorithm for the Kob-Andersen stochastic dynamics on regular lattices

Science.gov (United States)

Boccagna, Roberto

2017-07-01

The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)]; after defining the Markovian dynamics as in [W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993)] as well as the related interesting observables, we extend it to the more general framework of random regular graphs, listing at the same time some known analytical results [C. Toninelli, G. Biroli, D.S. Fisher, J. Stat. Phys. 120, 167 (2005)]. The purpose of this work is a dual one; firstly, we describe how bitwise operators can be used to build up the algorithm by carefully exploiting the way data are stored on a computer. Since it was first introduced [M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D 20, 1915 (1979); C. Rebbi, R.H. Swendsen, Phys. Rev. D 21, 4094 (1980)], this technique has been widely used to perform Monte Carlo simulations for Ising and Potts spin systems; however, it can be successfully adapted to more complex systems in which microscopic parameters may assume boolean values. Secondly, we introduce a random graph in which a characteristic parameter allows to tune the possible transition point. A consistent part is devoted to listing the numerical results obtained by running numerical simulations.

Stochastic calibration and learning in nonstationary hydroeconomic models

Science.gov (United States)

Maneta, M. P.; Howitt, R.

2014-05-01

Concern about water scarcity and adverse climate events over agricultural regions has motivated a number of efforts to develop operational integrated hydroeconomic models to guide adaptation and optimal use of water. Once calibrated, these models are used for water management and analysis assuming they remain valid under future conditions. In this paper, we present and demonstrate a methodology that permits the recursive calibration of economic models of agricultural production from noisy but frequently available data. We use a standard economic calibration approach, namely positive mathematical programming, integrated in a data assimilation algorithm based on the ensemble Kalman filter equations to identify the economic model parameters. A moving average kernel ensures that new and past information on agricultural activity are blended during the calibration process, avoiding loss of information and overcalibration for the conditions of a single year. A regularization constraint akin to the standard Tikhonov regularization is included in the filter to ensure its stability even in the presence of parameters with low sensitivity to observations. The results show that the implementation of the PMP methodology within a data assimilation framework based on the enKF equations is an effective method to calibrate models of agricultural production even with noisy information. The recursive nature of the method incorporates new information as an added value to the known previous observations of agricultural activity without the need to store historical information. The robustness of the method opens the door to the use of new remote sensing algorithms for operational water management.

Statistical learning in social action contexts.

Science.gov (United States)

Monroy, Claire; Meyer, Marlene; Gerson, Sarah; Hunnius, Sabine

2017-01-01

Sensitivity to the regularities and structure contained within sequential, goal-directed actions is an important building block for generating expectations about the actions we observe. Until now, research on statistical learning for actions has solely focused on individual action sequences, but many actions in daily life involve multiple actors in various interaction contexts. The current study is the first to investigate the role of statistical learning in tracking regularities between actions performed by different actors, and whether the social context characterizing their interaction influences learning. That is, are observers more likely to track regularities across actors if they are perceived as acting jointly as opposed to in parallel? We tested adults and toddlers to explore whether social context guides statistical learning and-if so-whether it does so from early in development. In a between-subjects eye-tracking experiment, participants were primed with a social context cue between two actors who either shared a goal of playing together ('Joint' condition) or stated the intention to act alone ('Parallel' condition). In subsequent videos, the actors performed sequential actions in which, for certain action pairs, the first actor's action reliably predicted the second actor's action. We analyzed predictive eye movements to upcoming actions as a measure of learning, and found that both adults and toddlers learned the statistical regularities across actors when their actions caused an effect. Further, adults with high statistical learning performance were sensitive to social context: those who observed actors with a shared goal were more likely to correctly predict upcoming actions. In contrast, there was no effect of social context in the toddler group, regardless of learning performance. These findings shed light on how adults and toddlers perceive statistical regularities across actors depending on the nature of the observed social situation and the

Transport in Stochastic Media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.; Thieberger, R.

1998-01-01

Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption

Stochastic Stability of Endogenous Growth: Theory and Applications

OpenAIRE

Boucekkine, Raouf; Pintus, Patrick; Zou, Benteng

2015-01-01

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differen- tial equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It’s shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncerta...

Stochastic models: theory and simulation.

Energy Technology Data Exchange (ETDEWEB)

Field, Richard V., Jr.

2008-03-01

Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

Stochastic diffusion models for substitutable technological innovations

NARCIS (Netherlands)

Wang, L.; Hu, B.; Yu, X.

2004-01-01

Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the

Informative sensor selection and learning for prediction of lower limb kinematics using generative stochastic neural networks.

Science.gov (United States)

Eunsuk Chong; Taejin Choi; Hyungmin Kim; Seung-Jong Kim; Yoha Hwang; Jong Min Lee

2017-07-01

We propose a novel approach of selecting useful input sensors as well as learning a mathematical model for predicting lower limb joint kinematics. We applied a feature selection method based on the mutual information called the variational information maximization, which has been reported as the state-of-the-art work among information based feature selection methods. The main difficulty in applying the method is estimating reliable probability density of input and output data, especially when the data are high dimensional and real-valued. We addressed this problem by applying a generative stochastic neural network called the restricted Boltzmann machine, through which we could perform sampling based probability estimation. The mutual informations between inputs and outputs are evaluated in each backward sensor elimination step, and the least informative sensor is removed with its network connections. The entire network is fine-tuned by maximizing conditional likelihood in each step. Experimental results are shown for 4 healthy subjects walking with various speeds, recording 64 sensor measurements including electromyogram, acceleration, and foot-pressure sensors attached on both lower limbs for predicting hip and knee joint angles. For test set of walking with arbitrary speed, our results show that our suggested method can select informative sensors while maintaining a good prediction accuracy.

Stochasticity in the Josephson map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.

1996-04-01

The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)

Expected utility and catastrophic risk in a stochastic economy-climate model

Energy Technology Data Exchange (ETDEWEB)

Ikefuji, M. [Institute of Social and Economic Research, Osaka University, Osaka (Japan); Laeven, R.J.A.; Magnus, J.R. [Department of Econometrics and Operations Research, Tilburg University, Tilburg (Netherlands); Muris, C. [CentER, Tilburg University, Tilburg (Netherlands)

2010-11-15

In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected utility with constant relative risk aversion (power utility); statisticians typically model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economy-climate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

KAUST Repository

Babuška, Ivo; Nobile, Fabio; Tempone, Raul

2010-01-01

This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.

Cancer survival analysis using semi-supervised learning method based on Cox and AFT models with L1/2 regularization.

Science.gov (United States)

Liang, Yong; Chai, Hua; Liu, Xiao-Ying; Xu, Zong-Ben; Zhang, Hai; Leung, Kwong-Sak

2016-03-01

One of the most important objectives of the clinical cancer research is to diagnose cancer more accurately based on the patients' gene expression profiles. Both Cox proportional hazards model (Cox) and accelerated failure time model (AFT) have been widely adopted to the high risk and low risk classification or survival time prediction for the patients' clinical treatment. Nevertheless, two main dilemmas limit the accuracy of these prediction methods. One is that the small sample size and censored data remain a bottleneck for training robust and accurate Cox classification model. In addition to that, similar phenotype tumours and prognoses are actually completely different diseases at the genotype and molecular level. Thus, the utility of the AFT model for the survival time prediction is limited when such biological differences of the diseases have not been previously identified. To try to overcome these two main dilemmas, we proposed a novel semi-supervised learning method based on the Cox and AFT models to accurately predict the treatment risk and the survival time of the patients. Moreover, we adopted the efficient L1/2 regularization approach in the semi-supervised learning method to select the relevant genes, which are significantly associated with the disease. The results of the simulation experiments show that the semi-supervised learning model can significant improve the predictive performance of Cox and AFT models in survival analysis. The proposed procedures have been successfully applied to four real microarray gene expression and artificial evaluation datasets. The advantages of our proposed semi-supervised learning method include: 1) significantly increase the available training samples from censored data; 2) high capability for identifying the survival risk classes of patient in Cox model; 3) high predictive accuracy for patients' survival time in AFT model; 4) strong capability of the relevant biomarker selection. Consequently, our proposed semi

Numerical Simulation of the Heston Model under Stochastic Correlation

Directory of Open Access Journals (Sweden)

Long Teng

2017-12-01

Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

1995-01-01

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....

Portfolio Management with Stochastic Interest Rates and Inflation Ambiguity

DEFF Research Database (Denmark)

Munk, Claus; Rubtsov, Alexey Vladimirovich

We solve a stock-bond-cash portfolio choice problem for a risk- and ambiguity-averse investor in a setting where the inflation rate and interest rates are stochastic. The expected inflation rate is unobservable, but the investor may learn about it from realized inflation and observed stock and bond......-Jacobi-Bellman equation in closed form and derive and illustrate a number of interesting properties of the solution. For example, ambiguity aversion affects the optimal portfolio through the correlation of price level with the stock index, a bond, and the expected inflation rate. Furthermore, unlike other settings...

Environmental vs Demographic Stochasticity in Population Growth

OpenAIRE

Braumann, C. A.

2010-01-01

Compares the effect on population growth of envinonmental stochasticity (random environmental variations described by stochastic differential equations) with demographic stochasticity (random variations in births and deaths described by branching processes and birth-and-death processes), in the density-independent and the density-dependent cases.

Alternative Asymmetric Stochastic Volatility Models

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2010-01-01

textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is

Transport stochastic multi-dimensional media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.

1996-01-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

Transport stochastic multi-dimensional media

Energy Technology Data Exchange (ETDEWEB)

Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

1996-12-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

Modelling and application of stochastic processes

CERN Document Server

1986-01-01

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

Turbulent response in a stochastic regime

International Nuclear Information System (INIS)

Molvig, K.; Freidberg, J.P.; Potok, R.; Hirshman, S.P.; Whitson, J.C.; Tajima, T.

1981-06-01

The theory for the non-linear, turbulent response in a system with intrinsic stochasticity is considered. It is argued that perturbative Eulerian theories, such as the Direct Interaction Approximation (DIA), are inherently unsuited to describe such a system. The exponentiation property that characterizes stochasticity appears in the Lagrangian picture and cannot even be defined in the Eulerian representation. An approximation for stochastic systems - the Normal Stochastic Approximation - is developed and states that the perturbed orbit functions (Lagrangian fluctuations) behave as normally distributed random variables. This is independent of the Eulerian statistics and, in fact, we treat the Eulerian fluctuations as fixed. A simple model problem (appropriate for the electron response in the drift wave) is subjected to a series of computer experiments. To within numerical noise the results are in agreement with the Normal Stochastic Approximation. The predictions of the DIA for this mode show substantial qualitative and quantitative departures from the observations

Stochastic modeling and analysis of telecoms networks

CERN Document Server

Decreusefond, Laurent

2012-01-01

This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an

Progressive image denoising through hybrid graph Laplacian regularization: a unified framework.

Science.gov (United States)

Liu, Xianming; Zhai, Deming; Zhao, Debin; Zhai, Guangtao; Gao, Wen

2014-04-01

Recovering images from corrupted observations is necessary for many real-world applications. In this paper, we propose a unified framework to perform progressive image recovery based on hybrid graph Laplacian regularized regression. We first construct a multiscale representation of the target image by Laplacian pyramid, then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered. On one hand, within each scale, a graph Laplacian regularization model represented by implicit kernel is learned, which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space. In this procedure, the intrinsic manifold structure is explicitly considered using both measured and unmeasured samples, and the nonlocal self-similarity property is utilized as a fruitful resource for abstracting a priori knowledge of the images. On the other hand, between two successive scales, the proposed model is extended to a projected high-dimensional feature space through explicit kernel mapping to describe the interscale correlation, in which the local structure regularity is learned and propagated from coarser to finer scales. In this way, the proposed algorithm gradually recovers more and more image details and edges, which could not been recovered in previous scale. We test our algorithm on one typical image recovery task: impulse noise removal. Experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state-of-the-art algorithms.

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-10-01

The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

Stochastic resonance during a polymer translocation process

International Nuclear Information System (INIS)

Mondal, Debasish; Muthukumar, M.

2016-01-01

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Is human failure a stochastic process?

International Nuclear Information System (INIS)

Dougherty, Ed M.

1997-01-01

Human performance results in failure events that occur with a risk-significant frequency. System analysts have taken for granted the random (stochastic) nature of these events in engineering assessments such as risk assessment. However, cognitive scientists and error technologists, at least those who have interest in human reliability, have, over the recent years, claimed that human error does not need this stochastic framework. Yet they still use the language appropriate to stochastic processes. This paper examines the potential for the stochastic nature of human failure production as the basis for human reliability analysis. It distinguishes and leaves to others, however, the epistemic uncertainties over the possible probability models for the real variability of human performance

Stochastic Switching Dynamics

DEFF Research Database (Denmark)

Simonsen, Maria

This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...

Stochastic singular optics

CSIR Research Space (South Africa)

Roux, FS

2013-09-01

Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...

An iterative method for Tikhonov regularization with a general linear regularization operator

NARCIS (Netherlands)

Hochstenbach, M.E.; Reichel, L.

2010-01-01

Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan

Hessian regularization based non-negative matrix factorization for gene expression data clustering.

Science.gov (United States)

Liu, Xiao; Shi, Jun; Wang, Congzhi

2015-01-01

Since a key step in the analysis of gene expression data is to detect groups of genes that have similar expression patterns, clustering technique is then commonly used to analyze gene expression data. Data representation plays an important role in clustering analysis. The non-negative matrix factorization (NMF) is a widely used data representation method with great success in machine learning. Although the traditional manifold regularization method, Laplacian regularization (LR), can improve the performance of NMF, LR still suffers from the problem of its weak extrapolating power. Hessian regularization (HR) is a newly developed manifold regularization method, whose natural properties make it more extrapolating, especially for small sample data. In this work, we propose the HR-based NMF (HR-NMF) algorithm, and then apply it to represent gene expression data for further clustering task. The clustering experiments are conducted on five commonly used gene datasets, and the results indicate that the proposed HR-NMF outperforms LR-based NMM and original NMF, which suggests the potential application of HR-NMF for gene expression data.

Dynamics of non-holonomic systems with stochastic transport

Science.gov (United States)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

Quantification of fetal heart rate regularity using symbolic dynamics

Science.gov (United States)

van Leeuwen, P.; Cysarz, D.; Lange, S.; Geue, D.; Groenemeyer, D.

2007-03-01

Fetal heart rate complexity was examined on the basis of RR interval time series obtained in the second and third trimester of pregnancy. In each fetal RR interval time series, short term beat-to-beat heart rate changes were coded in 8bit binary sequences. Redundancies of the 28 different binary patterns were reduced by two different procedures. The complexity of these sequences was quantified using the approximate entropy (ApEn), resulting in discrete ApEn values which were used for classifying the sequences into 17 pattern sets. Also, the sequences were grouped into 20 pattern classes with respect to identity after rotation or inversion of the binary value. There was a specific, nonuniform distribution of the sequences in the pattern sets and this differed from the distribution found in surrogate data. In the course of gestation, the number of sequences increased in seven pattern sets, decreased in four and remained unchanged in six. Sequences that occurred less often over time, both regular and irregular, were characterized by patterns reflecting frequent beat-to-beat reversals in heart rate. They were also predominant in the surrogate data, suggesting that these patterns are associated with stochastic heart beat trains. Sequences that occurred more frequently over time were relatively rare in the surrogate data. Some of these sequences had a high degree of regularity and corresponded to prolonged heart rate accelerations or decelerations which may be associated with directed fetal activity or movement or baroreflex activity. Application of the pattern classes revealed that those sequences with a high degree of irregularity correspond to heart rate patterns resulting from complex physiological activity such as fetal breathing movements. The results suggest that the development of the autonomic nervous system and the emergence of fetal behavioral states lead to increases in not only irregular but also regular heart rate patterns. Using symbolic dynamics to

Stochastic cooling at Fermilab

International Nuclear Information System (INIS)

Marriner, J.

1986-08-01

The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system

Stochastic inflation in phase space: is slow roll a stochastic attractor?

Energy Technology Data Exchange (ETDEWEB)

Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter; Taká č, Martin

2017-01-01

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter

2017-06-04

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Adversarial Reinforcement Learning in a Cyber Security Simulation}

OpenAIRE

Elderman, Richard; Pater, Leon; Thie, Albert; Drugan, Madalina; Wiering, Marco

2017-01-01

This paper focuses on cyber-security simulations in networks modeled as a Markov game with incomplete information and stochastic elements. The resulting game is an adversarial sequential decision making problem played with two agents, the attacker and defender. The two agents pit one reinforcement learning technique, like neural networks, Monte Carlo learning and Q-learning, against each other and examine their effectiveness against learning opponents. The results showed that Monte Carlo lear...

A Variance Minimization Criterion to Feature Selection Using Laplacian Regularization.

Science.gov (United States)

He, Xiaofei; Ji, Ming; Zhang, Chiyuan; Bao, Hujun

2011-10-01

In many information processing tasks, one is often confronted with very high-dimensional data. Feature selection techniques are designed to find the meaningful feature subset of the original features which can facilitate clustering, classification, and retrieval. In this paper, we consider the feature selection problem in unsupervised learning scenarios, which is particularly difficult due to the absence of class labels that would guide the search for relevant information. Based on Laplacian regularized least squares, which finds a smooth function on the data manifold and minimizes the empirical loss, we propose two novel feature selection algorithms which aim to minimize the expected prediction error of the regularized regression model. Specifically, we select those features such that the size of the parameter covariance matrix of the regularized regression model is minimized. Motivated from experimental design, we use trace and determinant operators to measure the size of the covariance matrix. Efficient computational schemes are also introduced to solve the corresponding optimization problems. Extensive experimental results over various real-life data sets have demonstrated the superiority of the proposed algorithms.

Quantization of dynamical systems and stochastic control theory

International Nuclear Information System (INIS)

Guerra, F.; Morato, L.M.

1982-09-01

In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior

On Lipschitzian quantum stochastic differential inclusions

International Nuclear Information System (INIS)

Ekhaguere, G.O.S.

1990-12-01

Quantum stochastic differential inclusions are introduced and studied within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus. Results concerning the existence of solutions of a Lipschitzian quantum stochastic differential inclusion and the relationship between the solutions of such an inclusion and those of its convexification are presented. These generalize the Filippov existence theorem and the Filippov-Wazewski Relaxation Theorem for classical differential inclusions to the present noncommutative setting. (author). 9 refs

Stochastic temperature and the Nicolai map

International Nuclear Information System (INIS)

Hueffel, H.

1989-01-01

Just as standard temperature can be related to the time coordinate of Euclidean space, a new concept of 'stochastic temperature' may be introduced by associating it to the Parisi-Wu time of stochastic quantization. The perturbative equilibrium limit for a self-interacting scalar field is studied, and a 'thermal' mass shift to one loop is shown. In addition one may interpret the underlying stochastic process as a Nicolai map at nonzero 'temperature'. 22 refs. (Author)

Stochastic Linear Quadratic Optimal Control Problems

International Nuclear Information System (INIS)

Chen, S.; Yong, J.

2001-01-01

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well

Regular Expression Pocket Reference

CERN Document Server

Stubblebine, Tony

2007-01-01

This handy little book offers programmers a complete overview of the syntax and semantics of regular expressions that are at the heart of every text-processing application. Ideal as a quick reference, Regular Expression Pocket Reference covers the regular expression APIs for Perl 5.8, Ruby (including some upcoming 1.9 features), Java, PHP, .NET and C#, Python, vi, JavaScript, and the PCRE regular expression libraries. This concise and easy-to-use reference puts a very powerful tool for manipulating text and data right at your fingertips. Composed of a mixture of symbols and text, regular exp

Stochastic programming with integer recourse

NARCIS (Netherlands)

van der Vlerk, Maarten Hendrikus

1995-01-01

In this thesis we consider two-stage stochastic linear programming models with integer recourse. Such models are at the intersection of two different branches of mathematical programming. On the one hand some of the model parameters are random, which places the problem in the field of stochastic

Stochastic quantization of gravity and string fields

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

The stochastic quantization method of Parisi and Wu is generalized so as to make it applicable to Einstein's theory of gravitation. The generalization is based on the existence of a preferred metric in field configuration space, involves Ito's calculus, and introduces a complex stochastic process adapted to Lorentzian spacetime. It implies formally the path integral measure of DeWitt, a causual Feynman propagator, and a consistent stochastic perturbation theory. The lineraized version of the theory is also obtained from the stochastic quantization of the free string field theory of Siegel and Zwiebach. (Author)

A regularized relaxed ordered subset list-mode reconstruction algorithm and its preliminary application to undersampling PET imaging

International Nuclear Information System (INIS)

Cao, Xiaoqing; Xie, Qingguo; Xiao, Peng

2015-01-01

List mode format is commonly used in modern positron emission tomography (PET) for image reconstruction due to certain special advantages. In this work, we proposed a list mode based regularized relaxed ordered subset (LMROS) algorithm for static PET imaging. LMROS is able to work with regularization terms which can be formulated as twice differentiable convex functions. Such a versatility would make LMROS a convenient and general framework for fulfilling different regularized list mode reconstruction methods. LMROS was applied to two simulated undersampling PET imaging scenarios to verify its effectiveness. Convex quadratic function, total variation constraint, non-local means and dictionary learning based regularization methods were successfully realized for different cases. The results showed that the LMROS algorithm was effective and some regularization methods greatly reduced the distortions and artifacts caused by undersampling. (paper)

Limites e possibilidades dos programas de aceleração de aprendizagem The limits and possibilities of including students from remedial learning programs in regular schooling

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Clarilza Prado de Sousa

1999-11-01

Full Text Available Pretendi neste trabalho analisar os limites e possibilidades da escola integrar alunos com atraso de escolaridade em processos de educação regular, que receberam apoio de programas de aceleração da aprendizagem. Baseada nas avaliações realizadas desses programas por professores do Programa de Estudos Pós-Graduados em Psicologia da Educação da PUCSP e por pesquisadores do Núcleo de Avaliação Educacional da Fundação Carlos Chagas, discuto os resultados efetivamente alcançados considerando duas categorias de análise. Na primeira categoria, analiso os efeitos da estratégia pedagógica promovida pelos programas, nas aprendizagens e progressos dos alunos participantes. Na segunda categoria, procuro analisar as possibilidades de integração/inclusão desses alunos no processo de educação regular. Finalmente, à guisa de conclusão, procuro fazer algumas considerações teórico-metodológicas. Distinguindo integração de inclusão, discuto os limites e possibilidades que as ações dos programas têm de realmente promoverem o desenvolvimento de uma escola sem exclusão.This article analyzes the limits and possibilities for schools to include students with schooling deficits who receive support from the accelerated learning programs, in their regular education processes. Based on evaluations of these programs done by professors from the Post Graduate Program in Educational Psychology of the Pontifical Catholic University of São Paulo and by researchers from the Nucleus for Educational Evaluation of the Carlos Chagas Foundation, the results will be discussed in two analytical categories. In the first category, I analyze the effects of the teaching strategies promoted by the programs on the learning and progress of the participating students. In the second category, I seek to analyze the possibilities for integration/inclusion of these students in the regular educational process. Finally by way of conclusion, I try to make some

Stochastic correlative firing for figure-ground segregation.

Science.gov (United States)

Chen, Zhe

2005-03-01

Segregation of sensory inputs into separate objects is a central aspect of perception and arises in all sensory modalities. The figure-ground segregation problem requires identifying an object of interest in a complex scene, in many cases given binaural auditory or binocular visual observations. The computations required for visual and auditory figure-ground segregation share many common features and can be cast within a unified framework. Sensory perception can be viewed as a problem of optimizing information transmission. Here we suggest a stochastic correlative firing mechanism and an associative learning rule for figure-ground segregation in several classic sensory perception tasks, including the cocktail party problem in binaural hearing, binocular fusion of stereo images, and Gestalt grouping in motion perception.

The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System

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Shaolin Ji

2013-01-01

Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.

Thermal mixtures in stochastic mechanics

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Guerra, F [Rome Univ. (Italy). Ist. di Matematica; Loffredo, M I [Salerno Univ. (Italy). Ist. di Fisica

1981-01-17

Stochastic mechanics is extended to systems in thermal equilibrium. The resulting stochastic processes are mixtures of Nelson processes. Their Markov property is investigated in some simple cases. It is found that in order to inforce Markov property the algebra of observable associated to the present must be suitably enlarged.

An e-learning course in medical immunology: does it improve learning outcome?

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Boye, Sondre; Moen, Torolf; Vik, Torstein

2012-01-01

E-learning is used by most medical students almost daily and several studies have shown e-learning to improve learning outcome in small-scale interventions. However, few studies have explored the effects of e-learning in immunology. To study the effect of an e-learning package in immunology on learning outcomes in a written integrated examination and to examine student satisfaction with the e-learning package. All second-year students at a Norwegian medical school were offered an animated e-learning package in basic immunology as a supplement to the regular teaching. Each student's log-on-time was recorded and linked with the student's score on multiple choice questions included in an integrated end-of-the-year written examination. Student satisfaction was assessed through a questionnaire. The intermediate-range students (interquartile range) on average scored 3.6% better on the immunology part of the examination per hour they had used the e-learning package (p = 0.0046) and log-on-time explained 17% of the variance in immunology score. The best and the less skilled students' examination outcomes were not affected by the e-learning. The e-learning was well appreciated among the students. Use of an e-learning package in immunology in addition to regular teaching improved learning outcomes for intermediate-range students.

Translating visual information into action predictions: Statistical learning in action and nonaction contexts.

Science.gov (United States)

Monroy, Claire D; Gerson, Sarah A; Hunnius, Sabine