127,403 research outputs found
Parabolic orbits of -nilpotent elements for classical groups
We consider the conjugation-action of the Borel subgroup of the symplectic or
the orthogonal group on the variety of nilpotent complex elements of nilpotency
degree in its Lie algebra. We translate the setup to a
representation-theoretic context in the language of a symmetric quiver algebra.
This makes it possible to provide a parametrization of the orbits via a
combinatorial tool that we call symplectic/orthogonal oriented link patterns.
We deduce information about numerology. We then generalize these
classifications to standard parabolic subgroups for all classical groups.
Finally, our results are restricted to the nilradical.Comment: comments welcom
Ancestral Causal Inference
Constraint-based causal discovery from limited data is a notoriously
difficult challenge due to the many borderline independence test decisions.
Several approaches to improve the reliability of the predictions by exploiting
redundancy in the independence information have been proposed recently. Though
promising, existing approaches can still be greatly improved in terms of
accuracy and scalability. We present a novel method that reduces the
combinatorial explosion of the search space by using a more coarse-grained
representation of causal information, drastically reducing computation time.
Additionally, we propose a method to score causal predictions based on their
confidence. Crucially, our implementation also allows one to easily combine
observational and interventional data and to incorporate various types of
available background knowledge. We prove soundness and asymptotic consistency
of our method and demonstrate that it can outperform the state-of-the-art on
synthetic data, achieving a speedup of several orders of magnitude. We
illustrate its practical feasibility by applying it on a challenging protein
data set.Comment: In Proceedings of Advances in Neural Information Processing Systems
29 (NIPS 2016
A knowledge representation meta-model for rule-based modelling of signalling networks
The study of cellular signalling pathways and their deregulation in disease
states, such as cancer, is a large and extremely complex task. Indeed, these
systems involve many parts and processes but are studied piecewise and their
literatures and data are consequently fragmented, distributed and sometimes--at
least apparently--inconsistent. This makes it extremely difficult to build
significant explanatory models with the result that effects in these systems
that are brought about by many interacting factors are poorly understood.
The rule-based approach to modelling has shown some promise for the
representation of the highly combinatorial systems typically found in
signalling where many of the proteins are composed of multiple binding domains,
capable of simultaneous interactions, and/or peptide motifs controlled by
post-translational modifications. However, the rule-based approach requires
highly detailed information about the precise conditions for each and every
interaction which is rarely available from any one single source. Rather, these
conditions must be painstakingly inferred and curated, by hand, from
information contained in many papers--each of which contains only part of the
story.
In this paper, we introduce a graph-based meta-model, attuned to the
representation of cellular signalling networks, which aims to ease this massive
cognitive burden on the rule-based curation process. This meta-model is a
generalization of that used by Kappa and BNGL which allows for the flexible
representation of knowledge at various levels of granularity. In particular, it
allows us to deal with information which has either too little, or too much,
detail with respect to the strict rule-based meta-model. Our approach provides
a basis for the gradual aggregation of fragmented biological knowledge
extracted from the literature into an instance of the meta-model from which we
can define an automated translation into executable Kappa programs.Comment: In Proceedings DCM 2015, arXiv:1603.0053
Chemoinformatics Research at the University of Sheffield: A History and Citation Analysis
This paper reviews the work of the Chemoinformatics Research Group in the Department of Information Studies at the University of Sheffield, focusing particularly on the work carried out in the period 1985-2002. Four major research areas are discussed, these involving the development of methods for: substructure searching in databases of three-dimensional structures, including both rigid and flexible molecules; the representation and searching of the Markush structures that occur in chemical patents; similarity searching in databases of both two-dimensional and three-dimensional structures; and compound selection and the design of combinatorial libraries. An analysis of citations to 321 publications from the Group shows that it attracted a total of 3725 residual citations during the period 1980-2002. These citations appeared in 411 different journals, and involved 910 different citing organizations from 54 different countries, thus demonstrating the widespread impact of the Group's work
Logic learning and optimized drawing: two hard combinatorial problems
Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures
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