Generalizing the hypergraph Laplacian via a diffusion process with mediators

Ballast material is a critical part of the safety of railways, such as padding tracks to prevent dynamic vibrations from causing trains to derail. The effectiveness of this material is closely tied to the percentage of fouling that is intermixed with the material. Generally, ballast is placed as compact as practical, but overtime, fouling of the ballast changes the composition of the placed material. Relative density could provide insight into the relative compactness and strength of the material. Unfortunately, the results of minimum or maximum density tests are not well documented in the existing literature. Although ASTM D4254 and D4253 do provide guidelines for minimum and maximum density testing of large particle diameters, there is minimal discussion in the literature regarding the anticipated error when testing with ballast and fouling. Tests to attempt to characterize this behavior, minimum and maximum density tests were run using Connecticut Granite ballast with granite stone dust used as a fouling material. The samples contained fouling at intervals of 0, 15, 30, 45, and 60% by mass and were placed in a 12-inch interior diameter cylinder mold in accordance with the ASTM standards. For each fouling condition, two operators each conducted 10 minimum density and 5 maximum density tests for a total of 100 minimum density tests and 50 maximum density tests. The effect of fouling, density, and operator, on the repeatability of the tests on ballast, is discussed.

Diffusion models have gained significant attention in the field of generative modeling due to their capability to produce high-quality samples. However, recent studies show that applying a uniform treatment to all distributions during the training of diffusion models is sub-optimal. In this paper, we present a comprehensive theoretical analysis of the forward process in diffusion models. Our findings indicate that distribution variations are not uniform throughout the diffusion process, with the sharpest changes occurring during the initial stages. Moreover, we observe that the initial distribution converges to a Gaussian distribution at an exponential rate, indicating that different initial distributions rapidly become quite similar during the forward diffusion process. Consequently, employing a uniform timestep sampling strategy does not effectively capture these dynamics, potentially leading to sub-optimal training outcomes for diffusion models. To remedy this, we introduce the Bidirectional Beta-Tuned Diffusion Model (BB-TDM). The BB-TDM leverages the Beta distribution to design the timestep sampling distribution and enhance the separation between different initial distributions during the diffusion process. By selecting appropriate parameters, the BB-TDM ensures that the timestep sampling distribution is aligned with the properties of the forward diffusion process and moderates the convergence speed of different initial distributions. Extensive experiments across various benchmark datasets on different diffusion models confirm the efficacy of the proposed BB-TDM.

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson in J Financ Quant Anal 18(1):141–148 (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same efficiency as the quadratic approximation of Barone-Adesi and Whaley in J Financ 42:301–320 (1987), with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston’s stochastic volatility model, our method is shown to be extremely efficient and fairly accurate.

Neutron reflectivity and Fourier transform infrared spectroscopy measurements are used to profile the deprotection reaction−diffusion front with nanometer resolution in a model photoresist polymer using three perfluoroalkane-based photoacid generators (PAG) with varying chain lengths. As expected, the spatial extent of the deprotection reaction front increases with decreasing PAG size. Although the total extent of deprotection increases with increasing postexposure bake time for each PAG, the reaction−diffusion of deprotection does not propagate continuously into the photoresist polymer. The form of the deprotection reaction front changes because the diffusion process is affected by the changing polymer composition. The data are well described by a reaction−diffusion model that includes a simple acid-trapping term and does not require a varying PAG diffusivity. This high-resolution profiling, together with modeling, illustrates details of the coupled diffusion and deprotection reaction processes that affe...

The rapid development of online social networks (OSNs) renders them a powerful platform for information diffusion on a massive scale. OSNs generate enormous propagation traces. An important question is how to model the real-world information diffusion process. Although considerable studies have been conducted in this field, the temporal characteristics have not been fully addressed yet. This thesis addresses the issue of modeling the temporal dynamics of the information diffusion process. Based on empirical findings drawn from large-scale propagation traces of a popular OSN in China, we demonstrate that the temporal characteristics has a significant impact on the diffusion dynamics. Hence, a series of new temporal information diffusion models have been proposed by incorporating these temporal features. Experimental results demonstrate that these proposed models are more accurate and practical than existing discrete diffusion models. Moreover, one application of information diffusion models, i.e., the revenue maximization problem, is studied. Specifically, the thesis consists of three major parts: 1) preliminaries, i.e., introduction of research platform and collected dataset, 2) modeling social influence diffusion from three different temporal aspects, and 3) monetizing OSNs through designing intelligent pricing strategies in the diffusion process to realize the goal of revenue maximization.
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\nFirstly, the research platform is introduced and the statistical properties of the data derived from this platform are investigated. We choose Renren, the dominant social network website in China, as our research platform and study its information propagation mechanisms. Specifically, we concentrate on the propagation of “sharing video” behaviors, and collect data on more than 2.8 million Renren users and over 209 million diffusion traces. The analysis result shows that the video access patterns in OSNs differ significantly from Youtube-like systems, which makes understanding the video propagation behaviors in OSNs an important research task.
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\nSecondly, the temporal modeling of information diffusion is explored. By investigating temporal features using real diffusion traces, we find that three factors should be considered in building realistic diffusion models, including, information propagation latency, multiple influential sources and user diversities. We then develop models to explain the information propagation process by incorporating these factors, and demonstrate that the models reflect reality well.
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\nFinally, revenue maximization in the information diffusion process is studied. Specifically, the pricing factor is explicitly incorporated into the product diffusion process. To realize the goal of revenue maximization, we develop a Dynamic Programming Based Heuristic (DPBH) to obtain the optimal pricing sequence. Application of the DPBH in the revenue maximization problem shows that it performs well in both the expected revenue achieved and in running time. This leads to fundamental ramifications to many related OSN marketing applications.

The forward-path method for pricing multi-asset American-style options under general diffusion processes

This study provides an examination of the effect of public news on inter-day exchange-rate return volatility. Unlike previous studies, the impacts ofboth U.S. and foreign macroeconomic news announcements are examined in the currency futures market for the Japanese yen, British pound, and Deutsche mark. Diffusion and jump-diffusion process models are developed which contain parameters conditional on the release of news. These models are estimated using the method of maximum likelihood, and are tested versus unconditional diffusion and jump-diffusion models using likelihood ratio tests. The results reveal that conditional variance diffusion and jump-diffusion process models dominate the equivalent non-conditional models. Over the period studied (January 1988–December 1990) U.S. merchandise trade balance and industrial production announcements had a significantly greater impact on trading period volatility than money supply or inflation announcements did. Foreign news was also found to have a substantially lower effect on foreign trading-period variance than U.S. news had on U.S. trading period variance. In addition, the correlation between the yen, pound, and mark was highest on days of U.S. macroeconomic news. Thus, this study provides evidence that the currency return generating process is not characterized by a simple diffusion process over trading and non-trading periods. Further, the release of U.S. and foreign macroeconomic news has been shown to provide additional understanding of the currency return process over and above that of more complex models such as a jump-diffusion process.

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann’s (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann’s problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann’s problem do not address the main theoretical question that historically motivated research in this area.

General References, Diffusion Processes, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov’s transformation, is described through theoretical results and numerical examples.

Limiting density behavior of quartz powders

Previous article Next article Haploid Populations Subject to Varying Environment: The Characteristic Values and the Rate of Loss of AllelesKeith GladstienKeith Gladstienhttps://doi.org/10.1137/0132065PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA class of stochastic matrices, arising in genetics, are considered. The characteristic values are obtained and related to the genetic process.[1] C. Cannings, The latent roots of certain Markov chains arising in genetics: a new approach. I. Haploid models, Advances in Appl. Probability, 6 (1974), 260–290 MR0343949 0284.60064 CrossrefGoogle Scholar[2] C. Cannings, The latent roots of certain Markov chains arising in genetics: a new approach. II. Further haploid models, Advances in Appl. Probability, 7 (1975), 264–282 MR0371430 0339.60067 CrossrefISIGoogle Scholar[3] A. B. Chia, Random mating in a population of cyclic size, J. Appl. Probability, 5 (1968), 21–30 MR0225583 0162.51901 CrossrefISIGoogle Scholar[4] William Feller, Diffusion processes in genetics, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 227–246 MR0046022 0045.09302 Google Scholar[5] Joseph Felsenstein, The rate of loss of multiple alleles in finite haploid populations, Theoret. Population Biology, 2 (1971), 391–403 10.1016/0040-5809(71)90028-1 MR0332215 0234.92010 CrossrefGoogle Scholar[6] Keith Gladstien, Loss of alleles in a haploid population with varying environment, Theoret. Population Biology, 10 (1976), 383–394 10.1016/0040-5809(76)90025-3 MR0496833 0346.92014 CrossrefISIGoogle Scholar[7] Keith Gladstien, The characteristic values and vectors for a class of stochastic matrices arising in genetics, SIAM J. Appl. Math., 34 (1978), 630–642 10.1137/0134050 MR0475977 0386.92004 LinkISIGoogle Scholar[8] Samuel Karlin, Equilibrium behavior of population genetic models with non-random mating. II. Pedigrees, homozygosity and stochastic models, J. Appl. Probability, 5 (1968), 487–566 MR0246657 0205.49601 CrossrefISIGoogle Scholar[9] S. Karlin, Rates of approach to homozygosity for finite stochastic models with variable population size, Amer. Naturalist, 102 (1968), 443–455 10.1086/282557 CrossrefISIGoogle Scholar[10] S. Wright, Evolution in Mendelain populations, Genetics, 16 (1931), 97–159 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Looking Forwards and Backwards in the Multi-Allelic Neutral Cannings Population ModelJournal of Applied Probability, Vol. 47, No. 03 | 14 July 2016 Cross Ref Looking Forwards and Backwards in the Multi-Allelic Neutral Cannings Population ModelJournal of Applied Probability, Vol. 47, No. 3 | 14 July 2016 Cross Ref The time back to the most recent common ancestor in exchangeable population modelsAdvances in Applied Probability, Vol. 36, No. 01 | 1 July 2016 Cross Ref The time back to the most recent common ancestor in exchangeable population modelsAdvances in Applied Probability, Vol. 36, No. 1 | 1 July 2016 Cross Ref Robustness results for the coalescentJournal of Applied Probability, Vol. 35, No. 02 | 14 July 2016 Cross Ref Robustness results for the coalescentJournal of Applied Probability, Vol. 35, No. 2 | 14 July 2016 Cross Ref Line-of-descent and genealogical processes, and their applications in population genetics modelsTheoretical Population Biology, Vol. 26, No. 2 | 1 Oct 1984 Cross Ref The Characteristic Values and Vectors for a Class of Stochastic Matrices Arising in GeneticsKeith GladstienSIAM Journal on Applied Mathematics, Vol. 34, No. 4 | 12 July 2006AbstractPDF (1212 KB) Volume 32, Issue 4| 1977SIAM Journal on Applied Mathematics707-895 History Submitted:29 April 1976Published online:12 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0132065Article page range:pp. 778-783ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Demand forecasting plays an important role in demand management, and product diffusion model had been used to forecast the demand of new products for several years. Bass diffusion model describes the empirical adoption curve by using two important factors, namely, the coefficients of innovation and imitation. In 1975, R-L model incorporated the “price” decision variable into diffusion model. A generalized Bass model incorporated price and advertising policies into the original Bass model to analyze empirical new product diffusion process. In this research a system dynamics diffusion model was constructed to model the dynamical diffusion process of a new product. In addition to the four factors, the effect of product brand was added into the system dynamics model. The model was tested and results revealed that the prediction capability of the proposed system dynamics model is better than those of Bass diffusion model, R-L model and generalized Bass model.