Quasi-regular sequences and optimal schedules for security games

We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time $t$ at a target $i$ of value $\alpha_i$, and if he leaves before the defender visits the target, his utility is $t \cdot \alpha_i$; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc. We show that optimal defender play for this continuous time security games reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol $i$: (1) $i$ constitutes a prescribed fraction $p_i$ of the sequence. (2) The occurrences of $i$ are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter $K$. We call such sequences $K$-quasi-regular. We show that, surprisingly, $2$-quasi-regular sequences suffice for optimal defender play. What is more, even randomized $2$-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. The question of the least $K$ for which deterministic $K$-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we show that deterministic $3$-quasi-regular sequences always exist. For $2 \leq K < 3$ we do not know whether deterministic $K$-quasi-regular sequences always exist.Comment: to appear in Proc. of SODA 201

Estimation of stratospheric input to the Arctic troposphere: 7Be and 10Be in aerosols at Alert, Canada

Concentrations of 7Be and 210Pb in 2 years of weekly high-volume aerosol samples collected at Alert, Northwest Territories, Canada, showed pronounced seasonal variations. We observed a broad winter peak in 210Pb concentration and a spring peak in 7Be. These peaks were similar in magnitude and duration to previously reported results for a number of stations in the Arctic Basin. Beryllium 10 concentrations (determined only during the first year of this study) were well correlated with those of 7Be; the atom ratio 10Be/7Be was nearly constant at 2.2 throughout the year. This relatively high value of 10Be/7Be indicates that the stratosphere must constitute an important source of both Be isotopes in the Arctic troposphere throughout the year. A simple mixing model based on the small seasonal variations of 10Be/7Be indicates an approximately twofold increase of stratospheric influence in the free troposphere in late summer. The spring maxima in concentrations of both Be isotopes at the surface apparently reflect vertical mixing in rather than stratospheric injections into the troposphere. We have merged the results of the Be-based mixing model with weekly O3 soundings to assess Arctic stratospheric impact on the surface O3 budget at Alert. The resulting estimates indicate that stratospheric inputs can account for a maximum of 10-15% of the 03 at the surface in spring and for less during the rest of the year. These estimates are most uncertain during the winter. The combination of Be isotopic measurements and O3 vertical profiles could allow quantification of the contributions of O3 from the Arctic stratosphere and lower latitude regions to the O3 budget in the Arctic troposphere. Although at present the lack of a quantitative understanding of the temporal variation of O3 lifetime in the Arctic troposphere precludes making definitive calculations, qualitative examples of the power of this approach are given

A convex relaxation for approximate global optimization in simultaneous localization and mapping

Modern approaches to simultaneous localization and mapping (SLAM) formulate the inference problem as a high-dimensional but sparse nonconvex M-estimation, and then apply general first- or second-order smooth optimization methods to recover a local minimizer of the objective function. The performance of any such approach depends crucially upon initializing the optimization algorithm near a good solution for the inference problem, a condition that is often difficult or impossible to guarantee in practice. To address this limitation, in this paper we present a formulation of the SLAM M-estimation with the property that, by expanding the feasible set of the estimation program, we obtain a convex relaxation whose solution approximates the globally optimal solution of the SLAM inference problem and can be recovered using a smooth optimization method initialized at any feasible point. Our formulation thus provides a means to obtain a high-quality solution to the SLAM problem without requiring high-quality initialization.Google (Firm) (Software Engineering Internship)United States. Office of Naval Research (Grants N00014-10-1-0936, N00014-11-1-0688 and N00014- 13-1-0588)National Science Foundation (U.S.) (Award IIS-1318392

Computation of nucleation of a non-equilibrium first-order phase transition using a rare-event algorithm

We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to efficiently measure transition times in rare-event processes in non-equilibrium systems, and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, are clearly found by this method.Comment: 12 pages, 10 figure

Late-season Insect Pests of Soybean in Louisiana: Preventive Management and Yield Enhancement (Bulletin #880)

The velvetbean caterpillar and the soybean looper are important pests of soybeans in Louisiana. These late-season soybean insect pests create the need for the continuous development of insecticide programs that are cost effective, maintain profitable yields and conserve natural enemies.https://digitalcommons.lsu.edu/agcenter_bulletins/1020/thumbnail.jp