Counting permutations by alternating descents

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can be expressed as the reciprocal of a sum involving Euler numbers. We give two proofs of the formula. The first uses a system of differential equations. The second proof derives the generating function directly from general permutation enumeration techniques, using noncommutative symmetric functions. The generating function is an "alternating" analogue of David and Barton's generating function for permutations with no increasing runs of length 3 or more. Our general results give further alternating analogues of permutation enumeration formulas, including results of Chebikin and Remmel

Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration

The thermal and nonthermal pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated. The nonthermal decay into pions of sigma mesons which are popularly produced in chiral symmetric phase leads to a low-momentum pion enhancement as a possible signature of chiral phase transition at finite temperature and density.Comment: 3 pages, 2 figure

Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration

The pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated in the framework of the Nambu-Jona-Lasinio model. The decay rate for the process sigma -> 2pion to the lowest order in a 1/N_c expansion is calculated as a function of temperature T and chemical potential mu. The thermal and nonthermal enhancements of pions generated by the decay before and after the freeze-out present only in the crossover region of the chiral symmetry transition. The strongest nonthermal enhancement is located in the vicinity of the endpoint of the first-order transition.Comment: Latex2e, 12 pages, 8 Postscript figures, submitted to Phys. Rev.

Shuffle-compatible permutation statistics

Since the early work of Richard Stanley, it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations. We formalize this notion of a shuffle-compatible permutation statistic and introduce the shuffle algebra of a shuffle-compatible permutation statistic, which encodes the distribution of the statistic over shuffles of permutations. This paper develops a theory of shuffle-compatibility for descent statistics (statistics that depend only on the descent set and length) which has close connections to the theory of $P$-partitions, quasisymmetric functions, and noncommutative symmetric functions. We use our framework to prove that many descent statistics are shuffle-compatible and to give explicit descriptions of their shuffle algebras, thus unifying past results of Stanley, Gessel, Stembridge, Aguiar-Bergeron-Nyman, and Petersen.Comment: 52 pages. To appear in Adv. Mat

Comment on ``Relativistic kinetic equations for electromagnetic, scalar and pseudoscalar interactions''

It is found that the extra quantum constraints to the spinor components of the equal-time Wigner function given in a recent paper by Zhuang and Heinz should vanish identically. We point out here the origin of the error and give an interpretation of the result. However, the principal idea of obtaining a complete equal-time transport theory by energy averaging the covariant theory remains valid. The classical transport equation for the spin density is also found to be incorrect. We give here the correct form of that equation and discuss briefly its structure.Comment: 5 pages LaTe

Turbulent shear-layer mixing: growth-rate compressibility scaling

A new shear-layer growth-rate compressibility-scaling parameter is proposed as an alternative to the total convective Mach number, Mc. This parameter derives from considerations of compressibility as a means of kinetic-to-thermal-energy conversion and can be significantly different from Mc for flows with far-from-unity free-stream-density and speed-of-sound ratios. Experimentally observed growth rates are well-represented by the new scaling

Active optical clock based on four-level quantum system

Active optical clock, a new conception of atomic clock, has been proposed recently. In this report, we propose a scheme of active optical clock based on four-level quantum system. The final accuracy and stability of two-level quantum system are limited by second-order Doppler shift of thermal atomic beam. To three-level quantum system, they are mainly limited by light shift of pumping laser field. These limitations can be avoided effectively by applying the scheme proposed here. Rubidium atom four-level quantum system, as a typical example, is discussed in this paper. The population inversion between $6S_{1/2}$ and $5P_{3/2}$ states can be built up at a time scale of $10^{-6}$s. With the mechanism of active optical clock, in which the cavity mode linewidth is much wider than that of the laser gain profile, it can output a laser with quantum-limited linewidth narrower than 1 Hz in theory. An experimental configuration is designed to realize this active optical clock.Comment: 5 page

The Effects of Evolutionary Adaptations on Spreading Processes in Complex Networks

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution. However, in real-life spreading processes, pathogens often evolve in response to changing environments and medical interventions and information is often modified by individuals before being forwarded. In this paper, we investigate the evolution of spreading processes on complex networks with the aim of i) revealing the role of evolution on the threshold, probability, and final size of epidemics; and ii) exploring the interplay between the structural properties of the network and the dynamics of evolution. In particular, we develop a mathematical theory that accurately predicts the epidemic threshold and the expected epidemic size as functions of the characteristics of the spreading process, the evolutionary dynamics of the pathogen, and the structure of the underlying contact network. In addition to the mathematical theory, we perform extensive simulations on random and real-world contact networks to verify our theory and reveal the significant shortcomings of the classical mathematical models that do not capture evolution. Our results reveal that the classical, single-type bond-percolation models may accurately predict the threshold and final size of epidemics, but their predictions on the probability of emergence are inaccurate on both random and real-world networks. This inaccuracy sheds the light on a fundamental disconnect between the classical bond-percolation models and real-life spreading processes that entail evolution. Finally, we consider the case when co-infection is possible and show that co-infection could lead the order of phase transition to change from second-order to first-order.Comment: Submitte

Markov modeling of moving target defense games

We introduce a Markov-model-based framework for Moving Target Defense (MTD) analysis. The framework allows modeling of broad range of MTD strategies, provides general theorems about how the probability of a successful adversary defeating an MTD strategy is related to the amount of time/cost spent by the adversary, and shows how a multi-level composition of MTD strategies can be analyzed by a straightforward combination of the analysis for each one of these strategies. Within the proposed framework we define the concept of security capacity which measures the strength or effectiveness of an MTD strategy: the security capacity depends on MTD specific parameters and more general system parameters. We apply our framework to two concrete MTD strategies

Double active region index-guided semiconductor laser

A buried crescent InGaAsP/InP laser with a double active layer was fabricated. The laser showed very high characteristic temperature T0 and highly nonlinear light versus current characteristics. A theoretical model using a rate equation approach showed good agreement with the experimental results