31,581 research outputs found
Differentiable Genetic Programming
We introduce the use of high order automatic differentiation, implemented via
the algebra of truncated Taylor polynomials, in genetic programming. Using the
Cartesian Genetic Programming encoding we obtain a high-order Taylor
representation of the program output that is then used to back-propagate errors
during learning. The resulting machine learning framework is called
differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic
regression, dCGP offers a new approach to the long unsolved problem of constant
representation in GP expressions. On several problems of increasing complexity
we find that dCGP is able to find the exact form of the symbolic expression as
well as the constants values. We also demonstrate the use of dCGP to solve a
large class of differential equations and to find prime integrals of dynamical
systems, presenting, in both cases, results that confirm the efficacy of our
approach
A Computational Algebra Approach to the Reverse Engineering of Gene Regulatory Networks
This paper proposes a new method to reverse engineer gene regulatory networks
from experimental data. The modeling framework used is time-discrete
deterministic dynamical systems, with a finite set of states for each of the
variables. The simplest examples of such models are Boolean networks, in which
variables have only two possible states. The use of a larger number of possible
states allows a finer discretization of experimental data and more than one
possible mode of action for the variables, depending on threshold values.
Furthermore, with a suitable choice of state set, one can employ powerful tools
from computational algebra, that underlie the reverse-engineering algorithm,
avoiding costly enumeration strategies. To perform well, the algorithm requires
wildtype together with perturbation time courses. This makes it suitable for
small to meso-scale networks rather than networks on a genome-wide scale. The
complexity of the algorithm is quadratic in the number of variables and cubic
in the number of time points. The algorithm is validated on a recently
published Boolean network model of segment polarity development in Drosophila
melanogaster.Comment: 28 pages, 5 EPS figures, uses elsart.cl
The Genetic Code as a Periodic Table: Algebraic Aspects
The systematics of indices of physico-chemical properties of codons and amino
acids across the genetic code are examined. Using a simple numerical labelling
scheme for nucleic acid bases, data can be fitted as low-order polynomials of
the 6 coordinates in the 64-dimensional codon weight space. The work confirms
and extends recent studies by Siemion of amino acid conformational parameters.
The connections between the present work, and recent studies of the genetic
code structure using dynamical symmetry algebras, are pointed out.Comment: 26 pages Latex, 10 figures (4 ps, 6 Tex). Refereed version, small
changes to discussion (conclusion unaltered). Minor alterations to format of
figures and tables. To appear in BioSystem
Symmetry and Minimum Principle at the Basis of the Genetic Code
The importance of the notion of symmetry in physics is well established:
could it also be the case for the genetic code? In this spirit, a model for the
Genetic Code based on continuous symmetries and entitled the "Crystal Basis
Model" has been proposed a few years ago. The present paper is a review of the
model, of some of its first applications as well as of its recent developments.
Indeed, after a motivated presentation of our mathematical model, we illustrate
its pertinence by applying it for the elaboration and verification of sum rules
for codon usage probabilities, as well as for establishing relations and some
predictions between physical-chemical properties of amino-acids. Then, defining
in this context a "bio-spin" structure for the nucleotides and codons, the
interaction between a couple of codon-anticodon can simply be represented by a
(bio) spin-spin potential. This approach will constitute the second part of the
paper where, imposing the minimum energy principle, an analysis of the
evolution of the genetic code can be performed with good agreement with the
generally accepted scheme. A more precise study of this interaction model
provides informations on codon bias, consistent with data.Comment: To appear in BIOMAT 2016, 326 - 362, 201
Dealing with Qualitative and Quantitative Features in Legal Domains
In this work, we enrich a formalism for argumentation by including a formal
characterization of features related to the knowledge, in order to capture
proper reasoning in legal domains. We add meta-data information to the
arguments in the form of labels representing quantitative and qualitative data
about them. These labels are propagated through an argumentative graph
according to the relations of support, conflict, and aggregation between
arguments.Comment: arXiv admin note: text overlap with arXiv:1903.0186
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