Diffusion Approximation Approach Research Articles

Smoluchowski–Kramers approximation with state dependent damping and highly random oscillation

<p style='text-indent:20px;'>The small mass limit (Smoluchowski–Kramers approximation) of class systems of ordinary differential equations describing motions of small mass particle with state dependent friction and high oscillation is derived by a diffusion approximation approach. In the small mass limit, due to the state dependent damping, one additional term appears in the limit equation, which leads to a stochastic differential equation (SDE) as the highly random oscillation appears as a multiplicative white noise.</p>

Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies

We consider a connection-level model proposed by Massoulié and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds on the weighted sum of the expected numbers of flows on different routes in heavy traffic. The bounds are linear in the number of critically loaded links in the network, and they hold for a class of phase-type file-size distributions; that is, the bounds are heavy-traffic insensitive to the distributions in this class. Our approach is Lyapunov drift based, which is different from the widely used diffusion approximation approach. A key technique we develop is to construct a novel inner product in the state space, which then allows us to obtain a multiplicative type of state-space collapse in steady state. Furthermore, this state-space collapse result implies the interchange of limits as a byproduct for the diffusion approximation of the unweighted proportionally fair sharing policy under phase-type file-size distributions, demonstrating the heavy-traffic insensitivity of the stationary distribution.

User Perceived Qos Provisioning for Video Streaming in Wireless OFDMA Systems: Admission Control and Resource Allocation

In this paper, we investigate a joint admission control (AC) and resource allocation (RA) scheme for providing quality of service (QoS) guarantees for video streaming in OFDMA networks. The QoS provisioning is posed as a network utility maximization (NUM) problem. We prove that the QoS requirements are mainly dominated by the average data rate with the aid of diffusion approximation approach, allowing us to decompose the NUM problem into two tractable sub-problems, namely, the AC and the RA sub-problems. We develop an AC algorithm, which enables us to select a maximum user set such that all selected users can meet their QoS requirements related to user perceived video quality during the video playback period. In addition, in order to handle the computational complexity, we further split the RA sub-problem into the constrained Markov decision process associated problems performed at users together with a transmission problem performed at the base station. Correspondingly, we develop a power and sub-carrier allocation algorithm to minimize the average power consumption. The decision of AC is made in a long timescale and depends on the average channel state information (CSI), whereas the decision of RA is made in a short timescale and is subject to both instantaneous CSI and queue state information. Simulation results demonstrate the advantages of the proposed algorithms.

Population Abundance of the Endangered Galapagos Sea Lion Zalophus wollebaeki in the Southeastern Galapagos Archipelago.

There is great concern regarding the population status of the endangered Galapagos sea lion (GSL) because it has drastically decreased over the last 30 years. We determined the population size and growth trend of the GSL in the Galapagos southeastern region (SER) at three population levels based on the available census data: 1) SER (2011–2015), including 13 rookeries on the four islands San Cristóbal (SC), Española, Floreana, and Santa Fe, comprising 58% of the archipelago’s population; 2) SC (2011–2015), including five rookeries, comprising 52% of the SER population; and 3) El Malecón (2005–2015), the largest rookery on SC and in the SER (43% of the population on SC and 22% in the SER). We also analyzed the influence of environmental variability on pup abundance in these rookeries. The current GSL population size in the SER, after applying correction factors to the counts, is estimated at approximately 2300–4100 individuals and has declined at an average annual rate (ʎ) of 8.7% over the last five years. A similar trend was determined for SC but at ʎ = 1.4% during the same period. For El Malecón, a count-based population viability analysis using a diffusion approximation approach showed that the population increased from 2005 to 2015 at ʎ = 2%. The interannual variability in pup abundance was associated with anomalies in sea surface temperature linked to oceanographic-atmospheric events, which impact the abundance and availability of prey, and ultimately may determine the population’s reproductive success. Since rookeries in the SER had different population trends, management actions should be implemented based on their specific conditions, giving priority to rookeries such as El Malecón, which, despite showing a slightly increasing population trend, still faces a high risk of extinction due to anthropogenic disturbances and environmental variability that may affect its growth and survival.

Inference of gorilla demographic and selective history from whole-genome sequence data.

Although population-level genomic sequence data have been gathered extensively for humans, similar data from our closest living relatives are just beginning to emerge. Examination of genomic variation within great apes offers many opportunities to increase our understanding of the forces that have differentially shaped the evolutionary history of hominid taxa. Here, we expand upon the work of the Great Ape Genome Project by analyzing medium to high coverage whole-genome sequences from 14 western lowland gorillas (Gorilla gorilla gorilla), 2 eastern lowland gorillas (G. beringei graueri), and a single Cross River individual (G. gorilla diehli). We infer that the ancestors of western and eastern lowland gorillas diverged from a common ancestor approximately 261 ka, and that the ancestors of the Cross River population diverged from the western lowland gorilla lineage approximately 68 ka. Using a diffusion approximation approach to model the genome-wide site frequency spectrum, we infer a history of western lowland gorillas that includes an ancestral population expansion of 1.4-fold around 970 ka and a recent 5.6-fold contraction in population size 23 ka. The latter may correspond to a major reduction in African equatorial forests around the Last Glacial Maximum. We also analyze patterns of variation among western lowland gorillas to identify several genomic regions with strong signatures of recent selective sweeps. We find that processes related to taste, pancreatic and saliva secretion, sodium ion transmembrane transport, and cardiac muscle function are overrepresented in genomic regions predicted to have experienced recent positive selection.

Optimization Analysis of the G/G/R Machine Repair Problem With Balking and Reneging

The G/G/R machine repair problem with balking and reneging via the diffusion approximation approach is investigated. Failed machines balk (do not enter) with a constant probability and renege (leave the queue after entering) according to a general distribution. Failure and repair times of the machines are also generally distributed. The approximate probability density functions of the number of failed machines in the system are developed using diffusion approximation approach. The Newton method and the direct search method are used, respectively, to determine the optimum number of repairmen as well as the optimum value of service rate, to maximize the profit function. Sensitivity analysis with numerical illustration is also provided.

Stock Price Fluctuations in an Agent-Based Model with Market Liquidity

We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is applied to characterize the continuous-time limit (as transaction intervals shorten) as a solution of the corresponding stochastic differential equation (SDE). In this paper we further make the assumption that some of the agents are bound by either short sale constraints or budget constraints. Then we show that the continuous-time process of the stock price can be derived from a certain SDE with oblique reflection. Moreover we find that the short sale (respectively, budget) constraint causes overpricing (respectively, underpricing).

Optical coherence tomography for quality assessment of embedded microchannels in alumina ceramic

Large-scale and cost-effective manufacturing of ceramic micro devices based on tape stacking requires the development of inspection systems to perform high-resolution in-process quality control of embedded manufactured cavities, metal structures and defects. With an optical coherence tomography (OCT) system operating at 1.3 μm and a dedicated automated line segmentation algorithm, layer thicknesses can be measured and laser-machined channels can be verified in alumina ceramics embedded at around 100 μm depth. Monte Carlo simulations are employed to analyze the abilities of OCT in imaging of the embedded channels. The light scattering parameters required as input data for simulations are evaluated from the integrating sphere measurements of collimated and diffuse transmittance spectra using a reconstruction algorithm based on refined diffusion approximation approach.

The joint allele frequency spectrum of multiple populations: A coalescent theory approach

The allele frequency spectrum is a series of statistics that describe genetic polymorphism, and is commonly used for inferring population genetic parameters and detecting natural selection. Population genetic theory on the allele frequency spectrum for a single population has been well studied using both coalescent theory and diffusion equations. Recently, the theory was extended to the joint allele frequency spectrum (JAFS) for three populations using diffusion equations and was shown to be very useful in inferring human demographic history. In this paper, I show that the JAFS can be analytically derived with coalescent theory for a basic model of two isolated populations and then extended to multiple populations and various complex scenarios, such as those involving population growth and bottleneck, migration, and positive selection. Simulation study is used to demonstrate the accuracy and applicability of the theoretical model. The coalescent theory-based approach for the JAFS can characterize the demographic history with comprehensive statistical models as the diffusion approach does, and in addition gains several novel advantages: the computational complexity of calculating the JAFS with coalescent theory is reduced, and thus it is feasible to analytically obtain the JAFS for multiple populations; the hitchhiking effect can be efficiently modeled in coalescent theory, enabling the development of methodologies for detecting selection via multi-population polymorphism data. As an alternative to the diffusion approximation approach, the coalescent theory for the JAFS also provides a foundation for population genetic inference with the advent of large-scale genomic polymorphism data.

Study on radiative heat transfer property of fiber assemblies using FTIR

Radiative heat transfer could be a significant contribution to the total heat transfer within the highly porous materials. This article reports on the use of a conventional instrument, viz. Fourier transform infrared (FTIR) spectroscopy, for the characterization of radiative heat properties of fiber assemblies with low bulk densities. Experimental measurements on spectral transmission with FTIR were performed on five types of fiber assemblies commonly used for insulating materials. From the measurements, radiative heat conductivity was determined by calculating extinction coefficient using Beer’s Law and applying the diffusion approximation approach. Bulk density, fiber arrangement, and temperature influences to radiative heat transfer were discussed. Results show that radiative heat conductivity decreases with bulk density and that of the random arranged fiber assemblies shows lower radiative heat conductivity than the random ball and parallel arranged fiber assemblies. Radiative heat conductivity is proportional to the cubic temperature. The existing theoretical model was modified by comparing theoretical and experimental radiative heat conductivity results.

A diffusion approximation model for wireless networks based on IEEE 802.11 standard

The article presents an analytical model of wireless networks using the IEEE 802.11 protocol to access the transport medium. The model allows to determine such key factors of the quality of service as transmission delays and losses. The model is based on diffusion approximation approach which was proposed three decades ago to model wired networks. We show that it can be adapted to take into consideration the input streams with general interarrival time distributions and servers with general service time distributions. The diffusion approximation has been chosen because of fairly general assumptions of models based on it, hard to be represented in Markov models. A queueing network model can have an arbitrary topology, the intensity of transmitted flows can be represented by non-Poisson (even self-similar) streams, the service times at nodes can be defined by general distributions. These assumptions are important: because of the CSMA/CA algorithm, the overall times needed to sent a packet are far from being exponentially distributed and therefore the flows between nodes are non-Poisson. Diffusion approximation allows us also to analyse the of transient behaviour of a network when traffic intensity is changing with time.

A Preliminary Model of Wood Stork Population Dynamics in the Southeastern United States

Abstract We modeled population dynamics and extinction probabilities for the endangered Wood Stork (Mycteria americana) using count data from synoptic aerial surveys, annual measures of productivity from throughout the southeastern U.S., and survival data from satellite-tagged juveniles. Using a simple, count-based diffusion approximation approach we were able to quantify an increasing population trend since 1976. High inter-year variability resulted in wide confidence intervals and we could not eliminate the possibility of long-term population decline in spite of recently measured population increases. We also used a stage-based population matrix model to incorporate observed differences in survival rates among age classes. Fledging success, and survival of fledglings, one, and two-year-old birds were estimated using data from the satellite telemetry study. Because the survival rates of three-year-olds and adults are presently unknown, we analyzed population dynamics over a range of these values. Long-te...

Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

The effect of population structure on the probability of fixation of a newly introduced mutant under weak selection is studied using a coalescent approach. Wright's island model in a framework of a finite number of demes is assumed and two selection regimes are considered: a beneficial allele model and a linear game among offspring. A first-order approximation of the fixation probability for a single mutant with respect to the intensity of selection is deduced. The approximation requires the calculation of expected coalescence times, under neutrality, for lineages starting from two or three sampled individuals. The results are obtained in a general setting without assumptions on the number of demes, the deme size or the migration rate, which allows for simultaneous coalescence or migration events in the genealogy of the sampled individuals. Comparisons are made with limit cases as the deme size or the number of demes goes to infinity or the migration rate goes to zero for which a diffusion approximation approach is possible. Conditions for selection to favor a mutant strategy replacing a resident strategy in the context of a linear game in a finite island population are addressed.

Radiation Parameterization for Three-Dimensional Inhomogeneous Cirrus Clouds: Application to Climate Models

Abstract A three-dimensional (3D) radiative transfer model has been developed to simulate the transfer of solar and thermal infrared radiation in inhomogeneous cirrus clouds. The model utilizes a diffusion approximation approach (four-term expansion in the intensity) for application to inhomogeneous media, employing Cartesian coordinates. The extinction coefficient, single-scattering albedo, and asymmetry factor are functions of spatial position and wavelength and are parameterized in terms of the ice water content and mean effective ice crystal size. The correlated k-distribution method is employed for incorporation of gaseous absorption in multiple-scattering atmospheres. Delta-function adjustment is used to account for the strong forward-diffraction nature in the phase function of ice particles to enhance computational accuracy. Comparisons of the model results with those from plane-parallel (PP) and other 3D models show reasonable agreement for both broadband and monochromatic results. Three-dimension...

Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models

Time-resolved light scattering profiles were measured from highly forward-scattering media in the spatial range of 5--15 transport mean free paths ${(l}_{t}).$ Experimental profiles were compared with theoretical predictions based on the non-Euclidean diffusion (NED) and conventional diffusion approximation (DA) equations. The NED model was found to be better in predicting scattered photon distribution over various temporal and spatial scales than the DA approach.

Comparative analysis for the M/K k/1 machine repair problem with spares

This paper deals with the M/E k/1 machine repair problem with spares under steady-state conditions. Spares are considered to be either cold standby, warm standby, or hot standby. We present exact formulas for the probability mass functions of the number of failed machines in the system. Approximate formulas for the probability density function of the number of failed machines in the system are obtained through diffusion approximation. A study of the derived exact results, compared to the approximate results, shows that the diffusion approximation approach is sufficiently accurate for practical use.

Comparative analysis for the G/G/R machine repair problem

Using approximate formulas for the probability density function of the number of failed machines in a G/G/R machine repair system obtained through diffusion approximation, a comparison between the approximate results with some of the exact existing results is made. The diffusion approximation approach is accurate enough for practical purposes and is a useful method for solving complex machine repair problems.