Dimensional Process Research Articles

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval [0,1] with dependence on a single parameter, λ. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on λ and the behavior of the initial data around 1. The second scaling leads to a measure-valued Fleming–Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method, utilizes the total variation distance to discriminate the transition probabilities of a high dimensional Markov process and a reduced order Markov process. The approximation is obtained by optimizing a linear functional defined in terms of transition probabilities of the reduced order Markov process over a total variation distance constraint. The transition probabilities of the approximated Markov process are given by a water-filling solution. The second method, utilizes total variation distance to discriminate the invariant probability of a Markov process and that of the approximating process. The approximation is obtained via two alternative formulations: (a) maximizing a functional of the occupancy distribution of the Markov process, and (b) maximizing the entropy of the approximating process invariant probability. For both formulations, once the reduced invariant probability is obtained, which does not correspond to a Markov process, a further approximation by a Markov process is proposed which minimizes the Kullback-Leibler divergence. These approximations are given by water-filling solutions. Finally, the theoretical results of both methods are applied to specific examples to illustrate the methodology, and the water-filling behavior of the approximations.

Expected Length of the Voronoi Path in a High Dimensional Poisson–Delaunay Triangulation

Let X be a d dimensional Poisson point process. We prove that the expected length of the Voronoi path between two points at distance 1 in the Delaunay triangulation associated with X is \(\sqrt{\frac{2d}{\pi }}+O(d^{-\frac{1}{2}})\) when \(d\rightarrow \infty \). In any dimension, we also provide a precise interval containing the actual value; in 3D the expected length is between 1.4977 and 1.50007.

Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and Wiener processes

In this paper, we study delayed reaction–diffusion Cohen–Grossberg neural networks driven by infinite dimensional Wiener processes. Based on semigroup theory, existence and uniqueness of mild solutions are proved under global Lipschitz conditions. Then, some criteria of global exponential stability are obtained by using Lyapunov method and Halanay inequality. Finally, some interesting examples are provided to show the feasibility and usefulness of the developed results.

Phase transitions for a planar quadratic contact process

We study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values λf for the process to survive from a finite set and λe for the existence of a nontrivial stationary distribution. Our first result comes from a standard block construction, while the second involves a comparison with the “generic population model” of Bramson and Gray (1991) [3]. An interesting new feature of our work is the suggestion that, as in the one dimensional contact process, edge speeds characterize critical values. We are able to prove the following for our quadratic contact process when the range is large but suspect they are true for two dimensional finite range attractive particle systems that are symmetric with respect to reflection in each axis. There is a speed c(θ) for the expansion of the process in each direction. If c(θ)>0 in all directions, then λ>λf, while if at least one speed is positive, then λ>λe. It is a challenging open problem to show that if some speed is negative, then the system dies out from any finite set.

High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model

(High dimensional) time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science. In this article, we separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via functional factor analysis. We propose a two-step estimation procedure. At the first step, we detect the deterministic trends of the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under various situations extending current variable selection studies. At the second step, we obtain the detrended low dimensional stochastic process, but it also poses an important question: is it justified, from an inferential point of view, to base further statistical inference on the estimated stochastic time series? We show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible, which finally allows one to study the dynamics of the whole high-dimensional system with a low dimensional representation together with the deterministic trend. We apply the method to our motivating empirical problems: studies of the dynamic behavior of temperatures (further used for pricing weather derivatives), implied volatilities and risk patterns and correlated brain activities (neuro-economics related) using fMRI data, where a panel version model is also presented.

Recurrence and transience properties of multi-dimensional diffusion processes in selfsimilar and semi-selfsimilar random environments

We consider $d$-dimensional diffusion processes in multi-parameter random environments which are given by values at different $d$ points of one-dimensional $\alpha $-stable or $(r, \alpha )$-semi-stable Levy processes. From the model, we derive some conditions of random environments that imply the dichotomy of recurrence and transience for the $d$-dimensional diffusion processes. The limiting behavior is quite different from that of a $d$-dimensional standard Brownian motion. We also consider the direct product of a one-dimensional diffusion process in a reflected non-positive Brownian environment and a one-dimensional standard Brownian motion. For the two-dimensional diffusion process, we show the transience property for almost all reflected Brownian environments.

Close Range Photogrammetry for Direct Multiple Feature Positioning Measurement without Targets

The main objective of this study is to present a new method to carry out measurements so as to improve the positioning verification step in the wind hub part dimensional validation process. This enhancement will speed up the measuring procedures for these types of parts. An industrial photogrammetry based system was applied to take advantage of its results, and new functions were added to existing capabilities. In addition to a new development based on photogrammetry modelling and image processing, a measuring procedure was defined based on optical and vision system considerations. A validation against a certified procedure by means of a laser-tracker has also been established obtaining deviations of ±0.125 μm/m.

Microscopy and FTIR investigations of the thermal gelation of methylcellulose in glycols

Methylcellulose is a well-known polymer due to its reverse thermal gel formation property in aqueous solutions. Support materials play an important role in the additive manufacturing of three dimensional parts using processes that utilise inkjet technology. This paper presents novel compositions of methylcellulose (MC) in non-aqueous solvents and investigates the thermal gel formation of these compositions. Compositions containing MC in different glycols (ethylene, propylene and butylene glycol) were prepared. Suitability of these compositions as reusable support materials for jetting based three dimensional printing processes have been previously established. In this paper, the mechanism of gelation of MC in three different glycols is explained and compared using experimental techniques such as heating and cooling between 25–150°C, hot stage microscopy and Fourier Transform Infrared (FTIR) spectroscopy. Based on the results, a generalised gel formation diagram for MC in glycols is presented and compared with aqueous MC gel formation. The results showed that MC forms gels in glycols upon cooling and the temperatures of gel formation/melting are different for each glycol. Understanding of the gel formation of these compositions can help in fine tuning these compositions for their performance during three dimensional printing.

Fractional Fick’s law for the boundary driven exclusion process with long jumps

A fractional Fick's law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.

A Data-Driven Holistic Approach to Fault Prognostics in a Cyclic Manufacturing Process

The complexity of manufacturing systems is increasing due to the increased requirements related to the variety and quality of the products, their complexity, and due to the general technological developments. In turn, the data related to the manufacturing processes is growing in size and in complexity. This presents new challenges for real-time monitoring, diagnostics, and prognostics of the processes. The challenges are addressed by new tools, methodologies, and concepts, collectively referred to as Big Data. The paper deals with the use of advanced methods for prognostics of infrequent faults on available but highly dimensional manufacturing process data. A holistic approach, which includes data generation, acquisition, storage, processing, and prognostics, is shown in a case of a plastic injection moulding process. Real industrial data acquired from five injection moulding machines and the Manufacturing Execution System within a period of six months is used. It is shown how the approach is able to tackle the high dimensionality and the large size of the data to create and evaluate prediction models for prognostics of the unplanned machine stops.

Extending expectancy-value theory predictions of achievement and aspirations in science: Dimensional comparison processes and expectancy-by-value interactions

Based on TIMSS data (18,047 Grade 8 students from the four OECD countries that collected data for multiple science domains), this study integrated dimensional comparison theory and expectancy-value theory and tested predictions about how self-concept and value are related to achievement and coursework aspirations across four science domains (physics, chemistry, earth science, and biology). First, strong support for social comparisons suggested that high achievement in a particular domain enhance students' motivation in the same domain, which in turn predicted domain-specific aspirations. Particularly, self-concept significantly interacted with value to predict aspirations. Second, in the processes underlying the formation of self-concept and intrinsic value, students tended to engage in negative dimensional comparisons between contrasting domains (physics vs. biology) but positive dimensional comparisons between assimilating domains (physics vs. chemistry). Similar dimensional comparison processes were evident for the effects of self-concept and intrinsic value on aspirations. The results generalized well across all countries.

Construction of Asymptotically Optimal Control for Crisscross Network from a Free Boundary Problem

An asymptotic framework for optimal control of multiclass stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP) and their equivalent workload formulations (EWF), has been developed by Harrison (1988). This framework has been implemented in many works for constructing asymptotically optimal control policies for a broad range of stochastic network models. To date all asymptotic optimality results for such networks correspond to settings where the solution of the EWF is a reflected Brownian motion in ℝ+ or a wedge in [Formula: see text]. In this work we consider a well studied stochastic network which is perhaps the simplest example of a model with more than one dimensional workload process. In the regime considered here, the singular control problem corresponding to the EWF does not have a simple form explicit solution. However, by considering an associated free boundary problem one can give a representation for an optimal controlled process as a two dimensional reflected Brownian motion in a Lipschitz domain whose boundary is determined by the solution of the free boundary problem. Using the form of the optimal solution we propose a sequence of control policies, given in terms of suitable thresholds, for the scaled stochastic network control problems and prove that this sequence of policies is asymptotically optimal. As suggested by the solution of the EWF, the policy we propose requires a server to idle under certain conditions which are specified in terms of thresholds determined from the free boundary.

Facial landmark automatic identification from three dimensional (3D) data by using Hidden Markov Model (HMM)

Landmark identification is one of the fundamental aspects and a necessary step of Three Dimensional (3D) data process. Numerous methods for landmark identification have been proposed, but none with high efficiency, good robustness and strong adaptability has been found yet. In this study, a novel method was developed and applied on a 120 subject's database to automatically identify facial landmarks from 3D facial scanned data. Spin Image (SI) is used to extract local feature and Hidden Markov Model (HMM) is adopted to implement the landmark identification procedure. Eleven HMMs were trained to identify different facial landmarks, respectively. We developed a three-hierarchy experiment to test the validity and reliability of the algorithm. Results show that SI is highly efficient and robust to extract facial feature. The maximum landmark recognition rate reached 95.9%. The influence of parameters in SI on the validity and reliability of landmark identification was also investigated. It was found that Bin Size of SI can improve or reduce Identification Accuracy Rate (IAR) by Bin Size value variation. The mean value of IAR increases with the Bin Size until Bin Size reaches 10, when IAR acquires its maximum value 100% and remains constant before Bin Size reaches 65. After that, IAR dropped with the increase of Bin Size, and the velocity of the drop keeps increasing until it reaches the minimum value. In contrast, Support Angle of SI influences IAR positively. Support Angle starts to function at the value of 10°. Then, IAR increases with it until Support Angle reaches the degree of 90, when IAR acquired and maintained a constant maximum value of 100%. At last, a comparison was made to address the superiority of HMM over Artificial Neural Network (ANN) on facial landmark identification and we figured out the direction of future work as well. Besides the parameters of SI as discussed in this study, we can investigate the influence of the point sampling granularity on the identification accuracy as well in the future. Relevance to industryProcessing the 3D anthropometric data in order to make it useful for the design of products and facilities is still a challenging problem. One of the typical difficulties is that there is no valid human anatomical landmarks identification method. The improvement of reliability and accuracy of the automatic 3D landmarks identification algorithm for various human body shapes will reduce the time and cost for performing manual landmark palpating and dimension extraction. This work is expected to bring benefits to human-dimension-related ergonomic design and improvement.

The Formalization of the Business Process Modeling Goals

In business process modeling the de facto standard BPMN has emerged. However, the applications of this notation have many subsets of elements and various extensions. Also, BPMN still coincides with many other modeling languages, forming a large set of available options for business process modeling languages and dialects. While, in general, the goal of modelers is a central notion in the choice of modeling languages and notations, in most researches that propose guidelines, techniques, and methods for business process modeling language evaluation and/or selection, the business process modeling goal is not formalized and not transparently taken into account. To overcome this gap, and to explicate and help to handle business process modeling complexity, the approach to formalize the business process modeling goal, and the supporting three dimensional business process modeling framework, are proposed.

How well do parents know their adolescent children? Parent inferences of student self-concepts reflect dimensional comparison processes

The internal/external frame of reference (I/E) model posits paradoxical relations between achievement and self-concept in mathematics and verbal domains. There is strong support for the I/E model based on student self-ratings, however, reviews of self-concept research claim that the I/E model does not apply to ratings by parents and significant others. We aimed to test these claims using parent inferred self-concepts. In contrast to widely cited claims, we found support for I/E model for both students (N = 486; aged 11–17; 57.2% female) and their parents (80.5% female). Math and verbal achievement had positive effects on self-concepts in the matching domain (e.g., math achievement predicting math self-concept) but negative effects for self-concepts in the non-matching domain (e.g., math achievement predicting verbal self-concept). Integrating conflicting claims, we found support for dimensional comparison processes for inferred self-concept ratings by parents, but not for parent perceptions of student abilities similar to the measures used that were the basis of previous claims.

Special Issue on INFORMS 2015 Annual Meeting

Special Issue on INFORMS 2015 Annual Meeting

Wastewater treatment by spiral wound reverse osmosis: Development and validation of a two dimensional process model

Reverse osmosis (RO) has become a significant method for removing salts and organic compounds from seawater and wastewater in recent decades. Spiral-wound module has been widely used due to a number of special features such as high packing density, premium separation and low operating cost. In this paper, a two-dimensional mathematical model is developed for the transport of dilute aqueous solutions through a spiral-wound RO module and the operational characteristics of the process under steady state conditions are analysed. The model is based on the solution-diffusion model coupled with the concentration polarization mechanism. This model yields a set of Differential and Algebraic Equations (DAEs), which are solved using the gPROMS software. The model is validated using experimental data from the literature for the rejection of dimethylphenol as solute in aqueous solutions. The model is then used to simulate the process under steady state conditions to gain deeper insight of the process.

Extending the internal/external frame of reference model to social studies: Self-concept and achievement in history and politics

Two studies with German secondary school students extend the internal/external frame of reference (I/E) model to multiple school subjects, by including history and politics as social studies subjects. Study 1 assessed students' self-concepts and achievements related to math, German, history, English (students' first foreign language), and physics. The cross-paths leading from history self-concept to math and verbal achievements and those leading from math and verbal achievements to history self-concept were non-significant arguing against the operation of dimensional comparison processes between math and verbal achievements in the formation of history self-concept. Study 2 included measures for students' self-concepts and achievements in math, English, physics, and politics as well as a history achievement. Politics achievement and self-concept were unrelated to math, English, and physics achievements and self-concepts. History achievement was positively related with politics self-concept. This finding indicates dimensional comparison processes leading to assimilation effects within the domain of social studies.

THE GENERALIZED INTERNAL/EXTERNAL FRAME OF REFERENCE MODEL: AN EXTENSION TO DIMENSIONAL COMPARISON THEORY

The dimensional comparison theory (DCT) is based on the internal/external frame of reference model (I/E model). The model focuses on the effects of external (e.g., “How good am I in math compared to my classmates?”) and internal, dimensional comparisons (e.g., “How good am I in math compared to English?”) on academic self-concepts with widespread consequences for students’ self-evaluation, motivation, and behavioral choices. This article presents an extension to the DCT: The proposal of a generalized internal/external frame of reference model (GI/E model that allows the application of previous findings on academic self-concepts to a variety of domain-specific comparison targets and standards. On the side of targets and standards it not only deals with the academic area but also with other areas, which are compared intra-individually. On the side of the consequences, it deals with other variables besides self-concepts, i.e. with motivational constructs, (learning) behaviors or personality characteristics as the outcomes of external and dimensional comparison processes. The present article closes with an examination and discussion of the contributions of the DCT by applying standards of good theories to it.