Comparison of non-linear optical susceptibilities of KNbO3 and LiNbO3

From the chemical bond viewpoint, second-order non-linear optical (NLO) tenser coefficients of KNbO3 and LiNbO3 crystals have been calculated. By using the bond-valence theory of complex crystals and the modified bond-charge model, we were able to determine contributions of each type of constituent chemical bond to the total second-order NLO susceptibility. The tenser values thus calculated are in good agreement with experimental data. From the comparison of NLO tenser coefficients of these two crystals, we found that the major NLO contributors are KO12 groups and LiO6 octahedra not the distorted NbO6 octahedra. The difference between their NLO properties arises from their different structural characters, and the high coordination number of constituent elements in KNbO3 makes its valence electrons become more delocalised compared with those of LiNbO3. (C) 1997 Elsevier Science Ltd. All rights reserved.

Effective response of a non-linear composite in external AC electric field

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets <(. . .)> denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

Study on system identification of linear and non-linear liquid chromatography separation

The paper proposes the identification method of linear and non-linear chromatographic system. The non-linear isotherms and lumped mass transfer coefficients of chromatography separating sorbitol and mannitol are determined. And the theoretical elution curves calculated by non-linear chromatographic model are more accurate than those calculated by linear chromatographic model.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Discovering Clusters in Motion Time-Series Data

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications.

Statistical Properties of Single and Competing Non-Linear Fast-Slow Oscillators in Noise

Statistical properties offast-slow Ellias-Grossberg oscillators are studied in response to deterministic and noisy inputs. Oscillatory responses remain stable in noise due to the slow inhibitory variable, which establishes an adaptation level that centers the oscillatory responses of the fast excitatory variable to deterministic and noisy inputs. Competitive interactions between oscillators improve the stability in noise. Although individual oscillation amplitudes decrease with input amplitude, the average to'tal activity increases with input amplitude, thereby suggesting that oscillator output is evaluated by a slow process at downstream network sites.

Emergence of Tri-Phasic Muscle Activation from the Non-linear Interactions of Central and Spinal Neural Network Circuits

The origin of the tri-phasic burst pattern, observed in the EMGs of opponent muscles during rapid self-terminated movements, has been controversial. Here we show by computer simulation that the pattern emerges from interactions between a central neural trajectory controller (VITE circuit) and a peripheral neuromuscularforce controller (FLETE circuit). Both neural models have been derived from simple functional constraints that have led to principled explanations of a wide variety of behavioral and neurobiological data, including, as shown here, the generation of tri-phasic bursts.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Addressing non-linear hardware limitations and extending network coverage area for power aware wireless sensor networks

Science Foundation Ireland (07/CE/11147); Irish Research Council for Science Engineering and Technology (Embark Initiative)

A distributed architecture for the monitoring and analysis of time series data

It is estimated that the quantity of digital data being transferred, processed or stored at any one time currently stands at 4.4 zettabytes (4.4 × 2 70 bytes) and this figure is expected to have grown by a factor of 10 to 44 zettabytes by 2020. Exploiting this data is, and will remain, a significant challenge. At present there is the capacity to store 33% of digital data in existence at any one time; by 2020 this capacity is expected to fall to 15%. These statistics suggest that, in the era of Big Data, the identification of important, exploitable data will need to be done in a timely manner. Systems for the monitoring and analysis of data, e.g. stock markets, smart grids and sensor networks, can be made up of massive numbers of individual components. These components can be geographically distributed yet may interact with one another via continuous data streams, which in turn may affect the state of the sender or receiver. This introduces a dynamic causality, which further complicates the overall system by introducing a temporal constraint that is difficult to accommodate. Practical approaches to realising the system described above have led to a multiplicity of analysis techniques, each of which concentrates on specific characteristics of the system being analysed and treats these characteristics as the dominant component affecting the results being sought. The multiplicity of analysis techniques introduces another layer of heterogeneity, that is heterogeneity of approach, partitioning the field to the extent that results from one domain are difficult to exploit in another. The question is asked can a generic solution for the monitoring and analysis of data that: accommodates temporal constraints; bridges the gap between expert knowledge and raw data; and enables data to be effectively interpreted and exploited in a transparent manner, be identified? The approach proposed in this dissertation acquires, analyses and processes data in a manner that is free of the constraints of any particular analysis technique, while at the same time facilitating these techniques where appropriate. Constraints are applied by defining a workflow based on the production, interpretation and consumption of data. This supports the application of different analysis techniques on the same raw data without the danger of incorporating hidden bias that may exist. To illustrate and to realise this approach a software platform has been created that allows for the transparent analysis of data, combining analysis techniques with a maintainable record of provenance so that independent third party analysis can be applied to verify any derived conclusions. In order to demonstrate these concepts, a complex real world example involving the near real-time capturing and analysis of neurophysiological data from a neonatal intensive care unit (NICU) was chosen. A system was engineered to gather raw data, analyse that data using different analysis techniques, uncover information, incorporate that information into the system and curate the evolution of the discovered knowledge. The application domain was chosen for three reasons: firstly because it is complex and no comprehensive solution exists; secondly, it requires tight interaction with domain experts, thus requiring the handling of subjective knowledge and inference; and thirdly, given the dearth of neurophysiologists, there is a real world need to provide a solution for this domain

Empirical Evidence of Conditional Heteroskedasticity in Vietnam’s Stock Returns Time Series

This paper confirms presence of GARCH(1,1) effect on stock return time series of Vietnam’s newborn stock market. We performed tests on four different time series, namely market returns (VN-Index), and return series of the first four individual stocks listed on the Vietnamese exchange (the Ho Chi Minh City Securities Trading Center) since August 2000. The results have been quite relevant to previously reported empirical studies on different markets.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.