Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

Stochastic models of IEEE 802.11e wireless net works with multimedia applications

We provide a survey of some of our recent results ([9], [13], [4], [6], [7]) on the analytical performance modeling of IEEE 802.11 wireless local area networks (WLANs). We first present extensions of the decoupling approach of Bianchi ([1]) to the saturation analysis of IEEE 802.11e networks with multiple traffic classes. We have found that even when analysing WLANs with unsaturated nodes the following state dependent service model works well: when a certain set of nodes is nonempty, their channel attempt behaviour is obtained from the corresponding fixed point analysis of the saturated system. We will present our experiences in using this approximation to model multimedia traffic over an IEEE 802.11e network using the enhanced DCF channel access (EDCA) mechanism. We have found that we can model TCP controlled file transfers, VoIP packet telephony, and streaming video in the IEEE802.11e setting by this simple approximation.

S-nets: A Petri net based model for performance evaluation of real-time scheduling algorithms

A new class of nets, called S-nets, is introduced for the performance analysis of scheduling algorithms used in real-time systems Deterministic timed Petri nets do not adequately model the scheduling of resources encountered in real-time systems, and need to be augmented with resource places and signal places, and a scheduler block, to facilitate the modeling of scheduling algorithms. The tokens are colored, and the transition firing rules are suitably modified. Further, the concept of transition folding is used, to get intuitively simple models of multiframe real-time systems. Two generic performance measures, called �load index� and �balance index,� which characterize the resource utilization and the uniformity of workload distribution, respectively, are defined. The utility of S-nets for evaluating heuristic-based scheduling schemes is illustrated by considering three heuristics for real-time scheduling. S-nets are useful in tuning the hardware configuration and the underlying scheduling policy, so that the system utilization is maximized, and the workload distribution among the computing resources is balanced.

Petri net-based modeling of a class of complex digital systems

We present through the use of Petri Nets, modeling techniques for digital systems realizable using FPGAs. These Petri Net models are used for logic validation at the logic design phase. The technique is illustrated by modeling practical circuits. Further, the utility of the technique with respect to timing analysis of the modeled digital systems is considered. Copyright (C) 1997 Elsevier Science Ltd

Multi-decadal variation of the net downward shortwave radiation over south Asia: The solar dimming effect

The solar radiation flux at the earth's surface has gone through decadal changes of decreasing and increasing trends over the globe. These phenomena known as dimming and brightening, respectively, have attracted the scientific interest in relation to the changes in radiative balance and climate. Despite the interest in the solar dimming/brightening phenomenon in various parts of the world, south Asia has not attracted great scientific attention so far. The present work uses the net downward shortwave radiation (NDSWR) values derived from satellites (Modern Era Retrospective-analysis for Research and Applications, MERRA 2D) in order to examine the multi-decadal variations in the incoming solar radiation over south Asia for the period of 1979-2004. From the analysis it is seen that solar dimming continues over south Asia with a trend of -0.54 Wm(-2) yr(-1). Assuming clear skies an average decrease of -0.05 Wm(-2)yr(-1) in NDSWR was observed, which is attributed to increased aerosol emissions over the region. There is evidence that the increase in cloud optical depth plays the major role for the solar dimming over the area. The cloud optical depth (MERRA retrievals) has increased by 10.7% during the study period, with the largest increase to be detected for the high-level (atmospheric pressure P < 400 hPa) clouds (31.2%). Nevertheless, the decrease in solar radiation and the role of aerosols and clouds exhibit large monthly and seasonal variations directly affected by the local monsoon system, the anthropogenic and natural aerosol emissions. All these aspects are examined in detail aiming at shedding light into the solar dimming phenomenon over a densely populated area. (C) 2011 Elsevier Ltd. All rights reserved.

Effect of Net-Fluence on waveguide formation in ultrafast laser inscribed chalcogenide glass

Waveguides were fabricated on GeGaSEr chalcogenide glass using ultrafast laser inscription method. The thermal diffusion model is discussed for understanding the light matter interaction and shown the effect of net-fluence in waveguide formation on chalcogenide glass. (C) 2012 Optical Society of America

Stabilization of Co-3 - Oxoclusters in a pcu Net: Synthesis, Structure, Solvent Exchange (Single Crystal to Single Crystal) and Magnetic Studies

The solvothermal reaction of CoCl(2)4H(2)O and 4,4-sulfonyldibenzoic acid (H(2)SDBA) resulted in the formation of a three-dimensional coordination polymer Co-3(C14H8O6S)(3)(DMA)(2)(MeOH)].DMA (Ia) consisting of trinuclear Co-3 oxo-cluster units. The Co-3 trimeric units are connected by SDBA(2-) anions leading to a three dimensional structure with a pcu topology. The terminal methanol molecules could be exchanged in a single crystal to single crystal (SCSC) fashion by other similar solvent molecules (ethanol, acetonitrile, water, ethyleneglycol). Magnetic studies on the parent compound, Ia, indicate antiferromagnetic interactions between the central metal atoms.