Discrete Steps Research Articles

Integrating machine learning with Markov chain and cellular automata models for modelling urban land use change

Modelling urban land use change is of profound concern to environmental scientists who have found cellular automata models very attractive for simulating urban dynamics. The quest for suitable predictive models to improve realistic simulation of urban land use change has resulted in the use of several notable cellular automata calibrations. Cellular automata model has become very attractive and one of the strongest models for urban growth simulation due to its simplicity and possibility of evolution. However, the inability of cellular automata to include driving forces of urban growth in the simulation process has warranted further cellular automata calibrations to minimize this weakness. To address this problem, and contrary to previous cellular automata calibrations, this research presents a novel integration of support vector machine, Markov chain and cellular automata for urban change modelling. Support vector machine is introduced as a machine learning technique to mine the impact of the explanatory variables that drive urban change. Markov chain is employed to mine the urban transition probabilities between the various urban epochs while cellular automata are used to implement the incremental discrete time steps based on neighbourhood interaction from an initial time to a future time. This modelling is implemented using Landsat data acquired in 1984, 2000 and 2015 over Lagos in Nigeria, Africa’s most populous city. Urban transitions (1984–2000 and 2000–2015) are used to simulate future urban state in 2030 and validation metrics include McNemar's test. The introduction of stochasticity into the model helps create the typical randomness inherent in the real world for deriving future urban forms through discrete cellular automata iterations. The high accuracy obtained in this experiment implies a substantial fit between the predicted and reference data. This outcome proves the robustness of this method for modelling urban change.

The Euler–Lagrange Approximation of the Mean Field Game for the Planning Problem

The paper presents a finite-difference analogue of the differential problem formulated in terms of the theory of ‘‘Mean Field Games’’ for solving the planning problem of convey to a given state. Here optimization problem is formulated as coupled pair of parabolic partial differential equations of the Kolmogorov (Fokker–Planck) and Hamilton–Jacobi–Bellman type. The proposed Euler–Lagrange finite-difference analogue inherits the basic properties of an optimization differential problem at a discrete level. As a result, it can serve as an approximation of the original differential problem when the discretization steps tend to zero, or as a self-contained optimization task with a finite set of participants. For the proposed analogue, the algorithm of monotonous minimization of the value functional is constructed and illustrated on a model economic task.

NOISY HIGH FREQUENCY DATA-BASED ESTIMATION OF VOLATILITY FUNCTION WITH APPLICATIONS

Diffusion models have been widely used to describe the stochastic dynamics of the underlying economic variables. Renò ( 2008 ) introduced a nonparametric estimator of the volatility function, which is based on the estimation of quadratic variation between observations by means of realized variance. However, they may be misleading when one uses intraday data to implement directly the estimator, because intraday data display microstructure effects that could seriously distort the estimation. To filter out the impact of microstructure noise on the estimation of the volatility function, in this paper we propose an improved estimator when there is microstructure noise in the observed price. Also, we show that the proposed estimator has the same asymptotic properties as the Renò estimator when the step of discretization inclines to zero. Some simulations and empirical applications on Shanghai Stock Exchange data from March 3, 2002 to December 31, 2008 are used to illustrate the finite sample performance of the proposed estimator.

Proton Transfer Management for Efficient Oxygen Evolution on α-Fe2O3 Electrode

The oxygen evolution reaction (OER, 2H2O → O2 + 4H+ + 4e-) has received considerable attention in recent years as a promising method for utilizing water as a sustainable electron source. By coupling the OER with a reduction half-reaction such as hydrogen evolution (2H+ + 2e- → H2) or carbon dioxide reduction (ex. CO2 + 8H+ + 8e- → CH4 + 2H2O), the intermittent energy from renewable sources, including solar energy or wind power, can be captured in the form of chemical fuels. However, driving the four-electron process to oxidize water to oxygen has proven difficult due to the large overpotential. Although RuO2 and IrO2 have been reported to show good catalytic performance, the scarcity and high costs associated with precious metals limit the large-scale applicability of these materials. Therefore, it is highly desirable to substitute them with catalysts derived from earth-abundant 3d metals such as Mn, Co, and Fe.This article reports the investigation of the OER mechanism of hematite (α-Fe2O3) to gain insight into the critical factors determining its electrocatalytic activity. Using spectroelectrochemimcal measurements, an intermediate species assignable to Fe4+ was identified as the precursor of OER across the entire pH range investigated (pH 4−13) [1,2]. The pH dependences of the onset potentials for OER and Fe4+ formation revealed that α-Fe2O3 showed higher catalytic activity under alkaline conditions and that there were two reaction mechanisms which switched at approximately pH 10. From the results of kinetic isotope effect experiments, it was found that the manner of proton and electron transfer during Fe4+ formation (Fe3+–OH → Fe4+=O + H+ + e-) was different between the two mechanisms. Whereas proton transfer and electron transfer proceed as discrete reaction steps at neutral pH, they proceed simultaneously at alkaline pH. Because the simultaneous transfer of proton and electron enables to avoid formation of high-energy protonated or deprotonated intermediates, the simultaneous transfer is energetically more favorable than the stepwise one, resulting in the higher activity under alkaline pH conditions. Notably, by adding appropriate pyridine derivatives as proton accepting reagents, the switching of the rate-determining step from the stepwise process to the simultaneous process was demonstrated [3]. As a result, a decrease in overpotential of 250 mV was achieved at pH 7 and the OER activity of α-Fe2O3 under neutral pH conditions became comparable to that under alkaline pH conditions. Furthermore, when the pyridine derivatives were replaced with a solid proton accepting material that is robust against anodic decomposition, the enhanced activity was maintained in the long-term operation [4]. These findings will be helpful to design active Fe-based OER catalysts and offer the opportunities to achieve high OER activity under neutral pH using 3d-metal catalysts which often show remarkable activities under alkaline pH conditions.[1] T. Takashima, K. Ishikawa, H. Irie, J. Phys. Chem. C, 120, 24827–24834 (2016).[2] T. Takashima, S. Hemmi, Q. Liu, H. Irie, Catal. Sci. Technol., in press.[3] T. Takashima, K. Ishikawa, H. Irie, Chem. Commun., 52, 14015–14018 (2016).[4] T. Takashima, K. Ishikawa, H. Irie, ACS Catal., 9, 9212–9215 (2019).

Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics

The paper studies asymptotics of inhomogeneous integral functionals of an ergodic diffusion process under the effect of discretization. Convergence to the corresponding functionals of the invariant distribution is shown for suitably chosen discretization steps, and the fluctuations are analyzed through central limit theorem and moderate deviation principle. The results will be particularly useful for understanding accuracy of an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. This is an infinite-time horizon problem, and the accuracy of numerical schemes in this context are comparatively much less studied than the ones used for generating approximate trajectories of diffusions over finite time intervals. The potential applications of these results also extend to other areas including mathematical physics, parameter inference of ergodic diffusions and analysis of multiscale dynamical systems with averaging.

SEMI-AUTOMATED DESIGN OF MICROSTRIP DUAL BAND COAXIAL FEED ANTENNA USING DIFFERENTIAL EVOLUTION ALGORITHM FOR WLAN APPLICATIONS

Traditional antenna design uses discrete steps manually to create and optimize the antenna structure. This approach costs both time and effort, especially when a complex antenna structure is on demand. The evolutionary algorithm emerges as a potential alternative method to formulate the antenna model as well as to optimize the structure so as to comply with the design requirements. In this paper, we propose a method for determining the surrogate model and dimensions of an ultra-wideband patch antenna using a differential evolution algorithm. This antenna is desired to work at the frequency range of 2.45GHz to 5.8GHz for WLAN applications. Through the evaluation of reflectivity and investigation of the algorithm,the surrogate model is obtained faster with optimized dimensions. The algorithm is investigated with different strategies to detect the best strategy when an object is a differential evolution applied.

Discrete event optimization of a vehicle charging station with multiple sockets

The relevance and presence of Electric Vehicles (EVs) are increasing all over the world since they seem an effective way to fight pollution and greenhouse gas emissions, especially in urban areas. One of the main issues related to EVs is the necessity of modifying the existing infrastructure to allow the installation of new charging stations (CSs). In this scenario, one of the most important problems is the definition of smart policies for the sequencing and scheduling of the vehicle charging process. The presence of intermittent energy sources and variable execution times represent just a few of the specific features concerning vehicle charging systems. Even though optimization problems regarding energy systems are usually considered within a discrete time setting, in this paper a discrete event approach is proposed. The fundamental reason for this choice is the necessity of limiting the number of the decision variables, which grows beyond reasonable values when a short time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles by a CS connected with a renewable energy source, a storage element, and the main grid. The objective function to be minimized results from the weighted sum of the (net) cost for purchasing energy from the external grid, the weighted tardiness of the services provided to the customers, and a cost related to the occupancy of the socket during the charging. The approach is tested on a real case study. The limited computational burden allows also the implementation in real-case applications.

Syncytia formation by SARS-CoV-2-infected cells.

Severe cases of COVID‐19 are associated with extensive lung damage and the presence of infected multinucleated syncytial pneumocytes. The viral and cellular mechanisms regulating the formation of these syncytia are not well understood. Here, we show that SARS‐CoV‐2‐infected cells express the Spike protein (S) at their surface and fuse with ACE2‐positive neighboring cells. Expression of S without any other viral proteins triggers syncytia formation. Interferon‐induced transmembrane proteins (IFITMs), a family of restriction factors that block the entry of many viruses, inhibit S‐mediated fusion, with IFITM1 being more active than IFITM2 and IFITM3. On the contrary, the TMPRSS2 serine protease, which is known to enhance infectivity of cell‐free virions, processes both S and ACE2 and increases syncytia formation by accelerating the fusion process. TMPRSS2 thwarts the antiviral effect of IFITMs. Our results show that SARS‐CoV‐2 pathological effects are modulated by cellular proteins that either inhibit or facilitate syncytia formation.

Low-Complexity Decentralized Algorithm for Aggregate Load Control of Thermostatic Loads

Thermostatically controlled loads such as refrigerators are exceptionally suitable as a flexible demand resource. This paper derives a decentralised load control algorithm for refrigerators. It is adapted from an existing continuous time control approach, with the aim to achieve low computational complexity and an ability to handle discrete time steps of variable length -- desirable features for embedding in appliances and high-throughput simulations. Simulation results of large populations of heterogeneous appliances illustrate the accurate aggregate control of power consumption and high computational efficiency. Tracking accuracy is quantified as a function of population size and time step size, and correlations in the tracking error are investigated. The controller is shown to be robust to errors in model specification and to sudden perturbations in the form of random refrigerator door openings.

New Insight Into Catalytic Mechanism of Glucose-6-Phosphate Dehydrogenase Enzyme: A DFT Study

The glucose-6-phosphate dehydrogenase (G6PD) enzyme plays a vital role in converting glucose-6-phosphate (G6P) to 6-phosphogluconolactone, as well as in reducing NADP([Formula: see text]) to NADPH. The Asp/His moiety of G6PD acts as a catalytic dyad in the active site of G6PD. This catalytic mechanism describes erythrocyte protection from oxidative stress and prevention of hemolysis; hence their exact understanding is important in the normal functioning of red blood cells. Herein, computational investigations were carried out to describe a plausible mechanism of the G6PD enzyme by using a series of DFT theoretical calculations using the M06-2X/6-31G ([Formula: see text], [Formula: see text]) basis set and performed in the following three discrete steps: (i) Proton transfer from His309 to Asp246, (ii) A subsequent proton transfer from G6P to His309, and (iii) A rate-limiting hydride transfer that reduces NADP([Formula: see text]) to NADPH. The final overall mechanism, therefore, results in the production of phosphogluconolactone and NADPH. The DFT calculations indicate that, in the absence of the His/Asp dyad, the chemical reaction changes from a low-energy sequential mechanism to the proposed concurrent mechanism with a very high energy barrier ([Formula: see text][Formula: see text]kcal[Formula: see text]mol[Formula: see text]). These results show that the Asp246 residue is responsible for transforming a high energy concurrent reaction into a low energy multistep sequential reaction in the G6PD enzyme for the production of NADPH. This work supports the study and design of the mechanism-based inhibitors and provides a detailed understanding of the catalytic mechanism of the enzyme thereby opening new possibilities towards an understanding of controlling detoxification processes due to premature breaking in red blood cells.

Interplay between Structure and Mechanism in Reductive Dissociative Electron Transfers to α,β -Epoxyketones.

The electrochemical reduction of several α,β -epoxyketones was studied using cyclic (linear sweep) voltammetry, convolution voltammetry, and homogeneous redox catalysis. The results were reconciled to pertinent theories of electron transfer. α,β -Epoxyketones undergo dissociative electron-transfer reactions with C-O bond cleavage, via both stepwise and concerted mechanisms, depending on their structure. For aliphatic ketones, the preferred mechanism of reduction is consistent with the "sticky" concerted model for dissociative electron transfer. Bond cleavage occurs simultaneously with electron transfer, and there is a residual, electrostatic interaction in the ring-opened (distonic) radical anion. In contrast, for aromatic ketones, because the ring-closed radical anions are resonance-stabilized and exist at energy minima, a stepwise mechanism operates (electron transfer and bond cleavage occur in discrete steps). The rate constants for ring opening are on the order of 108 s-1 , and not significantly affected by substituents on the 3-membered ring (consistent with C-O bond cleavage). These results and conclusions were fully supported and augmented by molecular orbital calculations.

$${{\mathcal{L}}}_{1}$$-Optimal Filtering of Markov Jump Processes. I. Exact Solution and Numerical Implementation Schemes

Part I of this research work is devoted to the development of a class of numerical solution algorithms for the filtering problem of Markov jump processes by indirect continuous-time observations corrupted by Wiener noises. The expected $${{\mathcal{L}}}_{1}$$ norm of the estimation error is chosen as an optimality criterion. The noise intensity depends on the state being estimated. The numerical solution algorithms involve not the original continuous-time observations, but the ones discretized by time. A feature of the proposed algorithms is that they take into account the probability of several jumps in the estimated state on the time interval of discretization. The main results are the statements on the accuracy of the approximate solution of the filtering problem, depending on the number of jumps taken into account for the estimated state, on the discretization step, and on the numerical integration scheme applied. These statements provide a theoretical basis for the subsequent analysis of particular numerical schemes to implement the solution of the filtering problem.

Neural network implementation of controllers for multi-channel objects synthesized by polynomial method

The implementation of neural network multichannel controllers synthesized by polynomial matrix decomposition is analysed. Objects and controllers are assumed to be linear; these allow them to be described by matrix transfer functions. The transfer function of the object is converted to the right polynomial matrix inter-simple decomposition. The transfer function of the controller is sought in the form of a left polynomial matrix of inter-simple decomposition that allows leading the characteristic matrix to the form of a linear matrix polynomial equation with two matrix indeterminates. This equation is solved by leading to a matrix equation with numeric matrix indeterminates. Then the controller equation is converted to a discrete equation. The discrete sampling step is chosen small enough to allow the systems with continuous and discrete controllers have sufficiently close transient processes. The discrete controller is converted to a structure including delay elements, adder units and amplification coefficients. Then this structure is presented in the form of a set of neurons. The operation of the algorithm is illustrated by the example of the synthesis of an unstable inverted pendulum control, which includes two PID controllers. Possible increases in neuro controller performance are demonstrated. Two PID controllers are combined into one neural network in order to further optimization.

An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression

We propose an iterative method to evaluate the roots of nonlinear equations. This Secant-based technique approximates the derivatives of the function numerically through a constant discretization step h disassociated from the iterative progression. The algorithm is developed, implemented, and tested. Its order of convergence is found to be h-dependent. The results obtained corroborate the theoretical deductions and evidence its excellent behavior. For infinitesimal h-values, the algorithm accelerates the convergence of the Secant method to order 2 (the one of the Newton-Raphson method) with no need for analytic expression of derivatives (the advantage of the Secant method).

Regulatory Frameworks for Development and Evaluation of Artificial Intelligence-Based Diagnostic Imaging Algorithms: Summary and Recommendations.

Although artificial intelligence (AI)-based algorithms for diagnosis hold promise for improving care, their safety and effectiveness must be ensured to facilitate wide adoption. Several recently proposed regulatory frameworks provide a solid foundation but do not address a number of issues that may prevent algorithms from being fully trusted. In this article, we review the major regulatory frameworks for software as a medical device applications, identify major gaps, and propose additional strategies to improve the development and evaluation of diagnostic AI algorithms. We identify the following major shortcomings of the current regulatory frameworks: (1) conflation of the diagnostic task with the diagnostic algorithm, (2) superficial treatment of the diagnostic task definition, (3) no mechanism to directly compare similar algorithms, (4) insufficient characterization of safety and performance elements, (5) lack of resources to assess performance at each installed site, and (6) inherent conflicts of interest. We recommend the following additional measures: (1) separate the diagnostic task from the algorithm, (2) define performance elements beyond accuracy, (3) divide the evaluation process into discrete steps, (4) encourage assessment by a third-party evaluator, (5) incorporate these elements into the manufacturers’ development process. Specifically, we recommend four phases of development and evaluation, analogous to those that have been applied to pharmaceuticals and proposed for software applications, to help ensure world-class performance of all algorithms at all installed sites. In the coming years, we anticipate the emergence of a substantial body of research dedicated to ensuring the accuracy, reliability, and safety of the algorithms.

Discretized Target Size Detection in Electrical Impedance Tomography Using Neural Network Classifier

Electrical impedance tomography (EIT) uses non-invasive and non-radiative imaging to detect inhomogeneous electrical properties in tissues. The inverse problem of EIT is a highly nonlinear, ill-posed problem, which causes inaccuracy in target size calculation. We propose a novel approach to discretize the target size and use a neural network (NN) classifier to classify the unknown size in discrete steps. The target size is discretized into distinct steps, and each step can be a unique class. The data is pre-processed with the cumulative distribution transform (CDT) to enhance distinguishability. First, the NN is trained with simulated datasets, divided into time difference (t-d) group and CDT group. After training, the NN classifier is tested by experimental data recorded in a phantom experiment. Linear discriminant analysis (LDA) is performed to assess the distinguishability of classes. There is a significant increase in distance between classes after the CDT pre-processing. The density of the classes has an upward trend with a higher degree of clustering after CDT pre-processing. The CDT data clustering into distinguishable classes is essential to excellent NN classification results. Such an approach is a significant paradigm shift by turning the cumbersome inverse calculation with uncertain accuracy into a classification problem with predetermined step errors. The accuracy and resolution can be further extended by increasing the discretization steps.

Introduction of the Operating Room Black Box in Gynecology: Development of a Procedural Framework for Total Laparoscopic Hysterectomy

Study Objective Operating room (OR) delays due to inefficiency can result from a chain of intraoperative events including technical factors, equipment failures or unavailability, and non-technical human factors. The newly developed Operating Room Black Box (ORBB) technology can be used to capture information during surgery which can be analyzed to potentially identify the root causes of delays and inefficiencies. We aimed to develop a procedural framework for total laparoscopic hysterectomy (TLH) in order to accurately and consistently capture the essential time points that occur during this complex laparoscopic procedure. Design Multi-disciplinary collaborative working group. Setting Canadian tertiary care academic hospital. Patients or Participants Team consisted of gynecologic surgeons, an anesthetist, an OR nurse and systems analysts. Interventions Multi-disciplinary working group collaborated to develop a procedural framework encompassing the critical steps and check points occurring during the course of a TLH. All phases of the operation were considered including pre-operative, intra-operative, and post-operative steps. Measurements and Main Results The completed framework consists of a series of procedural steps divided into three time phases: pre-operative, intraoperative and post-operative. Consensus from the group led to the identification of 7 discrete steps during the pre-operative phase, 11 intra-operative steps and 6 post-operative steps. Conclusion The development of a standardized procedural framework for TLH is the first step towards capturing data with the ORBB technology. The analysis of the captured data will allow us to analyze the non-technical skills and team performance in the OR, and ultimately develop a multi-disciplinary operating room “playbook” that can be utilized to minimize time delays and maximize OR utilization.

A derivation of Griffith functionals from discrete finite-difference models

We analyze a finite-difference approximation of a functional of Ambrosio–Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step delta is smaller than the ellipticity parameter varepsilon , we show the varGamma -convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no L^p fidelity term. Restricting to two dimensions, we also address the case in which a (linearized) constraint of non-interpenetration of matter is added in the limit functional, in the spirit of a recent work by Chambolle, Conti and Francfort.

Dealing with time in the multiple traveling salespersons problem with moving targets

The multiple traveling salespersons problem with moving targets is a generalization of the classical traveling salespersons problem, where the targets (nodes or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salespersons so that each target is reached exactly once within its visibility time window and the sum of all traveled distances of all salespersons is minimal. We present different modeling formulations for this TSP variant. The time requirements are modeled differently in each approach. Our goal is to examine what formulation is most suitable in terms of runtime to solve the multiple traveling salespersons problem with moving targets with exact methods. Computational experiments are carried out on randomly generated test instances to compare the different modeling approaches. The results for large-scale instances show, that the best way to model time requirements is to directly insert them into a formulation with discrete time steps.

GPU COMPUTING FOR 2D WAVE EQUATION BASED ON IMPLICIT FINITE DIFFERENCE SCHEMES

In this paper we will consider the numerical implementation of the 2d wave equation which is a fundamental equation in many engineering problems. An approximate solution of a function is calculated from discrete points in spatial grid based on discrete time steps. The initial values are given by the initial value condition. First we will interpret how to transform a differential equation into an implicit finitedifference equation, respectively, a set of finite-difference equations that can be used to calculate an approximate solution. Then we will change this algorithm to parallelize this task on GPU. Special focus is on improving the performance of the parallel algorithm. In addition, we will run the implemented parallel code on the GPU and serial code the central processor, calculate the acceleration based on the execution time. We present that the parallel code that runs on a GPU gives the expected results by comparing our results to those obtained by running serial code of the same simulation on the CPU. In fact, in some cases, simulations on the GPU are found to run 22 times faster than on a CPU