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David Smith

Publications and source records attributed to David Smith.

At least 91 records · Page 5Linked to original sources
arXiv2015

Approximations of injective modules and finitistic dimension

Let $Λ$ be an artin algebra and let $\mathcal{P}^{<\infty}_Λ$ the category of finitely generated right $Λ$-modules of finite projective dimension. We show that $\mathcal{P}^{<\infty}_Λ$ is contravariantly finite in $\rm mod\,Λ$ if and only if the direct sum $E$ of the indecomposable Ext-injective modules in $\mathcal{P}^{<\infty}_Λ$ form a tilting module in $\rm mod\,Λ$. Moreover, we show that in this case $E$ coincides with the direct sum of the minimal right $\mathcal{P}^{<\infty}_Λ$-approximations of the indecomposable $Λ$-injective modules and that the projective dimension of $E$ equal to the finitistic dimension of $Λ$.

math.RT↗
arXiv2015

Socially Optimal Coexistence of Wireless Body Area Networks Enabled by a Non-Cooperative Game

In this paper, we enable the coexistence of multiple wireless body area networks (BANs) using a finite repeated non-cooperative game for transmit power control. With no coordination amongst these personal sensor networks, the proposed game maximizes each network's packet delivery ratio (PDR) at low transmit power. In this context we provide a novel utility function, which gives reduced benefit to players with higher transmission power, and a subsequent reduction in radio interference to other coexisting BANs. Considering the purpose of inter-BAN interference mitigation, PDR is expressed as a compressed exponential function of inverse signal-to-interference-and-noise ratio (SINR), so it is essentially a function of transmit powers of all coexisting BANs. It is shown that a unique Nash Equilibrium (NE) exists, and hence there is a subgame-perfect equilibrium, considering best-response at each stage independent of history. In addition, the NE is proven to be the socially optimal solution across all action profiles. Realistic and extensive on- and inter-body channel models are employed. Results confirm the effectiveness of the proposed scheme in better interference management, greater reliability and reduced transmit power, when compared with other schemes that can be applied in BANs.

cs.NI↗
arXiv2015

The Application of Non-Cooperative Stackelberg Game Theory in Behavioral Science: Social Optimality with any Number of Players

Here we present a ground-breaking new postulate for game theory. The first part of this postulate contains the axiomatic observation that all games are created by a designer, whether they are: e.g., (dynamic/static) or (stationary/non-stationary) or (sequential/one-shot) non-cooperative games, and importantly, whether or not they are intended to represent a non-cooperative Stackelberg game, they can be mapped to a Stackelberg game. I.e., the game designer is the leader who is totally rational and honest, and the followers are mapped to the players of the designed game. If now the game designer, or "the leader" in the Stackelberg context, adopts a pure strategy, we postulate the following second part following from axiomatic observation of ultimate game leadership, where empirical insight leads to the second part of this postulate. Importantly, implementing a non-cooperative Stackelberg game, with a very honest and rational leader results in social optimality for all players (followers), assuming pure strategy across all followers and leader, and that the leader is totally rational, honest, and is able to achieve a minimum amount of competency in leading this game, with any finite number of iterations of leading this finite game.

cs.GT↗
arXiv2014

Lunar polar craters -- icy, rough or just sloping?

Circular Polarisation Ratio (CPR) mosaics from Mini-SAR on Chandrayaan-1 and Mini-RF on LRO are used to study craters near to the lunar north pole. The look direction of the detectors strongly affects the appearance of the crater CPR maps. Rectifying the mosaics to account for parallax also significantly changes the CPR maps of the crater interiors. It is shown that the CPRs of crater interiors in unrectified maps are biased to larger values than crater exteriors, because of a combination of the effects of parallax and incidence angle. Using the LOLA Digital Elevation Map (DEM), the variation of CPR with angle of incidence has been studied. For fresh craters, CPR~0.7 with only a weak dependence on angle of incidence or position interior or just exterior to the crater, consistent with dihedral scattering from blocky surface roughness. For anomalous craters, the CPR interior to the crater increases with both incidence angle and distance from the crater centre. Central crater CPRs are similar to those in the crater exteriors. CPR does not appear to correlate with temperature within craters. Furthermore, the anomalous polar craters have diameter-to-depth ratios that are lower than those of typical polar craters. These results strongly suggest that the high CPR values in anomalous polar craters are not providing evidence of significant volumes of water ice. Rather, anomalous craters are of intermediate age, and maintain sufficiently steep walls that deep regolith does not cover all rough surfaces.

astro-ph.EP↗
arXiv2013

Prioritizing Consumers in Smart Grid: A Game Theoretic Approach

This paper proposes an energy management technique for a consumer-to-grid system in smart grid. The benefit to consumers is made the primary concern to encourage consumers to participate voluntarily in energy trading with the central power station (CPS) in situations of energy deficiency. A novel system model motivating energy trading under the goal of social optimality is proposed. A single-leader multiple-follower Stackelberg game is then studied to model the interactions between the CPS and a number of energy consumers (ECs), and to find optimal distributed solutions for the optimization problem based on the system model. The CPS is considered as a leader seeking to minimize its total cost of buying energy from the ECs, and the ECs are the followers who decide on how much energy they will sell to the CPS for maximizing their utilities. It is shown that the game, which can be implemented distributedly, possesses a socially optimal solution, in which the benefits-sum to all consumers is maximized, as the total cost to the CPS is minimized. Numerical analysis confirms the effectiveness of the game.

eess.SY↗
arXiv2013

High-Angular-Resolution and High-Sensitivity Science Enabled by Beamformed ALMA

An international consortium is presently constructing a beamformer for the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile that will be available as a facility instrument. The beamformer will aggregate the entire collecting area of the array into a single, very large aperture. The extraordinary sensitivity of phased ALMA, combined with the extremely fine angular resolution available on baselines to the Northern Hemisphere, will enable transformational new very long baseline interferometry (VLBI) observations in Bands 6 and 7 (1.3 and 0.8 mm) and provide substantial improvements to existing VLBI arrays in Bands 1 and 3 (7 and 3 mm). The ALMA beamformer will have impact on a variety of scientific topics, including accretion and outflow processes around black holes in active galactic nuclei (AGN), tests of general relativity near black holes, jet launch and collimation from AGN and microquasars, pulsar and magnetar emission processes, the chemical history of the universe and the evolution of fundamental constants across cosmic time, maser science, and astrometry.

astro-ph.IM↗
arXiv2013

Coexistence and Interference Mitigation for Wireless Body Area Networks: Improvements using On-Body Opportunistic Relaying

Coexistence, and hence interference mitigation, across multiple wireless body area networks (WBANs) is an important problem as WBANs become more pervasive. Here, two-hop relay-assisted cooperative communications using opportunistic relaying (OR) is proposed for enhancement of coexistence for WBANs. Suitable time division multiple access (TDMA) schemes are employed for both intra-WBAN and inter-WBANs access protocols. To emulate actual conditions of WBAN use, extensive on-body and inter-body "everyday" channel measurements are employed. In addition, a realistic inter-WBAN channel model is simulated to investigate the effect of body shadowing and hub location on WBAN performance in enabling coexistence. When compared with single-link communications, it is found that opportunistic relaying can provide significant improvement, in terms of signal-to-interference+noise ratio (SINR), to outage probability and level crossing rate (LCR) into outages. However, average outage duration (AOD) is not affected. In addition a lognormal distribution shows a better fit to received SINR when the channel coherence time is small, and a Nakagami-m distribution is a more common fit when the channel is more stable. According to the estimated SINR distributions, theoretical outage probability, LCR and AOD are shown to match the empirical results well.

cs.NI↗
arXiv2012

Opportunistic Relaying in Wireless Body Area Networks: Coexistence Performance

In this paper, a cooperative two-hop communication scheme, together with opportunistic relaying (OR), is applied within a mobile wireless body area network (WBAN). Its effectiveness in interference mitigation is investigated in a scenario where there are multiple closely-located networks. Due to a typical WBAN's nature, no coordination is used among different WBANs. A suitable time-division-multiple-access (TDMA) is adopted as both an intra-network and also an inter-network access scheme. Extensive on-body and off-body channel gain measurements are employed to gauge performance, which are overlaid to simulate a realistic WBAN working environment. It is found that opportunistic relaying is able to improve the signal-to-interference-and-noise ratio (SINR) threshold value at outage probability of 10% by an average of 5 dB, and it is also shown that it can reduce level crossing rate (LCR) significantly at a low SINR threshold value. Furthermore, this scheme is more efficient when on-body channels fade less slowly.

cs.NI↗
arXiv2012

Planning under Continuous Time and Resource Uncertainty: A Challenge for AI

We outline a class of problems, typical of Mars rover operations, that are problematic for current methods of planning under uncertainty. The existing methods fail because they suffer from one or more of the following limitations: 1) they rely on very simple models of actions and time, 2) they assume that uncertainty is manifested in discrete action outcomes, 3) they are only practical for very small problems. For many real world problems, these assumptions fail to hold. In particular, when planning the activities for a Mars rover, none of the above assumptions is valid: 1) actions can be concurrent and have differing durations, 2) there is uncertainty concerning action durations and consumption of continuous resources like power, and 3) typical daily plans involve on the order of a hundred actions. This class of problems may be of particular interest to the UAI community because both classical and decision-theoretic planning techniques may be useful in solving it. We describe the rover problem, discuss previous work on planning under uncertainty, and present a detailed, but very small, example illustrating some of the difficulties of finding good plans.

cs.AI↗
arXiv2012

Optimal Limited Contingency Planning

For a given problem, the optimal Markov policy can be considerred as a conditional or contingent plan containing a (potentially large) number of branches. Unfortunately, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. For example, it may be that plans must later undergo more detailed simulation to verify correctness and safety, or that they must be simple enough to be understood and analyzed by humans. As a result, it may be necessary to limit consideration to plans with only a small number of branches. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning (OKP). It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a Partially Observable Markov Decision Process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

cs.AI↗
arXiv2012

Human sperm cells swimming in micro-channels

The migratory abilities of motile human spermatozoa in vivo are essential for natural fertility, but it remains a mystery what properties distinguish the tens of cells which find an egg from the millions of cells ejaculated. To reach the site of fertilization, sperm must traverse narrow and convoluted channels, filled with viscous fluids. To elucidate individual and group behaviors that may occur in the complex three-dimensional female tract environment, we examine the behavior of migrating sperm in assorted micro-channel geometries. Cells rarely swim in the central part of the channel cross-section, instead traveling along the intersection of the channel walls (`channel corners'). When the channel turns sharply, cells leave the corner, continuing ahead until hitting the opposite wall of the channel, with a distribution of departure angles, the latter being modulated by fluid viscosity. If the channel bend is smooth, cells depart from the inner wall when the curvature radius is less than a threshold value close to 150 micron. Specific wall shapes are able to preferentially direct motile cells. As a consequence of swimming along the corners, the domain occupied by cells becomes essentially 1-dimensional. This leads to frequent collisions and needs to be accounted for when modeling the behavior of populations of migratory cells and considering how sperm populate and navigate the female tract. The combined effect of viscosity and three-dimensional architecture should be accounted for in future in vitro studies of sperm chemoattraction.

physics.bio-ph↗
arXiv2011

Flat-face approximations of invisibility cloaks with planar metamaterial layers

Transformation optics (TO) is a powerful tool for the design of artiffcial materials with unprecedented optical properties. Here, we propose the approximation of TO structures of arbitrary shape by faceting, in which curved surfaces are approximated by at metamaterial layers that can be implemented by standard fabrication and stacking techniques. We illustrate the approximation approach for the specific example of a cylindrical invisibility cloak. First, we introduce a numerical method for the design of cloaks with arbitrary boundary shapes, and apply it to faceted shapes. Subsequently, we reduce the complexity of the metamaterials needed to implement the perfect faceted cloak by introducing several approximations, whose validity is quantified by an investigation of the scattering cross section.

physics.optics↗
arXiv2011

Mutation of cluster-tilting objects and potentials

We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This gives a close connection between 2-CY-tilted algebras and Jacobian algebras associated with quivers with potentials. We show that cluster-tilted algebras are Jacobian and also that they are determined by their quivers. There are similar results when dealing with tilting modules over 3-CY algebras. The nearly Morita equivalence for 2-CY-tilted algebras is shown to hold for the finite length modules over Jacobian algebras.

math.RT↗
arXiv2011

Friezes, Strings and Cluster Variables

To any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi-Yau tilted algebra, we prove that this Laurent polynomial coincides with the corresponding cluster character of the string module, up to an explicit normalising monomial factor.

math.AC↗
arXiv2011

Locating the LCROSS Impact Craters

The Lunar CRater Observations and Sensing Satellite (LCROSS) mission impacted a spent Centaur rocket stage into a permanently shadowed region near the lunar south pole. The Sheperding Spacecraft (SSC) separated \sim9 hours before impact and performed a small braking maneuver in order to observe the Centaur impact plume, looking for evidence of water and other volatiles, before impacting itself. This paper describes the registration of imagery of the LCROSS impact region from the mid- and near-infrared cameras onboard the SSC, as well as from the Goldstone radar. We compare the Centaur impact features, positively identified in the first two, and with a consistent feature in the third, which are interpreted as a 20 m diameter crater surrounded by a 160 m diameter ejecta region. The images are registered to Lunar Reconnaisance Orbiter (LRO) topographical data which allows determination of the impact location. This location is compared with the impact location derived from ground-based tracking and propagation of the spacecraft's trajectory and with locations derived from two hybrid imagery/trajectory methods. The four methods give a weighted average Centaur impact location of -84.6796\circ, -48.7093\circ, with a 1σ un- certainty of 115 m along latitude, and 44 m along longitude, just 146 m from the target impact site. Meanwhile, the trajectory-derived SSC impact location is -84.719\circ, -49.61\circ, with a 1σ uncertainty of 3 m along the Earth vector and 75 m orthogonal to that, 766 m from the target location and 2.803 km south-west of the Centaur impact. We also detail the Centaur impact angle and SSC instrument pointing errors. Six high-level LCROSS mission requirements are shown to be met by wide margins. We hope that these results facilitate further analyses of the LCROSS experiment data and follow-up observations of the impact region.

physics.space-ph↗
arXiv2010

Memory Metamaterials

The resonant elements that grant metamaterials their unique properties have the fundamental limitation of restricting their useable frequency bandwidth. The development of frequency-agile metamaterials has helped to alleviate these bandwidth restrictions by allowing real-time tuning of the metamaterial frequency response. We demonstrate electrically-controlled persistent frequency tuning of a metamaterial, allowing lasting modification of its response using a transient stimulus. This work demonstrates a form of memory capacitance which interfaces metamaterials with a class of devices known collectively as memory devices.

cond-mat.mes-hall↗
arXiv2009

Frises

Each acyclic graph, and more generally, each acyclic orientation of the graph associated to a Cartan matrix, allows to define a so-called frise; this is a collection of sequences over the positive natural numbers, one for each vertex of the graph. We prove that if these sequences satisfy a linear recurrence, then the Cartan matrix is of Dynkin type (if the sequences are bounded) or of Euclidean type (if the sequences are unbounded). We prove the converse in all cases, except for the exceptional Euclidean Cartan matrices; we show even that the sequences are rational over the positive natural numbers. We generalize these results by considering frises with variables; as a byproduct we obtain, for the Dynkin and Euclidean type A cases, explicit formulas for the cluster variables, over the semiring of Laurent polynomials over the positive natural numbers generated by the initial variables (which explains simultaneously positivity and the Laurent phenomenon). The general tool are the so-called SL_2-tilings of the plane; these are fillings of the whole discrete plane by elements of a ring, in such a way that each 2 by 2 connected submatrix is of determinant 1.

math.RA↗