Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Optimal forwarding in delay tolerant networks with multiple destinations

We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.

Method for Seismic Microzonation with Geotechnical Aspects

This study presents an overview of seismic microzonation and existing methodologies with a newly proposed methodology covering all aspects. Earlier seismic microzonation methods focused on parameters that affect the structure or foundation related problems. But seismic microzonation has generally been recognized as an important component of urban planning and disaster management. So seismic microzonation should evaluate all possible hazards due to earthquake and represent the same by spatial distribution. This paper presents a new methodology for seismic microzonation which has been generated based on location of study area and possible associated hazards. This new method consists of seven important steps with defined output for each step and these steps are linked with each other. Addressing one step and respective result may not be seismic microzonation, which is practiced widely. This paper also presents importance of geotechnical aspects in seismic microzonation and how geotechnical aspects affect the final map. For the case study, seismic hazard values at rock level are estimated considering the seismotectonic parameters of the region using deterministic and probabilistic seismic hazard analysis. Surface level hazard values are estimated considering site specific study and local site effects based on site classification/characterization. The liquefaction hazard is estimated using standard penetration test data. These hazard parameters are integrated in Geographical Information System (GIS) using Analytic Hierarchy Process (AHP) and used to estimate hazard index. Hazard index is arrived by following a multi-criteria evaluation technique - AHP, in which each theme and features have been assigned weights and then ranked respectively according to a consensus opinion about their relative significance to the seismic hazard. The hazard values are integrated through spatial union to obtain the deterministic microzonation map and probabilistic microzonation map for a specific return period. Seismological parameters are widely used for microzonation rather than geotechnical parameters. But studies show that the hazard index values are based on site specific geotechnical parameters.

Fuzzy data envelopment analysis for performance evaluation of an irrigation system

Sixteen irrigation subsystems of the Mahi Bajaj Sagar Project, Rajasthan, India, are evaluated and selection of the most suitable/best is made using data envelopment analysis (DEA) in both deterministic and fuzzy environments. Seven performance-related indicators, namely, land development works (LDW), timely supply of inputs (TSI), conjunctive use of water resources (CUW), participation of farmers (PF), environmental conservation (EC), economic impact (EI) and crop productivity (CPR) are considered. Of the seven, LDW, TSI, CUW, PF and EC are considered inputs, whereas CPR and EI are considered outputs for DEA modelling purposes. Spearman rank correlation coefficient values are also computed for various scenarios. It is concluded that DEA in both deterministic and fuzzy environments is useful for the present problem. However, the outcome of fuzzy DEA may be explored for further analysis due to its simple, effective data and discrimination handling procedure. It is inferred that the present study can be explored for similar situations with suitable modifications.

The precision with which single cells of Dictyostelium discoideum can locate a source of cyclic AMP

When stimulated by a point source of cyclic AMP, a starved amoeba of Dictyostelium discoideum responds by putting out a hollow balloon-like membrane extension followed by a pseudopod. The effect of the stimulus is to influence the position where either of these protrusions is made on the cell rather than to cause them to be made. Because the pseudopod forms perpendicular to the cell surface, its location is a measure of the precision with which the cell can locate the cAMP source. Cells beyond 1 h of starvation respond non-randomly with a precision that improves steadily thereafter. A cell that is starved for 1-2 h can locate the source accurately 43% of the time; and if starved for 6-7 h, 87% of the time. The response always has a high scatter; population-level heterogeneity reflects stochasticity in single cell behaviour. From the angular distribution of the response its maximum information content is estimated to be 2-3 bits. In summary, we quantitatively demonstrate the stochastic nature of the directional response and the increase in its accuracy over time.

Efficient Cache Exploration Method for a Tiled Chip Multiprocessor

Past studies use deterministic models to evaluate optimal cache configuration or to explore its design space. However, with the increasing number of components present on a chip multiprocessor (CMP), deterministic approaches do not scale well. Hence, we apply probabilistic genetic algorithms (GA) to determine a near-optimal cache configuration for a sixteen tiled CMP. We propose and implement a faster trace based approach to estimate fitness of a chromosome. It shows up-to 218x simulation speedup over the cycle-accurate architectural simulation. Our methodology can be applied to solve other cache optimization problems such as design space exploration of cache and its partitioning among applications/ virtual machines.

Characterizing drought using the reliability-resilience-vulnerability concept

This study borrows the measures developed for the operation of water resources systems as a means of characterizing droughts in a given region. It is argued that the common approach of assessing drought using a univariate measure (severity or reliability) is inadequate as decision makers need assessment of the other facets considered here. It is proposed that the joint distribution of reliability, resilience, and vulnerability (referred to as RRV in a reservoir operation context), assessed using soil moisture data over the study region, be used to characterize droughts. Use is made of copulas to quantify the joint distribution between these variables. As reliability and resilience vary in a nonlinear but almost deterministic way, the joint probability distribution of only resilience and vulnerability is modeled. Recognizing the negative association between the two variables, a Plackett copula is used to formulate the joint distribution. The developed drought index, referred to as the drought management index (DMI), is able to differentiate the drought proneness of a given area when compared to other areas. An assessment of the sensitivity of the DMI to the length of the data segments used in evaluation indicates relative stability is achieved if the data segments are 5years or longer. The proposed approach is illustrated with reference to the Malaprabha River basin in India, using four adjoining Climate Prediction Center grid cells of soil moisture data that cover an area of approximately 12,000 km(2). (C) 2013 American Society of Civil Engineers.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Optimal incentive timing strategies for product marketing on social networks

We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to potential buyers (influence) and b) referral rewards for customers who influence potential buyers to make the purchase (exploit connections). The problem is to determine the optimal timing of these programs over a finite time horizon. In contrast to algorithmic perspective popular in the literature, we take a mean-field approach and formulate the problem as a continuous-time deterministic optimal control problem. We show that the optimal strategy for the seller has a simple structure and can take both forms, namely, influence-and-exploit and exploit-and-influence. We also show that in some cases it may optimal for the seller to deploy incentive programs mostly for low degree nodes. We support our theoretical results through numerical studies and provide practical insights by analyzing various scenarios.

Influence of Spatial Variation of Hydraulic Conductivity of Municipal Solid Waste on Performance of Bioreactor Landfill

The current study analyzes the leachate distribution in the Orchard Hills Landfill, Davis Junction, Illinois, using a two-phase flow model to assess the influence of variability in hydraulic conductivity on the effectiveness of the existing leachate recirculation system and its operations through reliability analysis. Numerical modeling, using finite-difference code, is performed with due consideration to the spatial variation of hydraulic conductivity of the municipal solid waste (MSW). The inhomogeneous and anisotropic waste condition is assumed because it is a more realistic representation of the MSW. For the reliability analysis, the landfill is divided into 10 MSW layers with different mean values of vertical and horizontal hydraulic conductivities (decreasing from top to bottom), and the parametric study is performed by taking the coefficients of variation (COVs) as 50, 100, 150, and 200%. Monte Carlo simulations are performed to obtain statistical information (mean and COV) of output parameters of the (1) wetted area of the MSW, (2) maximum induced pore pressure, and (3) leachate outflow. The results of the reliability analysis are used to determine the influence of hydraulic conductivity on the effectiveness of the leachate recirculation and are discussed in the light of a deterministic approach. The study is useful in understanding the efficiency of the leachate recirculation system. (C) 2013 American Society of Civil Engineers.

Seismic hazard analysis of Lucknow considering local and active seismic gaps

The Himalayas are one of very active seismic regions in the world where devastating earthquakes of 1803 Bihar-Nepal, 1897 Shillong, 1905 Kangra, 1934 Bihar-Nepal, 1950 Assam and 2011 Sikkim were reported. Several researchers highlighted central seismic gap based on the stress accumulation in central part of Himalaya and the non-occurrence of earthquake between 1905 Kangra and 1934 Bihar-Nepal. The region has potential of producing great seismic event in the near future. As a result of this seismic gap, all regions which fall adjacent to the active Himalayan region are under high possible seismic hazard due to future earthquakes in the Himalayan region. In this study, the study area of the Lucknow urban centre which lies within 350 km from the central seismic gap has been considered for detailed assessment of seismic hazard. The city of Lucknow also lies close to Lucknow-Faizabad fault having a seismic gap of 350 years. Considering the possible seismic gap in the Himalayan region and also the seismic gap in Lucknow-Faizabad fault, the seismic hazard of Lucknow has been studied based on deterministic and the probabilistic seismic hazard analysis. Results obtained show that the northern and western parts of Lucknow are found to have a peak ground acceleration of 0.11-0.13 g, which is 1.6- to 2.0-fold higher than the seismic hazard compared to the other parts of Lucknow.

Scheduling for Fading Channels Under Partial Channel Information

We consider a scheduler for the downlink of a wireless channel when only partial channel-state information is available at the scheduler. We characterize the network stability region and provide two throughput-optimal scheduling policies. We also derive a deterministic bound on the mean packet delay in the network. Finally, we provide a throughput-optimal policy for the network under QoS constraints when real-time and rate-guaranteed data traffic may be present.

Experimental Study on Substrate Noise Effects of a Pulsed Clocking Scheme on PLL Performance

In this brief, the substrate noise effects of a pulsed clocking scheme on the output spur level, the phase noise, and the peak-to-peak (Pk-Pk) deterministic period jitter of an integer-N charge-pump phase-locked loop (PLL) are demonstrated experimentally. The phenomenon of noise coupling to the PLL is also explained through experiments. The PLL output frequency is 500 MHz and it is implemented in the 0.13-mu m CMOS technology. Measurements show a reduction of 12.53 dB in the PLL output spur level at an offset of 5 MHz and a reduction of 107 ps in the Pk-Pk deterministic period jitter upon reducing the duty cycle of the signal injected into the substrate from 50% to 20%. The results of the analyses suggest that using a pulsed clocking scheme for digital systems in mixed-signal integration along with other isolation techniques helps reduce the substrate noise effects on sensitive analog/radio-frequency circuits.

Optimal Forwarding in Delay-Tolerant Networks With Multiple Destinations

We study the tradeoff between delivery delay and energy consumption in a delay-tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the message and the number of destinations that have received the message. We formulate the problem as a controlled continuous-time Markov chain and derive the optimal closed-loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ordinary differential equation (ODE) (i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open-loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed-loop policy.

Seismic microzonation of a nuclear power plant site with detailed geotechnical, geophysical and site effect studies

This paper highlights the seismic microzonation carried out for a nuclear power plant site. Nuclear power plants are considered to be one of the most important and critical structures designed to withstand all natural disasters. Seismic microzonation is a process of demarcating a region into individual areas having different levels of various seismic hazards. This will help in identifying regions having high seismic hazard which is vital for engineering design and land-use planning. The main objective of this paper is to carry out the seismic microzonation of a nuclear power plant site situated in the east coast of South India, based on the spatial distribution of the hazard index value. The hazard index represents the consolidated effect of all major earthquake hazards and hazard influencing parameters. The present work will provide new directions for assessing the seismic hazards of new power plant sites in the country. Major seismic hazards considered for the evaluation of the hazard index are (1) intensity of ground shaking at bedrock, (2) site amplification, (3) liquefaction potential and (4) the predominant frequency of the earthquake motion at the surface. The intensity of ground shaking in terms of peak horizontal acceleration (PHA) was estimated for the study area using both deterministic and probabilistic approaches with logic tree methodology. The site characterization of the study area has been carried out using the multichannel analysis of surface waves test and available borehole data. One-dimensional ground response analysis was carried out at major locations within the study area for evaluating PHA and spectral accelerations at the ground surface. Based on the standard penetration test data, deterministic as well as probabilistic liquefaction hazard analysis has been carried out for the entire study area. Finally, all the major earthquake hazards estimated above, and other significant parameters representing local geology were integrated using the analytic hierarchy process and hazard index map for the study area was prepared. Maps showing the spatial variation of seismic hazards (intensity of ground shaking, liquefaction potential and predominant frequency) and hazard index are presented in this work.