Synchrony and Desynchrony in Integrate-and-Fire Oscillators
Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrate-and-fire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrate-and-fire oscillators. We illustrate that a LEGION architecture with integrate-and-fire oscillators can be similarly used to address image analysis.

title: Synchrony and Desynchrony in Neural Oscillator Networks
abstract: An novel class of locally excitatory, globally inhibitory oscillator networks is proposed. The model of each oscillator corresponds to a standard relaxation oscillator with two time scales. The network exhibits a mechanism of selective gating, whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern, while preventing others from jumping up. We show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks. Computer simulations demonstrate the network's promising ability for segmenting multiple input patterns in real time. This model lays a physical foundation for the oscillatory correlation theory of feature binding, and may provide an effective computational framework for scene segmentation and figure/ground segregation.

title: Oriented statistical nonlinear smoothing filter
abstract: This paper presents a nonlinear smoothing method which is based on an orientation-sensitive probability measure. By incorporating geometrical constraints through the coupling structure, we obtain a robust nonlinear smoothing algorithm. Even when noise is substantial the proposed smoothing algorithm can still preserve salient boundaries. Compared with anisotropic diffusive approaches, the proposed nonlinear algorithm not only performs better in preserving boundaries but also has a non-uniform stable state, whereby reliable results are available within a fixed number of iterations independent of images. A system using the proposed method and LEGION network has been developed and applied in noisy image segmentation and hydrographic feature extraction from digital ortho-photo quadrangles. Experimental results using synthetic and real images are provided.

title: Synchronization in Relaxation Oscillator Networks with Conduction Delays
abstract: We study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase-lag synchrony. Our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays. We analyze the system of two coupled oscillators and derive phase compression rates. This analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony. The numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions. The robustness of the proposed mechanism is verified with respect to different nullclines, variations in parameter values, and initial conditions.

title: Singing Voice Separation from Monaural Recordings
abstract: Separating singing voice from music accompaniment has wide applications in areas such as automatic lyrics recognition and alignment, singer identification, and music information retrieval. Compared to the extensive studies of speech separation, singing voice separation has been little explored. We propose a system to separate singing voice from music accompaniment from monaural recordings. The system has three stages. The singing voice detection stage partitions and classifies an input into vocal and non-vocal portions. Then the predominant pitch detection stage detects the pitch contour of the singing voice for vocal portions. Finally the separation stage uses the detected pitch contour to group the time-frequency segments of the singing voice. Quantitative results show that the system performs well in singing voice separation.

title: An oscillatory correlation model of human motion perception
abstract: An oscillatory correlation model of human motion perception is proposed based on the integration of motion and luminance information. The model is composed of two parallel pathways that segment the input scene based on motion and luminance, respectively. Combining these segmentations, the model refines the motion estimates in the integration stage to obtain the final segmentation in the motion pathway. For segmentation, LEGION (locally excitatory globally inhibitory oscillator network) is employed whereby the phases of oscillators are used for region labeling. The model performance is demonstrated using a set of psychophysical data.

title: Semantics modeling based image retrieval system using neural networks
abstract: Semantics based image retrieval techniques show a promising direction to the development of CBIR systems. To design such systems, semantics modeling is one of the most difficult tasks. This paper aims to develop a semantics modeling approach using neural networks. In our work, a neural network is utilized to memorize the semantic patterns within the images. An intelligent image retrieval system is designed based on this model. User's relevance feedback is used for enhancing the retrieval performance. Experimental results from the prototype system demonstrate the effectiveness of the proposed approach.

title: Stability analysis of biological systems with real solution classification
abstract: This paper presents a new and general approach for analyzing the stability of a large class of biological networks, modeled as autonomous systems of differential equations, using real solving and solution classification. The proposed approach, based on the classical technique of linearization from the qualitative theory of ordinary differential equations yet with exact symbolic computation, is applied to analyzing the local stability of the Cdc2-cyclin B/Wee1 system and the Mos/MEK/p42 MAPK cascade, two well-known models for cell and protein signaling that have been studied extensively in the literature. We provide rigorous proofs and generalizations for some of the previous results established experimentally and report our new findings.

title: Nonlinear quantification scheduling in image computation
abstract: Computing the set of states reachable in one step from a given set of states, i.e. image computation, is a crucial step in several symbolic verification algorithms, including model checking and reachability analysis. So far, the best methods for quantification scheduling in image computation, with a conjunctively partitioned transition relation, have been restricted to a linear schedule. This results in a loss of flexibility during image computation. We view image computation as a problem of constructing an optimal parse tree for the image set. The optimality of a parse tree is defined by the largest BDD that is encountered during the computation of the tree. We present dynamic and static versions of a new algorithm, VarScore, which exploits the flexibility offered by the parse tree approach to the image computation. We show by extensive experimentation that our techniques outperform the best known techniques so far.

title: Hardware-software partitioning of real-time operating systems using Hopfield neural networks
abstract: The hardware–software automated partitioning of a real-time operating system in the system-on-a-chip (SoC-RTOS partitioning) is a NP-complete problem, and a crucial step in the hardware–software co-design of SoC. In this paper, a new model for SoC-RTOS partitioning is introduced, which can help in understanding the essence of the SoC-RTOS partitioning. A discrete Hopfield neural network approach for implementing the SoC-RTOS partitioning is proposed, where a novel energy function, operating equation and coefficients of the neural network are redefined. Simulations are carried out with comparison to other optimization techniques. Experimental results demonstrate the feasibility and effectiveness of the proposed method.

title: Decomposing Algebraic Varieties
abstract: An algebraic variety is a geometric figure defined by the zeros of a set of multivariate polynomials. This paper explains how to adapt two general zero decomposition methods for efficient decomposition of affine algebraic varieties into unmixed and irreducible components. Two devices based on Grobner bases are presented for computing the generators of the saturated ideals of triangular sets. We also discuss a few techniques and variants which, when properly used, may speed up the decomposition. Experiments for a set of examples are reported with comparison to show the performance and effectiveness of such techniques, variants and the whole decomposition methods. Several theoretical results are stated along with the description of algorithms. The paper ends with a brief mention of some applications of variety decomposition.