A High Reliability Asymptotic Approach for Packet Inter-Delivery Time Optimization in Cyber-Physical Systems

In cyber-physical systems such as automobiles, measurement data from sensor nodes should be delivered to other consumer nodes such as actuators in a regular fashion. But, in practical systems over unreliable media such as wireless, it is a significant challenge to guarantee small enough inter-delivery times for different clients with heterogeneous channel conditions and inter-delivery requirements. In this paper, we design scheduling policies aiming at satisfying the inter-delivery requirements of such clients. We formulate the problem as a risk-sensitive Markov Decision Process (MDP). Although the resulting problem involves an infinite state space, we first prove that there is an equivalent MDP involving only a finite number of states. Then we prove the existence of a stationary optimal policy and establish an algorithm to compute it in a finite number of steps. However, the bane of this and many similar problems is the resulting complexity, and, in an attempt to make fundamental progress, we further propose a new high reliability asymptotic approach. In essence, this approach considers the scenario when the channel failure probabilities for different clients are of the same order, and asymptotically approach zero. We thus proceed to determine the asymptotically optimal policy: in a two-client scenario, we show that the asymptotically optimal policy is a "modified least time-to-go" policy, which is intuitively appealing and easily implementable; in the general multi-client scenario, we are led to an SN policy, and we develop an algorithm of low computational complexity to obtain it. Simulation results show that the resulting policies perform well even in the pre-asymptotic regime with moderate failure probabilities

On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.Comment: 15 pages, 3 figure

On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields

Recently, Gupta et.al. [GKKS2013] proved that over Q any $n^{O(1)}$-variate and $n$-degree polynomial in VP can also be computed by a depth three $\Sigma\Pi\Sigma$ circuit of size $2^{O(\sqrt{n}\log^{3/2}n)}$. Over fixed-size finite fields, Grigoriev and Karpinski proved that any $\Sigma\Pi\Sigma$ circuit that computes $Det_n$ (or $Perm_n$) must be of size $2^{\Omega(n)}$ [GK1998]. In this paper, we prove that over fixed-size finite fields, any $\Sigma\Pi\Sigma$ circuit for computing the iterated matrix multiplication polynomial of $n$ generic matrices of size $n\times n$, must be of size $2^{\Omega(n\log n)}$. The importance of this result is that over fixed-size fields there is no depth reduction technique that can be used to compute all the $n^{O(1)}$-variate and $n$-degree polynomials in VP by depth 3 circuits of size $2^{o(n\log n)}$. The result [GK1998] can only rule out such a possibility for depth 3 circuits of size $2^{o(n)}$. We also give an example of an explicit polynomial ($NW_{n,\epsilon}(X)$) in VNP (not known to be in VP), for which any $\Sigma\Pi\Sigma$ circuit computing it (over fixed-size fields) must be of size $2^{\Omega(n\log n)}$. The polynomial we consider is constructed from the combinatorial design. An interesting feature of this result is that we get the first examples of two polynomials (one in VP and one in VNP) such that they have provably stronger circuit size lower bounds than Permanent in a reasonably strong model of computation. Next, we prove that any depth 4 $\Sigma\Pi^{[O(\sqrt{n})]}\Sigma\Pi^{[\sqrt{n}]}$ circuit computing $NW_{n,\epsilon}(X)$ (over any field) must be of size $2^{\Omega(\sqrt{n}\log n)}$. To the best of our knowledge, the polynomial $NW_{n,\epsilon}(X)$ is the first example of an explicit polynomial in VNP such that it requires $2^{\Omega(\sqrt{n}\log n)}$ size depth four circuits, but no known matching upper bound

Thermal conductivity of comets

A value is described for the thermal conductivity of the frost layer and for the water-ice solid debris mixture. The value of the porous structure is discussed as a function of depth only. Graphs show thermal conductivity as a function of depth and temperature at constant porosity and density

Electronic states of PrCoO3_3: X-ray photoemission spectroscopy and LDA+U density of states studies

Electronic states of PrCoO$_3$ are studied using x-ray photoemission spectroscopy. Pr 3d$_{5/2}$ core level and valence band (VB) were recorded using Mg K$_\beta$ source. The core level spectrum shows that the 3d$_{5/2}$ level is split into two components of multiplicity 4 and 2, respectively due to coupling of the spin states of the hole in 3d$_{5/2}$ with Pr 4f holes spin state. The observed splitting is 4.5 eV. The VB spectrum is interpreted using density of states (DOS) calculations under LDA and LDA+U. It is noted that LDA is not sufficient to explain the observed VB spectrum. Inclusion of on-site Coulomb correlation for Co 3d electrons in LDA+U calculations gives DOS which is useful in qualitative explanation of the ground state. However, it is necessary to include interactions between Pr 4f electrons to get better agreement with experimental VB spectrum. It is seen that the VB consists of Pr 4f, Co 3d and O 2p states. Pr 4f, Co 3d and O 2p bands are highly mixed indicating strong hybridization of these three states. The band near the Fermi level has about equal contributions from Pr 4f and O 2p states with somewhat smaller contribution from Co 3d states. Thus in the Zaanen, Sawatzky, and Allen scheme PrCoO$_3$ can be considered as charge transfer insulator. The charge transfer energy $\Delta$ can be obtained using LDA DOS calculations and the Coulomb-exchange energy U' from LDA+U. The explicit values for PrCoO$_3$ are $\Delta$ = 3.9 eV and U' = 5.5 eV; the crystal field splitting and 3d bandwidth of Co ions are also found to be 2.8 and 1.8 eV, respectively.Comment: 12 pages, 7 figures; to appear J. Phys.: Condens. Matte

Effects of exenatide and liraglutide on heart rate, blood pressure and body weight : systematic review and meta-analysis

Objectives: To synthesise current evidence for the effects of exenatide and liraglutide on heart rate, blood pressure and body weight. Design: Meta-analysis of available data from randomised controlled trials comparing Glucagon-like peptide-1 (GLP-1) analogues with placebo, active antidiabetic drug therapy or lifestyle intervention. Participants: Patients with type 2 diabetes. Outcome measures: Weighted mean differences between trial arms for changes in heart rate, blood pressure and body weight, after a minimum of 12-week follow-up. Results: 32 trials were included. Overall, GLP-1 agonists increased the heart rate by 1.86 beats/min (bpm) (95% CI 0.85 to 2.87) versus placebo and 1.90 bpm (1.30 to 2.50) versus active control. This effect was more evident for liraglutide and exenatide long-acting release than for exenatide twice daily. GLP-1 agonists decreased systolic blood pressure by −1.79 mm Hg (−2.94 to −0.64) and −2.39 mm Hg (−3.35 to −1.42) compared to placebo and active control, respectively. Reduction in diastolic blood pressure failed to reach statistical significance (−0.54 mm Hg (−1.15 to 0.07) vs placebo and −0.50 mm Hg (−1.24 to 0.24) vs active control). Body weight decreased by −3.31 kg (−4.05 to −2.57) compared to active control, but by only −1.22 kg (−1.51 to −0.93) compared to placebo. Conclusions: GLP-1 analogues are associated with a small increase in heart rate and modest reductions in body weight and blood pressure. Mechanisms underlying the rise in heart rate require further investigation

A rapidly expanding Bose-Einstein condensate: an expanding universe in the lab

We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have taken place at the end of inflation.Comment: 12 pages, 7 figure

Opto-mechanical micro-macro entanglement

We propose to create and detect opto-mechanical entanglement by storing one component of an entangled state of light in a mechanical resonator and then retrieving it. Using micro-macro entanglement of light as recently demonstrated experimentally, one can then create opto-mechanical entangled states where the components of the superposition are macroscopically different. We apply this general approach to two-mode squeezed states where one mode has undergone a large displacement. Based on an analysis of the relevant experimental imperfections, the scheme appears feasible with current technology.Comment: 7 pages, 6 figures, to appear in PRL, submission coordinated with Sekatski et al. who reported on similar result

COBE ground segment attitude determination

The Cosmic Background Explorer (COBE) spacecraft was launched in November 1989 by NASA to survey the sky for primordial radiation left from the Big Bang explosion. The success of the mission requires an accurate determination of the spacecraft attitude. While the accuracy of the attitude obtained from the attitude sensors is adequate for two of the experiments, the higher accuracy required by the Diffuse Infrared Background Experiment (DIRBE) is obtained by using the DIRBE instrument as a special type of star sensor. Presented here is an overview of the attitude processing algorithms used at the Cosmology Data Analysis Center (CDAC) and the results obtained from the flight data