A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Finding the Leftmost Critical Factorization on Unordered Alphabet

We present a linear time and space algorithm computing the leftmost critical factorization of a given string on an unordered alphabet.Comment: 13 pages, 13 figures (accepted to Theor. Comp. Sci.

Little Boxes: A Dynamic Optimization Approach for Enhanced Cloud Infrastructures

The increasing demand for diverse, mobile applications with various degrees of Quality of Service requirements meets the increasing elasticity of on-demand resource provisioning in virtualized cloud computing infrastructures. This paper provides a dynamic optimization approach for enhanced cloud infrastructures, based on the concept of cloudlets, which are located at hotspot areas throughout a metropolitan area. In conjunction, we consider classical remote data centers that are rigid with respect to QoS but provide nearly abundant computation resources. Given fluctuating user demands, we optimize the cloudlet placement over a finite time horizon from a cloud infrastructure provider's perspective. By the means of a custom tailed heuristic approach, we are able to reduce the computational effort compared to the exact approach by at least three orders of magnitude, while maintaining a high solution quality with a moderate cost increase of 5.8% or less

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitaries. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.Comment: Added references to NMR refocusing and to earlier work by Leung et al and Jones and Knil

Oscillatory secular modes: The thermal micropulses

Stars in the narrow mass range of about 2.5 and 3.5 solar masses can develop a thermally unstable He-burning shell during its ignition phase. We study, from the point of view secular stability theory, these so called thermal micropulses and we investigate their properties; the thermal pulses constitute a convenient conceptual laboratory to look thoroughly into the physical properties of a helium-burning shell during the whole thermally pulsing episode. Linear stability analyses were performed on a large number of 3 solar-mass star models at around the end of their core helium-burning and the beginning of the double-shell burning phase. The stellar models were not assumed to be in thermal equilibrium. The thermal mircopulses, and we conjecture all other thermal pulse episodes encountered by shell-burning stars, can be understood as the nonlinear finite-amplitude realization of an oscillatory secular instability that prevails during the whole thermal pulsing episode. Hence, the cyclic nature of the thermal pulses can be traced back to a linear instability concept.Comment: To be published - essentially footnote-free - in Astronomy & Astrophysic

Global bifurcation for the Whitham equation

We prove the existence of a global bifurcation branch of $2\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of H\"older class $C^{\alpha}$, $\alpha < \frac{1}{2}$. Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spectral scheme for computing approximations to those waves is put forward, and several numerical results along the global bifurcation branch are presented, including the presence of a turning point and a `highest', cusped wave. Both analytic and numerical results are compared to traveling-wave solutions of the KdV equation