507 research outputs found
Optimal synchronization of ABD networks
We present in this paper a simple and efficient synchronizer algorithm for Asynchonous Bounded Delay Networks. In these networks each processor has a local clock, and the message delay is bounded by a known constant. The algorithm improves on an earlier synchronizer for this network model, presented by Cou et al. Moreover, using a mathematical model for this type of synchronizer, we show that the round time of new synchronizer is optimal
Electromagnetic Oscillations in a Driven Nonlinear Resonator: A New Description of Complex Nonlinear Dynamics
Many intriguing properties of driven nonlinear resonators, including the
appearance of chaos, are very important for understanding the universal
features of nonlinear dynamical systems and can have great practical
significance. We consider a cylindrical cavity resonator driven by an
alternating voltage and filled with a nonlinear nondispersive medium. It is
assumed that the medium lacks a center of inversion and the dependence of the
electric displacement on the electric field can be approximated by an
exponential function. We show that the Maxwell equations are integrated exactly
in this case and the field components in the cavity are represented in terms of
implicit functions of special form. The driven electromagnetic oscillations in
the cavity are found to display very interesting temporal behavior and their
Fourier spectra contain singular continuous components. To the best of our
knowledge, this is the first demonstration of the existence of a singular
continuous (fractal) spectrum in an exactly integrable system.Comment: 5 pages, 3 figure
Sierpinski signal generates spectra
We investigate the row sum of the binary pattern generated by the Sierpinski
automaton: Interpreted as a time series we calculate the power spectrum of this
Sierpinski signal analytically and obtain a unique rugged fine structure with
underlying power law decay with an exponent of approximately 1.15. Despite the
simplicity of the model, it can serve as a model for spectra in a
certain class of experimental and natural systems like catalytic reactions and
mollusc patterns.Comment: 4 pages (4 figs included). Accepted for publication in Physical
Review
Synchronizing automata with random inputs
We study the problem of synchronization of automata with random inputs. We
present a series of automata such that the expected number of steps until
synchronization is exponential in the number of states. At the same time, we
show that the expected number of letters to synchronize any pair of the famous
Cerny automata is at most cubic in the number of states
Steady Stokes flow with long-range correlations, fractal Fourier spectrum, and anomalous transport
We consider viscous two-dimensional steady flows of incompressible fluids
past doubly periodic arrays of solid obstacles. In a class of such flows, the
autocorrelations for the Lagrangian observables decay in accordance with the
power law, and the Fourier spectrum is neither discrete nor absolutely
continuous. We demonstrate that spreading of the droplet of tracers in such
flows is anomalously fast. Since the flow is equivalent to the integrable
Hamiltonian system with 1 degree of freedom, this provides an example of
integrable dynamics with long-range correlations, fractal power spectrum, and
anomalous transport properties.Comment: 4 pages, 4 figures, published in Physical Review Letter
Exact scaling in the expansion-modification system
This work is devoted to the study of the scaling, and the consequent
power-law behavior, of the correlation function in a mutation-replication model
known as the expansion-modification system. The latter is a biology inspired
random substitution model for the genome evolution, which is defined on a
binary alphabet and depends on a parameter interpreted as a \emph{mutation
probability}. We prove that the time-evolution of this system is such that any
initial measure converges towards a unique stationary one exhibiting decay of
correlations not slower than a power-law. We then prove, for a significant
range of mutation probabilities, that the decay of correlations indeed follows
a power-law with scaling exponent smoothly depending on the mutation
probability. Finally we put forward an argument which allows us to give a
closed expression for the corresponding scaling exponent for all the values of
the mutation probability. Such a scaling exponent turns out to be a piecewise
smooth function of the parameter.Comment: 22 pages, 2 figure
Shuffling cards, factoring numbers, and the quantum baker's map
It is pointed out that an exactly solvable permutation operator, viewed as
the quantization of cyclic shifts, is useful in constructing a basis in which
to study the quantum baker's map, a paradigm system of quantum chaos. In the
basis of this operator the eigenfunctions of the quantum baker's map are
compressed by factors of around five or more. We show explicitly its connection
to an operator that is closely related to the usual quantum baker's map. This
permutation operator has interesting connections to the art of shuffling cards
as well as to the quantum factoring algorithm of Shor via the quantum order
finding one. Hence we point out that this well-known quantum algorithm makes
crucial use of a quantum chaotic operator, or at least one that is close to the
quantization of the left-shift, a closeness that we also explore
quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to
the quantum bakers map. To appear in J. Phys.
Detectability of non-differentiable generalized synchrony
Generalized synchronization of chaos is a type of cooperative behavior in
directionally-coupled oscillators that is characterized by existence of stable
and persistent functional dependence of response trajectories from the chaotic
trajectory of driving oscillator. In many practical cases this function is
non-differentiable and has a very complex shape. The generalized synchrony in
such cases seems to be undetectable, and only the cases, in which a
differentiable synchronization function exists, are considered to make sense in
practice. We show that this viewpoint is not always correct and the
non-differentiable generalized synchrony can be revealed in many practical
cases. Conditions for detection of generalized synchrony are derived
analytically, and illustrated numerically with a simple example of
non-differentiable generalized synchronization.Comment: 8 pages, 8 figures, submitted to PR
Therapeutic limitations in tumor-specific CD8+ memory T cell engraftment
BACKGROUND: Adoptive immunotherapy with cytotoxic T lymphocytes (CTL) represents an alternative approach to treating solid tumors. Ideally, this would confer long-term protection against tumor. We previously demonstrated that in vitro-generated tumor-specific CTL from the ovalbumin (OVA)-specific OT-I T cell receptor transgenic mouse persisted long after adoptive transfer as memory T cells. When recipient mice were challenged with the OVA-expressing E.G7 thymoma, tumor growth was delayed and sometimes prevented. The reasons for therapeutic failures were not clear. METHODS: OT-I CTL were adoptively transferred to C57BL/6 mice 21 – 28 days prior to tumor challenge. At this time, the donor cells had the phenotypical and functional characteristics of memory CD8+ T cells. Recipients which developed tumor despite adoptive immunotherapy were analyzed to evaluate the reason(s) for therapeutic failure. RESULTS: Dose-response studies demonstrated that the degree of tumor protection was directly proportional to the number of OT-I CTL adoptively transferred. At a low dose of OT-I CTL, therapeutic failure was attributed to insufficient numbers of OT-I T cells that persisted in vivo, rather than mechanisms that actively suppressed or anergized the OT-I T cells. In recipients of high numbers of OT-I CTL, the E.G7 tumor that developed was shown to be resistant to fresh OT-I CTL when examined ex vivo. Furthermore, these same tumor cells no longer secreted a detectable level of OVA. In this case, resistance to immunotherapy was secondary to selection of clones of E.G7 that expressed a lower level of tumor antigen. CONCLUSIONS: Memory engraftment with tumor-specific CTL provides long-term protection against tumor. However, there are several limitations to this immunotherapeutic strategy, especially when targeting a single antigen. This study illustrates the importance of administering large numbers of effectors to engraft sufficiently efficacious immunologic memory. It also demonstrates the importance of targeting several antigens when developing vaccine strategies for cancer
- …