Abstract:
In this paper we revisit the results of Loynes (1962) on stability of queues for ergodic arrivals and services, and show examples when the arrivals are bounded and ergodic, the service rate is constant, and under stability the limit distribution has larger than exponential tail.

Abstract:
The fold recognition methods are promissing tools for capturing the structure of a protein by its amino acid residues sequence but their use is still restricted by the needs of huge computational resources and suitable efficient algorithms as well. In the recent version of FROST (Fold Recognition Oriented Search Tool) package the most efficient algorithm for solving the Protein Threading Problem (PTP) is implemented due to the strong collaboration between the SYMBIOSE group in IRISA and MIG in Jouy-en-Josas. In this paper, we present the diverse components of FROST, emphasizing on the recent advances in formulating and solving new versions of the PTP and on the way of solving on a computer cluster a million of instances in a easonable time.

Abstract:
We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline how the two-dimensional risk model with a general two-dimensional claim size distribution (hence without ordering of claim sizes) is related to a known Riemann boundary value problem.

Abstract:
Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very different intervals. Sometimes, this is evident even within a single given field of investigation making very difficult (and inaccurate) the assessment of scientific papers. On the other hand, the problem can be recast in the same framework which has allowed to efficiently cope with the ordering of web-pages, i.e., to formulate the PageRank of Google. For this reason, we call such problem the PaperRank problem, here solved by using a similar approach to that employed by PageRank. The obtained solution, which is mathematically grounded, will be used to compare the usual heuristics of the number of citations with a new one here proposed. Some numerical tests show that the new heuristics is much more reliable than the currently used ones, based on the bare number of citations. Moreover, we show that our model improves on recently proposed ones.

Abstract:
To advance Thomson problem we generalize physical principles suggested by Caspar and Klug (CK) to model icosahedral capsids. Proposed simplest distortions of the CK spherical arrangements yield new-type trial structures very close to the lowest energy ones. In the region 600

Abstract:
The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of binary sequences and thereby prove various conjectures, explain numerical evidence presented by other authors, and bring together within a single framework results previously appearing in scattered form. We exhibit, for the first time, families of skew-symmetric sequences whose asymptotic merit factor is as large as the best known value (an algebraic number greater than 6.34) for all binary sequences; this is interesting in light of Golay's conjecture that the subclass of skew-symmetric sequences has asymptotically optimal merit factor. Our methods combine Fourier analysis, estimation of character sums, and estimation of the number of lattice points in polyhedra.

Abstract:
We consider a recent model with sub-millimeter sized extra dimensions, where the field that determines the size of the extra dimensions (the radion) also acts as an inflaton. The radion is also a stable modulus, and its coherent oscillations can potentially overclose the Universe. It has been suggested that a second round of late inflation can solve this problem, however we find that this scenario does not allow for sufficient reheating of the Universe.

Abstract:
We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For the spatially confined particle, we show that the problem admits a solution in the form of an eigenvalue problem of a compact and self-adjoint time of arrival operator derived by a quantization of the classical time of arrival, which is canonically conjugate with the Hamiltonian in closed subspace of the Hilbert space.

Abstract:
We show that a short period of late D-term inflation can solve the cosmological moduli (radion) problem of (asymmetric) inflation at the TeV scale. Late inflation happens after the large compact dimensions are stabilized which is crucial for obtaining the extremely small Hubble constant and inflaton mass required.

Abstract:
The initial motivation of this text was to provide an up to date translation of the monograph [45] written in french by the first author, taking account of more recent developments of infinite dimensional dynamics based on the {\L}ojasiewicz gradient inequality. In order to keep the present work within modest size bounds and to make it available to the readers without too much delay, we decided to make a first volume entirely dedicated to the so-called convergence problem for autonomous systems of dissipative type. We hope that this volume will help the interested reader to make the connection between the rather simple background developed in the french monograph and the rather technical specialized literature on the convergence problem which grew up rather fast in the recent years.