To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.

Abstract It has been recently suggested by Jiang and Walrand that adaptive carrier sense multiple access (CSMA) can achieve optimal utility without any message passing in wireless networks. In this paper, after a survey of recent work on random access, a generalization of this algorithm is considered. In the continuous‐time model, a proof is presented of the convergence of these adaptive CSMA algorithms to be arbitrarily close to utility optimality, without assuming that the network dynamics converge to an equilibrium in between consecutive CSMA parameter updates. In the more realistic, slotted‐time model, the impact of collisions on the utility achieved is characterized, and the tradeoff between optimality and short‐term fairness is quantified. Copyright © 2009 John Wiley & Sons, Ltd.

It has been recently suggested by Jiang andWalrand that adaptive carrier sense multiple access (CSMA) can achieve optimal utility without any message passing in wireless networks. In this paper, a generalization of this algorithm is considered. In the continuous-time model, a proof is presented of t

The flow-level stability and performance of data networks with utility-maximizing allocations are studied in this paper. Similarly to prior works on flow-level models, exogenous data arrivals with finite workloads are considered. However, to model many realistic situations, the rate region, which constrains the feasibility of resource allocation, may be either nonconvex or time-varying. When the rate region is fixed but nonconvex, sufficient and necessary conditions are characterized for stability for a class ofalpha-fair allocation policies, which coincide when the set of allocated rate vectors have continuous contours. When the rate region is time-varying according to a Markovian stationary and ergodic process, the precise stability region is obtained. In both cases, the size of the stability region depends on the resource allocation policy, in particular, on the fairness parameteralphainalpha-fair utility maximization. This is in sharp contrast with the substantial existing literature on stability under fixed and convex rate regions, in which the stability region coincides with the rate region for many utility-based resource allocation schemes, independent of the value of the fairness parameter. It is further shown that for networks which consist of flows from two different classes underalpha-fair allocations, there exists a tradeoff between the stability region and the fairness parameteralpha. Moreover, the impact of this fairness-stability tradeoff on the system performance, e.g., average throughput and mean flow response time, is studied, and numerical experiments that illustrate the new stability region and the performance versus fairness tradeoff are presented.

A model for wireless networks with slotted-Aloha-type random access and with multihop flow routes is considered. The goal is to devise distributed algorithms for utility-optimal end-to-end throughput allocation and queueing stability. A class of queue back-pressure random access algorithms (QBRAs), in which actual queue lengths of the flows in each node's close neighborhood are used to determine the nodes' channel access probabilities, is studied. This is in contrast to some previously proposed algorithms, which are based on deterministic optimization formulations and are oblivious to actual queues. QBRA is also substantially different from the well-studied ldquoMaxWeightrdquo type scheduling algorithms, even though both use the concept of back-pressure. For the model with infinite backlog at each flow source, it is shown that QBRA, combined with simple congestion control local to each source, leads to optimal end-to-end throughput allocation within the network saturation throughput region achievable by random access, without end-to-end message passing. This scheme is generalized to the case with minimum flow rate constraints. For the model with stochastic exogenous arrivals, it is shown that QBRA ensures stability of the queues as long as nominal loads of the nodes are within the saturation throughput region. Simulation comparison of QBRA and the queue oblivious random-access algorithms, shows that QBRA reduces end-to-end delays.

This paper introduces a new rate-2, full-diversity space-time code for four transmit antennas and one receive antenna. The 4times4 codeword matrix consists of four 2times2 Alamouti blocks with entries fromQ(i,radic5) , and these blocks can be viewed as quaternions which in turn represent rotations inR3. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a common underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and theE8lattice.

In this paper we characterize flow-level stochastic stability for networks with non-convex or time-varying rate regions underresource allocation based on utility maximization. Similar to prior works on flow-level stability, we consider exogenous data arrivals with finite workloads. However, to model many realistic situations, the rate region, which constrains the feasibility of resource allocation, may be either non-convex or time-varying. When the rate region is fixed but non-convex, we derive sufficient and necessary conditions for stability, which coincide when the set of allocated rate vectors has continuous contours. When the rate region is time-varying according to some stationary, ergodic process, we derive the precise stability region. In both cases,the size of the stability region depends on the resource allocation policy, in particular, on the fairness parameter in ∝-fair utility maximization. This is in sharp contrast with the substantial existing literature on stability under fixed and convex rate regions, in which the stability region coincides with the rate region for many utility-based resource allocation schemes, independently of the value of the fairness parameter. We further investigate the tradeoff between fairness and stability when rate region is non-convex or time-varying. Numerical examples of both wired and wireless networks are provided to illustrate the new stability regions and tradeoffs proved in the paper.

This paper introduces a new full-rate, full-diversity space-time code for 4 transmit antennas. The 4times4 codeword matrix consists of four 2times2 Alamouti blocks with entries from Q(i, radic5), and these blocks can be viewed as quaternions which in turn represent rotations in R3. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a similar underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the E8lattice