Exact averages of central values of triple product L-functions

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla

Decoherence-free quantum-information processing using dipole-coupled qubits

We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located in the Dicke limit. Although our proposal is general to any system of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV) centers in diamond as an experimental context for our theoretical results.Comment: 7 pages, 5 figure

Distributed CSMA with pairwise coding

We consider distributed strategies for joint routing, scheduling, and network coding to maximize throughput in wireless networks. Network coding allows for an increase in network throughput under certain routing conditions. We previously developed a centralized control policy to jointly optimize for routing and scheduling combined with a simple network coding strategy using max-weight scheduling (MWS) [9]. In this work we focus on pairwise network coding and develop a distributed carrier sense multiple access (CSMA) policy that supports all arrival rates allowed by the network subject to the pairwise coding constraint. We extend our scheme to optimize for packet overhearing to increase the number of beneficial coding opportunities. Simulation results show that the CSMA strategy yields the same throughput as the optimal centralized policy of [9], but at the cost of increased delay. Moreover, overhearing provides up to an additional 25% increase in throughput on random topologies.United States. Dept. of Defense. Assistant Secretary of Defense for Research & EngineeringUnited States. Air Force (Air Force Contract FA8721-05-C-0002

Optimal routing and scheduling for a simple network coding scheme

We consider jointly optimal routing, scheduling, and network coding strategies to maximize throughput in wireless networks. While routing and scheduling techniques for wireless networks have been studied for decades, network coding is a relatively new technique that allows for an increase in throughput under certain topological and routing conditions. In this work we introduce k-tuple coding, a generalization of pairwise coding with next-hop decodability, and fully characterize the region of arrival rates for which the network queues can be stabilized under this coding strategy. We propose a dynamic control policy for routing, scheduling, and k-tuple coding, and prove that our policy is throughput optimal subject to the k-tuple coding constraint. We provide analytical bounds on the coding gain of our policy, and present numerical results to support our analytical findings. We show that most of the gains are achieved with pairwise coding, and that the coding gain is greater under 2-hop than 1-hop interference. Simulations show that under 2-hop interference our policy yields median throughput gains of 31% beyond optimal scheduling and routing on random topologies with 16 nodes.National Science Foundation (U.S.) (grant CNS-0915988)United States. Office of Naval Research (grant N00014-12-1-0064)United States. Office of Naval Research. Multidisciplinary University Research Initiative (grant number W911NF-08-1-0238)United States. Air ForceUnited States. Dept. of Defense (Contract No. FA8721-05-C-0002

In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at http://www.eurico.web.co

Perspectives: Quantum Mechanics on Phase Space

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum Structures Association; Denver, Colorado; 17-22 July, 200

The Contribution of Pre-Existing Depression to the Acute Cognitive Sequelae of Mild Traumatic Brain Injury

Frontotemporal abnormalities and cognitive dysfunction, especially in verbal memory and information processing speed, occur in both mild traumatic brain injury (mTBI) and depression. Study 1 investigated the effect of depression on cognitive performance in a sample at risk of sustaining mTBI.Seventy-eight male undergraduates completed the Depression Anxiety Stress Scales (DASS), Digit Symbol Substitution Test (DSS), Hopkins Verbal Learning Test (HVLT), and Speed of Comprehension Test. A oneway analysis of covariance (using the top 25% and bottom 25% of DASS Depression subscale scorers) showed that HVLT recognition was significantly worse in the high scorers. Study 2 examined the effects of injury type and pre-existing depression on cognitive performance in a prospective emergency department sample (within 24 hours of injury). Fifty-eight participants with mTBI (29 with depression, 29 without depression) and 47 control participants (18 with depression, 29 without depression) completed the DSS, HVLT, and Speed of Comprehension Test. Participants with mTBI performed worse than controls (uninjured and orthopaedic-injured participants) on all tests. Participants with depression did not perform worse than participants without depression on the tests. However, there was a significant univariate interaction for HVLT recognition, participants in the mTBI group with depression exhibited worse recognition compared to participants without depression. Since word recognition was impaired in participants who were more depressed in both samples, this suggests that it is a consistent finding. More importantly, the results of Study 2 indicate that depression may interact with mTBI to impair word recognition during the acute phase after head injury