Bio-PEPA: A framework for the modelling and analysis of biological systems

In this work we present Bio-PEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. Bio-PEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analyses can be carried out. Bio-PEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered and extended to our language. Finally, we show the translation of a biological model into the new language and we report some analysis results.     

Equivalences for a biological process algebra

This paper investigates Bio-PEPA, the stochastic process algebra for biological modelling developed by Ciocchetta and Hillston. It focuses on Bio-PEPA with levels where molecular counts are grouped or concentrations are discretised into a finite number of levels. Basic properties of well-defined Bio-PEPA systems are established after which equivalences used for the stochastic process algebra PEPA are considered for Bio-PEPA, and are shown to be identical for well-defined Bio-PEPA systems. Two new semantic equivalences parameterised by functions, called g-bisimilarity and weak g-bisimilarity are introduced. Different functions lead to different equivalences for Bio-PEPA. Congruence is shown for both forms of g-bisimilarity under certain reasonable conditions on the function and the use of these equivalences are demonstrated with a biologically-motivated example where two similar species are treated as a single species, and modelling of alternative pathways in the MAPK kinase signalling cascade.     

A semantic equivalence for Bio-PEPA based on discretisation of continuous values

Bio-PEPA is a process algebra for modelling biological systems. An important aspect of Bio-PEPA is the ability it provides to discretise concentrations resulting in a smaller, more manageable state space. The discretisation is based on a step size which determines the size of each discrete level and also the number of levels. This paper considers the relationship between two discretisations of the same Bio-PEPA model that differ only in the step size and hence the number of levels, by using the idea of equivalence from concurrency and process algebra. We present a novel behavioural semantic equivalence, compression bisimilarity, and investigate when this equates two discretisations of the same model and the circumstances in which this equivalence is a congruence with respect to the synchronisation operator.     

A Novel Space Variant Image Representation

Traditionally, in machine vision images are represented using cartesian coordinates with uniform sampling along the axes. On the contrary, biological vision systems represent images using polar coordinates with non-uniform sampling. For various advantages provided by space-variant representations many researchers are interested in space-variant computer vision. In this direction the current work proposes a novel and simple space variant representation of images. The proposed representation is compared with the classical log-polar mapping. The log-polar representation is motivated by biological vision having the characteristic of higher resolution at the fovea and reduced resolution at the periphery. On the contrary to the log-polar, the proposed new representation has higher resolution at the periphery and lower resolution at the fovea. Our proposal is proved to be a better representation in navigational scenarios such as driver assistance systems and robotics. The experimental results involve analysis of optical flow fields computed on both proposed and log-polar representations. Additionally, an egomotion estimation application is also shown as an illustrative example. The experimental analysis comprises results from synthetic as well as real sequences.     

Neural memories and search engines

In this article, we show the existence of a formal convergence between the matrix models of biological memories and the vector space models designed to extract information from large collections of documents. We first show that, formally, the term-by-document matrix (a mathematical representation of a set of codified documents) can be interpreted as an associative memory. In this framework, the dimensionality reduction of the term-by-document matrices produced by the latent semantic analysis (LSA) has a common factor with the matrix biological memories. This factor consists in the generation of a statistical ‘conceptualisation’ of data using little dispersed weighted averages. Then, we present a class of matrix memory that built up thematic blocks using multiplicative contexts. The thematic memories define modular networks that can be acceded using contexts as passwords. This mathematical structure emphasises the contacts between LSA and matrix memory models and invites to interpret LSA, and similar procedures, as a reverse engineering applied on context-deprived cognitive products, or on biological objects (e.g. genomes) selected during large evolutionary processes.     

基因序列图形表达及聚类分析应用研究

在基因序列图形表达模型研究的基础上，提出了一种新的非退化的基因图形三维表示方法。该表达方法不仅避免了图形的重叠和交叉，同时还保留了序列的生物学特征。利用该表达方法对H5N1病毒基因序列进行数字特征的提取并引入基于多维PFS判别函数进行模糊聚类分析应用。在聚类分析过程中直接利用数字特征矩阵作为分析数据，分析结果表明：利用文中所给图形表达建立基因序列数字特征矩阵进行的聚类分析具有一定的合理性。     

一类模拟生物复眼几何结构的数据处理方法--方向量子化表示的理论

基于对生物复眼几何结构的模拟,提出一类新颖而有效的数据处理方法－方向量子化方法,该方法适宜于处理由高维数据所表示的凸体的菜,上仍乘法有效、适用广泛、半动态维护简便和易于在各种并行计算模型上实现等优点,理论分析和数值模拟表明：这一方法理论基础坚实,计算稳定可靠,具有广阔的应用前景。     

Pattern recognition methods for advanced stochastic protein sequence analysis using HMMs

Currently, Profile Hidden Markov Models (Profile HMMs) are the methodology of choice for probabilistic protein family modeling. Unfortunately, despite substantial progress the general problem of remote homology analysis is still far from being solved. In this article we propose new approaches for robust protein family modeling by consequently exploiting general pattern recognition techniques. A new feature based representation of amino acid sequences serves as the basis for semi-continuous protein family HMMs. Due to this paradigm shift in processing biological sequences the complexity of family models can be reduced substantially resulting in less parameters which need to be trained. This is especially favorable when only little training data is available as in most current tasks of molecular biology research. In various experiments we prove the superior performance of advanced stochastic protein family modeling for remote homology analysis which is especially relevant for e.g. drug discovery applications.     

Reconstructing an image from its edge representation

In this paper, we show that a new edge detection scheme developed from the notion of transition in nonlinear physics, associated with the precise computation of its quantitative parameters (most notably singularity exponents) provide enhanced performances in terms of reconstruction of the whole image from its edge representation; moreover it is naturally robust to noise. The study of biological vision in mammals state the fact that major information in an image is encoded in its edges, the idea further supported by neurophysics. The first conclusion that can be drawn from this stated fact is that of being able to reconstruct accurately an image from the compact representation of its edge pixels. The paper focuses on how the idea of edge completion can be assessed quantitatively from the framework of reconstructible systems when evaluated in a microcanonical formulation; and how it redefines the adequation of edge as candidates for compact representation. In the process of doing so, we also propose an algorithm for image reconstruction from its edge feature and show that this new algorithm outperforms the well-known ‘state-of-the-art’ techniques, in terms of compact representation, in majority of the cases.     

Robust stability and instability of biochemical networks with parametric uncertainty

Parameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model’s behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we develop a new method for robustness analysis of the dynamical behaviour. As a first step, we provide a characterization of non-robust perturbations as a system of polynomial equalities and inequalities. In the second step, we apply the Positivstellensatz and Handelman representation of polynomials to check for the non-existence of solutions to this system, which can be relaxed to solving a linear program. Thereby, a solution to the linear program yields a robustness certificate for the considered dynamical behaviour. With these robustness certificates, we propose an algorithm to compute a lower robustness bound corresponding to a level of parametric uncertainty up to which no local bifurcations can occur. The applicability of the proposed method to biochemical network models is illustrated by analysing the robustness of oscillations in a model of the NF-κB signalling pathway. The results may be used to define a level of confidence in the observed model behaviour under parametric uncertainty, making them valuable for evaluating dynamical models of biological networks.     

Gene expression and fast construction of distributed evolutionary representation

The gene expression process in nature produces different proteins in different cells from different portions of the DNA. Since proteins control almost every important activity in a living organism, at an abstract level, gene expression can be viewed as a process that evaluates the merit or "fitness" of the DNA. This distributed evaluation of the DNA would not be possible without a decomposed representation of the fitness function defined over the DNAs. This paper argues that, unless the living body was provided with such a representation, we have every reason to believe that it must have an efficient mechanism to construct this distributed representation. This paper demonstrates polynomial-time computability of such a representation by proposing a class of efficient algorithms. The main contribution of this paper is two-fold. On the algorithmic side, it offers a way to scale up evolutionary search by detecting the underlying structure of the search space. On the biological side, it proves that the distributed representation of the evolutionary fitness function in gene expression can be computed in polynomial-time. It advances our understanding about the representation construction in gene expression from the perspective of computing. It also presents experimental results supporting the theoretical performance of the proposed algorithms.     

Interactive Modeling and Authoring of Climbing Plants

We present a novel system for the interactive modeling of developmental climbing plants with an emphasis on efficient control and plausible physics response. A plant is represented by a set of connected anisotropic particles that respond to the surrounding environment and to their inner state. Each particle stores biological and physical attributes that drive growth and plant adaptation to the environment such as light sensitivity, wind interaction, and physical obstacles. This representation allows for the efficient modeling of external effects that can be induced at any time without prior analysis of the plant structure. In our framework we exploit this representation to provide powerful editing capabilities that allow to edit a plant with respect to its structure and its environment while maintaining a biologically plausible appearance. Moreover, we couple plants with Lagrangian fluid dynamics and model advanced effects, such as the breaking and bending of branches. The user can thus interactively drag and prune branches or seed new plants in dynamically changing environments. Our system runs in real‐time and supports up to 20 plant instances with 25k branches in parallel. The effectiveness of our approach is demonstrated through a number of interactive experiments, including modeling and animation of different species of climbing plants on complex support structures.     

Do cortical maps adapt to optimize information density?

Topographic maps are found in many biological and artificial neural systems. In biological systems, some parts of these can form a significantly expanded representation of their sensory input, such as the representation of the fovea in the visual cortex. We propose that a cortical feature map should be organized to optimize the efficiency of information transmission through it. This leads to a principle of uniform cortical information density across the map as the desired optimum. An expanded representation in the cortex for a particular sensory area (i.e. a high magnification factor) means that a greater information density is concentrated in that sensory area, leading to finer discrimination thresholds. Improvement may ultimately be limited by the construction of the sensors themselves. This approach gives a good fit to threshold versus cortical area data of Recanzone et al on owl monkeys trained on a tactile frequency-discrimination task.     

Comparative Analysis of Text Representation Methods Using Classification

In our work, we review and empirically evaluate five different raw methods of text representation that allow automatic processing of Wikipedia articles. The main contribution of the article—evaluation of approaches to text representation for machine learning tasks—indicates that the text representation is fundamental for achieving good categorization results. The analysis of the representation methods creates a baseline that cannot be compensated for even by sophisticated machine learning algorithms. It confirms the thesis that proper data representation is a prerequisite for achieving high-quality results of data analysis. Evaluation of the text representations was performed within the Wikipedia repository by examination of classification parameters observed during automatic reconstruction of human-made categories. For that purpose, we use a classifier based on a support vector machines method, extended with multilabel and multiclass functionalities. During classifier construction we observed parameters such as learning time, representation size, and classification quality that allow us to draw conclusions about text representations. For the experiments presented in the article, we use data sets created from Wikipedia dumps. We describe our software, called Matrix’u, which allows a user to build computational representations of Wikipedia articles. The software is the second contribution of our research, because it is a universal tool for converting Wikipedia from a human-readable form to a form that can be processed by a machine. Results generated using Matrix’u can be used in a wide range of applications that involve usage of Wikipedia data.     

Coding, analysis, interpretation, and recognition of facialexpressions

We describe a computer vision system for observing facial motion by using an optimal estimation optical flow method coupled with geometric, physical and motion-based dynamic models describing the facial structure. Our method produces a reliable parametric representation of the face's independent muscle action groups, as well as an accurate estimate of facial motion. Previous efforts at analysis of facial expression have been based on the facial action coding system (FACS), a representation developed in order to allow human psychologists to code expression from static pictures. To avoid use of this heuristic coding scheme, we have used our computer vision system to probabilistically characterize facial motion and muscle activation in an experimental population, thus deriving a new, more accurate, representation of human facial expressions that we call FACS+. Finally, we show how this method can be used for coding, analysis, interpretation, and recognition of facial expressions     

Deontic logic in the representation of law: Towards a methodology

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of a methodology for its use in the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions.Deontic logic and the theory of normative positions are of relevance to legal knowledge representation, but also to the analysis and. representation of normative systems generally. The emphasis of the paper is on legal knowledge representation, but we seek to place the discussion within the context of a broader range of issues concerning the role of deontic logic in Computer Science.     

Toward data representation with spiking neurons

Notable advances in the understanding of neural processing were made when sensory systems were investigated from the viewpoint of adaptation to the statistical structure of their input space. For this purpose, mathematical methods for data representation were used. Here, we point out that emphasis on the input structure has been at the cost of the biological plausibility of the corresponding neuron models which process the natural stimuli. The signal transformation of the data representation methods does not correspond well to the signal transformations happening at the single-cell level in neural systems. Hence, we now propose data representation by means of spiking neuron models. We formulate the data representation problem as an optimization problem and derive the fundamental quantities for an iterative learning scheme. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

非负矩阵分解在微阵列数据分类和聚类发现中的应用

基因芯片是微阵列技术的典型代表,它具有高通量的特性和同时检测全部基因组基因表达水平的能力。应用微阵列芯片的一个主要目的是基因表达模式的发现,即在基因组水平发现功能相似,生物学过程相关的基因簇;或者将样本分类,发现样本的各种亚型。例如根据基因表达水平对癌症样本进行分类,发现疾病的分子亚型。非负矩阵分解NMF方法是一种非监督的、非正交的、基于局部表示的矩阵分解方法。近年来这种方法被越来越多地应用在微阵列数据的分类分析和聚类发现中。系统地介绍了非负矩阵分解的原理、算法和应用,分解结果的生物学解释,分类结果的质量评估和基于NMF算法的分类软件。总结并评估了NMF方法在微阵列数据分类和聚类发现应用中的表现。     

The virtual feedback problem in hierarchical representations of combinational circuits

Orders of magnitude of space and time can be saved if hierarchical algorithms are used for automatic synthesis and analysis of regular VLSI circuits. When we tried to apply this technique to compiled simulation of large regular combinational circuits, we observed that hierarchical representations of acyclic circuits often contain cycles. In this paper we study the question of whether this undesired property is necessary or not. We prove, that there are combinational circuits, which have a succinct cyclic hierarchical representation, but where each acyclic hierarchical representation is large. This negative result may be weakened, if we allow the circuits structure to be changed but not its behavior. We also discuss the effect of these observations on hierarchical simulation techniques and the complexity of pragmatic approaches such as the construction of a smallest acyclic refinement of a hierarchical representation.This work was supported by Deutsche Forschungsgemeinschaft under contract SFB 124 B1