Energy Efficient and Reliable ARQ Scheme (ER-ACK) for Mission Critical M2M/IoT Services

Wireless sensor networks (WSNs) are the main infrastructure for machine to machine (M2M) and Internet of thing (IoT). Since various sophisticated M2M/IoT services have their own quality-of-service (QoS) requirements, reliable data transmission in WSNs is becoming more important. However, WSNs have strict constraints on resources due to the crowded wireless frequency, which results in high collision probability. Therefore a more efficient data delivering scheme that minimizes both the transmission delay and energy consumption is required. This paper proposes energy efficient and reliable data transmission ARQ scheme, called energy efficient and reliable ACK (ER-ACK), to minimize transmission delay and energy consumption at the same time. The proposed scheme has three aspects of advantages compared to the legacy ARQ schemes such as ACK, NACK and implicit-ACK (I-ACK). It consumes smaller energy than ACK, has smaller transmission delay than NACK, and prevents the duplicated retransmission problem of I-ACK. In addition, resource considered reliability (RCR) is suggested to quantify the improvement of the proposed scheme, and mathematical analysis of the transmission delay and energy consumption are also presented. The simulation results show that the ER-ACK scheme achieves high RCR by significantly reducing transmission delay and energy consumption

On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

Performance of distributed mechanisms for flow admission in wireless adhoc networks

Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth quality-of-service (QoS) requirements can be satisfied. We are especially interested in algorithms which have low communication overhead and low processing complexity. The interference in the network is modeled using a conflict graph whose vertices correspond to the communication links in the network. Two links are adjacent in this graph if and only if they interfere with each other due to being in the same vicinity and hence cannot be simultaneously active. The problem of scheduling the transmission of the various links is then essentially a fractional, weighted vertex coloring problem, for which upper bounds on the fractional chromatic number are sought using only localized information. We recall some distributed algorithms for this problem, and then assess their worst-case performance. Our results on this fundamental problem imply that for some well known classes of networks and interference models, the performance of these distributed algorithms is within a bounded factor away from that of an optimal, centralized algorithm. The performance bounds are simple expressions in terms of graph invariants. It is seen that the induced star number of a network plays an important role in the design and performance of such networks.Comment: 21 pages, submitted. Journal version of arXiv:0906.378

Incremental proximal methods for large scale convex optimization

Laboratory for Information and Decision Systems Report LIDS-P-2847We consider the minimization of a sum∑m [over]i=1 fi (x) consisting of a large number of convex component functions fi . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components.We also discuss applications in a few contexts, including signal processing and inference/machine learning.United States. Air Force Office of Scientific Research (grant FA9550-10-1-0412

Approximate policy iteration: A survey and some new methods

We consider the classical policy iteration method of dynamic programming (DP), where approximations and simulation are used to deal with the curse of dimensionality. We survey a number of issues: convergence and rate of convergence of approximate policy evaluation methods, singularity and susceptibility to simulation noise of policy evaluation, exploration issues, constrained and enhanced policy iteration, policy oscillation and chattering, and optimistic and distributed policy iteration. Our discussion of policy evaluation is couched in general terms and aims to unify the available methods in the light of recent research developments and to compare the two main policy evaluation approaches: projected equations and temporal differences (TD), and aggregation. In the context of these approaches, we survey two different types of simulation-based algorithms: matrix inversion methods, such as least-squares temporal difference (LSTD), and iterative methods, such as least-squares policy evaluation (LSPE) and TD (λ), and their scaled variants. We discuss a recent method, based on regression and regularization, which rectifies the unreliability of LSTD for nearly singular projected Bellman equations. An iterative version of this method belongs to the LSPE class of methods and provides the connecting link between LSTD and LSPE. Our discussion of policy improvement focuses on the role of policy oscillation and its effect on performance guarantees. We illustrate that policy evaluation when done by the projected equation/TD approach may lead to policy oscillation, but when done by aggregation it does not. This implies better error bounds and more regular performance for aggregation, at the expense of some loss of generality in cost function representation capability. Hard aggregation provides the connecting link between projected equation/TD-based and aggregation-based policy evaluation, and is characterized by favorable error bounds.National Science Foundation (U.S.) (No.ECCS-0801549)Los Alamos National Laboratory. Information Science and Technology InstituteUnited States. Air Force (No.FA9550-10-1-0412

Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Sparsity and cosparsity for audio declipping: a flexible non-convex approach

This work investigates the empirical performance of the sparse synthesis versus sparse analysis regularization for the ill-posed inverse problem of audio declipping. We develop a versatile non-convex heuristics which can be readily used with both data models. Based on this algorithm, we report that, in most cases, the two models perform almost similarly in terms of signal enhancement. However, the analysis version is shown to be amenable for real time audio processing, when certain analysis operators are considered. Both versions outperform state-of-the-art methods in the field, especially for the severely saturated signals

Polymer-induced tubulation in lipid vesicles

A mechanism of extraction of tubular membranes from a lipid vesicle is presented. A concentration gradient of anchoring amphiphilic polymers generates tubes from bud-like vesicle protrusions. We explain this mechanism in the framework of the Canham-Helfrich model. The energy profile is analytically calculated and a tube with a fixed length, corresponding to an energy minimum, is obtained in a certain regime of parameters. Further, using a phase-field model, we corroborate these results numerically. We obtain the growth of tubes when a polymer source is added, and the bud-like shape after removal of the polymer source, in accordance with recent experimental results

Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Iterative Approximate Consensus in the presence of Byzantine Link Failures

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consen- sus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [22, 21, 23, 12]. However, to the best of our knowledge, we are the first to consider approximate consensus in the presence of Byzan- tine links. We extend our past work that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable [22, 21]. In particular, we prove a tight necessary and sufficient condition on the underlying com- munication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609