213 research outputs found
Application of The Method of Elastic Maps In Analysis of Genetic Texts
Abstract - Method of elastic maps ( http://cogprints.ecs.soton.ac.uk/archive/00003088/ and
http://cogprints.ecs.soton.ac.uk/archive/00003919/ )
allows us to construct efficiently 1D, 2D and 3D non-linear approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. We describe the idea of the method and demonstrate its applications in analysis of genetic sequences. The animated 3D-scatters are available on our web-site: http://www.ihes.fr/~zinovyev/7clusters/
We found the universal cluster structure of genetic sequences, and demonstrated the thin structure of these clusters for coding regions. This thin structure is related to different translational efficiency
The General Approximation Theorem
A general approximation theorem is proved. It uniformly envelopes both the classical Stone theorem and approximation of functions of several variables by means of superpositions and linear combinations of functions of one variable. This theorem is interpreted as a statement on universal approximating possibilities ( approximating omnipotence ) of arbitrary nonlinearity. For the neural networks, our result states that the function of neuron activation must be nonlinear, and nothing els
High Order Orthogonal Tensor Networks: Information Capacity and Reliability
Neural networks based on construction of orthogonal projectors in the tensor power of space of signals are described. A sharp estimate of their ultimate information capacity is obtained. The number of stored prototype patterns (prototypes) can many times exceed the number of neurons. A comparison with the error control codes is mad
Elastic principal manifolds and their practical applications
Principal manifolds serve as useful tool for many practical applications.
These manifolds are defined as lines or surfaces passing through "the middle"
of data distribution. We propose an algorithm for fast construction of grid
approximations of principal manifolds with given topology. It is based on
analogy of principal manifold and elastic membrane. The first advantage of this
method is a form of the functional to be minimized which becomes quadratic at
the step of the vertices position refinement. This makes the algorithm very
effective, especially for parallel implementations. Another advantage is that
the same algorithmic kernel is applied to construct principal manifolds of
different dimensions and topologies. We demonstrate how flexibility of the
approach allows numerous adaptive strategies like principal graph constructing,
etc. The algorithm is implemented as a C++ package elmap and as a part of
stand-alone data visualization tool VidaExpert, available on the web. We
describe the approach and provide several examples of its application with
speed performance characteristics.Comment: 26 pages, 10 figures, edited final versio
The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007
In special coordinates (codon position--specific nucleotide frequencies)
bacterial genomes form two straight lines in 9-dimensional space: one line for
eubacterial genomes, another for archaeal genomes. All the 348 distinct
bacterial genomes available in Genbank in April 2007, belong to these lines
with high accuracy. The main challenge now is to explain the observed high
accuracy. The new phenomenon of complementary symmetry for codon
position--specific nucleotide frequencies is observed. The results of analysis
of several codon usage models are presented. We demonstrate that the
mean--field approximation, which is also known as context--free, or complete
independence model, or Segre variety, can serve as a reasonable approximation
to the real codon usage. The first two principal components of codon usage
correlate strongly with genomic G+C content and the optimal growth temperature
respectively. The variation of codon usage along the third component is related
to the curvature of the mean-field approximation. First three eigenvalues in
codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and
archaeal genomes codon usage is clearly distributed along two third order
curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct
bacterial genomes available in Genbank in April 200
Back-propagation of accuracy
In this paper we solve the problem: how to determine maximal allowable
errors, possible for signals and parameters of each element of a network
proceeding from the condition that the vector of output signals of the network
should be calculated with given accuracy? "Back-propagation of accuracy" is
developed to solve this problem. The calculation of allowable errors for each
element of network by back-propagation of accuracy is surprisingly similar to a
back-propagation of error, because it is the backward signals motion, but at
the same time it is very different because the new rules of signals
transformation in the passing back through the elements are different. The
method allows us to formulate the requirements to the accuracy of calculations
and to the realization of technical devices, if the requirements to the
accuracy of output signals of the network are known.Comment: 4 pages, 5 figures, The talk given on ICNN97 (The 1997 IEEE
International Conference on Neural Networks, Houston, USA
Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory
We use the entropy production variational method to associate a one particle
distribution function to the assumed known energy-momentum and entropy currents
describing a relativistic conformal fluid. Assuming a simple form for the
collision operator we find this one particle distribution function explicitly,
and show that this method of linking the hydro and kinetic description is a non
trivial generalization of Grad's ansatz. The resulting constitutive relations
are the same as in the conformal dissipative type theories discussed in J.
Peralta-Ramos and E. Calzetta, Phys. Rev. D {\bfseries 80}, 126002 (2009). Our
results may prove useful in the description of freeze-out in ultrarelativistic
heavy-ion collisions.Comment: v2: 23 pages, no figures, accepted in Phys. Rev.
Thermodynamic Tree: The Space of Admissible Paths
Is a spontaneous transition from a state x to a state y allowed by
thermodynamics? Such a question arises often in chemical thermodynamics and
kinetics. We ask the more formal question: is there a continuous path between
these states, along which the conservation laws hold, the concentrations remain
non-negative and the relevant thermodynamic potential G (Gibbs energy, for
example) monotonically decreases? The obvious necessary condition, G(x)\geq
G(y), is not sufficient, and we construct the necessary and sufficient
conditions. For example, it is impossible to overstep the equilibrium in
1-dimensional (1D) systems (with n components and n-1 conservation laws). The
system cannot come from a state x to a state y if they are on the opposite
sides of the equilibrium even if G(x) > G(y). We find the general
multidimensional analogue of this 1D rule and constructively solve the problem
of the thermodynamically admissible transitions.
We study dynamical systems, which are given in a positively invariant convex
polyhedron D and have a convex Lyapunov function G. An admissible path is a
continuous curve along which does not increase. For x,y from D, x\geq y (x
precedes y) if there exists an admissible path from x to y and x \sim y if
x\geq y and y\geq x. The tree of G in D is a quotient space D/~. We provide an
algorithm for the construction of this tree. In this algorithm, the restriction
of G onto the 1-skeleton of (the union of edges) is used. The problem of
existence of admissible paths between states is solved constructively. The
regions attainable by the admissible paths are described.Comment: Extended version, 31 page, 9 figures, 69 cited references, many minor
correction
Decay and coherence of two-photon excited yellow ortho-excitons in Cu2O
Photoluminescence excitation spectroscopy has revealed a novel, highly
efficient two-photon excitation method to produce a cold, uniformly distributed
high density excitonic gas in bulk cuprous oxide. A study of the time evolution
of the density, temperature and chemical potential of the exciton gas shows
that the so called quantum saturation effect that prevents Bose-Einstein
condensation of the ortho-exciton gas originates from an unfavorable ratio
between the cooling and recombination rates. Oscillations observed in the
temporal decay of the ortho-excitonic luminescence intensity are discussed in
terms of polaritonic beating. We present the semiclassical description of
polaritonic oscillations in linear and non-linear optical processes.Comment: 14 pages, 12 figure
- …