General Stochastic Approach Research Articles

Effective hydrogen supply chain management framework considering nonlinear multi-stage process uncertainties

The large amount of carbon emitted due to industrial development is posing serious climate change. Under these circumstances, hydrogen energy is being used as a major energy source and is attracting attention as an alternative energy to fossil fuels, characterized by high carbon emissions. While the use of hydrogen has the obvious benefit of a low carbon footprint, the hydrogen production process possesses a high carbon footprint difference depending on the source of utilized electricity. This study considers several situations arising in an electrolysis-based hydrogen supply chain network (HSCN). A multi-stage stochastic programming (SP) is modeled to consider the uncertainty of demand and transportation capacity generated in HSCN. Moreover, a typical stochastic model has a chain rule between the decision variables resulting from nonlinearity and uncertainty, and these features make it difficult to derive an effective solution. Thus, in this study, a new methodology, Weighted Scenario Sample Average Approximation (WSSAA), is proposed to derive an effective solution for the multistage SP model considering various scenarios under the hydrogen supply chain. While a general stochastic programming approach fails to generate feasible solutions with volatile HSCN uncertainties, the proposed WSSAA framework provides feasible decisions considering multiple scenarios. The effectiveness of the proposed model applied with WSSAA is demonstrated through comparative experiments over the models used in existing studies.

LARGE PLATONIC MARKETS WITH DELAYS

The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large Platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modeling of markets, where the observed information is delayed, while the latter provides the opportunity to defer the indexed time of a received asset price. Both delays may be designed randomly and inhomogeneously over time. We show that delayed markets are equipped with a fundamental theorem of asset pricing and our main result is inheritance of the no asymptotic Lp-free lunch condition under both delay types. Eventually, we suggest an approach to verify absence of Lp-free lunch on markets with multiple brokers endowed with deviating trading speeds.

Computational micromechanics of porous brittle solids

Porous brittle solids evidence complex mechanical behavior, where localized failure patterns originate from mechanical processes on the microstructural level. In order to investigate the failure mechanics of porous brittle solids, we outline a general stochastic and numerical microstructure-based approach. To this end, we generate random porous microstructures by level-cutting Gaussian random fields, and conduct numerical simulations using the material point method. This allows investigating both small and large deformation characteristics of irregular porous media where a segmentation into grains and bonds is ambiguous. We demonstrate the versatility of our approach by examining elasticity and failure as a function of a wide range of porosities, from 20% to 80%. Observing that onset of failure can be well described through the second order work, we show that the stress at failure follows a power law similar to that of the elastic modulus. Moreover, we propose that the failure envelope can be approximated by a simple quadratic fitting curve, and that plastic deformation appears to be governed by an associative plastic flow rule. Finally, large deformation simulations reveal a transition in the mode of localization of the deformation, from compaction bands for highly porous samples to shear bands for denser ones.

An Exactly Solvable Stochastic Kinetic Theory of Single-Molecule Force Experiments.

The unfolding of a protein in single-molecule pulling experiments subjected to a constant force (force-clamp) and constant velocity (force-ramp) is analyzed by introducing an exactly solvable two-state kinetic model framed based on the general stochastic approach of discrete state and continuous time formulation. The effect of perturbation is interpreted in the presence of dynamic disorder, resulting from intrinsic conformational fluctuations, by deriving an exact analytical expression for the unfolding time distribution, which in turn allowed us to calculate the expressions for the quantities of experimental interest explicitly. In particular, the novelty of our method lies in the fact that it reduced the need for a lengthy calculation, contrary to the previous dynamic disorder studies, and provides a fairly concise but sufficient mathematical analysis, which becomes much easier to implement quantitatively. We tested our results against the measured data from a number of force unfolding experiments on various proteins, ubiquitin, titin, and filamin, and the force unzipping of DNA and observed excellent agreement in each case. This asserts the reliability of the present technique, which suggests a plausible extension of the stochastic kinetic theory in single-molecule force experiments beyond its present-day widespread implications.

Anomalous diffusion for neuronal growth on surfaces with controlled geometries.

Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned polydimethylsiloxane surfaces. We use fluorescence microscopy to image neurons, quantify their dynamics, and demonstrate that the substrate geometrical patterns cause strong directional alignment of axons. We quantify axonal growth and report a general stochastic approach that quantitatively describes the motion of growth cones. The growth cone dynamics is described by Langevin and Fokker-Planck equations with both deterministic and stochastic contributions. We show that the deterministic terms contain both the angular and speed dependence of axonal growth, and that these two contributions can be separated. Growth alignment is determined by surface geometry, and it is quantified by the deterministic part of the Langevin equation. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: speed and angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from Brownian motion (Ornstein-Uhlenbeck process) at earlier times to anomalous dynamics (superdiffusion) at later times. The superdiffusive regime is characterized by non-Gaussian speed distributions and power law dependence of the axonal mean square length and the velocity correlation functions. These results demonstrate the importance of geometrical cues in guiding axonal growth, and could lead to new methods for bioengineering novel substrates for controlling neuronal growth and regeneration.

Role of geometrical cues in neuronal growth.

Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micropatterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds, and damping coefficients. We demonstrate that axonal dynamics displays a crossover from an Ornstein-Uhlenbeck process to a nonlinear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide insight into the role of curvature sensing proteins and their interactions with geometrical cues.

Exact and Efficient Sampling of Conditioned Walks

A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.

Stochastic Simulation of Utility-Scale Storage Resources in Power Systems With Integrated Renewable Resources

We report on the extension of a general stochastic simulation approach for power systems with integrated renewable resources to also incorporate the representation of utility-scale storage resources. The extended approach deploys models of the energy storage resources to emulate their scheduling and operations in the transmission-constrained hourly day-ahead markets. To this end, we formulate a scheduling optimization problem to determine the operational schedule of the controllable storage resources in coordination with the demands and the various supply resources, including the conventional and renewable resources. The incorporation of the scheduling optimization problem into the Monte Carlo simulation framework takes full advantage of the structural characteristics in the construction of the so-called sample paths for the stochastic simulation approach and to ensure its numerical tractability. The extended methodology has the capability to quantify the power system economics, emissions and reliability variable effects over longer-term periods for power systems with the storage resources. Applications of the approach include planning and investment studies and the formulation and analysis of policy. We illustrate the capabilities and effectiveness of the simulation approach on representative study cases on modified IEEE 118 and WECC 240-bus systems. These results provide valuable insights into the impacts of energy storage resources on the performance of power systems with integrated wind resources.

Statistical modeling and forecasting of fruit crop phenology under climate change

Phenology, the study of the association between biological development stages and variations in climate, has greatly increased in importance because of concerns arising from climate change. This paper presents a general stochastic approach to the modeling of the relationship between phenological events and climate variables, and gives a prediction method based on this approach to provide full predictive distributions for future events. The proposed methods are then applied to the modeling and prediction of the bloom dates of six high‐valued fruit crops. In particular, we use our approach to explore how the bloom dates are related to the accumulation of growing degree days, to provide a sensible estimate of an important parameter Tbase in phenological study, and to assess the prediction of bloom dates with a leave‐one‐out procedure. Most importantly, the impact of future climate change on bloom dates is studied with temperature outputs from well‐established coupled global climate models under a high greenhouse gases scenario. Copyright © 2014 John Wiley & Sons, Ltd.

Spreading dynamics on complex networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

A Spatial Clustering Approach for Stochastic Fracture Network Modelling

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia.

Modelling Coagulation Systems: A Stochastic Approach

A general stochastic approach to the description of coagulating aerosol system is developed. As the object of description one can consider arbitrary mesoscopic values (number of aerosol clusters, their size etc). The birth-and-death formalism for a number of clusters can be regarded as a partial case of the generalized storage model. An application of the storage model to the number of monomers in a cluster is discussed.

A Stochastic Model for Calibrating the Survival Benefit of Screen-Detected Cancers

Comparison of the survival of clinically detected and screen-detected cancer cases from either population-based service screening programs or opportunistic screening is often distorted by both lead-time and length biases. Both are correlated with each other and are also affected by measurement errors and tumor attributes such as regional lymph node spread. We propose a general stochastic approach to calibrate the survival benefit of screen-detected cancers related to both biases, measurement errors, and tumor attributes. We apply our proposed method to breast cancer screening data from one arm of the Swedish Two-County trial in the trial period together with the subsequent service screening for the same cohort. When there is no calibration, the results—assuming a constant (exponentially distributed) post-lead-time hazard rate (i.e., a homogeneous stochastic process)—show a 57% reduction in breast cancer death over 25 years. After correction, the reduction was 30%, with approximately 12% of the overestimation being due to lead-time bias and 15% due to length bias. The additional impacts of measurement errors (sensitivity and specificity) depend on the type of the proposed model and follow-up time. The corresponding analysis when the Weibull distribution was applied—relaxing the assumption of a constant hazard rate—yielded similar findings and lacked statistical significance compared with the exponential model. The proposed calibration approach allows the benefit of a service cancer screening program to be fairly evaluated. This article has supplementary materials online.

Stochastic Models of User-Contributory Web Sites

We describe a general stochastic processes-based approach to modeling user-contributory web sites, where users create, rate and share content. These models describe aggregate measures of activity and how they arise from simple models of individual users. This approach provides a tractable method to understand user activity on the web site and how this activity depends on web site design choices, especially the choice of what information about other users' behaviors is shown to each user. We illustrate this modeling approach in the context of user-created content on the news rating site Digg.

A General Stochastic Calculus Approach to Insider Trading

The purpose of this paper is to present a general stochastic calculus approach to insider trading. We consider a market driven by a standard Brownian motion $B(t)$ on a filtered probability space $\displaystyle (\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$, with $\F_t\subset\G_t$ for all $t\in [0,T]$, $T>0$ being a fixed terminal time. By an {\it insider} in this market we mean a person who has access to a filtration (information) $\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly bigger than the filtration $\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$. In this context an insider strategy is represented by an $\H_t$-adapted process $\phi(t)$ and we interpret all anticipating integrals as the forward integral defined in [23] and [25]. We consider an optimal portfolio problem with general utility for an insider with access to a general information $\H_t \supset\G_t$ and show that if an optimal insider portfolio $\pi^*(t)$ of this problem exists, then $B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement of filtration property holds. This is a converse of previously known results in this field. Moreover, if $\pi^*$ exists we obtain an explicit expression in terms of $\pi^*$ for the semimartingale decomposition of $B(t)$ with respect to $\H_t$. This is a generalization of results in [16], [20] and [2].

General framework for the behaviour of continuously observed open quantum systems

We develop the general quantum stochastic approach for the description of quantum measurements continuous in time. The framework that we introduce encompasses the various particular models for continuous-time measurements considered previously in the physical and the mathematical literature.

General stochastic approach to the description of coagulating aerosol systems and stochastic storage model

General stochastic approach to the description of coagulating aerosol systems and stochastic storage model

A Stochastic Approach to Tracer Kinetics

The single compartment well-mixed model ( SCWMM ) which has been used in almost all dynamic studies in nuclear medicine is, in fact , strictly accurate only in the case of a steady state obtained by means of constant administration of long-lived isotopes. That is the reason why SCWMM is not a good predictor of the behaviour of short-lived isotopes and why the distribution and transport of short- and long-lived isotopes in various situations has not yet been discussed in general terms. The aim of this paper is to do that by means of a more general stochastic approach. This more general approach takes into account the distribution and transport of tracer in the system, not requiring a hypothesis of good mixing and providing a possibility of making corrections due to decay in the case of short-lived isotopes studies.

The Influence of Additional Orientation Mechanisms on the Theory of Streaming Birefringence

The problem of determining the orientation distribution function of rigid particles of arbitrary shape is formulated in a general stochastic approach to consider any acting orientation mechanism, stochastic or deterministic. The effect of the various orientation mechanisms on the partial differential equation of the problem is analysed. A particular orientation mechanism acting on rigid ellipsoidal macromolecules in addition to the hydrodynamic and the Brownian effects is considered in Couette flow: a force field in the radial direction x, varying linearly with x. It is shown that the effect of a uniform electric field in the radial direction on polarizable ellipsoidal particles is of this nature. The corresponding steady-state orientation distribution function is determined to the third order for the case of predominant Brownian influence, and the theory of streaming birefringence of a dilute suspension of rigid ellipsoidal macromolecules in Couette flow is generalised to include the influence of the additional orientation mechanism: the direction of the isocline and the amount of birefringence are calculated to the second order.