Forward Backward Research Articles

Looking for B→Xsℓ+ℓ− in a nonminimal universal extra dimensional model

Non-vanishing boundary localised terms significantly modify the mass spectrum and various interactions among the Kaluza-Klein excited states of 5-Dimensional Universal Extra Dimensional scenario. In this scenario we compute the contributions of Kaluza-Klein excitations of gauge bosons and third generation quarks for the decay process $B\rightarrow X_s\ell^+\ell^-$ incorporating next-to-leading order QCD corrections. We estimate branching ratio as well as Forward Backward asymmetry associated with this decay process. Considering the constraints from some other $b \to s$ observables and electroweak precision data we show that significant amount of parameter space of this scenario has been able to explain the observed experimental data for this decay process. From our analysis we put lower limit on the size of the extra dimension by comparing our theoretical prediction for branching ratio with the corresponding experimental data. Depending on the values of free parameters of the present scenario, lower limit on the inverse of the radius of compactification ($R^{-1}$) can be as high as $\geq 760$ GeV. {Even this value could slightly be higher if we project the upcoming measurement by Belle II experiment.} Unfortunately, the Forward Backward asymmetry of this decay process would not provide any significant limit on $R^{-1}$ in the present model.

The kernel Kalman rule

Enabling robots to act in unstructured and unknown environments requires versatile state estimation techniques. While traditional state estimation methods require known models and make strong assumptions about the dynamics, such versatile techniques should be able to deal with high dimensional observations and non-linear, unknown system dynamics. The recent framework for nonparametric inference allows to perform inference on arbitrary probability distributions. High-dimensional embeddings of distributions into reproducing kernel Hilbert spaces are manipulated by kernelized inference rules, most prominently the kernel Bayes’ rule (KBR). However, the computational demands of the KBR do not scale with the number of samples. In this paper, we present two techniques to increase the computational efficiency of non-parametric inference. First, the kernel Kalman rule (KKR) is presented as an approximate alternative to the KBR that estimates the embedding of the state based on a recursive least squares objective. Based on the KKR we present the kernel Kalman filter (KKF) that updates an embedding of the belief state and learns the system and observation models from data. We further derive the kernel forward backward smoother (KFBS) based on a forward and backward KKF and a smoothing update in Hilbert space. Second, we present the subspace conditional embedding operator as a sparsification technique that still leverages from the full data set. We apply this sparsification to the KKR and derive the corresponding sparse KKF and KFBS algorithms. We show on nonlinear state estimation tasks that our approaches provide a significantly improved estimation accuracy while the computational demands are considerably decreased.

Convergence of a Relaxed Inertial Forward–Backward Algorithm for Structured Monotone Inclusions

In a Hilbert space $${{\mathcal {H}}}$$ , we study the convergence properties of a class of relaxed inertial forward–backward algorithms. They aim to solve structured monotone inclusions of the form $$Ax + Bx \ni 0$$ where $$A:{{\mathcal {H}}}\rightarrow 2^{{\mathcal {H}}}$$ is a maximally monotone operator and $$B:{{\mathcal {H}}}\rightarrow {{\mathcal {H}}}$$ is a cocoercive operator. We extend to this class of problems the acceleration techniques initially introduced by Nesterov, then developed by Beck and Teboulle in the case of structured convex minimization (FISTA). As an important element of our approach, we develop an inertial and parametric version of the Krasnoselskii–Mann theorem, where joint adjustment of the inertia and relaxation parameters plays a central role. This study comes as a natural extension of the techniques introduced by the authors for the study of relaxed inertial proximal algorithms. An illustration is given to the inertial Nash equilibration of a game combining non-cooperative and cooperative aspects.

An Inertial Parallel and Asynchronous Forward–Backward Iteration for Distributed Convex Optimization

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they are synchronous by construction. Introducing asynchronicity in the updates can resolve several issues that appear in the synchronous case, like load imbalances in the computations or failing communication links. However, and to the best of our knowledge, there are no instances of asynchronous versions of commonly known algorithms combined with inertial acceleration techniques. In this work, we propose an inertial asynchronous and parallel fixed-point iteration, from which several new versions of existing convex optimization algorithms emanate. Departing from the norm that the frequency of the coordinates’ updates should comply to some prior distribution, we propose a scheme, where the only requirement is that the coordinates update within a bounded interval. We prove convergence of the sequence of iterates generated by the scheme at a linear rate. One instance of the proposed scheme is implemented to solve a distributed optimization load sharing problem in a smart grid setting, and its superiority with respect to the nonaccelerated version is illustrated.

Strong convergence results for convex minimization and monotone variational inclusion problems in Hilbert space

In this paper, we propose a new modification of the Gradient Projection Algorithm and the Forward–Backward Algorithm. Using our proposed algorithms, we establish two strong convergence theorems for solving convex minimization problem, monotone variational inclusion problem and fixed point problem for demicontractive mappings in a real Hilbert space. Furthermore, we apply our results to solve split feasibility and optimal control problems. We also give two numerical examples of our algorithm in real Euclidean space of dimension 4 and in an infinite dimensional Hilbert space, to show the efficiency and advantage of our results.

Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities

ABSTRACTWe propose two modified Tseng's extragradient methods (also known as Forward–Backward–Forward methods) for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under mild and standard conditions, we obtain the weak and strong convergence of the proposed methods. Numerical examples for illustrating the behaviour of the proposed methods are also presented

HIV drug resistance: Insights from mathematical modelling

In 2013 the World Health Organization recommended the initiation of antiretroviral therapy (ART) to any person who tests HIV positive irrespective of his/her CD4+ count. However, implementation of the new guidelines poses a lot of challenges especially in Sub-Sahara Africa such as: drug side effects, drug resistance-mutations and significant financial burdens. Most importantly, it has been established that HIV resistance and subsequent virologic failure occur in a substantial proportion of HIV-infected patients receiving HAART. This study therefore, seeks to investigate the emergence of drug resistant HIV virus during treatment with the aim of determining the proper use of HIV therapy that would lessen drug resistance. To carry out the analysis a ten dimensional in-vivo mathematical model is proposed for HIV dynamics. The model is formulated in such away that it takes into account two virus strain, that is, the wild type as well as the naive type HIV virus. The in-vivo model is shown to be both biologically meaningful and mathematically well posed. The existence of unique infection-free equilibrium point is determined and both its local and global stability investigated. In addition, the basic reproduction number for each viral strain is computed using the next generation matrix method. An optimal control model is proposed and analysed by applying Pontryagin maximum principle, to obtain the optimal drug combination for HIV treatment. Here two drugs, that is, Reverse Transcriptase inhibitor and Protease inhibitor are used as the controls in the model. We provide an objective function for the minimisation of the number of wild type HIV virus and the drug resistant virus as well as the costs associated with the use of Reverse Transcriptase inhibitor and protease inhibitor. The forward backward sweep method is applied to numerically solve the optimality system. From the numerical simulations, it is evident that protease inhibitor is the most effective drug in controlling HIV infection. The results suggest that prolonged use of HAART leads to development of drug resistant and that people with drug-resistant infection could play a core role in the epidemic of HIV.

Stability and Accuracy Analysis of $$\theta $$ Scheme for a Convolutional Integro-Differential Equation

Spatially long-range interactions for linearly elastic media resulting in dispersion relations are modelled by an integro-differential equation of convolution type (IDE) that incorporate non-local effects. This type of IDE is nonstandard (hence, it is almost impossible to obtain exact solutions) and plays an important role in modeling various applied science and engineering problems. In this article, such an IDE describing a linear elastic wave phenomenon has been studied. First, a discrete equivalent of the model IDE in space is proposed and then a class of forward backward average one step \(\theta \) scheme for the semi-discrete time dependent numerical method has been developed. Further, stability and accuracy of the developed method has been analyzed rigorously.

A fast splitting method for efficient Split Bregman iterations

In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward–Backward algorithm. Beside proving the convergence of the method, numerical tests, carried out on different imaging applications, prove the accuracy and computational efficiency of the proposed algorithm.

Massive MIMO-OFDM Channel Estimation via Distributed Compressed Sensing

Massive multiple-input multiple-output orthogonal frequency division multiplexing (mMIMO-OFDM) channel estimation is considered recently utilizing compressed sensing (CS) based methods. Here, we proposed to use the joint sparsity of mMIMO-OFDM channels using stage-wise forward backward pursuit (StFBP) algorithm. In order to increase the speed of convergence and accuracy of estimation, we proposed to gather multiple good atoms in each step and to exploit common sparsity in the system model, respectively. Furthermore, the backward steps improve the accuracy by omitting bad previously gathered atoms. Simulation results represent the superiority of the proposed StFBP approach rather than the conventional CS-based and non-CS-based approaches.

Inertial Alternating Generalized Forward–Backward Splitting for Image Colorization

In this paper, we propose a novel accelerated alternating optimization scheme to solve block biconvex nonsmooth problems whose objectives can be split into smooth (separable) regularizers and simple coupling terms. The proposed method performs a Bregman distance-based generalization of the well-known forward–backward splitting for each block, along with an inertial strategy which aims at getting empirical acceleration. We discuss the theoretical convergence of the proposed scheme and provide numerical experiments on image colorization.

Forward–backward SDEs with distributional coefficients

Forward–backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of solution and show its existence and in certain cases its uniqueness. Moreover we establish a link with PDE theory via a non-linear Feynman–Kac formula. The associated semi-linear parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated.

Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations

This is the second part of our series papers on the deferred correction method for forward backward stochastic differential equations. In this work, we extend our previous work in Tang et al. (Numer Math Theory Methods Appl 10(2):222–242, 2017) to solve second-order forward backward stochastic differential equations (2FBSDEs). More precisely, we propose a class of explicit deferred correction schemes for 2FBSDEs. The key feature is that the simple Euler scheme is used as an initialization. Then, by a simple deferred correction iteration scheme, one can obtain an approximated solution with very high accuracy. Yet in each iteration, the computational complexity is always comparable to the Euler solver. Numerical examples are presented to show the effectiveness of the proposed scheme. We believe that the scheme proposed in this work is promising when dealing with 2FBSDEs in moderate dimensions.

Chou-Yang Model for Forward-Backward Multiplicity Correlations at 7 TeV using Generalized Multiplicity Distribution.

The basis of the Chou-Yang model is made up of a stochastic and non-stochastic distribution and has been successful in describing forward-backward multiplicities.[1] This project examines data drawn from CERN’s 7 TeV run where we revist the Chou-Yang model’s components. It also approaches phenomenological descriptions for cluster sizes from forward-backward multiplicaity correlation strength by the E735 collaboration.[6] For the stochastic binomial component, it examines the variance of the charge asymmetry parameter z with regards to fixed total charged multiplicities n. The fitting of the Generalized Multiplicity distribution along with the linear least square fitting of the forward backward multiplicity is analysed. The parameters for the Generalized Multiplicity Distribution is presented along with an investigation on the cluster size r.[3] This serves as an extention to the work done by W.Y Wang’sWeighted GMD model at7TeV, however the nonweighted GMD model is used here.[7]

A Performance Comparison of Centralized and Distributed Spectrum Management Techniques in Elastic Optical Networks

Elastic optical networks (EONs) have emerged to provide higher spectrum efficiency than traditional Dense Wavelength-Division-Multiplexing (DWDM) by utilizing enabling technologies such as flexible spectrum grid, Orthogonal Frequency Division Multiplexing (OFDM), and distance adaptive rate and modulation. The choice of the control-plane is an important consideration when deploying any new technology, especially in optical networks. This paper considers generic distributed and centralized spectrum assignment policies in conjunction with the accompanying connection set-up signaling protocols in EONs. A network simulator for Generalized Multiprotocol Label Switching (GMPLS) was developed with Forward Reservation Protocol and Backward Reservation Protocol signaling methods. These signaling techniques are used with the First Fit (FF) and Random Fit (RF) Routing and Spectrum Allocation (RSA) algorithms. The paper discusses control elements (central and distributed architectures) decisions under busy hour and normal network conditions and presents a comprehensive performance analysis of key performance metrics such as connection success rate, connection establishment time, and capacity requirement.

采用模拟PID控制的DFB激光器温度控制系统研制

The control precision and stability of emitting wavelength of distributed feedback laser directly determines the measurement accuracy of detection system that uses infrared distributed feedback laser excitation light source as the core section. A temperature control system of distributed feedback laser was developed utilizing analog PID control. Simulated proportional-integral-differential temperature forward control module and real-time temperature backward acquisition module were adopted to control temperature. Emitting wavelength of 2 049 nm DFB laser was used in temperature control experiment. Results show that system temperature control stability is 0.05℃, and the stability time is less than 30 s. Meanwhile, spectrum test experiment was conducted using the developed temperature control system to control the proposed distributed feedback laser. The results show that the emitting wavelength of laser is linear with its working temperature while the laser drive current is fixed.

Saint-Venant Model Analysis of Trapezoidal Open Channel Water Flow using Finite Difference Method

This study aims to compare the flow characteristics in rectangular and trapezoidal open channel by investigating the effects of Manning coefficient, channel bottom slope, channel width, and channel side slope which represented by modified Saint-Venant equation according to the channel cross section, which are rectangular and trapezoidal, and the slope of channel friction using the Manning coefficient. The equation is solved numerically by using finite difference methods with Forward Time Backward Space approach. The model is simulated by using python-based desktop application to show the flow characteristics. Computational results are displayed in the form of summaries, tables, two-dimensional graphics, and three-dimensional graphics. Validation is done by comparing computational results data with data from the other studies that have been done before and concluded that the simulation results have been valid and indicate compliance with the prior studies. The simulation results show that trapezoidal channel is better at minimizing the risk of flooding than rectangular channel in consideration of smaller discharge, smaller velocity, and lower water level.

Effect of Yoga on Immune Parameters, Cognitive Functions, and Quality of Life among HIV-Positive Children/Adolescents: A Pilot Study.

Context:HIV/AIDS individuals have problems relating to immune system, quality of life (QOL), and cognitive functions (CFs). Yoga is found to be useful in similar conditions. Hardly, any work is reported on yoga for HIV-positive adults/adolescents. Hence, this study is important.Aim:The aim of the study is to determine the effect of yoga on immune parameters, CFs, and QOL of HIV-positive children/adolescents.Settings and Design:Single-group, pre–post study with 4-month yoga intervention.Methods:The study had 18 children from an HIV/AIDS rehabilitation center for children/adolescents. CD4, CD8, CD4/CD8 ratio, and viral loads were studied. CF tests included six letter cancellation test, symbol digit modalities test, digit-span forward backward test, and Stroop tests. QOL was assessed using PedsQL-QOL and fatigue questionnaire. Depression was assessed using CDI2-SR.Statistical Analysis Used:t-test and Wilcoxon signed-rank tests, as applicable.Results:The study included 18 children/adolescents. There was improvement in general health of the participants. There was statistically significant increase in CD4 cells counts (p = 0.039) and significant decrease in viral load (p = 0.041). CD4/CD8 ratio moved to normal range. QOL significantly improved. CFs had mixed results with improved psychomotor performance (PP) and reduced executive functions.Conclusions:There was improvement in general health and immune parameters. While depression increased, QOL improved. CFs showed mixed results with improved PP and reduced executive functions.

Infinite horizon mean-field type forward backward stochastic delay differential game with Poisson jump processes

Infinite horizon mean-field type forward backward stochastic delay differential game with Poisson jump processes

Risk-Sensitive Mean Field Games via the Stochastic Maximum Principle

In this paper, we consider risk-sensitive mean field games via the risk-sensitive maximum principle. The problem is analyzed through two sequential steps: (i) risk-sensitive optimal control for a fixed probability measure, and (ii) the associated fixed-point problem. For step (i), we use the risk-sensitive maximum principle to obtain the optimal solution, which is characterized in terms of the associated forward–backward stochastic differential equation (FBSDE). In step (ii), we solve for the probability law induced by the state process with the optimal control in step (i). In particular, we show the existence of the fixed point of the probability law of the state process determined by step (i) via Schauder’s fixed-point theorem. After analyzing steps (i) and (ii), we prove that the set of N optimal distributed controls obtained from steps (i) and (ii) constitutes an approximate Nash equilibrium or $$\epsilon $$-Nash equilibrium for the N player risk-sensitive game, where $$\epsilon \rightarrow 0$$ as $$N \rightarrow \infty $$ at the rate of $$O(\frac{1}{N^{1/(n+4)}})$$. Finally, we discuss extensions to heterogeneous (non-symmetric) risk-sensitive mean field games.