Backward Approaches Research Articles

The relationship between the backward and forward equations of stochastic neutron transport and associated matters

The relationship between the forward and backward equations of probability balance for neutron transport are discussed and, in particular, we show the close relationship between the characteristics of the forward equation to the main equations of the backward approach. The well-known failure of the backward method to handle feedback is also noted and possible origins proposed, although this curious feature remains an open question. A comparison of the backward and forward approaches is gone into in some detail and their relative advantages and disadvantages highlighted. We illustrate the matter by the discussion of a problem of an energy burst due to a ramp insertion of reactivity. This problem leads to a transition from the stochastic region to the deterministic one and shows how the backward equation may be used in tandem with a deterministic set of equations without violating the restriction on the backward method. The problems arising from a spatially varying source are also discussed with reference to the backward equations and their undoubted superiority over the forward equations is stressed.

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability approaches for safety certification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While backward reachability strategies have been developed for systems without NN components, the nonlinearities in NN activation functions and general noninvertibility of NN weight matrices make backward reachability for NFLs a challenging problem. To avoid the difficulties associated with propagating sets backward through NNs, we introduce a framework that leverages standard forward NN analysis tools to efficiently find over-approximations to backprojection (BP) sets, i.e., sets of states for which an NN policy will lead a system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

Angular velocity around the longitudinal axis in combination with head movements of springboard divers during twisted somersaults

ABSTRACT The ability of springboard divers to perform and control difficult elements with multiple twisted somersaults before entering the water is of great interest for coaches and researchers. In order to produce twists within somersaults, divers use both ‘contact’ and ‘aerial’ techniques. After completing body axes rotations, head movements seem to be important, as they enable visual information in the air. The current study aims at investigating angular velocities around the longitudinal axis in combination with head movements of 13 springboard divers during twisted somersaults. Divers performed forward and backward somersaults with different numbers of half twists. The results revealed maximum longitudinal axis angular velocities between 500°/s and 1300°/s. Moreover, results showed that the use of contact technique was greater in twisted somersaults with backward approaches, and thus higher angular velocities could be achieved. While finishing the twists, head movements in the opposite direction to the longitudinal axis rotation occurred, which allow divers to orient themselves. Twist speeds influenced athletes’ head movements to have greater angles and greater rotational velocities. Therefore, it is concluded that fast head movements are necessary in difficult twisted dives to allow orientation in the short phase between finishing the twist and entering the water surface.

Designing local air pollution policies focusing on mobility and heating to avoid a targeted number of pollution-related deaths: Forward and backward approaches combining air pollution modeling, health impact assessment and cost-benefit analysis.

Policies aiming at decreasing air pollutants (e.g., fine particulate matter, PM2.5) are often designed without targeting an explicit health benefit nor carrying out cost-benefit analyses. We developed a transdisciplinary backward and forward approach at the conurbation level: from health objectives set by local decision-makers, we estimated which reductions in PM2.5 exposures and emissions would allow to reach them, and identified urban policies leading to these reductions (backward approach). We finally conducted health impact and cost-benefit analyses of these policies (forward approach). The policies were related to the most emitting sectors in the considered area (Grenoble, France), wood heating and transport sectors. The forward approach also considered the health impact and co-benefits of these policies related to changes in physical activity and CO2 emissions. Decision-makers set three health targets, corresponding to decreases by 33% to 67% in PM2.5-attributable mortality in 2030, compared to 2016. A decrease by 42% in PM2.5 exposure (from 13.9µg/m3) was required to reach the decrease by 67% in PM2.5-attributable mortality. For each Euro invested, the total benefit was about 30€ for policies focusing on wood heating, and 1 to 68€ for traffic policies. Acting on a single sector was not enough to attain a 67% decrease in PM2.5-attributable mortality. This target could be achieved by replacing all inefficient wood heating equipment by low-emission pellet stoves and reducing by 36% the traffic of private motorized vehicles. This would require to increase the share of active modes (walking, biking…), inducing increases in physical activity and additional health benefits beyond the initial target. Annual net benefits were between €484 and €629 per capita for policies with report on active modes, compared to between €162 and €270 without. Urban policies strongly reducing air pollution-attributable mortality can be identified by our approach. Such policies can be cost-efficient.

The Utility of Sentinel-2 Spectral Data in Quantifying Above-Ground Carbon Stock in an Urban Reforested Landscape

The transformation of the natural landscape into an impervious surface due to urbanization has often been considered an important driver of environmental change, affecting essential urban ecological processes and ecosystem services. Continuous forest degradation and deforestation due to urbanization have led to an increase in atmospheric carbon emissions, risks, and impacts associated with climate change within urban landscapes and beyond them. Hence, urban reforestation has become a reliable long-term alternative for carbon sink and climate change mitigation. However, there is an urgent need for spatially accurate and concise quantification of these forest carbon stocks in order to understand and effectively monitor the accumulation and progress on such ecosystem services. Hence, this study sought to examine the prospect of Sentinel-2 spectral data in quantifying carbon stock in a reforested urban landscape using the random forest ensemble. Results show that Sentinel-2 spectral data estimated reforested forest carbon stock to an RMSE between 0.378 and 0.466 t·ha−1 and R2 of 79.82 and 77.96% using calibration and validation datasets. Based on random forest variable selection and backward elimination approaches, the red-edge normalized difference vegetation index, enhanced vegetation index, modified simple ratio index, and normalized difference vegetation index were the best subset of predictor variables of carbon stock. These findings demonstrate the value and prospects of Sentinel-2 spectral data for predicting carbon stock in reforested urban landscapes. This information is critical for adopting informed management policies and plans for optimizing urban reforested landscapes carbon sequestration capacity and improving their climate change mitigation potential.

Which specific urban policies should be implemented by local authorities to achieve a health objective seeking reducing air pollution-attributable mortality?

BACKGROUND AND AIM: Public policies aiming at decreasing air pollutants such as fine particulate matter (PM2.5) are often designed without targeting an explicit health benefit and without carrying out cost-benefit analyses, therefore possibly limiting their adoption. We therefore developed a transdisciplinary backward and forward approach. METHODS: We first defined health objectives (corresponding to decreases by 33%, 50% and 67% in PM2.5-attributable mortality in 2030 compared to 2016), then identified which PM2.5 reductions and urban policies allowed to meet the health targets (backward approach), and finally conducted health impact and cost-benefit analyses of these policies (forward approach). The urban policies were related to wood heating and traffic, the two main emitting sectors in the considered area (Grenoble conurbation, France). The forward approach also considered the health and economic impacts related to changes in physical activity and carbon dioxide emissions. RESULTS:We showed that the most ambitious health target (-67%) could be achieved in 2030 by replacing all inefficient wood heating equipment by pellet stoves and by reducing by 36% the traffic of private motorized vehicles. Such a reduction in traffic requires to increase active modes share (walking, ...), which would also induce substantial increases in physical activity, and additional health benefits beyond the initial health target. Wood heating system replacement and the strategies maximizing active mobility, which are those that did not require massive investment in public transport, were the most cost-effective policies. Many benefits would be linked to the increase in physical activity: annual net benefits were between €468 and €615 per capita for policies with report on active modes, compared to between €151 and €258 for those without. CONCLUSIONS:Urban policies strongly reducing air pollution-attributable mortality can be identified by backward transdisciplinary approaches, and they can be cost-efficient. To our knowledge, such approach has not previously been carried out at the city or national level. KEYWORDS: Dispersion model, economic analysis, fine particulate matter (PM2.5), health impact assessment, transportation modal shift

ПРОБЛЕМИ СТРУКТУРИЗАЦІЇ СУЧАСНОЇ СИСТЕМИ ПУБЛІЧНИХ ФІНАНСІВ

The article is devoted to a number of important methodological problems faced by domestic scientific researchers and policy-makers specializing in the public finance. Ukraine remains one of the few countries whose legislation lacks regulations that plainly defines the concept of the public finance system, its structure and principles of operation. The author draws attention to the fact that despite significant number of scientific studies, focused on selected components of the public finance system, Ukrainian scientists still confront with lack of fundamental works dedicated to the internal structure of public finance. A very simplified and backward approaches are dominated even in the papers of leading Ukrainian scientists. As a rule, they are mechanically borrowed from fundamental scientific works from the end of the previous century. It is a significant failure, because public finance system is characterized by a high dynamic of internal transformation. This leads to constant changes in the structure of the system and the links between its components. The problems relate to structuring of the public finance system are often perceived as a sheer theoretical topic that hasn’t practical value for researchers. In this work, the author tries to argue for the opposite thesis. The public finance system is an integral phenomenon. The lack of a clear vision of the internal structure of the public finance system does not allow to understand its complexity and the links between its constituent components. In practical terms, this problem has become a key factor of the fragmentation of the Ukrainian public finance system, which in turn has a very negative impact on the effectiveness of the mechanisms of mobilization, redistribution and financial resources’ expenditure. Understanding of this object, as well as its structure, allows one better realize the functioning of its individual elements and mechanisms of its functioning. The author draws attention to the fact that the public finance system is a dynamic object that develops in accordance with certain patterns. In this light, the internal structure of public finance is in the process of permanent transformation as well. Based on this conclusion, the author studies how the structure of public finance looks in a modern state.

Combination of Backward and Forward Approaches for Future Prediction by Business Intelligence Tools

Business intelligence tools now play an important role in data collection, processing and analyses of organizations. Managers may use outputs of such tools and make improved decisions. To provide an even better situation for managers, business intelligence tools may be used to predict future and display present and past statuses of the organization. Available business intelligence tools predict future based on historical data, i.e., they are said to enjoy backward approaches. In this study, it was tried to change extrapolation of historical trends according to our expectations of future events so that forward approaches could be employed for prediction purposes.

Identification of uncertainty sources in distributed hydrological modelling: Case study of the Grote Nete catchment in Belgium

The quest for good practice in modelling merits thorough and sustained attention since good practice increases the credibility and impact of the information, and insight that modelling seeks to generate. This paper presents the findings of an evaluation whose goal was to understand the uncertainty in applying a distributed hydrological model to the Grote Nete catchment in Flanders, Belgium. Uncertainties were selected for investigation depending on how significantly they affected the model's decision variables. A Fault Tree was used to determine various combinations of inputs, mathematical code, and human error failures that could result in a specified risk. A combination of forward and backward approaches was used in developing the Fault Tree. Eleven events were identified as contributing to the top event. A total of 7 gates were used to describe the Fault Tree. A critical path analysis was carried out for the events and established their rank or order of significance. Three measures of importance were applied, namely the F-Vesely, the Birnbaum, and the B-Proschan importance measures. Model development of distributed models involves considerable uncertainty. Many of these dependencies arise naturally and their correct evaluation is crucial to the accurate analysis of the modelling system reliability.

Stable blowup for the cubic wave equation in higher dimensions

We consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data. We prove that there exists an open set of initial data such that the corresponding solution exists in a backward light-cone and approaches the ODE blowup profile.

Type-2 Fuzzy Rule-Based Expert System for Diagnosis of Spinal Cord Disorders

The majority of people have experienced pain in their low back or neck in their lives. In this paper a type-2 fuzzy rule based expert system is presented for diagnosing the spinal cord disorders. The interval type-2 fuzzy logic system permits us to handle the high uncertainty of diagnosing the type of disorder and its severity. The spinal cord disorders are studied in five categories using historical data and clinical symptoms of the patients. The main novelty of this paper lies in presentation of the interval type-2 fuzzy hybrid rule-based system, which is a combination of the forward and backward chaining approaches in its inference engine and avoids unnecessary medical questions. Using of parametric operations for fuzzy calculations increases the robustness of the system and the compatibility of the diagnosis with a wide range of physicians’ diagnosis. The outputs of the system are comprised of type of disorder, location and severity as well as the necessity of taking a M.R. Image. A comparison of the performance of the developed system with the expert shows an acceptable accuracy of the system in diagnosing the disorders and determining the necessity of the M.R. Image.

The Analysis of Forward and Backward Dynamic Programming for Multistage Graph

Dynamic programming is an optimization approach that divides the complex problems into the simple sequences of problems in which they are interrelated leading to decisions. In the dynamic programming, there is no standard formula that can be used to make a certain formulation. In this paper we use forward and backward method to find path which have the minimum cost and to know whether they make the same final decision. Convert the problem into several successive sequential stages starting on from stages 1,2,3 and 4 for forward dynamic programming and the step back from stage 4.3,2,1 for backward dynamic programming and interconnected with a decision rule in each stage. Find the optimal solution with cost principle at next stage. Based on the characteristics of the dynamic programming, the case is divided into several stages and the decision is has to be made (xk) at each stage. The results obtained at a stage are used for the states in the next stage so that at the forward stage 1, f1 (s) is obtained and used as a consideration of the decision in the next stage. In the backward, used firstly stage 4, f4 (s) is obtained and used as a consideration of the decision in the next stage. Cost forward and backward always increase steadily, because the cost in the next stage depends on the cost in the previous stage and formed the decision of each stage by taking the smallest fk value. Therefore the forward and backward approaches have the same result.

Future Prospects for Energy Technologies: Insights from Expert Elicitations

Expert elicitation is a process for eliciting subjective probability distributions from experts about items of interest to decision makers. These methods have been increasingly applied in the energy domain to collect information on the future cost and performance of specific energy technologies and the associated uncertainty. This article reviews the existing expert elicitations on energy technologies with three main objectives: (1) to provide insights on expert elicitation methods and how they compare/complement other approaches to inform public energy decision making; (2) to review all recent elicitation exercises about future technology costs; and (3) to discuss the main results from these expert elicitations, in terms of implied rates of cost reduction and the role of R&D investments in shaping these reductions, and compare it with insights from backward looking approaches. We argue that the emergence of data on future energy costs through expert elicitations provides the opportunity for more transparent and robust analyses incorporating technical uncertainty to assess energy and climate change mitigation policies.

An Exposition of Process Theory and Critique of Mohr’s (1982) Conceptualization Thereof

Championed by Whitehead (1979), a process metaphysics has been forwarded as one way of conceptualizing the fundamental nature of our existence. On an applied level, we might use the notion of process within the framework of scientific method to advance our knowledge of how we might take steps to create particular outcomes or states that we desire within organizations. We discuss both forward and backward looking approaches to developing process theory. Ultimately, though, in this paper, we present discussion of the limits of Mohr’s (1982) conceptualization of process theory and show (1) how his discussion focuses on a subset or limited view of process (and would render invisible other alternatives) and (2) how such limitation of view retards the accumulation of knowledge regarding individuals and organizations as a storehouse of process approaches toward achieving specified results.

Performance evaluation of single layer HDR video transmission pipelines

Thanks to the recent developments in both High Dynamic Range (HDR) content creation and HDR consumer displays, HDR technology is now mature enough for consumer TV broadcasting. Considering that HDR displays have been introduced to the consumer market just recently, backward compatible broadcasting approaches that can also address the Standard Dynamic Range (SDR) displays are preferred during this transition period. While several backward compatible single layer approaches have been proposed for HDR content delivery, there is no comprehensive study on the subjective quality of the delivered content on both SDR and HDR displays. In this work, we investigate the performance of two single layer HDR delivery pipelines, namely HDR10 and SDR10 through three sets of subjective test experiments. The effect of different video preprocessing and post-processing methods used in the HDR10 and SDR10 pipelines on the visual quality of the HDR and SDR outputs is investigated in these comprehensive tests. The analysis of the results shows that the HDR10 pipeline can achieve superior HDR quality compared to that of the SDR10 while the SDR subjective quality of the HDR10 pipeline is comparable to that of the SDR10 pipeline. Therefore, it is concluded that HDR10 can be used as a backward compatible single layer pipeline addressing both HDR and SDR displays. It is also shown in this work that by addressing the display in 4:4:4 mode, the SDR subjective quality of the HDR10 pipeline is further improved compared to the 4:2:0 mode. The findings of this work can be used as guidelines for addressing both HDR and SDR displays with HDR10 pipeline.

A New Approach for Parameter Estimation of Autoregressive Models Using Adaptive Network-Based Fuzzy Inference System (ANFIS)

Time series modeling plays an important role in different fields of science and engineering such as hydrology and water resources management. The proper estimation of the parameters in time series models is one of the essential steps of modeling. Yule–Walker, least square, Burge and forward–backward approaches are known, and common methods of parameter estimation are used in many time series studies. Recently, intelligent techniques such as adaptive network-based fuzzy inference system (ANFIS) have been used for time series modeling. Review of previous researches, especially in the field of hydrological time series, shows that these systems are often used as intelligent forecasting systems; indeed, they were considered as a black box. In this study, using ANFIS and its basic concepts, a new approach is devised for parameter estimation of autoregressive (AR) models. Performance of this approach is evaluated through the Akaike information criterion; also its application has been surveyed in time series forecasting by naturalized inflow of the Zayandehrud dam located in central Iran. Results show that the proposed approach has a good and effective performance for parameter estimation of AR models which can be depicted as a new “intelligent approach.” In addition, this capability of ANFIS in parameter estimation is a new application of ANFIS that was not addressed in the past. Also, the new driven method from ANFIS shows that this system can be employed as a parameter estimator for time series models such as AR models.

Combining forward and backward mortality estimation

Demographers often form estimates by combining information from two data sources—a challenging problem when one or both data sources are incomplete. A classic example entails the construction of death probabilities, which requires death counts for the subpopulations under study and corresponding base population estimates. Approaches typically entail ‘back projection', as in Wrigley and Schofield's seminal analysis of historical English data, or ‘inverse’ or ‘forward projection’ as used by Lee in his important reanalysis of that work, both published in the 1980s. Our paper shows how forward and backward approaches can be optimally combined, using a generalized method of moments (GMM) framework. We apply the method to the estimation of death probabilities for relatively small subpopulations within the United States (men born 1930–39 by state of birth by birth cohort by race), combining data from vital statistics records and census samples.

Empirical-Markovian model for predicting the overlay design thickness for asphalt concrete pavement

An Empirical-Markovian model has been developed to predict the overlay design thickness for asphalt concrete pavement from relevant design parameters. The Empirical-Markovian model mainly predicts the structural capacity of overlaid pavement as a function of the structural capacity associated with original pavement, annual traffic growth rate, rehabilitation scheduling time, and two calibration constants. The structural capacity is evaluated using either the structural number or gravel equivalent deployed by the American Association of State Highway and Transportation Officials and Caltrans design methods for flexible pavement, respectively. The Empirical-Markovian model provides the practitioner with two options as related to the performance of overlaid pavement. The first option enforces the performance of overlaid pavement to be similar to that of the original pavement, an objective achieved by requiring the deterioration transition probabilities for overlaid pavement to be the same as the corresponding ones for original pavement. The second option imposes improved performance of overlaid pavement compared to that of the original pavement, an objective accomplished by requiring the deterioration transition probabilities of overlaid pavement to be lower than the corresponding values associated with original pavement. The two calibration constants can be estimated by either minimising the sum of squared errors applied to historical records of pavement distress (forward approach) or a backward solution of the developed Empirical-Markovian model mainly relying on historical records of pavement rehabilitation. Two case studies are presented to demonstrate the use of both forward and backward approaches with results seem to be in line with the common practice.

Response variable selection in principal response curves using permutation testing

Principal response curves analysis (PRC) is widely applied to experimental multivariate longitudinal data for the study of time-dependent treatment effects on the multiple outcomes or response variables (RVs). Often, not all of the RVs included in such a study are affected by the treatment and RV-selection can be used to identify those RVs and so give a better estimate of the principal response. We propose four backward selection approaches, based on permutation testing, that differ in whether coefficient size is used or not in ranking the RVs. These methods are expected to give a more robust result than the use of a straightforward cut-off value for coefficient size. Performance of all methods is demonstrated in a simulation study using realistic data. The permutation testing approach that uses information on coefficient size of RVs speeds up the algorithm without affecting its performance. This most successful permutation testing approach removes roughly 95 % of the RVs that are unaffected by the treatment irrespective of the characteristics of the data set and, in the simulations, correctly identifies up to 97 % of RVs affected by the treatment.

Stable blowup for wave equations in odd space dimensions

We consider semilinear wave equations with focusing power nonlinearities in odd space dimensions d≥5. We prove that for every p>d+3d−1 there exists an open set of radial initial data in Hd+12×Hd−12 such that the corresponding solution exists in a backward lightcone and approaches the ODE blowup profile. The result covers the entire range of energy supercritical nonlinearities and extends our previous work for the three-dimensional radial wave equation to higher space dimensions.