499 research outputs found

### A "metric" complexity for weakly chaotic systems

We consider the number of Bowen sets which are necessary to cover a large
measure subset of the phase space. This introduce some complexity indicator
characterizing different kind of (weakly) chaotic dynamics. Since in many
systems its value is given by a sort of local entropy, this indicator is quite
simple to be calculated. We give some example of calculation in nontrivial
systems (interval exchanges, piecewise isometries e.g.) and a formula similar
to the Ruelle-Pesin one, relating the complexity indicator to some initial
condition sensitivity indicators playing the role of positive Lyapunov
exponents.Comment: 15 pages, no figures. Articl

### Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function
S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov
exponents or systems that exhibit strong intermittent behavior with
``flights'', trappings, weak mixing, etc. The important part of the new notions
is the first appearance of epsilon-separation of initially close trajectories.
The complexity function is similar to the propagator p(t0,x0;t,x) with a
replacement of x by the natural lengths s of trajectories, and its introduction
does not assume of the space-time independence in the process of evolution of
the system. A special stress is done on the choice of variables and the
replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider
time-algebraic and space-algebraic complexity and some mixed cases. It is shown
that for typical cases the entropy function S(epsilon;xi,eta) possesses
invariants (alpha,beta) that describe the fractal dimensions of the space-time
structures of trajectories. The invariants (alpha,beta) can be linked to the
transport properties of the system, from one side, and to the Riemann
invariants for simple waves, from the other side. This analog provides a new
meaning for the transport exponent mu that can be considered as the speed of a
Riemann wave in the log-phase space of the log-space-time variables. Some other
applications of new notions are considered and numerical examples are
presented.Comment: 27 pages, 6 figure

### Extensive parallelism in protein evolution

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

### Recurrence and algorithmic information

In this paper we initiate a somewhat detailed investigation of the
relationships between quantitative recurrence indicators and algorithmic
complexity of orbits in weakly chaotic dynamical systems. We mainly focus on
examples.Comment: 26 pages, no figure

### Complexity for extended dynamical systems

We consider dynamical systems for which the spatial extension plays an
important role. For these systems, the notions of attractor, epsilon-entropy
and topological entropy per unit time and volume have been introduced
previously. In this paper we use the notion of Kolmogorov complexity to
introduce, for extended dynamical systems, a notion of complexity per unit time
and volume which plays the same role as the metric entropy for classical
dynamical systems. We introduce this notion as an almost sure limit on orbits
of the system. Moreover we prove a kind of variational principle for this
complexity.Comment: 29 page

### Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies

Existing sequence alignment algorithms use heuristic scoring schemes which
cannot be used as objective distance metrics. Therefore one relies on measures
like the p- or log-det distances, or makes explicit, and often simplistic,
assumptions about sequence evolution. Information theory provides an
alternative, in the form of mutual information (MI) which is, in principle, an
objective and model independent similarity measure. MI can be estimated by
concatenating and zipping sequences, yielding thereby the "normalized
compression distance". So far this has produced promising results, but with
uncontrolled errors. We describe a simple approach to get robust estimates of
MI from global pairwise alignments. Using standard alignment algorithms, this
gives for animal mitochondrial DNA estimates that are strikingly close to
estimates obtained from the alignment free methods mentioned above. Our main
result uses algorithmic (Kolmogorov) information theory, but we show that
similar results can also be obtained from Shannon theory. Due to the fact that
it is not additive, normalized compression distance is not an optimal metric
for phylogenetics, but we propose a simple modification that overcomes the
issue of additivity. We test several versions of our MI based distance measures
on a large number of randomly chosen quartets and demonstrate that they all
perform better than traditional measures like the Kimura or log-det (resp.
paralinear) distances. Even a simplified version based on single letter Shannon
entropies, which can be easily incorporated in existing software packages, gave
superior results throughout the entire animal kingdom. But we see the main
virtue of our approach in a more general way. For example, it can also help to
judge the relative merits of different alignment algorithms, by estimating the
significance of specific alignments.Comment: 19 pages + 16 pages of supplementary materia

### Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page

### Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (Ă˘â€°0.1Ă˘â‚¬ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced

### M-GCAT: interactively and efficiently constructing large-scale multiple genome comparison frameworks in closely related species

BACKGROUND: Due to recent advances in whole genome shotgun sequencing and assembly technologies, the financial cost of decoding an organism's DNA has been drastically reduced, resulting in a recent explosion of genomic sequencing projects. This increase in related genomic data will allow for in depth studies of evolution in closely related species through multiple whole genome comparisons. RESULTS: To facilitate such comparisons, we present an interactive multiple genome comparison and alignment tool, M-GCAT, that can efficiently construct multiple genome comparison frameworks in closely related species. M-GCAT is able to compare and identify highly conserved regions in up to 20 closely related bacterial species in minutes on a standard computer, and as many as 90 (containing 75 cloned genomes from a set of 15 published enterobacterial genomes) in an hour. M-GCAT also incorporates a novel comparative genomics data visualization interface allowing the user to globally and locally examine and inspect the conserved regions and gene annotations. CONCLUSION: M-GCAT is an interactive comparative genomics tool well suited for quickly generating multiple genome comparisons frameworks and alignments among closely related species. M-GCAT is freely available for download for academic and non-commercial use at:

### Bioinstructive implantable scaffolds for rapid in vivo manufacture and release of CAR-T cells

Despite their clinical success, chimeric antigen receptor (CAR)-T cell therapies for B cell malignancies are limited by lengthy, costly and labor-intensive ex vivo manufacturing procedures that might lead to cell products with heterogeneous composition. Here we describe an implantable Multifunctional Alginate Scaffold for T Cell Engineering and Release (MASTER) that streamlines in vivo CAR-T cell manufacturing and reduces processing time to a single day. When seeded with human peripheral blood mononuclear cells and CD19-encoding retroviral particles, MASTER provides the appropriate interface for viral vector-mediated gene transfer and, after subcutaneous implantation, mediates the release of functional CAR-T cells in mice. We further demonstrate that in vivo-generated CAR-T cells enter the bloodstream and control distal tumor growth in a mouse xenograft model of lymphoma, showing greater persistence than conventional CAR-T cells. MASTER promises to transform CAR-T cell therapy by fast-tracking manufacture and potentially reducing the complexity and resources needed for provision of this type of therapy

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