On Packet Scheduling with Adversarial Jamming and Speedup

In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these properties in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of $\phi+1\approx 2.618$ on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in $[1,4)$ and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. and the lower bound by Anta et al.Comment: Appeared in Proc. of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

The Exemption Status of the Bona Fide Pledgee of Unregistered Securities Under the Securities Act of 1933

The number of connections of photovoltaic (PV) to distribution network is increasing. Very few PV connection guidelines that distribution system operators (DSOs) can refer to have been found. This paper deals with network planning guidelines for distribution networks with PV. The paper aims to identify planning rules that are relatively easy to implement.QC 20140625</p

Sobre la existencia del producto de medidas valoradas en espacios localmente convexos : una condición necesaria

A necessary condition is given for the existente of the tensor product of certain measures valued in locally convex spaces

On Evidence-based Risk Management in Requirements Engineering

Background: The sensitivity of Requirements Engineering (RE) to the context makes it difficult to efficiently control problems therein, thus, hampering an effective risk management devoted to allow for early corrective or even preventive measures. Problem: There is still little empirical knowledge about context-specific RE phenomena which would be necessary for an effective context- sensitive risk management in RE. Goal: We propose and validate an evidence-based approach to assess risks in RE using cross-company data about problems, causes and effects. Research Method: We use survey data from 228 companies and build a probabilistic network that supports the forecast of context-specific RE phenomena. We implement this approach using spreadsheets to support a light-weight risk assessment. Results: Our results from an initial validation in 6 companies strengthen our confidence that the approach increases the awareness for individual risk factors in RE, and the feedback further allows for disseminating our approach into practice.Comment: 20 pages, submitted to 10th Software Quality Days conference, 201

Open-charm meson spectroscopy

We present a theoretical framework that accounts for the new $D_J$ and $D_{sJ}$ mesons measured in the open-charm sector. These resonances are properly described if considered as a mixture of conventional $P-$wave quark-antiquark states and four-quark components. The narrowest states are basically $P-$wave quark-antiquark mesons, while the dominantly four-quark states are shifted above the corresponding two-meson threshold, being broad resonances. We study the electromagnetic decay widths as basic tools to scrutiny their nature. The proposed explanation incorporates in a natural way the most recently discovered mesons in charmonium spectroscopy.Comment: 15 pages, 5 tables. Accepted for publication in Phys. Rev.

Geometric Phases and Mielnik's Evolution Loops

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.Comment: 11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS GFMR 11/9