Drift rate control of a Brownian processing system

A system manager dynamically controls a diffusion process Z that lives in a finite interval [0,b]. Control takes the form of a negative drift rate \theta that is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ=dX-\theta(Z) dt+dL-dU, where X is a (0,\sigma) Brownian motion, and L and U are increasing processes that enforce a lower reflecting barrier at Z=0 and an upper reflecting barrier at Z=b, respectively. The cumulative cost process increases according to the differential relationship d\xi =c(\theta(Z)) dt+p dU, where c(\cdot) is a nondecreasing cost of control and p>0 is a penalty rate associated with displacement at the upper boundary. The objective is to minimize long-run average cost. This problem is solved explicitly, which allows one to also solve the following, essentially equivalent formulation: minimize the long-run average cost of control subject to an upper bound constraint on the average rate at which U increases. The two special problem features that allow an explicit solution are the use of a long-run average cost criterion, as opposed to a discounted cost criterion, and the lack of state-related costs other than boundary displacement penalties. The application of this theory to power control in wireless communication is discussed.Comment: Published at http://dx.doi.org/10.1214/105051604000000855 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time $(1+\epsilon)$-approximation algorithm that yields an $(e+\epsilon)$-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with \emph{optimal }cost at $1+\epsilon$ speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most $\log n$ many classes. This algorithm allows the jobs even to have up to $\log n$ many distinct release dates.Comment: 2 pages, 1 figur

Spectral Analysis and the Dynamic Response of Complex Networks

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network characteristics: random networks follow Wigner's semicircular law whereas scale-free networks exhibit a triangular distribution. In this paper we show that the spectral density of hierarchical networks follow a very different pattern, which can be used as a fingerprint of modularity. Of particular importance is the value $\rho(0)$, related to the homeostatic response of the network: it is maximum for random and scale free networks but very small for hierarchical modular networks. It is also large for an actual biological protein-protein interaction network, demonstrating that the current leading model for such networks is not adequate.Comment: 4 pages 14 figure

An analytically solvable model of probabilistic network dynamics

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur

Conflict-Free Coloring Made Stronger

In FOCS 2002, Even et al. showed that any set of $n$ discs in the plane can be Conflict-Free colored with a total of at most $O(\log n)$ colors. That is, it can be colored with $O(\log n)$ colors such that for any (covered) point $p$ there is some disc whose color is distinct from all other colors of discs containing $p$. They also showed that this bound is asymptotically tight. In this paper we prove the following stronger results: \begin{enumerate} \item [(i)] Any set of $n$ discs in the plane can be colored with a total of at most $O(k \log n)$ colors such that (a) for any point $p$ that is covered by at least $k$ discs, there are at least $k$ distinct discs each of which is colored by a color distinct from all other discs containing $p$ and (b) for any point $p$ covered by at most $k$ discs, all discs covering $p$ are colored distinctively. We call such a coloring a {\em $k$-Strong Conflict-Free} coloring. We extend this result to pseudo-discs and arbitrary regions with linear union-complexity. \item [(ii)] More generally, for families of $n$ simple closed Jordan regions with union-complexity bounded by $O(n^{1+\alpha})$, we prove that there exists a $k$-Strong Conflict-Free coloring with at most $O(k n^\alpha)$ colors. \item [(iii)] We prove that any set of $n$ axis-parallel rectangles can be $k$-Strong Conflict-Free colored with at most $O(k \log^2 n)$ colors. \item [(iv)] We provide a general framework for $k$-Strong Conflict-Free coloring arbitrary hypergraphs. This framework relates the notion of $k$-Strong Conflict-Free coloring and the recently studied notion of $k$-colorful coloring. \end{enumerate} All of our proofs are constructive. That is, there exist polynomial time algorithms for computing such colorings

Proposing "b-Parity" - a New Approximate Quantum Number in Inclusive b-jet Production - as an Efficient Probe of New Flavor Physics

We consider the inclusive reaction \ell^+ \ell^- -> nb +X (n = number of b-jets) in lepton colliders for which we propose a useful approximately conserved quantum number b_P=(-1)^n that we call b-Parity (b_P). We make the observation that the Standard Model (SM) is essentially b_P-even since SM b_P-violating signals are necessarily CKM suppressed. In contrast new flavor physics can produce b_P=-1 signals whose only significant SM background is due to b-jet misidentification. Thus, we show that b-jet counting, which relies primarily on b-tagging, becomes a very simple and sensitive probe of new flavor physics (i.e., of b_P-violation).Comment: 5 pages using revtex, 2 figures embadded in the text using epsfig. As will appear in Phys.Rev.Lett.. Considerable improvement was made in the background calculation as compared to version 1, by including purity parameters, QCD effects and 4-jets processe

Be-implanted (GaAl)As stripe geometry lasers

GaAl)As double-heterostructure stripe geometry lasers have been fabricated using Be ion implantation. Pulsed threshold currents as low as 21 mA have been found. The light-vs-current characteristics were kink-free up to 10 mW output power and the measured differential quantum efficiency was 45%

Detecting Hands in Egocentric Videos: Towards Action Recognition

Recently, there has been a growing interest in analyzing human daily activities from data collected by wearable cameras. Since the hands are involved in a vast set of daily tasks, detecting hands in egocentric images is an important step towards the recognition of a variety of egocentric actions. However, besides extreme illumination changes in egocentric images, hand detection is not a trivial task because of the intrinsic large variability of hand appearance. We propose a hand detector that exploits skin modeling for fast hand proposal generation and Convolutional Neural Networks for hand recognition. We tested our method on UNIGE-HANDS dataset and we showed that the proposed approach achieves competitive hand detection results