Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite

On the emergence and evolution of artificial cell signaling networks

This PhD project is concerned with the evolution of Cell Signaling Networks (CSNs) in silico. CSNs are complex biochemical networks responsible for the coordination of cellular activities. We are investigating the possibility to build an evolutionary simulation platform that would allow the spontaneous emergence and evolution of Artificial Cell Signaling Networks (ACSNs). From a practical point of view, realizing and evolving ACSNs may provide novel computational paradigms for a variety of application areas. This work may also contribute to the biological understanding of the origins and evolution of real CSNs

Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.Comment: Darwinian Neurodynamics. Submitted as a two part paper to Living Machines 2013 Natural History Museum, Londo

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors

In silico transitions to multicellularity

The emergence of multicellularity and developmental programs are among the major problems of evolutionary biology. Traditionally, research in this area has been based on the combination of data analysis and experimental work on one hand and theoretical approximations on the other. A third possibility is provided by computer simulation models, which allow to both simulate reality and explore alternative possibilities. These in silico models offer a powerful window to the possible and the actual by means of modeling how virtual cells and groups of cells can evolve complex interactions beyond a set of isolated entities. Here we present several examples of such models, each one illustrating the potential for artificial modeling of the transition to multicellularity.Comment: 21 pages, 10 figures. Book chapter of Evolutionary transitions to multicellular life (Springer

Non-perturbative effects and the refined topological string

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.Comment: 38 pages, 5 figure

Explaining Adaptation in Genetic Algorithms With Uniform Crossover: The Hyperclimbing Hypothesis

The hyperclimbing hypothesis is a hypothetical explanation for adaptation in genetic algorithms with uniform crossover (UGAs). Hyperclimbing is an intuitive, general-purpose, non-local search heuristic applicable to discrete product spaces with rugged or stochastic cost functions. The strength of this heuristic lie in its insusceptibility to local optima when the cost function is deterministic, and its tolerance for noise when the cost function is stochastic. Hyperclimbing works by decimating a search space, i.e. by iteratively fixing the values of small numbers of variables. The hyperclimbing hypothesis holds that UGAs work by implementing efficient hyperclimbing. Proof of concept for this hypothesis comes from the use of a novel analytic technique involving the exploitation of algorithmic symmetry. We have also obtained experimental results that show that a simple tweak inspired by the hyperclimbing hypothesis dramatically improves the performance of a UGA on large, random instances of MAX-3SAT and the Sherrington Kirkpatrick Spin Glasses problem.Comment: 22 pages, 5 figure

Revisiting Waiting Times in DNA evolution

Transcription factors are short stretches of DNA (or $k$-mers) mainly located in promoters sequences that enhance or repress gene expression. With respect to an initial distribution of letters on the DNA alphabet, Behrens and Vingron consider a random sequence of length $n$ that does not contain a given $k$-mer or word of size $k$. Under an evolution model of the DNA, they compute the probability $\mathfrak{p}_n$ that this $k$-mer appears after a unit time of 20 years. They prove that the waiting time for the first apparition of the $k$-mer is well approximated by $T_n=1/\mathfrak{p}_n$. Their work relies on the simplifying assumption that the $k$-mer is not self-overlapping. They observe in particular that the waiting time is mostly driven by the initial distribution of letters. Behrens et al. use an approach by automata that relaxes the assumption related to words overlaps. Their numerical evaluations confirms the validity of Behrens and Vingron approach for non self-overlapping words, but provides up to 44% corrections for highly self-overlapping words such as $\mathtt{AAAAA}$. We devised an approach of the problem by clump analysis and generating functions; this approach leads to prove a quasi-linear behaviour of $\mathfrak{p}_n$ for a large range of values of $n$, an important result for DNA evolution. We present here this clump analysis, first by language decomposition, and next by an automaton construction; finally, we describe an equivalent approach by construction of Markov automata.Comment: 19 pages, 3 Figures, 2 Table

SNOMED CT standard ontology based on the ontology for general medical science

Background: Systematized Nomenclature of Medicine—Clinical Terms (SNOMED CT, hereafter abbreviated SCT) is acomprehensive medical terminology used for standardizing the storage, retrieval, and exchange of electronic healthdata. Some efforts have been made to capture the contents of SCT as Web Ontology Language (OWL), but theseefforts have been hampered by the size and complexity of SCT. Method: Our proposal here is to develop an upper-level ontology and to use it as the basis for defining the termsin SCT in a way that will support quality assurance of SCT, for example, by allowing consistency checks ofdefinitions and the identification and elimination of redundancies in the SCT vocabulary. Our proposed upper-levelSCT ontology (SCTO) is based on the Ontology for General Medical Science (OGMS). Results: The SCTO is implemented in OWL 2, to support automatic inference and consistency checking. Theapproach will allow integration of SCT data with data annotated using Open Biomedical Ontologies (OBO) Foundryontologies, since the use of OGMS will ensure consistency with the Basic Formal Ontology, which is the top-levelontology of the OBO Foundry. Currently, the SCTO contains 304 classes, 28 properties, 2400 axioms, and 1555annotations. It is publicly available through the bioportal athttp://bioportal.bioontology.org/ontologies/SCTO/. Conclusion: The resulting ontology can enhance the semantics of clinical decision support systems and semanticinteroperability among distributed electronic health records. In addition, the populated ontology can be used forthe automation of mobile health applications