Stability analysis of biological systems with real solution classification
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: GEOTHER: A Geometry Theorem Prover

title: On Wu's Method for Proving Constructive Geometric Theorems
abstract: In 1977 Wu Wen-tsiin discovered an efficient method for mechanical theorem proving. This method has been applied to prove and discover theorems in various kinds of geometries. Based on an extension of one of Wu's algorithmic procedures, the author implemented a prover CPS for proving so-called constructive geometric theorems, as well as a general theorem prover PS. Using this prover we proved more than one hundred non-trivial theorems and discovered also a number of interesting ones. This paper is a summarization of our early work, as a abbreviation of the chapter 2 from my Chinese doctoral dissertation.

title: Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
abstract: This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods and their implementations to deal with problems from the local theory of surfaces. We show how to prove known geometric theorems and to derive unknown relations automatically. In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li. Moreover, we provide symmetric expressions for Li's relation and clarify his statement. Some examples of theorem proving and computational difficulties encountered in our experiments are also discussed.

title: A Strategy for Speeding-up the Computation of Characteristic Sets
abstract: In this note a strategy is presented that speeds up the computation of characteristic sets several times in many cases. We test the possibility of success for this strategy in the quasi-sense by 50 examples, where the strategy succeeds in 58 and fails in 23 of the 81 completed cases. The speed-up of the strategy, while successful, ranges from a few to hundred times, whereas in the failure case the computation may be slightly slowed down (not less than 0.6 times).

title: A simple method for implicitizing rational curves and surfaces
abstract: This paper presents a simple method for converting rational parametric equations of curves and surfaces into implicit equations. The method proceeds via writing out the implicit polynomial F of estimated degree with indeterminate coefficients u i , substituting the rational expressions for the given parametric curve or surface into F to yield a rational expression g / h in the parameter s (or s and t ), equating the coefficients of g in terms of s (and t ) to 0 to generate a sparse, partially triangular system of linear equations in u i with constant coefficients, and finally solving the linear system for u i . If a nontrivial solution is found, then an implicit polynomial is obtained; otherwise, one repeats the same process, increasing the degree of F . Our experiments show that this simple method is efficient. It performs particularly well in the presence of base points and may detect the dependency of parameters incidentally.

title: Automated Abstraction Refinement for Model Checking Large State Spaces Using SAT Based Conflict Analysis
abstract: We introduce a SAT based automatic abstraction refinement framework for model checking systems with several thousand state variables in the cone of influence of the specification. The abstract model is constructed by designating a large number of state variables as invisible. In contrast to previous work where invisible variables were treated as free inputs we describe a computationally more advantageous approach in which the abstract transition relation is approximated by pre-quantifying invisible variables during image computation. The abstract counterexamples obtained from model-checking the abstract model are symbolically simulated on the concrete system using a state-of-the-art SAT checker. If no concrete counterexample is found, a subset of the invisible variables is reintroduced into the system and the process is repeated. The main contribution of this paper are two new algorithms for identifying the relevant variables to be reintroduced. These algorithms monitor the SAT checking phase in order to analyze the impact of individual variables. Our method is complete for safety properties (AGp) in the sense that - performance permitting - a property is either verified or disproved by a concrete counterexample. Experimental results are given to demonstrate the power of our method on real-world designs.

title: Perceptual organization based on temporal dynamics
abstract: This paper presents a computational model for perceptual organization. A figure-ground segregation network is proposed based on a novel boundary pair representation. The system solves the figure-ground segregation problem through temporal evolution. Gestalt-like grouping rules are incorporated by modulating connections, which determines the temporal behavior and thus the perception of the system. The results are then fed to a surface completion module based on local diffusion. Different perceptual phenomena, such as modal and a modal completion, virtual contours, grouping and shape decomposition are explained by the model with a fixed set of parameters. Computationally, the system eliminates combinatorial optimization, which is common to many existing computational approaches. It also accounts for more examples that are consistent with psychological experiments. In addition, the boundary-pair representation is consistent with well-known on- and off-center cell responses and thus biologically more plausible.

title: Modelling the perceptual segregation of double vowels with a network of neural oscillators
abstract: The ability of listeners to identify two simultaneously presented vowels can be introducing a difference in fundamental frequency (F0) between the vowels. We propose an explanation for this phenomenon in the form of a computational model of concurrent sound segregation, which is motivated by neurophysiological evidence of oscillatory firing activity in the auditory cortex and thalamus. More specifically, the model represents the perceptual grouping of auditory frequency channels as synchronised (phase-locked zero phase lag) oscillations in a neural network. Computer simulations on a vowel set used in psychophysical studies confirm that the model qualitatively matches the performance of human listeners; vowel identification performance increases with increasing difference in F0. Additionally, the model is able to replicate other findings relating to the perception of harmonic complexes in which one component is mistuned.

title: A neuro-fuzzy approach for diagnosis of antibody deficiency syndrome
abstract: This paper presents a neuro-fuzzy approach for diagnosis of antibody deficiency syndrome, where a new neuro-fuzzy network with fuzzy activation functions (FAFs) at hidden layer is used. The FAFs capturing some essential information on pattern distributions, can be adaptively constructed using training examples. To improve the generalization capability and reduce the model complexity, a heuristic method for feature selection is proposed by measuring the size of non-overlapped areas of the FAFs. The effectiveness of our proposed techniques is investigated by an immunology clinical data set collected from the University of California, Irvine (UCI) immunology laboratory.

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.