We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of $n$ identical particles that are randomly distributed on the real line and have zero initial speeds. Particles begin to move
under the forces of mutual attraction. When particles collide, they stick together forming a new particle, called cluster, whose mass and speed are defined by the laws of conservation. We are interested in the asymptotic behavior of $K_n(t)$ as $nto infty$, where $K_n(t)$ denotes the number of clusters at time $t$ in the system with $n$ initial particles. Our main result is a functional limit theorem for $K_n(t)$. Its proof is based on the discovered localization property of the aggregation process, which states that the behavior of each particle is essentially defined by the motion of neighbor particles.
The formation of quasi-2D spin-wave waveforms in longitudinally magnetized stripes of ferrimagnetic film was observed by using time- and space-resolved Brillouin light scattering technique. In the linear regime it was found that the confinement decre
ases the amplitude of dynamic magnetization near the lateral stripe edges. Thus, the so-called effective dipolar pinning of dynamic magnetization takes place at the edges. In the nonlinear regime a new stable spin wave packet propagating along a waveguide structure, for which both transversal instability and interaction with the side walls of the waveguide are important was observed. The experiments and a numerical simulation of the pulse evolution show that the shape of the formed waveforms and their behavior are strongly influenced by the confinement.
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length $n$ with
$m$-state HMM can be as low as $Theta(mlog n)$, without a significant slow-down compared to the classical Viterbi algorithm. Classical Viterbi algorithm requires $O(mn)$ space, which is impractical for analysis of long DNA sequences (such as complete human genome chromosomes) and for continuous data streams. We also experimentally demonstrate the performance of the on-line Viterbi algorithm on a simple HMM for gene finding on both simulated and real DNA sequences.
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper,
we study the number of positive steady states of a general multisite phosphorylation-dephosphorylation cycle, and how the number of positive steady states varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (in particular, this implies that for n=2, including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.
We describe a new algorithm, the $(k,ell)$-pebble game with colors, and use it obtain a characterization of the family of $(k,ell)$-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs. Special inst
ances of sparse graphs appear in rigidity theory and have received increased attention in recent years. In particular, our colored pebbles generalize and strengthen the previous results of Lee and Streinu and give a new proof of the Tutte-Nash-Williams characterization of arboricity. We also present a new decomposition that certifies sparsity based on the $(k,ell)$-pebble game with colors. Our work also exposes connections between pebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and Westermann and Hendrickson.
Precision tests of the Kobayashi-Maskawa model of CP violation are discussed, pointing out possible signatures for other sources of CP violation and for new flavor-changing operators. The current status of the most accurate tests is summarized.
The quadratic pion scalar radius, la r^2ra^pi_s, plays an important role for present precise determinations of pipi scattering. Recently, Yndurain, using an Omn`es representation of the null isospin(I) non-strange pion scalar form factor, obtains la
r^2ra^pi_s=0.75pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn`es equations, la r^2ra^pi_s=0.61pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndurains method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input pipi phase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is la r^2ra_s^pi=0.65pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 pipi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.
Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of non-zero elements, is presented and analysed using methods of statistical physic
s. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code.
We investigate the effect of tuning the phonon energy on the correlation effects in models of electron-phonon interactions using DMFT. In the regime where itinerant electrons, instantaneous electron-phonon driven correlations and static distortions c
ompete on similar energy scales, we find several interesting results including (1) A crossover from band to Mott behavior in the spectral function, leading to hybrid band/Mott features in the spectral function for phonon frequencies slightly larger than the band width. (2) Since the optical conductivity depends sensitively on the form of the spectral function, we show that such a regime should be observable through the low frequency form of the optical conductivity. (3) The resistivity has a double kondo peak arrangement
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible tak
ing into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics . In conclusion we propose an example of formal quantum coherence.
