Gupta, Gautam; Jung, Yoon Chul
Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced
that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances. Conclusion We provide an indication of the conditions under which such an optimal enumeration approach is likely to be feasible, suggesting that these strategies are usable for relatively large numbers of taxa, although with stricter limits on numbers of variable sites. The work thus provides methodology suitable for provably optimal solution of some harder instances that resist all prior approaches. PMID:23343437
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
Poos, Alexandra M.; Maicher, André; Dieckmann, Anna K.; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
Li, Zukui; Ding, Ran; Floudas, Christodoulos A.
Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263
Li, Y P; Huang, G H
In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management. PMID:16678336
The problem consists in selecting the sites on the river where reservoirs and hydroelectric power plants are to be built and then determining the type and size of the projected installations. The solution obviously depends on the amount of money the utility is willing to invest, which itself is a function of what the new installations will produce. It is therefore necessary to solve the problem for all possible amounts of firm energy produced, since it is not known at the outset which production level the utility will select. This is done in the paper by a parametric mixed-integer linear programming (MILP) method whose efficiency derives from the fact that the branch-and-bound algorithm for selecting the sites to be developed (and consuming most of the computer time) is solved a minimum number of times. Between the points where the MILP problem is solved, LP parametric analysis is applied.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398
Siew, Lam Weng; Jaaman, Saiful Hafizah Hj.; Ismail, Hamizun bin
Enhanced index tracking is a popular form of portfolio management in stock market investment. Enhanced index tracking aims to construct an optimal portfolio to generate excess return over the return achieved by the stock market index without purchasing all of the stocks that make up the index. The objective of this paper is to construct an optimal portfolio using mixed-integer programming model which adopts regression approach in order to generate higher portfolio mean return than stock market index return. In this study, the data consists of 24 component stocks in Malaysia market index which is FTSE Bursa Malaysia Kuala Lumpur Composite Index from January 2010 until December 2012. The results of this study show that the optimal portfolio of mixed-integer programming model is able to generate higher mean return than FTSE Bursa Malaysia Kuala Lumpur Composite Index return with only selecting 30% out of the total stock market index components.
Woodruff, David L.; Watson, Jean-Paul
Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its widespread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer, multi-stage case. Intricate, configurable, and parallel decomposition strategies are frequently required to achieve tractable run-times. We simultaneously address both of these factors in our PySP software package, which is part of the COIN-OR Coopr open-source Python project for optimization. To formulate a stochastic program in PySP, the user specifies both the deterministic base model and the scenario tree with associated uncertain parameters in the Pyomo open-source algebraic modeling language. Given these two models, PySP provides two paths for solution of the corresponding stochastic program. The first alternative involves writing the extensive form and invoking a standard deterministic (mixed-integer) solver. For more complex stochastic programs, we provide an implementation of Rockafellar and Wets Progressive Hedging algorithm. Our particular focus is on the use of Progressive Hedging as an effective heuristic for approximating general multi-stage, mixed-integer stochastic programs. By leveraging the combination of a high-level programming language (Python) and the embedding of the base deterministic model in that language (Pyomo), we are able to provide completely generic and highly configurable solver implementations. PySP has been used by a number of research groups, including our own, to rapidly prototype and solve difficult stochastic programming problems.
Sawyer, Charles S.; Ahlfeld, David P.; King, Alan J.
A three-dimensional groundwater flow management model for making decisions on the design of hydrodynamic control of a groundwater flow system using a combination of extraction and/or injection wells is developed. The model takes into account constraints imposed on the system to stop the horizontal spread of contaminants and to ensure a net upward flow in areas where downward vertical gradients exist. The mathematical formulation of the groundwater remediation problem as a mixed-integer model and the strategy for solving the model are presented. Numerical results are presented for the Toms River Plant site, which is modeled as a five-layer aquifer system with interconnecting aquitards. A sensitivity analysis on the relative magnitude of the continuous operating costs and the fixed-charge costs is also presented.
Zhang, Huiling; Huang, Qingsheng; Bei, Zhendong; Wei, Yanjie; Floudas, Christodoulos A
In this article, we present COMSAT, a hybrid framework for residue contact prediction of transmembrane (TM) proteins, integrating a support vector machine (SVM) method and a mixed integer linear programming (MILP) method. COMSAT consists of two modules: COMSAT_SVM which is trained mainly on position-specific scoring matrix features, and COMSAT_MILP which is an ab initio method based on optimization models. Contacts predicted by the SVM model are ranked by SVM confidence scores, and a threshold is trained to improve the reliability of the predicted contacts. For TM proteins with no contacts above the threshold, COMSAT_MILP is used. The proposed hybrid contact prediction scheme was tested on two independent TM protein sets based on the contact definition of 14 Å between Cα-Cα atoms. First, using a rigorous leave-one-protein-out cross validation on the training set of 90 TM proteins, an accuracy of 66.8%, a coverage of 12.3%, a specificity of 99.3% and a Matthews' correlation coefficient (MCC) of 0.184 were obtained for residue pairs that are at least six amino acids apart. Second, when tested on a test set of 87 TM proteins, the proposed method showed a prediction accuracy of 64.5%, a coverage of 5.3%, a specificity of 99.4% and a MCC of 0.106. COMSAT shows satisfactory results when compared with 12 other state-of-the-art predictors, and is more robust in terms of prediction accuracy as the length and complexity of TM protein increase. COMSAT is freely accessible at http://hpcc.siat.ac.cn/COMSAT/. PMID:26756402
This work presents a method of finding near global optima to minimum-time trajectory generation problem for systems that would be linear if it were not for the presence of Coloumb friction. The required final state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that they can overcome the maximum static Coloumb friction force. Other than the previous work for generating minimum-time trajectories for non redundant robotic manipulators for which the path in joint space is already specified, this work represents, to the best of the authors' knowledge, the first approach for generating near global optima for minimum-time problems involving a nonlinear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the nonlinear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.
Tang, Jiafu; Liu, Yang; Fung, Richard; Luo, Xinggang
Manufacturers have a legal accountability to deal with industrial waste generated from their production processes in order to avoid pollution. Along with advances in waste recovery techniques, manufacturers may adopt various recycling strategies in dealing with industrial waste. With reuse strategies and technologies, byproducts or wastes will be returned to production processes in the iron and steel industry, and some waste can be recycled back to base material for reuse in other industries. This article focuses on a recovery strategies optimization problem for a typical class of industrial waste recycling process in order to maximize profit. There are multiple strategies for waste recycling available to generate multiple byproducts; these byproducts are then further transformed into several types of chemical products via different production patterns. A mixed integer programming model is developed to determine which recycling strategy and which production pattern should be selected with what quantity of chemical products corresponding to this strategy and pattern in order to yield maximum marginal profits. The sales profits of chemical products and the set-up costs of these strategies, patterns and operation costs of production are considered. A simulated annealing (SA) based heuristic algorithm is developed to solve the problem. Finally, an experiment is designed to verify the effectiveness and feasibility of the proposed method. By comparing a single strategy to multiple strategies in an example, it is shown that the total sales profit of chemical products can be increased by around 25% through the simultaneous use of multiple strategies. This illustrates the superiority of combinatorial multiple strategies. Furthermore, the effects of the model parameters on profit are discussed to help manufacturers organize their waste recycling network.
Background This paper presents a Mixed Integer Programming (MIP) model for designing the layout of the Intensive Care Units' (ICUs) patient care space. In particular, this MIP model was developed for optimizing the layout for materials to be used in interventions. This work was developed within the framework of a joint project between the Madrid Technical Unverstity and the Medical Emergency Services of the Madrid Regional Government (SUMMA 112). Methods The first task was to identify the relevant information to define the characteristics of the new vehicles and, in particular, to obtain a satisfactory interior layout to locate all the necessary materials. This information was gathered from health workers related to ICUs. With that information an optimization model was developed in order to obtain a solution. From the MIP model, a first solution was obtained, consisting of a grid to locate the different materials needed for the ICUs. The outcome from the MIP model was discussed with health workers to tune the solution, and after slightly altering that solution to meet some requirements that had not been included in the mathematical model, the eventual solution was approved by the persons responsible for specifying the characteristics of the new vehicles. According to the opinion stated by the SUMMA 112's medical group responsible for improving the ambulances (the so-called "coaching group"), the outcome was highly satisfactory. Indeed, the final design served as a basis to draw up the requirements of a public tender. Results As a result from solving the Optimization model, a grid was obtained to locate the different necessary materials for the ICUs. This grid had to be slightly altered to meet some requirements that had not been included in the mathematical model. The results were discussed with the persons responsible for specifying the characteristics of the new vehicles. Conclusion The outcome was highly satisfactory. Indeed, the final design served as a basis
Irmeilyana, Puspita, Fitri Maya; Indrawati
The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.
Winebrake, James J; Corbett, James J; Wang, Chengfeng; Farrell, Alexander E; Woods, Pippa
Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emissions of oxides of nitrogen (NOx) and particulate matter (PM) from primarily unregulated diesel engines. This paper explores technical solutions to reduce pollution from passenger ferries operating in the New York-New Jersey Harbor. The paper discusses and demonstrates a mixed-integer, non-linear programming model used to identify optimal control strategies for meeting NOx and PM reduction targets for 45 privately owned commuter ferries in the harbor. Results from the model can be used by policy-makers to craft programs aimed at achieving least-cost reduction targets. PMID:15887889
Henriques, David; Rocha, Miguel; Saez-Rodriguez, Julio; Banga, Julio R.
Motivation: Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters. Results: In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two-component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cells. Supplementary information: Supplementary data are available at Bioinformatics online. Contact: firstname.lastname@example.org or email@example.com PMID:26002881
Armutlu, Pelin; Ozdemir, Muhittin E; Uney-Yuksektepe, Fadime; Kavakli, I Halil; Turkay, Metin
Background A priori analysis of the activity of drugs on the target protein by computational approaches can be useful in narrowing down drug candidates for further experimental tests. Currently, there are a large number of computational methods that predict the activity of drugs on proteins. In this study, we approach the activity prediction problem as a classification problem and, we aim to improve the classification accuracy by introducing an algorithm that combines partial least squares regression with mixed-integer programming based hyper-boxes classification method, where drug molecules are classified as low active or high active regarding their binding activity (IC50 values) on target proteins. We also aim to determine the most significant molecular descriptors for the drug molecules. Results We first apply our approach by analyzing the activities of widely known inhibitor datasets including Acetylcholinesterase (ACHE), Benzodiazepine Receptor (BZR), Dihydrofolate Reductase (DHFR), Cyclooxygenase-2 (COX-2) with known IC50 values. The results at this stage proved that our approach consistently gives better classification accuracies compared to 63 other reported classification methods such as SVM, Naïve Bayes, where we were able to predict the experimentally determined IC50 values with a worst case accuracy of 96%. To further test applicability of this approach we first created dataset for Cytochrome P450 C17 inhibitors and then predicted their activities with 100% accuracy. Conclusion Our results indicate that this approach can be utilized to predict the inhibitory effects of inhibitors based on their molecular descriptors. This approach will not only enhance drug discovery process, but also save time and resources committed. PMID:18834515
Guo, P.; Huang, G. H.; Li, Y. P.
In this study, an inexact fuzzy-chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is developed for flood diversion planning under multiple uncertainties. A concept of the distribution with fuzzy boundary interval probability is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets and probability distributions. IFCTIP integrates the inexact programming, two-stage stochastic programming, integer programming and fuzzy-stochastic programming within a general optimization framework. IFCTIP incorporates the pre-regulated water-diversion policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised targets are violated. More importantly, it can facilitate dynamic programming for decisions of capacity-expansion planning under fuzzy-stochastic conditions. IFCTIP is applied to a flood management system. Solutions from IFCTIP provide desired flood diversion plans with a minimized system cost and a maximized safety level. The results indicate that reasonable solutions are generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of flood flows.
Li, Rui; Emmerich, Michael T M; Eggermont, Jeroen; Bäck, Thomas; Schütz, M; Dijkstra, J; Reiber, J H C
Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems. PMID:22122384
Ko, Andi Setiady; Chang, Ni-Bin
Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time. PMID:17395362
Han, Kyung T.; Rudner, Lawrence M.
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
Valicka, C.; Hart, W.; Rintoul, M.
Remote sensing systems have expanded the set of capabilities available for and critical to national security. Cooperating, high-fidelity sensing systems and growing mission applications have exponentially increased the set of potential schedules. A definitive lack of advanced tools places an increased burden on operators, as planning and scheduling remain largely manual tasks. This is particularly true in time-critical planning activities where operators aim to accomplish a large number of missions through optimal utilization of single or multiple sensor systems. Automated scheduling through identification and comparison of alternative schedules remains a challenging problem applicable across all remote sensing systems. Previous approaches focused on a subset of sensor missions and do not consider ad-hoc tasking. We have begun development of a robust framework that leverages the Pyomo optimization modeling language for the design of a tool to assist sensor operators planning under the constraints of multiple concurrent missions and uncertainty. Our scheduling models have been formulated to address the stochastic nature of ad-hoc tasks inserted under a variety of scenarios. Operator experience is being leveraged to select appropriate model objectives. Successful development of the framework will include iterative development of high-fidelity mission models that consider and expose various schedule performance metrics. Creating this tool will aid time-critical scheduling by increasing planning efficiency, clarifying the value of alternative modalities uniquely provided by multi-sensor systems, and by presenting both sets of organized information to operators. Such a tool will help operators more quickly and fully utilize sensing systems, a high interest objective within the current remote sensing operations community. Preliminary results for mixed-integer programming formulations of a sensor scheduling problem will be presented. Assumptions regarding sensor geometry
Hartman-Baker, Rebecca J; Busch, Ingrid Karin; Hilliard, Michael R; Middleton, Richard S; Schultze, Michael
In this paper, we describe our experience with solving difficult mixed-integer linear programming problems (MILPs) on the petaflop Cray XT5 system at the National Center for Computational Sciences at Oak Ridge National Laboratory. We describe the algorithmic, software, and hardware needs for solving MILPs and present the results of using PICO, an open-source, parallel, mixed-integer linear programming solver developed at Sandia National Laboratories, to solve canonical MILPs as well as problems of interest arising from the logistics and supply chain management field.
Smalley, Hannah K; Keskinocak, Pinar; Swann, Julie; Hinman, Alan
In addition to improved sanitation, hygiene, and better access to safe water, oral cholera vaccines can help to control the spread of cholera in the short term. However, there is currently no systematic method for determining the best allocation of oral cholera vaccines to minimize disease incidence in a population where the disease is endemic and resources are limited. We present a mathematical model for optimally allocating vaccines in a region under varying levels of demographic and incidence data availability. The model addresses the questions of where, when, and how many doses of vaccines to send. Considering vaccine efficacies (which may vary based on age and the number of years since vaccination), we analyze distribution strategies which allocate vaccines over multiple years. Results indicate that, given appropriate surveillance data, targeting age groups and regions with the highest disease incidence should be the first priority, followed by other groups primarily in order of disease incidence, as this approach is the most life-saving and cost-effective. A lack of detailed incidence data results in distribution strategies which are not cost-effective and can lead to thousands more deaths from the disease. The mathematical model allows for what-if analysis for various vaccine distribution strategies by providing the ability to easily vary parameters such as numbers and sizes of regions and age groups, risk levels, vaccine price, vaccine efficacy, production capacity and budget. PMID:26458806
Kania, Adhe; Sidarto, Kuntjoro Adji
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
Skulovich, Olya; Bent, Russell; Judi, David; Perelman, Lina Sela; Ostfeld, Avi
Despite their potential catastrophic impact, transients are often ignored or presented ad hoc when designing water distribution systems. To address this problem, we introduce a new piece-wise function fitting model that is integrated with mixed integer programming to optimally place and size surge tanks for transient control. The key features of the algorithm are a model-driven discretization of the search space, a linear approximation nonsmooth system response surface to transients, and a mixed integer linear programming optimization. Results indicate that high quality solutions can be obtained within a reasonable number of function evaluations and demonstrate the computational effectiveness of the approach through two case studies. The work investigates one type of surge control devices (closed surge tank) for a specified set of transient events. The performance of the algorithm relies on the assumption that there exists a smooth relationship between the objective function and tank size. Results indicate the potential of the approach for the optimal surge control design in water systems.
Tam, Margaret; Glenn Lightsey, E.
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Li, J. C.; Gong, B.; Wang, H. G.
Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design-determining well placement, number of fracturing stages, and fracture lengths-is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.
Gorissen, Bram L; den Hertog, Dick; Hoffmann, Aswin L
Current inverse treatment planning methods that optimize both catheter positions and dwell times in prostate HDR brachytherapy use surrogate linear or quadratic objective functions that have no direct interpretation in terms of dose-volume histogram (DVH) criteria, do not result in an optimum or have long solution times. We decrease the solution time of the existing linear and quadratic dose-based programming models (LP and QP, respectively) to allow optimizing over potential catheter positions using mixed integer programming. An additional average speed-up of 75% can be obtained by stopping the solver at an early stage, without deterioration of the plan quality. For a fixed catheter configuration, the dwell time optimization model LP solves to optimality in less than 15 s, which confirms earlier results. We propose an iterative procedure for QP that allows us to prescribe the target dose as an interval, while retaining independence between the solution time and the number of dose calculation points. This iterative procedure is comparable in speed to the LP model and produces better plans than the non-iterative QP. We formulate a new dose-volume-based model that maximizes V(100%) while satisfying pre-set DVH criteria. This model optimizes both catheter positions and dwell times within a few minutes depending on prostate volume and number of catheters, optimizes dwell times within 35 s and gives better DVH statistics than dose-based models. The solutions suggest that the correlation between the objective value and the clinical plan quality is weak in the existing dose-based models. PMID:23363622
Sendín, J O H; Exler, O; Banga, J R
In this contribution, the authors consider multi-criteria optimisation problems arising from the field of systems biology when both continuous and integer decision variables are involved. Mathematically, they are formulated as mixed-integer non-linear programming problems. The authors present a novel solution strategy based on a global optimisation approach for dealing with this class of problems. Its usefulness and capabilities are illustrated with two metabolic engineering case studies. For these problems, the authors show how the set of optimal solutions (the so-called Pareto front) is successfully and efficiently obtained, providing further insight into the systems under consideration regarding their optimal manipulation. PMID:20500003
Guo, P; Huang, G H
In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada. PMID:19800164
Cheung, Kar-Ming; Lee, Charles H.
We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.
Lee, Charles H.; Cheung, Kar-Ming
Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.
Wu, Juan; Ge, Xueqian
Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.
Lei, Yang; Li, Shurong; Zhang, Xiaodong; Zhang, Qiang; Guo, Lanlei
Polymer flooding is one of the most important technologies for enhanced oil recovery. In this article, a mixed-integer optimal control model of distributed parameter systems (DPS) for the injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding and some inequalities constraints, such as polymer concentration and injection amount limitation. The control variables are the volume size, the injection concentration of each slug and the terminal flooding time. For the constant injection rate, the slug size is determined by the integer time stage length, and thus the integer variables are introduced in the DPS. To cope with the optimal control problem (OCP) of this DPS, a mixed-integer iterative dynamic programming incorporating a special truncation procedure to handle integer restrictions on stage lengths is proposed. First, the OCP with variable time stage lengths is transformed into a fixed time stage problem by introducing a normalised time variable. Then, the optimisation procedure is carried out at each stage and preceded backwards in a systematic way. Finally, the numerical results of an example illustrate the effectiveness of the proposed method.
Zhang, Jin; Tang, Guo-jin; Luo, Ya-Zhong; Li, Hai-yang
The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates single phase parameters and phase connecting parameters simultaneously, is proposed to improve the rendezvous mission's overall performance. The design variables are composed of integers and continuous-valued numbers. The integer part consists of the parameters for station-keeping and sensor-switching, the number of maneuvers in each rendezvous phase and the number of repeating periods to start the rendezvous mission. The continuous part consists of the orbital transfer time and the station-keeping duration. The objective function is a combination of the propellant consumed, the sun angle which represents the power available, and the terminal precision of each rendezvous phase. The operational requirements for the spacecraft-ground communication, sun illumination and the sensor transition are considered. The simple genetic algorithm, which is a combination of the integer-coded and real-coded genetic algorithm, is chosen to obtain the optimal solution. A practical rendezvous mission planning problem is solved by the proposed method. The results show that the method proposed can solve the integral rendezvous mission planning problem effectively, and the solution obtained can satisfy the operational constraints and has a good overall performance.
DiMaggio, Peter A.
A novel methodology for the de novo identification of peptides by mixed-integer optimization and tandem mass spectrometry is presented in this article. The various features of the mathematical model are presented and examples are used to illustrate the key concepts of the proposed approach. Several problems are examined to illustrate the proposed method's ability to address (1) residue-dependent fragmentation properties and (2) the variability of resolution in different mass analyzers. A preprocessing algorithm is used to identify important m/z values in the tandem mass spectrum. Missing peaks, resulting from residue-dependent fragmentation characteristics, are dealt with using a two-stage algorithmic framework. A cross-correlation approach is used to resolve missing amino acid assignments and to identify the most probable peptide by comparing the theoretical spectra of the candidate sequences that were generated from the MILP sequencing stages with the experimental tandem mass spectrum. PMID:19412358
Linderoth, Jeff T.; Luedtke, James R.
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Problems involving both discrete and nonlinear components are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems. This research project added to the understanding of this area by making a number of fundamental advances. First, the work demonstrated many novel, strong, tractable relaxations designed to deal with non-convexities arising in mathematical formulation. Second, the research implemented the ideas in software that is available to the public. Finally, the work demonstrated the importance of these ideas on practical applications and disseminated the work through scholarly journals, survey publications, and conference presentations.
Webb, W. A.
A computer model is described which uses mixed-integer linear programming to provide optimal DSN spacecraft schedules given a mission set and specified scheduling requirements. A solution technique is proposed which uses Bender's Method and a heuristic starting algorithm.
Bravo, Héctor Corrada; Wright, Stephen; Eng, Kevin H.; Keles, Sündüz; Wahba, Grace
We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used to formulate estimation as instances of well-studied numerical optimization problems. In particular, our estimates are based on projection, where the covariance estimate is the nearest tree-structured covariance matrix to an observed sample covariance matrix. The problem is posed as a linear or quadratic mixed-integer program (MIP) where a setting of the integer variables in the MIP specifies a set of tree topologies of the structured covariance matrix. We solve these problems to optimality using efficient and robust existing MIP solvers. We present a case study in phylogenetic analysis of gene expression and a simulation study comparing our method to distance-based tree estimating procedures. PMID:22081761
Webb, W. A.
A computer model is described which uses mixed-integer linear programming to provide optimal DSN spacecraft schedules given a mission set and specified scheduling requirements. A solution technique is proposed which uses Bender's method and a heuristic starting algorithm.
Cheng, Guanhui; Huang, Guohe Gordon; Dong, Cong
To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can
Liu, Songsong; Simaria, Ana S; Farid, Suzanne S; Papageorgiou, Lazaros G
Chromatography operations are identified as critical steps in a monoclonal antibody (mAb) purification process and can represent a significant proportion of the purification material costs. This becomes even more critical with increasing product titers that result in higher mass loads onto chromatography columns, potentially causing capacity bottlenecks. In this work, a mixed-integer nonlinear programming (MINLP) model was created and applied to an industrially relevant case study to optimize the design of a facility by determining the most cost-effective chromatography equipment sizing strategies for the production of mAbs. Furthermore, the model was extended to evaluate the ability of a fixed facility to cope with higher product titers up to 15 g/L. Examination of the characteristics of the optimal chromatography sizing strategies across different titer values enabled the identification of the maximum titer that the facility could handle using a sequence of single column chromatography steps as well as multi-column steps. The critical titer levels for different ratios of upstream to dowstream trains where multiple parallel columns per step resulted in the removal of facility bottlenecks were identified. Different facility configurations in terms of number of upstream trains were considered and the trade-off between their cost and ability to handle higher titers was analyzed. The case study insights demonstrate that the proposed modeling approach, combining MINLP models with visualization tools, is a valuable decision-support tool for the design of cost-effective facility configurations and to aid facility fit decisions. 2013. PMID:23956206
Damci Kurt, Pelin
This dissertation conducts theoretical and computational research to solve challenging problems in application areas such as supply chain and power systems. The first part of the dissertation studies a transportation problem with market choice (TPMC) which is a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We show that TPMC is strongly NP-complete. We consider a version of the problem with a service level constraint on the maximum number of markets that can be rejected and show that if the original problem is polynomial, its cardinality-constrained version is also polynomial. We propose valid inequalities for mixed-integer cover and knapsack sets with variable upper bound constraints, which appear as substructures of TPMC and use them in a branch-and-cut algorithm to solve this problem. The second part of this dissertation studies a unit commitment (UC) problem in which the goal is to minimize the operational cost of power generators over a time period subject to physical constraints while satisfying demand. We provide several exponential classes of multi-period ramping and multi-period variable upper bound inequalities. We prove the strength of these inequalities and describe polynomial-time separation algorithms. Computational results show the effectiveness of the proposed inequalities when used as cuts in a branch-and-cut algorithm to solve the UC problem. The last part of this dissertation investigates the effects of uncertain wind power on the UC problem. A two-stage robust model and a three-stage stochastic program are compared.
Yin, Sisi; Nishi, Tatsushi
Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.
Wang, Bin; Chiang, Hsiao-Dong
Many applications of smart grid can be formulated as constrained optimization problems. Because of the discrete controls involved in power systems, these problems are essentially mixed-integer nonlinear programs. In this paper, we review the Trust-Tech-based methodology for solving mixed-integer nonlinear optimization. Specifically, we have developed a two-stage Trust-Tech-based methodology to systematically compute all the local optimal solutions for constrained mixed-integer nonlinear programming (MINLP) problems. In the first stage, for a given MINLP problem this methodology starts with the construction of a new, continuous, unconstrained problem through relaxation and the penalty function method. A corresponding dynamical system is then constructed to search for a set of local optimal solutions for the unconstrained problem. In the second stage, a reduced constrained NLP is defined for each local optimal solution by determining and fixing the values of integral variables of the MINLP problem. The Trust-Tech-based method is used to compute a set of local optimal solutions for these reduced NLP problems, from which the optimal solution of the original MINLP problem is determined. A numerical simulation of several testing problems is provided to illustrate the effectiveness of our proposed method.
Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.
In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean -Paul; Wets, Roger J.-B.; Woodruff, David L.
We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.
When wood is to be utilized as a raw material for furniture, buildings, etc., it must be dried from approximately 100% to 6% moisture content. This is achieved at least partly in a drying kiln. Heat for this purpose is provided by electrical means, or by steam from boilers fired with wood chips or oil. By making a close examination of monitored values from an actual drying kiln it has been possible to optimize the use of steam and electricity using the so called mixed integer programming technique. Owing to the operating schedule for the drying kiln it has been necessary to divide the drying process in very short time intervals, i.e., a number of minutes. Since a drying cycle takes about two or three weeks, a considerable mathematical problem is presented and this has to be solved.
Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao
A “Smart House” is a highly energy-optimized house equipped with photovoltaic systems (PV systems), electric battery systems, fuel cell cogeneration systems (FC systems), electric vehicles (EVs) and so on. Smart houses are attracting much attention recently thanks to their enhanced ability to save energy by making full use of renewable energy and by achieving power grid stability despite an increased power draw for installed PV systems. Yet running a smart house's power system, with its multiple power sources and power storages, is no simple task. In this paper, we consider the problem of power scheduling for a smart house with a PV system, an FC system and an EV. We formulate the problem as a mixed integer programming problem, and then extend it to a stochastic programming problem involving recourse costs to cope with uncertain electricity demand, heat demand and PV power generation. Using our method, we seek to achieve the optimal power schedule running at the minimum expected operation cost. We present some results of numerical experiments with data on real-life demands and PV power generation to show the effectiveness of our method.
Baran, Ismet; Tutum, Cem C.; Hattel, Jesper H.
In this paper thermo-chemical simulation of the pultrusion process of a composite rod is first used as a validation case to ensure that the utilized numerical scheme is stable and converges to results given in literature. Following this validation case, a cylindrical die block with heaters is added to the pultrusion domain of a composite part and thermal contact resistance (TCR) regions at the die-part interface are defined. Two optimization case studies are performed on this new configuration. In the first one, optimal die radius and TCR values are found by using a hybrid genetic algorithm based on a sequential combination of a genetic algorithm (GA) and a local search technique to fit the centerline temperature of the composite with the one calculated in the validation case. In the second optimization study, the productivity of the process is improved by using a mixed integer genetic algorithm (MIGA) such that the total number of heaters is minimized while satisfying the constraints for the maximum composite temperature, the mean of the cure degree at the die exit and the pulling speed.
Munguia, Lluis-Miquel; Oxberry, Geoffrey; Rajan, Deepak
Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. In order to overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We also show promising results on the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. Finally, we expect the performance of PIPS-SBB to improve furthermore » as more functionality is added in the future.« less
Shoemaker, Christine; Wan, Ying
Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).
Guo, P.; Huang, G.H.
In this study, an interval-parameter semi-infinite fuzzy-chance-constrained mixed-integer linear programming (ISIFCIP) approach is developed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing interval-parameter semi-infinite programming (ISIP) and fuzzy-chance-constrained programming (FCCP) by incorporating uncertainties expressed as dual uncertainties of functional intervals and multiple uncertainties of distributions with fuzzy-interval admissible probability of violating constraint within a general optimization framework. The binary-variable solutions represent the decisions of waste-management-facility expansion, and the continuous ones are related to decisions of waste-flow allocation. The interval solutions can help decision-makers to obtain multiple decision alternatives, as well as provide bases for further analyses of tradeoffs between waste-management cost and system-failure risk. In the application to the City of Regina, Canada, two scenarios are considered. In Scenario 1, the City's waste-management practices would be based on the existing policy over the next 25 years. The total diversion rate for the residential waste would be approximately 14%. Scenario 2 is associated with a policy for waste minimization and diversion, where 35% diversion of residential waste should be achieved within 15 years, and 50% diversion over 25 years. In this scenario, not only landfill would be expanded, but also CF and MRF would be expanded. Through the scenario analyses, useful decision support for the City's solid-waste managers and decision-makers has been generated. Three special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it is useful for tackling multiple uncertainties expressed as intervals, functional intervals, probability distributions, fuzzy sets, and their
Nolle, Lars; Biegler-König, Friedrich; Deeskow, Peter
In order to optimise the energy production in a fleet of power plants, it is necessary to solve a mixed integer optimisation problem. Traditionally, the continuous parts of the problem are linearized and a Simplex scheme is applied. Alternatively, heuristic "bionic" optimisation methods can be used without having to linearize the problem. Weare going to demonstrate this approach by modelling power plant blocks with fast Neural Networks and optimising the operation of multi-block power plants over one day with Simulated Annealing.
Permutation tests (see Permutation Based Inference) for the linear model have applications in behavioral studies when traditional parametric assumptions about the error term in a linear model are not tenable. Improved validity of Type I error rates can be achieved with properly constructed permutation tests. Perhaps more importantly, increased statistical power, improved robustness to effects of outliers, and detection of alternative distributional differences can be achieved by coupling permutation inference with alternative linear model estimators. For example, it is well-known that estimates of the mean in linear model are extremely sensitive to even a single outlying value of the dependent variable compared to estimates of the median [7, 19]. Traditionally, linear modeling focused on estimating changes in the center of distributions (means or medians). However, quantile regression allows distributional changes to be estimated in all or any selected part of a distribution or responses, providing a more complete statistical picture that has relevance to many biological questions ...
Zou, Meng; Zhang, Peng-Jun; Wen, Xin-Yu; Chen, Luonan; Tian, Ya-Ping; Wang, Yong
Multi-biomarker panels can capture the nonlinear synergy among biomarkers and they are important to aid in the early diagnosis and ultimately battle complex diseases. However, identification of these multi-biomarker panels from case and control data is challenging. For example, the exhaustive search method is computationally infeasible when the data dimension is high. Here, we propose a novel method, MILP_k, to identify serum-based multi-biomarker panel to distinguish colorectal cancers (CRC) from benign colorectal tumors. Specifically, the multi-biomarker panel detection problem is modeled by a mixed integer programming to maximize the classification accuracy. Then we measured the serum profiling data for 101 CRC patients and 95 benign patients. The 61 biomarkers were analyzed individually and further their combinations by our method. We discovered 4 biomarkers as the optimal small multi-biomarker panel, including known CRC biomarkers CEA and IL-10 as well as novel biomarkers IMA and NSE. This multi-biomarker panel obtains leave-one-out cross-validation (LOOCV) accuracy to 0.7857 by nearest centroid classifier. An independent test of this panel by support vector machine (SVM) with threefold cross validation gets an AUC 0.8438. This greatly improves the predictive accuracy by 20% over the single best biomarker. Further extension of this 4-biomarker panel to a larger 13-biomarker panel improves the LOOCV to 0.8673 with independent AUC 0.8437. Comparison with the exhaustive search method shows that our method dramatically reduces the searching time by 1000-fold. Experiments on the early cancer stage samples reveal two panel of biomarkers and show promising accuracy. The proposed method allows us to select the subset of biomarkers with best accuracy to distinguish case and control samples given the number of selected biomarkers. Both receiver operating characteristic curve and precision-recall curve show our method's consistent performance gain in accuracy. Our method
Purnomo, Muhammad Ridwan Andi; Satrio Wiwoho, Yoga
Facility layout becomes one of production system factor that should be managed well, as it is designated for the location of production. In managing the layout, designing the layout by considering the optimal layout condition that supports the work condition is essential. One of the method for facility layout optimization is Mixed Integer Programming (MIP). In this study, the MIP is solved using Lingo 9.0 software and considering quantitative and qualitative objectives to be achieved simultaneously: minimizing material handling cost, maximizing closeness rating, and minimizing re-layout cost. The research took place in Rekayasa Wangdi as a make to order company, focusing on the making of concrete brick dough stirring machine with 10 departments involved. The result shows an improvement in the new layout for 333,72 points of objective value compared with the initial layout. As the conclusion, the proposed MIP is proven to be used to model facility layout problem under multi objective consideration for a more realistic look.
Villante, F. L.; Ricci, B.
We present a new approach to studying the properties of the Sun. We consider small variations of the physical and chemical properties of the Sun with respect to standard solar model predictions and we linearize the structure equations to relate them to the properties of the solar plasma. By assuming that the (variation of) present solar composition can be estimated from the (variation of) nuclear reaction rates and elemental diffusion efficiency in the present Sun, we obtain a linear system of ordinary differential equations which can be used to calculate the response of the Sun to an arbitrary modification of the input parameters (opacity, cross sections, etc.). This new approach is intended to be a complement to the traditional methods for solar model (SM) calculation and allows us to investigate in a more efficient and transparent way the role of parameters and assumptions in SM construction. We verify that these linear solar models recover the predictions of the traditional SMs with a high level of accuracy.
Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph
A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics
Moody, D.W.; Maddock, Thomas; Karlinger, M.R.; Lloyd, J.J.
Because the use of the Mathematical Programming System -Extended (MPSX) to solve large linear and mixed integer programs requires the preparation of many input data cards, a matrix generator program to produce the MPSX input data from a much more limited set of data may expedite the use of the mixed integer programming optimization technique. The Model Definition and Control Program (MODCQP) is intended to assist a planner in preparing MPSX input data for the Puerto Rico Water Resources Planning Model. The model utilizes a mixed-integer mathematical program to identify a minimum present cost set of water resources projects (diversions, reservoirs, ground-water fields, desalinization plants, water treatment plants, and inter-basin transfers of water) which will meet a set of future water demands and to determine their sequence of construction. While MODCOP was specifically written to generate MPSX input data for the planning model described in this report, the program can be easily modified to reflect changes in the model's mathematical structure.
Duke, E. L.
The Derivation and Definition of a Linear Model program, LINEAR, provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models. LINEAR was developed to provide a standard, documented, and verified tool to derive linear models for aircraft stability analysis and control law design. Linear system models define the aircraft system in the neighborhood of an analysis point and are determined by the linearization of the nonlinear equations defining vehicle dynamics and sensors. LINEAR numerically determines a linear system model using nonlinear equations of motion and a user supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. LINEAR is capable of extracting both linearized engine effects, such as net thrust, torque, and gyroscopic effects and including these effects in the linear system model. The point at which this linear model is defined is determined either by completely specifying the state and control variables, or by specifying an analysis point on a trajectory and directing the program to determine the control variables and the remaining state variables. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to provide easy selection of state, control, and observation variables to be used in a particular model. Thus, the order of the system model is completely under user control. Further, the program provides the flexibility of allowing alternate formulations of both the state and observation equations. Data describing the aircraft and the test case is input to the program through a terminal or formatted data files. All data can be modified interactively from case to case. The aerodynamic model can be defined in two ways: a set of nondimensional stability and control derivatives for the flight point of
Rashid, Kashif; Ambani, Saumil; Cetinkaya, Eren
Many real-world optimization problems comprise objective functions that are based on the output of one or more simulation models. As these underlying processes can be time and computation intensive, the objective function is deemed expensive to evaluate. While methods to alleviate this cost in the optimization procedure have been explored previously, less attention has been given to the treatment of expensive constraints. This article presents a methodology for treating expensive simulation-based nonlinear constraints alongside an expensive simulation-based objective function using adaptive radial basis function techniques. Specifically, a multiquadric radial basis function approximation scheme is developed, together with a robust training method, to model not only the costly objective function, but also each expensive simulation-based constraint defined in the problem. The article presents the methodology developed for expensive nonlinear constrained optimization problems comprising both continuous and integer variables. Results from various test cases, both analytical and simulation-based, are presented.
Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.
Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.
Baliban, Richard C; Dimaggio, Peter A; Plazas-Mayorca, Mariana D; Garcia, Benjamin A; Floudas, Christodoulos A
A novel protein identification framework, PILOT_PROTEIN, has been developed to construct a comprehensive list of all unmodified proteins that are present in a living sample. It uses the peptide identification results from the PILOT_SEQUEL algorithm to initially determine all unmodified proteins within the sample. Using a rigorous biclustering approach that groups incorrect peptide sequences with other homologous sequences, the number of false positives reported is minimized. A sequence tag procedure is then incorporated along with the untargeted PTM identification algorithm, PILOT_PTM, to determine a list of all modification types and sites for each protein. The unmodified protein identification algorithm, PILOT_PROTEIN, is compared to the methods SEQUEST, InsPecT, X!Tandem, VEMS, and ProteinProspector using both prepared protein samples and a more complex chromatin digest. The algorithm demonstrates superior protein identification accuracy with a lower false positive rate. All materials are freely available to the scientific community at http://pumpd.princeton.edu. PMID:22788846
Yao, Weigang; Liou, Meng-Sing
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Generalized linear models (GLMs), as defined by J. A. Nelder and R. W. M. Wedderburn (1972), unify a class of regression models for categorical, discrete, and continuous response variables. As an extension of classical linear models, GLMs provide a common body of theory and methodology for some seemingly unrelated models and procedures, such as…
Baghaei, Purya; Kubinger, Klaus D.
The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…
By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty examples from the literature. |
Hussain, Mushtaq Taleb; Ramli, Razamin; Khalid, Ruzelan
The decrement of input proportions in DEA model is associated with its input reduction. This reduction is apparently good for economy since it could reduce unnecessary cost resources. However, in some situations the reduction of relevant inputs such as labour could create social problems. Such inputs should thus be maintained or increased. This paper develops an advanced radial DEA model dealing with mixed integer linear programming to improve integer output values through the combination of inputs. The model can deal with real input values and integer output values. This model is valuable for situations dealing with input combination to improve integer output values as faced by most organizations.
Serroyen, Jan; Molenberghs, Geert; Verbeke, Geert; Davidian, Marie
While marginal models, random-effects models, and conditional models are routinely considered to be the three main modeling families for continuous and discrete repeated measures with linear and generalized linear mean structures, respectively, it is less common to consider non-linear models, let alone frame them within the above taxonomy. In the latter situation, indeed, when considered at all, the focus is often exclusively on random-effects models. In this paper, we consider all three families, exemplify their great flexibility and relative ease of use, and apply them to a simple but illustrative set of data on tree circumference growth of orange trees. PMID:20160890
Liu, Guodong; Starke, Michael R; Zhang, Xiaohu; Tomsovic, Kevin
This paper proposes a distribution optimal power flow (D-OPF) model for the operation of microgrids. The proposed model minimizes not only the operating cost, including fuel cost, purchasing cost and demand charge, but also several performance indices, including voltage deviation, network power loss and power factor. It co-optimizes the real and reactive power form distributed generators (DGs) and batteries considering their capacity and power factor limits. The D-OPF is formulated as a mixed-integer linear programming (MILP). Numerical simulation results show the effectiveness of the proposed model.
Viterna, L. A.; Ferencz, D.
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ
This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.
Lu, Wenbin; Zhang, Hao Helen
We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernel-weighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unified manner. We show that with a proper choice of the kernel bandwidth parameter, one can obtain the consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established as well. We further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness. To facilitate the implementation of the new procedure, an iterative algorithm is developed. Numerical examples are given to illustrate the finite-sample performance of the procedure. PMID:20802823
Lu, Wenbin; Zhang, Hao Helen
We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernel-weighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unified manner. We show that with a proper choice of the kernel bandwidth parameter, one can obtain the consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established as well. We further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness. To facilitate the implementation of the new procedure, an iterative algorithm is developed. Numerical examples are given to illustrate the finite-sample performance of the procedure. PMID:20802823
Li,Y.; Krinsky, S.; Rehak, M.
In this paper, we discuss an algorithm for constructing a numerical linear optics model for dipole magnets from a 3D field map. The difference between the numerical model and K. Brown's analytic approach is investigated and clarified. It was found that the optics distortion due to the dipoles' fringe focusing must be properly taken into account to accurately determine the chromaticities. In NSLS-II, there are normal dipoles with 35-mm gap and dipoles for infrared sources with 90-mm gap. This linear model of the dipole magnets is applied to the NSLS-II lattice design to match optics parameters between the DBA cells having dipoles with different gaps.
Brennan, Robert L.
In 1955, R. Levine introduced two linear equating procedures for the common-item non-equivalent populations design. His procedures make the same assumptions about true scores; they differ in terms of the nature of the equating function used. In this paper, two parameterizations of a classical congeneric model are introduced to model the variables…
Ker, H. W.
Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…
Kallosh, Renata; Karlsson, Anna; Mosk, Benjamin; Murli, Divyanshu
We derive supersymmetry/supergravity models with constrained orthogonal nilpotent superfields from the linear models in the formal limit where the masses of the sgoldstino, inflatino and sinflaton tend to infinity. The case where the sinflaton mass remains finite leads to a model with a `relaxed' constraint, where the sinflaton remains an independent field. Our procedure is equivalent to a requirement that some of the components of the curvature of the moduli space tend to infinity.
Warne, Russell T.; Li, Yan; McKyer, E. Lisako J.; Condie, Rachel; Diep, Cassandra S.; Murano, Peter S.
Researchers in nutrition research often use cluster or multistage sampling to gather participants for their studies. These sampling methods often produce violations of the assumption of data independence that most traditional statistics share. Hierarchical linear modeling is a statistical method that can overcome violations of the independence…
Arendacká, Barbora; Täubner, Angelika; Eichstädt, Sascha; Bruns, Thomas; Elster, Clemens
In Annex H.5, the Guide to the Evaluation of Uncertainty in Measurement (GUM)  recognizes the necessity to analyze certain types of experiments by applying random effects ANOVA models. These belong to the more general family of linear mixed models that we focus on in the current paper. Extending the short introduction provided by the GUM, our aim is to show that the more general, linear mixed models cover a wider range of situations occurring in practice and can be beneficial when employed in data analysis of long-term repeated experiments. Namely, we point out their potential as an aid in establishing an uncertainty budget and as means for gaining more insight into the measurement process. We also comment on computational issues and to make the explanations less abstract, we illustrate all the concepts with the help of a measurement campaign conducted in order to challenge the uncertainty budget in calibration of accelerometers.
Ferencz, Donald C.; Viterna, Larry A.
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Barajas-Solano, D. A.; Wohlberg, B.; Vesselinov, V. V.; Tartakovsky, D. M.
We present a novel parameter estimation methodology for transient models of geophysical systems with uncertain, spatially distributed, heterogeneous and piece-wise continuous parameters.The methodology employs a bayesian approach to propose an inverse modeling problem for the spatial configuration of the model parameters.The likelihood of the configuration is formulated using sparse measurements of both model parameters and transient states.We propose using total variation regularization (TV) as the prior reflecting the heterogeneous, piece-wise continuity assumption on the parameter distribution.The maximum a posteriori (MAP) estimator of the parameter configuration is then computed by minimizing the negative bayesian log-posterior using a linearized functional minimization approach. The computation of the MAP estimator is a large-dimensional nonlinear minimization problem with two sources of nonlinearity: (1) the TV operator, and (2) the nonlinear relation between states and parameters provided by the model's governing equations.We propose a a hybrid linearized functional minimization (LFM) algorithm in two stages to efficiently treat both sources of nonlinearity.The relation between states and parameters is linearized, resulting in a linear minimization sub-problem equipped with the TV operator; this sub-problem is then minimized using the Alternating Direction Method of Multipliers (ADMM). The methodology is illustrated with a transient saturated groundwater flow application in a synthetic domain, stimulated by external point-wise loadings representing aquifer pumping, together with an array of discrete measurements of hydraulic conductivity and transient measurements of hydraulic head.We show that our inversion strategy is able to recover the overall large-scale features of the parameter configuration, and that the reconstruction is improved by the addition of transient information of the state variable.
Duke, Eugene L.; Patterson, Brian P.; Antoniewicz, Robert F.
This report documents a FORTRAN program that provides a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.
Yousefi, Ali; Dibazar, Alireza A; Berger, Theodore W
In this research, temporal processing in brain neural circuitries is addressed by a dynamic model of synaptic connections in which the synapse model accounts for both pre- and post-synaptic processes determining its temporal dynamics and strength. Neurons, which are excited by the post-synaptic potentials of hundred of the synapses, build the computational engine capable of processing dynamic neural stimuli. Temporal dynamics in neural models with dynamic synapses will be analyzed, and learning algorithms for synaptic adaptation of neural networks with hundreds of synaptic connections are proposed. The paper starts by introducing a linear approximate model for the temporal dynamics of synaptic transmission. The proposed linear model substantially simplifies the analysis and training of spiking neural networks. Furthermore, it is capable of replicating the synaptic response of the non-linear facilitation-depression model with an accuracy better than 92.5%. In the second part of the paper, a supervised spike-in-spike-out learning rule for synaptic adaptation in dynamic synapse neural networks (DSNN) is proposed. The proposed learning rule is a biologically plausible process, and it is capable of simultaneously adjusting both pre- and post-synaptic components of individual synapses. The last section of the paper starts with presenting the rigorous analysis of the learning algorithm in a system identification task with hundreds of synaptic connections which confirms the learning algorithm's accuracy, repeatability and scalability. The DSNN is utilized to predict the spiking activity of cortical neurons and pattern recognition tasks. The DSNN model is demonstrated to be a generative model capable of producing different cortical neuron spiking patterns and CA1 Pyramidal neurons recordings. A single-layer DSNN classifier on a benchmark pattern recognition task outperforms a 2-Layer Neural Network and GMM classifiers while having fewer numbers of free parameters and
Roth, K.; Jury, W. A.
A unified linear theory for the transport of adsorbing solutes through soils is presented and applied to analyze movement of napropamide through undisturbed soil columns. The transport characteristics of the soil are expressed in terms of the travel time distribution of the mobile phase which is then used to incorporate local interaction processes. This approach permits the analysis of all linear transport processes, not only the small subset for which a differential description is known. From a practical point of view, it allows the direct use of measured concentrations or fluxes of conservative solutes to characterize the mobile phase without first subjecting them to any model. For complicated flow regimes, this may vastly improve the identification of models and estimation of their parameters for the local adsorption processes.
Elliott, S J; Ghandchi Tehrani, M; Langley, R S
The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a 'quasi-linear' model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the nth power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system's response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea. PMID:26303921
Belcastro, Celeste (Technical Monitor); Hogge, Edward F.
The Linear Autoland Simulink model was created to be a modular test environment for testing of control system components in commercial aircraft. The input variables, physical laws, and referenced frames used are summarized. The state space theory underlying the model is surveyed and the location of the control actuators described. The equations used to realize the Dryden gust model to simulate winds and gusts are derived. A description of the pseudo-random number generation method used in the wind gust model is included. The longitudinal autopilot, lateral autopilot, automatic throttle autopilot, engine model and automatic trim devices are considered as subsystems. The experience in converting the Airlabs FORTRAN aircraft control system simulation to a graphical simulation tool (Matlab/Simulink) is described.
Inamdar, A. R.; Lele, S. K.; Jacobson, M. Z.
It is widely acknowledged that the large uncertainties in predictions of climate impact of linear contrails stem from inadequate parametrization of contrails in GCMs. But, the parameter space on which contrail dynamics and optical properties depend is very large and spanning it using high fidelity LES is prohibitively expensive. This study leverages the large dataset of LES done so far to understand the most important physical process that governs the evolution of contrails in different stages of its life and proposes a simple, low-cost and robust ODE model to capture the evolution of quantities of interest such as ice mass, vortex downwash and contrail cross-sectional dimensions. A direct consequence of modeling the contrail using parameters impacting the most important physical process is the reduction of the original parameter space to only those groupings of parameters that impact linear contrails independently. We are able to capture the most prominent features of the contrail at every stage of the life of the contrail - the induction of the jet exhaust by the trailing vortex pair, the vortex downwash and eventual destruction and the subsequent spreading of the contrail by ambient turbulence. A simplified version of GATOR-GCMOM - a GCM - is initialized using inputs from the new ODE model to test if the inclusion of the impact of the aforementioned parameter groups has significant persistent effects. Results from the GATOR-GCMOM box model calculations show which parameter groupings show persistent effects.
Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.
An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.
Bart, J.; Collins, B.; Morrison, R.I.G.
We describe a simple and robust method for estimating trends in population size. The method may be used with Breeding Bird Survey data, aerial surveys, point counts, or any other program of repeated surveys at permanent locations. Surveys need not be made at each location during each survey period. The method differs from most existing methods in being design based, rather than model based. The only assumptions are that the nominal sampling plan is followed and that sample size is large enough for use of the t-distribution. Simulations based on two bird data sets from natural populations showed that the point estimate produced by the linear model was essentially unbiased even when counts varied substantially and 25% of the complete data set was missing. The estimating-equation approach, often used to analyze Breeding Bird Survey data, performed similarly on one data set but had substantial bias on the second data set, in which counts were highly variable. The advantages of the linear model are its simplicity, flexibility, and that it is self-weighting. A user-friendly computer program to carry out the calculations is available from the senior author.
Eight subjects time-shared performance of two compensatory tracking tasks under conditions when both were of constant difficulty, and when the control order of one task (designated primary) was varied over time within a trial. On line performance feedback was presented on half of the trials. The data are interpreted in terms of a linear model of the operator's attention allocation system, and suggest that this allocation is strongly suboptimal. Furthermore, the limitations in reallocating attentional resources between tasks, in response to difficulty fluctuations were not reduced by augmented performance feedback. Some characteristics of the allocation system are described, and reasons for its limitations suggested.
We introduce and discuss kinetic models for wealth distribution which include both taxation and uniform redistribution. The evolution of the continuous density of wealth obeys a linear Boltzmann equation where the background density represents the action of an external subject on the taxation mechanism. The case in which the mean wealth is conserved is analyzed in full details, by recovering the analytical form of the steady states. These states are probability distributions of convergent random series of a special structure, called perpetuities. Among others, Gibbs distribution appears as steady state in case of total taxation and uniform redistribution.
Vitello, P; Souers, P C
For non-ideal explosives a wide range of behavior is observed in experiments dealing with differing sizes and geometries. A predictive detonation model must be able to reproduce many phenomena including such effects as: variations in the detonation velocity with the radial diameter of rate sticks; slowing of the detonation velocity around gentle corners; production of dead zones for abrupt corner turning; failure of small diameter rate sticks; and failure for rate sticks with sufficiently wide cracks. Most models have been developed to explain one effect at a time. Often, changes are made in the input parameters used to fit each succeeding case with the implication that this is sufficient for the model to be valid over differing regimes. We feel that it is important to develop a model that is able to fit experiments with one set of parameters. To address this we are creating a new generation of models that are able to produce better fitting to individual data sets than prior models and to simultaneous fit distinctly different regimes of experiments. Presented here are details of our new Piece Wise Linear reactive flow model applied to LX-17.
Ryoo, Ji Hoon
Model building or model selection with linear mixed models (LMMs) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are codependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multilevel or…
Miyamoto, U; Yahikozawa, S
The idea that a space-time metric emerges as a Fisher-Rao "information metric" of instanton moduli space has been examined in several field theories, such as the Yang-Mills theories and nonlinear σ models. In this paper, we report that the flat Euclidean or Minkowskian metric, rather than an anti-de Sitter metric that generically emerges from instanton moduli spaces, can be obtained as the Fisher-Rao metric from a nontrivial solution of the massive Klein-Gordon field (a linear σ model). This realization of the flat space from the simple field theory would be useful to investigate the ideas that relate the space-time geometry with the information geometry. PMID:23004729
This report considers the use of linear models for analyzing data related to reliability and safety issues of the type usually associated with nuclear power plants. The report discusses some of the general results of linear regression analysis, such as the model assumptions and properties of the estimators of the parameters. The results are motivated with examples of operational data. Results about the important case of a linear regression model with one covariate are covered in detail. This case includes analysis of time trends. The analysis is applied with two different sets of time trend data. Diagnostic procedures and tests for the adequacy of the model are discussed. Some related methods such as weighted regression and nonlinear models are also considered. A discussion of the general linear model is also included. Appendix A gives some basic SAS programs and outputs for some of the analyses discussed in the body of the report. Appendix B is a review of some of the matrix theoretic results which are useful in the development of linear models.
Kim, W.; Kurdila, A. J.; Stepanyan, V.; Inman, D. J.; Vignola, J.
In this paper, we consider a linear piezoelectric structure which employs a fast-switched, capacitively shunted subsystem to yield a tunable vibration absorber or energy harvester. The dynamics of the system is modeled as a hybrid system, where the switching law is considered as a control input and the ambient vibration is regarded as an external disturbance. It is shown that under mild assumptions of existence and uniqueness of the solution of this hybrid system, averaging theory can be applied, provided that the original system dynamics is periodic. The resulting averaged system is controlled by the duty cycle of a driven pulse-width modulated signal. The response of the averaged system approximates the performance of the original fast-switched linear piezoelectric system. It is analytically shown that the averaging approximation can be used to predict the electromechanically coupled system modal response as a function of the duty cycle of the input switching signal. This prediction is experimentally validated for the system consisting of a piezoelectric bimorph connected to an electromagnetic exciter. Experimental results show that the analytical predictions are observed in practice over a fixed "effective range" of switching frequencies. The same experiments show that the response of the switched system is insensitive to an increase in switching frequency above the effective frequency range.
Bostan, Mohamad; Hadi Afshar, Mohamad; Khadem, Majed
This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for
Korovinskiy, D. B.; Ivanov, I. B.; Semenov, V. S.; Erkaev, N. V.; Kiehas, S. A.
Kink-like magnetotail flapping oscillations in a Harris-like current sheet with earthward growing normal magnetic field component Bz are studied by means of time-dependent 2D linearized MHD numerical simulations. The dispersion relation and two-dimensional eigenfunctions are obtained. The results are compared with analytical estimates of the double-gradient model, which are found to be reliable for configurations with small Bz up to values ˜ 0.05 of the lobe magnetic field. Coupled with previous results, present simulations confirm that the earthward/tailward growth direction of the Bz component acts as a switch between stable/unstable regimes of the flapping mode, while the mode dispersion curve is the same in both cases. It is confirmed that flapping oscillations may be triggered by a simple Gaussian initial perturbation of the Vz velocity.
Glas, Cees A. W.; Hendrawan, Irene
Methods for testing hypotheses concerning the regression parameters in linear models for the latent person parameters in item response models are presented. Three tests are outlined: A likelihood ratio test, a Lagrange multiplier test and a Wald test. The tests are derived in a marginal maximum likelihood framework. They are explicitly formulated…
Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.
This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
Alippi, A.; Bettucci, A.; Biagioni, A.; Conclusio, D.; D'Orazio, A.; Germano, M.; Passeri, D.
Tensegrity models for the cytoskeleton structure of living cells is largely used nowadays for interpreting the biochemical response of living tissues to mechanical stresses. Microtubules, microfilaments and filaments are the microscopic cell counterparts of struts (microtubules) and cables (microfilaments and filaments) in the macroscopic world: the formers oppose to compression, the latters to tension, thus yielding an overall structure, light and highly deformable. Specific cell surface receptors, such as integrins, act as the coupling elements that transmit the outside mechanical stress state into the cell body. Reversible finite deformations of tensegrity structures have been widely demonstrated experimentally and in a number of living cell simulations. In the present paper, the bistability behaviour of two general models, the linear bar oscillator and the icosahedron, is studied, as they are both obtained from mathematical simulation, the former, and from larger scale experiments, the latter. The discontinuity in the frequency response of the oscillation amplitude and the lateral bending of the resonance curves are put in evidence, as it grows larger as the driving amplitude increases, respectively.
Wohlberg, Brendt; Tartakovsky, Daniel M.; Dentz, Marco
Heterogeneous aquifers typically consist of multiple lithofacies, whose spatial arrangement significantly affects flow and transport. The estimation of these lithofacies is complicated by the scarcity of data and by the lack of a clear correlation between identifiable geologic indicators and attributes. We introduce a new inverse-modeling approach to estimate both the spatial extent of hydrofacies and their properties from sparse measurements of hydraulic conductivity and hydraulic head. Our approach is to minimize a functional defined on the vectors of values of hydraulic conductivity and hydraulic head fields defined on regular grids at a user-determined resolution. This functional is constructed to (i) enforce the relationship between conductivity and heads provided by the groundwater flow equation, (ii) penalize deviations of the reconstructed fields from measurements where they are available, and (iii) penalize reconstructed fields that are not piece-wise smooth. We develop an iterative solver for this functional that exploits a local linearization of the mapping from conductivity to head. This approach provides a computationally efficient algorithm that rapidly converges to a solution. A series of numerical experiments demonstrates the robustness of our approach.
Guo, P; Huang, G H
In this study, a solid waste decision-support system was developed for the long-term planning of waste management in the City of Regina, Canada. Interactions among various system components, objectives, and constraints will be analyzed. Issues concerning planning for cost-effective diversion and prolongation of the landfill will be addressed. Decisions of system-capacity expansion and waste allocation within a multi-facility, multi-option, and multi-period context will be obtained. The obtained results would provide useful information and decision-support for the City's solid waste management and planning. In the application, four scenarios are considered. Through the above scenario analyses under different waste-management policies, useful decision support for the City's solid waste managers and decision makers was generated. Analyses for the effects of varied policies (for allowable waste flows to different facilities) under 35 and 50% diversion goals were also undertaken. Tradeoffs among system cost and constraint-violation risk were analyzed. Generally, a policy with lower allowable waste-flow levels corresponded to a lower system cost under advantageous conditions but, at the same time, a higher penalty when such allowances were violated. A policy with higher allowable flow levels corresponded to a higher cost under disadvantageous conditions. The modeling results were useful for (i) scheduling adequate time and capacity for long-term planning of the facility development and/or expansion in the city's waste management system, (ii) adjusting of the existing waste flow allocation patterns to satisfy the city's diversion goal, and (iii) generating of desired policies for managing the city's waste generation, collection and disposal. PMID:19818549
Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad
In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models. PMID:26837750
Holdaway, Dan; Kim, Jong G.; Errico, Ron; Gelaro, Ronald; Mahajan, Rahul
Global Modeling and Assimilation Office (GMAO) is close to having a working 4DVAR system and has developed a linearized version of GEOS-5.This talk outlines a series of improvements made to the linearized dynamics, physics and trajectory.Of particular interest is the development of linearized cloud microphysics, which provides the framework for 'all-sky' data assimilation.
Rakheja, S; Gurram, R; Gouw, G J
Hand-arm vibration (HAV) models serve as an effective tool to assess the vibration characteristics of the hand-tool system and to evaluate the attenuation performance of vibration isolation mechanisms. This paper describes a methodology to identify the parameters of HAV models, whether linear or nonlinear, using mechanical impedance data and a nonlinear programming based optimization technique. Three- and four-degrees-of-freedom (DOF) linear, piecewise linear and nonlinear HAV models are formulated and analyzed to yield impedance characteristics in the 5-1000 Hz frequency range. A local equivalent linearization algorithm, based upon the principle of energy similarity, is implemented to simulate the nonlinear HAV models. Optimization methods are employed to identify the model parameters, such that the magnitude and phase errors between the computed and measured impedance characteristics are minimum in the entire frequency range. The effectiveness of the proposed method is demonstrated through derivations of models that correlate with the measured X-axis impedance characteristics of the hand-arm system, proposed by ISO. The results of the study show that a linear model cannot predict the impedance characteristics in the entire frequency range, while a piecewise linear model yields an accurate estimation. PMID:8253830
Brosius, Hans-Bernd; Kepplinger, Hans Mathias
A content analysis of major German television news shows and 53 weekly surveys on 16 issues were used to compare linear and nonlinear models as ways to describe the relationship between media coverage and the public agenda. Results indicate that nonlinear models are in some cases superior to linear models in terms of explained variance. (34…
In eighth grade, students usually learn about forces in science class and linear relationships in math class, crucial topics that form the foundation for further study in science and engineering. An activity that links these two fundamental concepts involves measuring the distance a spring stretches as a function of how much weight is suspended…
Herman, James D.
Linear regression examines the relationship between one or more independent (predictor) variables and a dependent variable. By using a particular formula, regression determines the weights needed to minimize the error term for a given set of predictors. With one predictor variable, the relationship between the predictor and the dependent variable…
Jensen, Patrick T.; Curtiss, H. C., Jr.; Mckillip, Robert M., Jr.
An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.
Regan, Timothy F.; Lewandowski, Edward J.
The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.
Levison, W. H.; Junker, A. M.; Kenner, K.
A study is being conducted to explore use of the steady state visual-evoke electrocortical response as an indicator of cognitive task loading. Application of linear descriptive modeling to steady state Visual Evoked Response (VER) data is summarized. Two aspects of linear modeling are reviewed: (1) unwrapping the phase-shift portion of the frequency response, and (2) parsimonious characterization of task-loading effects in terms of changes in model parameters. Model-based phase unwrapping appears to be most reliable in applications, such as manual control, where theoretical models are available. Linear descriptive modeling of the VER has not yet been shown to provide consistent and readily interpretable results.
Moraga, RocíO.; GarcíA-GonzáLez, Javier; Parrilla, Ernesto; Nogales, Sergio
In a competitive environment, operation and planning decisions of generating units are decentralized. Therefore the management of hydroelectric generation resources requires the development of advanced planning and scheduling tools adapted to the particular needs of each company. This paper presents a method for considering natural water transfers through a pipeline in the context of a midterm hydro scheduling model. The main complexity of gravitational transfer modeling resides in considering the nonlinear relation between the water levels in the connected reservoirs and the transfer flow. The methodology proposed consists first in simplifying the problem by means of a change of variables, subsequently using a piecewise linear approximation of the transfer flow equation in order to consider it within a mixed integer linear programming tool, and ultimately adjusting the final solution. The proposed methodology is currently being used to manage the Sil River hydro basin in the northwest of Spain, with satisfactory results, as shown in the case study.
Stoll, Brady; Brinkman, Gregory; Townsend, Aaron; Bloom, Aaron
Renewable energy integration studies have been published for many different regions exploring the question of how higher penetration of renewable energy will impact the electric grid. These studies each make assumptions about the systems they are analyzing; however the effect of many of these assumptions has not been yet been examined and published. In this paper we analyze the impact of modeling assumptions in renewable integration studies, including the optimization method used (linear or mixed-integer programming) and the temporal resolution of the dispatch stage (hourly or sub-hourly). We analyze each of these assumptions on a large and a small system and determine the impact of each assumption on key metrics including the total production cost, curtailment of renewables, CO2 emissions, and generator starts and ramps. Additionally, we identified the impact on these metrics if a four-hour ahead commitment step is included before the dispatch step and the impact of retiring generators to reduce the degree to which the system is overbuilt. We find that the largest effect of these assumptions is at the unit level on starts and ramps, particularly for the temporal resolution, and saw a smaller impact at the aggregate level on system costs and emissions. For each fossil fuel generator type we measured the average capacity started, average run-time per start, and average number of ramps. Linear programming results saw up to a 20% difference in number of starts and average run time of traditional generators, and up to a 4% difference in the number of ramps, when compared to mixed-integer programming. Utilizing hourly dispatch instead of sub-hourly dispatch saw no difference in coal or gas CC units for either start metric, while gas CT units had a 5% increase in the number of starts and 2% increase in the average on-time per start. The number of ramps decreased up to 44%. The smallest effect seen was on the CO2 emissions and total production cost, with a 0.8% and 0
We analyze the two-dimensional supersymmetric linear σ-model with U(1) gauge symmetries that includes a Calabi-Yau phase and a possible Landau-Ginzburg phase. We demonstrate the topology changing transitions among the generic vacua of various linear σ-models. In the supersymmetric transition the determinantal contraction naturally arises.
Tongue, B. H.
The linearized equations of motion of a helicopter in contact with the ground have solutions which can be linearly stable or unstable, depending on the system parameters. The present study includes physical non-linearities in the helicopter model. This allows one to determine if a steady-state response exists and, if so, what the frequency and amplitude of the oscillations will be. In this way, one can determine how serious the linearly unstable operating regime is and whether destructive oscillations are possible when the system is in the linearly stable regime. The present analysis applies to helicopters having fully articulated rotors.
Lushnikov, A. A.; Kagan, A. I.
The Malthus process of population growth is reformulated in terms of the probability w(n,t) to find exactly n individuals at time t assuming that both the birth and the death rates are linear functions of the population size. The master equation for w(n,t) is solved exactly. It is shown that w(n,t) strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of w(n,t).
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Merfeld, D M; Zupan, L; Peterka, R J
Because sensory systems often provide ambiguous information, neural processes must exist to resolve these ambiguities. It is likely that similar neural processes are used by different sensory systems. For example, many tasks require neural processing to distinguish linear acceleration from gravity, but Einstein's equivalence principle states that all linear accelerometers must measure both linear acceleration and gravity. Here we investigate whether the brain uses internal models, defined as neural systems that mimic physical principles, to help estimate linear acceleration and gravity. Internal models may be used in motor contro, sensorimotor integration and sensory processing, but direct experimental evidence for such models is limited. To determine how humans process ambiguous gravity and linear acceleration cues, subjects were tilted after being rotated at a constant velocity about an Earth-vertical axis. We show that the eye movements evoked by this post-rotational tilt include a response component that compensates for the estimated linear acceleration even when no actual linear acceleration occurs. These measured responses are consistent with our internal model predictions that the nervous system can develop a non-zero estimate of linear acceleration even when no true linear acceleration is present. PMID:10217143
Bennett, Ted D.; Yu, Fengling
A linear radiation model is developed that overcomes the analytical complexity in phase of thermal emission spectroscopy. It is shown that the linear radiation model can result in a simple algebraic relation between the phase of thermal emission and four coating properties, enabling these properties to be determined by nonlinear regression analysis of experimental measurements. Suitability of the linear radiation model to various measurement conditions is explored, and the model is applied to the phase of thermal emission measurements performed on a thermal barrier coating.
Roweis, S; Ghahramani, Z
Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models. PMID:9950734
Archer, W.E.; Deveney, M.F.; Nagel, R.L.
Transformers models for simulation with Pspice and Analogy`s Saber are being developed using experimental B-H Loop and network analyzer measurements. The models are evaluated for accuracy and convergence using several test circuits. Results are presented which demonstrate the effects on circuit performance from magnetic core losses eddy currents and mechanical stress on the magnetic cores.
Mirzaesmaeeli, H; Elkamel, A; Douglas, P L; Croiset, E; Gupta, M
A novel deterministic multi-period mixed-integer linear programming (MILP) model for the power generation planning of electric systems is described and evaluated in this paper. The model is developed with the objective of determining the optimal mix of energy supply sources and pollutant mitigation options that meet a specified electricity demand and CO(2) emission targets at minimum cost. Several time-dependent parameters are included in the model formulation; they include forecasted energy demand, fuel price variability, construction lead time, conservation initiatives, and increase in fixed operational and maintenance costs over time. The developed model is applied to two case studies. The objective of the case studies is to examine the economical, structural, and environmental effects that would result if the electricity sector was required to reduce its CO(2) emissions to a specified limit. PMID:20149519
Sheppard, J.C.; Helm, R.H.; Lee, M.J.; Woodley, M.D.
Models for computer control of the SLAC three-kilometer linear accelerator and damping rings have been developed as part of the control system for the Stanford Linear Collider. Some of these models have been tested experimentally and implemented in the control program for routine linac operations. This paper will describe the development and implementation of these models, as well as some of the operational results.
Abrahart, R. J.; See, L. M.
Two recent studies have suggested that neural network modelling offers no worthwhile improvements in comparison to the application of weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. The potential of an artificial neural network to perform simple non-linear hydrological transformations under controlled conditions is examined in this paper. Eight neural network models were developed: four full or partial emulations of a recognised non-linear hydrological rainfall-runoff model; four solutions developed on an identical set of inputs and a calculated runoff coefficient output. The use of different input combinations enabled the competencies of solutions developed on a reduced number of parameters to be assessed. The selected hydrological model had a limited number of inputs and contained no temporal component. The modelling process was based on a set of random inputs that had a uniform distribution and spanned a modest range of possibilities. The initial cloning operations permitted a direct comparison to be performed with the equation-based relationship. It also provided more general information about the power of a neural network to replicate mathematical equations and model modest non-linear relationships. The second group of experiments explored a different relationship that is of hydrological interest; the target surface contained a stronger set of non-linear properties and was more challenging. Linear modelling comparisons were performed against traditional least squares multiple linear regression solutions developed on identical datasets. The reported results demonstrate that neural networks are capable of modelling non-linear hydrological processes and are therefore appropriate tools for hydrological modelling.
Filisetti, A.; Serra, R.; Carletti, T.; Villani, M.; Poli, I.
We consider generic protocells models allowing linear and non-linear kinetics for the main involved chemical reactions. We are interested in understanding if and how the protocell division and the metabolism do synchronise to give rise to sustainable evolution of the protocell.
Groves, Kevin S.; Vance, Charles M.
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.
A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.
Kim, Kion; Şentürk, Damla; Li, Runze
We consider the recent history functional linear models, relating a longitudinal response to a longitudinal predictor where the predictor process only in a sliding window into the recent past has an effect on the response value at the current time. We propose an estimation procedure for recent history functional linear models that is geared towards sparse longitudinal data, where the observation times across subjects are irregular and total number of measurements per subject is small. The proposed estimation procedure builds upon recent developments in literature for estimation of functional linear models with sparse data and utilizes connections between the recent history functional linear models and varying coefficient models. We establish uniform consistency of the proposed estimators, propose prediction of the response trajectories and derive their asymptotic distribution leading to asymptotic point-wise confidence bands. We include a real data application and simulation studies to demonstrate the efficacy of the proposed methodology. PMID:21691421
Bechtel, Gordon G.
It is the purpose of this paper to suggest the orthogonal analysis of variance as a device for simplifying either the analytic or iterative problem of finding LS (least squares) estimates for the parameters of particular nonlinear models. (Author/RK)
Suontama, M; van der Werf, J H J; Juga, J; Ojala, M
Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success
Barajas-Solano, D. A.; Wohlberg, B. E.; Vesselinov, V. V.; Tartakovsky, D. M.
We present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Aspnes, D. E.
Bond models, also known as polarizable-point or mechanical models, have a long history in optics, starting with the Clausius-Mossotti relation but more accurately originating with Ewald's largely forgotten work in 1912. These models describe macroscopic phenomena such as dielectric functions and nonlinear-optical (NLO) susceptibilities in terms of the physics that takes place in real space, in real time, on the atomic scale. Their strengths lie in the insights that they provide and the questions that they raise, aspects that are often obscured by quantum-mechanical treatments. Statics versions were used extensively in the late 1960's and early 1970's to correlate NLO susceptibilities among bulk materials. Interest in NLO applications revived with the 2002 work of Powell et al., who showed that a fully anisotropic version reduced by more than a factor of 2 the relatively large number of parameters necessary to describe secondharmonic- generation (SHG) data for Si(111)/SiO2 interfaces. Attention now is focused on the exact physical meaning of these parameters, and to the extent that they represent actual physical quantities.
Hall, Ryan; Desai, Priyanka; Kang, Beomgoo; Katzarova, Maria; Huang, Qifan; Lee, Sanghoon; Chang, Taihyun; Venerus, David; Mays, Jimmy; Schieber, Jay; Larson, Ronald
We compare predictions of two of the most advanced versions of the tube model, namely the Hierarchical model by Wang et al. (J. Rheol. 54:223, 2010) and the BOB (branch-on-branch) model by Das et al. (J. Rheol. 50:207-234, 2006), against linear viscoelastic data on blends of monodisperse star and monodisperse linear polybutadiene polymers. The star was carefully synthesized/characterized by temperature gradient interaction chromatography, and rheological data in the high frequency region were obtained through time-temperature superposition. We found massive failures of both the Hierarchical and BOB models to predict the terminal relaxation behavior of the star/linear blends, despite their success in predicting the rheology of the pure star and pure linear. This failure occurred regardless of the choices made concerning constraint release, such as assuming arm retraction in fat or skinny tubes, or allowing for disentanglement relaxation to cut off the constraint release Rouse process at long times. The failures call into question whether constraint release can be described as a combination of constraint release Rouse processes and dynamic tube dilation within a canonical tube model of entanglement interactions.
Lansing, F. L.
An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.
Carfora, M.; Marzuoli, A.
We review our recent work describing, in terms of the Wasserstein geometry over the space of probability measures, the embedding of the Ricci flow in the renormalization group flow for dilatonic non-linear sigma models.
Sherman, Rivi; Pnueli, Amir
This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms.
Sun, Xiaoqiang; Cai, Yingfeng; Wang, Shaohua; Liu, Yanling; Chen, Long
The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical (MLD) modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller (HMPC) is tuned based on online mixed-integer quadratic optimization (MIQP). Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology (MPT), thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.
Esteley, Cristina; Villarreal, Monica; Alagia, Humberto
This research report presents a study of the work of agronomy majors in which an extension of linear models to non-linear contexts can be observed. By linear models we mean the model y=a.x+b, some particular representations of direct proportionality and the diagram for the rule of three. Its presence and persistence in different types of problems…
Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.
Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651
Narvand, A.; Soleimani, P.; Raissi, Sadigh
In many circumstances, the quality of a process or product is best characterized by a given mathematical function between a response variable and one or more explanatory variables that is typically referred to as profile. There are some investigations to monitor auto-correlated linear and nonlinear profiles in recent years. In the present paper, we use the linear mixed models to account autocorrelation within observations which is gathered on phase II of the monitoring process. We undertake that the structure of correlated linear profiles simultaneously has both random and fixed effects. The work enhanced a Hotelling's T 2 statistic, a multivariate exponential weighted moving average (MEWMA), and a multivariate cumulative sum (MCUSUM) control charts to monitor process. We also compared their performances, in terms of average run length criterion, and designated that the proposed control charts schemes could effectively act in detecting shifts in process parameters. Finally, the results are applied on a real case study in an agricultural field.
Daniele, C. J.; Krosel, S. M.
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
Waaben, S.; Federico, J.; Moskowitz, I.
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
Hartley, D.S. III.
This paper is the fourth in a series of reports on the breakthrough research in historical validation of attrition in conflict. Significant defense policy decisions, including weapons acquisition and arms reduction, are based in part on models of conflict. Most of these models are driven by their attrition algorithms, usually forms of the Lanchester square and linear laws. None of these algorithms have been validated. The results of this paper confirm the results of earlier papers, using a large database of historical results. The homogeneous linear-logarithmic Lanchestrian attrition model is validated to the extent possible with current initial and final force size data and is consistent with the Iwo Jima data. A particular differential linear-logarithmic model is described that fits the data very well. A version of Helmbold's victory predicting parameter is also confirmed, with an associated probability function. 37 refs., 73 figs., 68 tabs.
Taleghani, Barmac K.; Campbell, Joel F.
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Dao, Thanh-Son; McPhee, John
An electrochemical cell is a multidisciplinary system which involves complex chemical, electrical, and thermodynamical processes. The primary objective of this paper is to develop a linear graph-theoretical modeling for the dynamic description of electrochemical systems through the representation of the system topologies. After a brief introduction to the topic and a review of linear graphs, an approach to develop linear graphs for electrochemical systems using a circuitry representation is discussed, followed in turn by the use of the branch and chord transformation techniques to generate final dynamic equations governing the system. As an example, the application of linear graph theory to modeling a nickel metal hydride (NiMH) battery will be presented. Results show that not only the number of equations are reduced significantly, but also the linear graph model simulates faster compared to the original lumped parameter model. The approach presented in this paper can be extended to modeling complex systems such as an electric or hybrid electric vehicle where a battery pack is interconnected with other components in many different domains.
One of the most commonly used models for describing phosphorus (P) sorption to soils is the nonlinear Langmuir model. To avoid the difficulties in fitting the nonlinear Langmuir equation to sorption data, linearized versions are commonly used. Although concerns have been raised in the past regarding...
Martinez-Luaces, Victor E.
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Casasent, D.; Ghosh, A.
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of ...
Md. S. Roni; Sandra D. Eksioglu; Erin Searcy; Krishna Jha
We propose a framework for designing the supply chain network for biomass co-firing in coal-fired power plants. This framework is inspired by existing practices with products with similar physical characteristics to biomass. We present a hub-and-spoke supply chain network design model for long-haul delivery of biomass. This model is a mixed integer linear program solved using benders decomposition algorithm. Numerical analysis indicates that 100 million tons of biomass are located within 75 miles from a coal plant and could be delivered at $8.53/dry-ton; 60 million tons of biomass are located beyond 75 miles and could be delivered at $36/dry-ton.
Kushairi, S.; Omar, A. R.; Schmidt, R.; Isa, A. A. Mat; Hudha, K.; Azizan, M. A.
A quarter of an active trailer suspension system having the characteristics of a double wishbone type was modeled as a complex multi-body dynamic system in MSC.ADAMS. Due to the complexity of the model, a linearized version is considered in this paper. A model reduction technique is applied to the linear model, resulting in a reduced-order model. Based on this simplified model, a Proportional-Integral-Derivative (PID) controller was designed in MATLAB/Simulink environment; primarily to reduce excessive roll motions and thus improving the ride comfort. Simulation results show that the output signal closely imitates the input signal in multiple cases - demonstrating the effectiveness of the controller.
Fan, Ruzong; Wang, Yifan; Mills, James L; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao
Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study. PMID:24130119
Hartley, D.S. III.
This paper is the fourth in a series of reports on the breakthrough research in historical validation of attrition in conflict. Significant defense policy decisions, including weapons acquisition and arms reduction, are based in part on models of conflict. Most of these models are driven by their attrition algorithms, usually forms of the Lanchester square and linear laws. None of these algorithms have been validated. The results of this paper confirm the results of earlier papers, using a large database of historical results. The homogeneous linear-logarithmic Lanchestrian attrition model is validated to the extent possible with current initial and final force size data and is consistent with the Iwo Jima data. A particular differential linear-logarithmic model is described that fits the data very well. A version of Helmbold's victory predicting parameter is also confirmed, with an associated probability function. The implications of these findings are potentially far-reaching. Two-sided daily attrition data on a large number of battles is needed to absolutely confirm these results. Such a confirmation will require that numerous computer conflict models containing square and linear law based attrition algorithms be reexamined. It is conceivable that complex mixed, heterogeneous, square plus linear law algorithms may produce the same results as a homogeneous mixed linear-logarithmic law algorithm; however, such an occurrence is by no means assured. Even without such absolute confirmation, the results of this research allow the analysis of combat data for the effects of training, weather, leadership, and other human factors, unencumbered by the force size effects.
Weissbrod, Omer; Geiger, Dan; Rosset, Saharon
Linear mixed models (LMMs) and their extensions have recently become the method of choice in phenotype prediction for complex traits. However, LMM use to date has typically been limited by assuming simple genetic architectures. Here, we present multikernel linear mixed model (MKLMM), a predictive modeling framework that extends the standard LMM using multiple-kernel machine learning approaches. MKLMM can model genetic interactions and is particularly suitable for modeling complex local interactions between nearby variants. We additionally present MKLMM-Adapt, which automatically infers interaction types across multiple genomic regions. In an analysis of eight case-control data sets from the Wellcome Trust Case Control Consortium and more than a hundred mouse phenotypes, MKLMM-Adapt consistently outperforms competing methods in phenotype prediction. MKLMM is as computationally efficient as standard LMMs and does not require storage of genotypes, thus achieving state-of-the-art predictive power without compromising computational feasibility or genomic privacy. PMID:27302636
Reed, D. A.; Patrick, M. L.
A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.
Zhu, W. D.; Ren, H.
Based on a recent asymptotic analysis of a nonlinear model of a slack cable, a computationally efficient, linear model is developed for calculating the natural frequencies, mode shapes, and dynamic responses of stationary elevator traveling and compensation cables. The linear cable model consists of two vertical cable segments connected by a half-circular lower loop. The two vertical cable segments are modeled as a string with a variable tension due to the weight of the cable. The horizontal displacements of the cable segments consist of boundary-induced displacements and relative elastic displacements, where the boundary-induced displacements are interpolated from the displacements of the two lower ends of the cable segments, and the relative elastic displacements satisfy the corresponding homogeneous boundary conditions of the cable segments. The horizontal displacement of the lower loop is interpolated from those of the two lower ends of the two cable segments, and the bending stiffness of the lower loop is modeled by a spring with a constant stiffness, which can be calculated from the nonlinear model. Given a car position, the natural frequencies and mode shapes of an elevator traveling or compensation cable are calculated using the linear model and compared with those from the nonlinear model. The calculated natural frequencies are also compared with those from a full-scale experiment. In addition, the dynamic responses of a cable under a boundary excitation are calculated and compared with those from the nonlinear model. There is a good agreement between the predictions from the linear and nonlinear models and between the measured natural frequencies from the full-scale experiment and the corresponding calculated ones.
Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex
Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.
Ikegami, Takashi; Iwafune, Yumiko; Ogimoto, Kazuhiko
The high penetration of variable renewable generation such as Photovoltaic (PV) systems will cause the issue of supply-demand imbalance in a whole power system. The activation of the residential power usage, storage and generation by sophisticated scheduling and control using the Home Energy Management System (HEMS) will be needed to balance power supply and demand in the near future. In order to evaluate the applicability of the HEMS as a distributed controller for local and system-wide supply-demand balances, we developed an optimum operation scheduling model of domestic electric appliances using the mixed integer linear programming. Applying this model to several houses with dynamic electricity prices reflecting the power balance of the total power system, it was found that the adequate changes in electricity prices bring about the shift of residential power usages to control the amount of the reverse power flow due to excess PV generation.
Acidified vegetable products with a pH above 3.3 must be pasteurized to assure the destruction of acid resistant pathogenic bacteria. The times and temperatures needed to assure a five log reduction by pasteurization have previously been determined using a non-linear (Weibull) model. Recently, the F...
Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich
A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process' amount of dynamic behavior.
Stapleton, Laura M.; Lissitz, Robert W.
This paper presents results from a comparison of the multiple regression (MR) approach to examining faculty salary equity (with clusters for the various disciplines) and hierarchical linear modeling (HLM) for the same problem. The comparison was done in two steps. First, a practical example of applying both techniques, using empirical data, is…
Wagler, Amy E.
Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…
Young, John W.
A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure,…
The following paper is presented in viewgraph format and covers topics including: (1) linear state feedback control system; (2) Kalman filter state estimation; (3) relation between residual and stochastic part of output; (4) obtaining Kalman filter gain; (5) state estimation under unknown system model and unknown noises; and (6) relationship between filter Markov parameters and system Markov parameters.
Dell'Oro, Filippo; Giorgi, Claudio; Pata, Vittorino
We consider the coupled linear system describing the vibrations of a string-beam system related to the well-known Lazer-McKenna suspension bridge model. For ɛ > 0 and k > 0, the decay properties of the solution semigroup are discussed in dependence of the nonnegative parameters γ and h, which are responsible for the damping effects.
Bizdadea, Constantin; Cioroianu, Eugen M.; Danehkar, Ashbiz; Iordache, Marius; Saliu, Solange O.; Sararu, Silviu C.
The case of couplings in D = 5 between a simple, maximal BF model and the dual formulation of linearized gravity is considered. All the possible interactions are exhausted by means of computing the 'free' local BRST cohomology in ghost number zero.
Sandblom, J; Ring, A; Eisenman, G
By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425
We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...
Fujikawa, Kazuo; Oh, C. H.; Zhang, Chengjie
We re-examine d = 4 hidden-variables model for a system of two spin-1/2 particles in view of the concrete model of Hardy, who analyzed the criterion of entanglement without referring to inequality. The basis of our analysis is the linearity of the probability measure related to the Born probability interpretation, which excludes noncontextual hidden-variables model in d≥3. To be specific, we note the inconsistency of the noncontextual hidden-variables model in d = 4 with the linearity of the quantum mechanical probability measure in the sense <ψ|aṡσ ⊗b ṡσ|ψ>+ <ψ|a ṡσ ⊗b‧ ṡσ|ψ> = <ψ|aṡσ⊗(b + b‧)ṡσ|ψ> for noncollinear b and b‧. It is then shown that Hardy's model in d = 4 does not lead to a unique mathematical expression in the demonstration of the discrepancy of local realism (hidden-variables model) with entanglement and thus his proof is incomplete. We identify the origin of this nonuniqueness with the nonuniqueness of translating quantum mechanical expressions into expressions in hidden-variables model, which results from the failure of the above linearity of the probability measure. In contrast, if the linearity of the probability measure is strictly imposed, which tantamounts to asking that the noncontextual hidden-variables model in d = 4 gives the Clauser-Horne-Shimony-Holt (CHSH) inequality ||≤2 uniquely, it is shown that the hidden-variables model can describe only separable quantum mechanical states; this conclusion is in perfect agreement with the so-called Gisin's theorem which states that ||≤2 implies separable states.
Meshkat, Nicolette; Sullivant, Seth; Eisenberg, Marisa
Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology. PMID:26337290
Schultz, J.F.; Hemez, F.M.
This research presents a new method to improve analytical model fidelity for non-linear systems. The approach investigates several mechanisms to assist the analyst in updating an analytical model based on experimental data and statistical analysis of parameter effects. The first is a new approach at data reduction called feature extraction. This is an expansion of the update metrics to include specific phenomena or character of the response that is critical to model application. This is an extension of the classical linear updating paradigm of utilizing the eigen-parameters or FRFs to include such devices as peak acceleration, time of arrival or standard deviation of model error. The next expansion of the updating process is the inclusion of statistical based parameter analysis to quantify the effects of uncertain or significant effect parameters in the construction of a meta-model. This provides indicators of the statistical variation associated with parameters as well as confidence intervals on the coefficients of the resulting meta-model, Also included in this method is the investigation of linear parameter effect screening using a partial factorial variable array for simulation. This is intended to aid the analyst in eliminating from the investigation the parameters that do not have a significant variation effect on the feature metric, Finally an investigation of the model to replicate the measured response variation is examined.
Hu, Y.; Yurkovich, S.
The advent of hybrid and plug-in hybrid electric vehicles has created a demand for more precise battery pack management systems (BMS). Among methods used to design various components of a BMS, such as state-of-charge (SoC) estimators, model based approaches offer a good balance between accuracy, calibration effort and implementability. Because models used for these approaches are typically low in order and complexity, the traditional approach is to identify linear (or slightly nonlinear) models that are scheduled based on operating conditions. These models, formally known as linear parameter varying (LPV) models, tend to be difficult to identify because they contain a large amount of coefficients that require calibration. Consequently, the model identification process can be very laborious and time-intensive. This paper describes a comprehensive identification algorithm that uses linear-algebra-based subspace methods to identify a parameter varying state variable model that can describe the input-to-output dynamics of a battery under various operating conditions. Compared with previous methods, this approach is much faster and provides the user with information on the order of the system without placing an a priori structure on the system matrices. The entire process and various nuances are demonstrated using data collected from a lithium ion battery, and the focus is on applications for energy storage in automotive applications.
Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.
Olcer, Fahri Ersel
Recent developments on individual blade control (IBC) and physics based reduced order models of various on-blade control (OBC) actuation concepts are opening up opportunities to explore innovative rotor control strategies for improved rotor aerodynamic performance, reduced vibration and BVI noise, and improved rotor stability, etc. Further, recent developments in computationally efficient algorithms for the extraction of Linear Time Invariant (LTI) models are providing a convenient framework for exploring integrated flight and rotor control, while accounting for the important couplings that exist between body and low frequency rotor response and high frequency rotor response. Formulation of linear time invariant (LTI) models of a nonlinear system about a periodic equilibrium using the harmonic domain representation of LTI model states has been studied in the literature. This thesis presents an alternative method and a computationally efficient scheme for implementation of the developed method for extraction of linear time invariant (LTI) models from a helicopter nonlinear model in forward flight. The fidelity of the extracted LTI models is evaluated using response comparisons between the extracted LTI models and the nonlinear model in both time and frequency domains. Moreover, the fidelity of stability properties is studied through the eigenvalue and eigenvector comparisons between LTI and LTP models by making use of the Floquet Transition Matrix. For time domain evaluations, individual blade control (IBC) and On-Blade Control (OBC) inputs that have been tried in the literature for vibration and noise control studies are used. For frequency domain evaluations, frequency sweep inputs are used to obtain frequency responses of fixed system hub loads to a single blade IBC input. The evaluation results demonstrate the fidelity of the extracted LTI models, and thus, establish the validity of the LTI model extraction process for use in integrated flight and rotor control
Palya, William L; Walter, Donald; Kessel, Robert; Lucke, Robert
The observed steady-state behavioral dynamics supported by unsignaled periods of reinforcement within repeating 2,000-s trials were modeled with a linear transfer function. These experiments employed improved schedule forms and analytical methods to improve the precision of the measured transfer function, compared to previous work. The refinements include both the use of multiple reinforcement periods that improve spectral coverage and averaging of independently determined transfer functions. A linear analysis was then used to predict behavior observed for three different test schedules. The fidelity of these predictions was determined. PMID:11831782
Henneberg, S. A.; Cowley, S. C.; Wilson, H. R.
The explosive, filamentary plasma eruptions described by the non-linear ideal MHD ballooning model is tested quantitatively against experimental observations of ELMs in MAST. The equations describing this model were derived by Wilson and Cowley for tokamak-like geometry which includes two differential equations: the linear ballooning equation which describes the spatial distribution along the field lines and the non-linear ballooning mode envelope equation, which is a two-dimensional, non-linear differential equation which can involve fractional temporal-derivatives, but is often second-order in time and space. To employ the second differential equation for a specific geometry one has to evaluate the coefficients of the equation which is non-trivial as it involves field line averaging of slowly converging functions. We have solved this system for MAST, superimposing the solutions of both differential equations and mapping them onto a MAST plasma. Comparisons with the evolution of ELM filaments in MAST will be reported in order to test the model. The support of the EPSRC for the FCDT (Grant EP/K504178/1), of Euratom research and training programme 2014-2018 (No 633053) and of the RCUK Energy Programme [grant number EP/I501045] is gratefully acknowledged.
Johnston, A.H.; Plaag, R.E.
Mechanisms for total dose degradation of linear circuits are discussed, including bulk effects, oxide charge buildup and recombination at the Si-SiO/sub 2/ interface. The dependence of damage on bias, dose, particle type and energy is used in conjunction with two-dimensional modeling to identify the failure mechanism in a specific linear device type. The importance of surface recombination is demonstrated along with the absence of bias dependence. Bulk damage is shown to be important for high energy electron irradiation because of wide-base pnp transistors. This causes substantial differences in device failure between electron and cobalt-60 environments that need to be taken into account for test standards and data bases that include commercial bipolar integrated circuits. Valid test methodologies for linear device must consider the energy and particle type present in the actual environment.
Rodricks, Neena; Kirkland, Laurel E.
Hyperspectral spectroscopy can be used remotely to measure emitted radiation from minerals and rocks at a series of narrow and continuous wavelength bands resulting in a continuous spectrum for each pixel, thereby providing ample spectral information to identify and distinguish spectrally unique materials. Linear mixture modeling ("spectral unmixing"), a commonly used method, is based on the theory that the radiance in the thermal infrared region (8-12 μm) from a multi-mineral surface can be modeled as a linear combination of the endmembers. A linear mixture model can thus potentially model the minerals present on planetary surfaces. It works by scaling the endmember spectra so that the sum of the scaled endmember spectra matches the measured spectrum with the smallest "error" (difference). But one of the drawbacks of this established method is that mathematically, a fit with an inverted spectrum is valid, which effectively returns a negative abundance of a material. Current models usually address the problem by elimination of endmembers that have negative scale factors. Eliminating the negative abundance problem is not a major issue when the endmembers are known. However, identifying unknown target composition (like on Mars) can be a problem. The goal of this study is to improve the understanding and find a subsequent solution of the negative abundance problem for Mars analog field data obtained from airborne and ground spectrometers. We are using a well-defined library of spectra to test the accuracy of hyperspectral analysis for the identification of minerals on planetary surfaces.
Aspinwall, Paul S.; Plesser, M. Ronen
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
Background Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure. Results We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided. Conclusion The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward. PMID:19788745
Lombriser, Lucas; Taylor, Andy
We study the model space generated by the time-dependent operator coefficients in the effective field theory of the cosmological background evolution and perturbations of modified gravity and dark energy models. We identify three classes of modified gravity models that reduce to Newtonian gravity on the small scales of linear theory. These general classes contain enough freedom to simultaneously admit a matching of the concordance model background expansion history. In particular, there exists a large model space that mimics the concordance model on all linear quasistatic subhorizon scales as well as in the background evolution. Such models also exist when restricting the theory space to operators introduced in Horndeski scalar-tensor gravity. We emphasize that whereas the partially shielded scenarios might be of interest to study in connection with tensions between large and small scale data, with conventional cosmological probes, the ability to distinguish the fully shielded scenarios from the concordance model on near-horizon scales will remain limited by cosmic variance. Novel tests of the large-scale structure remedying this deficiency and accounting for the full covariant nature of the alternative gravitational theories, however, might yield further insights on gravity in this regime. PMID:25658988
Costa, Jorge C.; Tiago, Carlos M.; Pimenta, Paulo M.
This work develops a kinematically linear shell model departing from a consistent nonlinear theory. The initial geometry is mapped from a flat reference configuration by a stress-free finite deformation, after which, the actual shell motion takes place. The model maintains the features of a complete stress-resultant theory with Reissner-Mindlin kinematics based on an inextensible director. A hybrid displacement variational formulation is presented, where the domain displacements and kinematic boundary reactions are independently approximated. The resort to a flat reference configuration allows the discretization using 2-D Multiple Fixed Least-Squares (MFLS) on the domain. The consistent definition of stress resultants and consequent plane stress assumption led to a neat formulation for the analysis of shells. The consistent linear approximation, combined with MFLS, made possible efficient computations with a desired continuity degree, leading to smooth results for the displacement, strain and stress fields, as shown by several numerical examples.
Ponzi, A.; Yasutomi, A.; Kaneko, K.
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Pegram, Geoff; Sinclair, Scott
A pilot study using real time rainfall data as input to a parsimonious linear distributed flood forecasting model is presented. The aim of the study is to deliver an operational system capable of producing flood forecasts, in real time, for the Mgeni and Mlazi catchments near the city of Durban in South Africa. The forecasts can be made at time steps which are of the order of a fraction of the catchment response time. To this end, the model is formulated in Finite Difference form in an equation similar to an Auto Regressive Moving Average (ARMA) model; it is this formulation which provides the required computational efficiency. The ARMA equation is a discretely coincident form of the State-Space equations that govern the response of an arrangement of linear reservoirs. This results in a functional relationship between the reservoir response con- stants and the ARMA coefficients, which guarantees stationarity of the ARMA model. Input to the model is a combined "Best Estimate" spatial rainfall field, derived from a combination of weather RADAR and Satellite rainfield estimates with point rain- fall given by a network of telemetering raingauges. Several strategies are employed to overcome the uncertainties associated with forecasting. Principle among these are the use of optimal (double Kalman) filtering techniques to update the model states and parameters in response to current streamflow observations and the application of short term forecasting techniques to provide future estimates of the rainfield as input to the model.
Gorelick, Steven M.; Gustafson, Sven-Ake
Mathematical models for the problem of maintaining a specified groundwater quality while permitting solute waste disposal at various facilities distributed over space are discussed. The pollutants are assumed to be chemically inert and their concentrations in the groundwater are governed by linear equations for advection and diffusion. The aim is to determine a disposal policy which maximises the total amount of pollutants released during a fixed time T while meeting the condition that the concentration everywhere is below prescribed levels.
Gordon, Sheldon P.
This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…
Erdemir, Ovgucan Karadag; Sucu, Meral
In this paper generalized linear model (GLM) and credibility theory which are frequently used in nonlife insurance pricing are combined for reliability analysis. Using full credibility standard, GLM is associated with limited fluctuation credibility approach. Comparison criteria such as asymptotic variance and credibility probability are used to analyze the credibility of risk classes. An application is performed by using one-year claim frequency data of a Turkish insurance company and results of credible risk classes are interpreted.
Steen, David; Stadler, Michael; Cardoso, Gonçalo; Groissböck, Markus; DeForest, Nicholas; Marnay, Chris
Thermal energy storage (TES) and distributed generation technologies, such as combined heat and power (CHP) or photovoltaics (PV), can be used to reduce energy costs and decrease CO2 emissions from buildings by shifting energy consumption to times with less emissions and/or lower energy prices. To determine the feasibility of investing in TES in combination with other distributed energy resources (DER), mixed integer linear programming (MILP) can be used. Such a MILP model is the well-established Distributed Energy Resources Customer Adoption Model (DER-CAM); however, it currently uses only a simplified TES model to guarantee linearity and short run-times. Loss calculations are based only on the energy contained in the storage. This paper presents a new DER-CAM TES model that allows improved tracking of losses based on ambient and storage temperatures, and compares results with the previous version. A multi-layer TES model is introduced that retains linearity and avoids creating an endogenous optimization problem. The improved model increases the accuracy of the estimated storage losses and enables use of heat pumps for low temperature storage charging. Ultimately,results indicate that the previous model overestimates the attractiveness of TES investments for cases without possibility to invest in heat pumps and underestimates it for some locations when heat pumps are allowed. Despite a variation in optimal technology selection between the two models, the objective function value stays quite stable, illustrating the complexity of optimal DER sizing problems in buildings and microgrids.
Brookes, Matthew J; Gibson, Andrew M; Hall, Stephen D; Furlong, Paul L; Barnes, Gareth R; Hillebrand, Arjan; Singh, Krish D; Holliday, Ian E; Francis, Sue T; Morris, Peter G
A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields). PMID:15528094
Esteley, Cristina B.; Villarreal, Monica E.; Alagia, Humberto R.
Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…
Sahin, Rubina; Tapadia, Kavita
The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG < 0) and endothermic (ΔH > 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area. PMID:26676015
Huber, Christian; Shafei, Babak; Parmigiani, Andrea
Pore-scale processes exert a strong control on the transport of reactants in porous media at the continuum scale. As such, pore-scale numerical models can offer a more quantitative understanding of the coupling between transport and reaction and yield parameterized constitutive equations to introduce pore-scale corrections into macroscopic (continuum) reactive transport models. In the present study, we present a new pore-scale model for the advection and diffusion of reactants in porous media with complex topologies. The model is based on the lattice Boltzmann method and couples a fluid flow solver to an optimal advection-diffusion transport model. Internal solid-fluid boundaries (grain boundaries) are explicitly part of the numerical domain, which allows the algorithm to solve for surface reactions independently from the surface shape and orientation of the grains. Thus, the approach is well suited for the treatment of heterogeneous reactions in complex pore structures. We present single and multispecies reactive transport applications of the model. In the first application we study the permeability change of a porous medium associated with a given porosity change during dissolution and precipitation using linear reaction kinetics. We show that, for a given porous medium, the correlation between porosity and permeability changes depends on the transport regime (the ratio of advective to diffusive transport) and the reaction rate. Finally, we carry out simulations of multispecies reactive transport, focusing on the case of calcium carbonate dissolution/precipitation. Our results highlight the difference between pH dependent and independent reaction rates for heterogeneous reactions in complex geometries at the pore scale.
Kulczycki, Eric A.; Johnson, Joseph R.; Bayard, David S.; Elfes, Alberto; Quadrelli, Marco B.
In order to explore Titan, a moon of Saturn, airships must be able to traverse the atmosphere autonomously. To achieve this, an accurate model and accurate control of the vehicle must be developed so that it is understood how the airship will react to specific sets of control inputs. This paper explains how longitudinal aircraft stability derivatives can be used with airship parameters to create a linear model of the airship solely by combining geometric and aerodynamic airship data. This method does not require system identification of the vehicle. All of the required data can be derived from computational fluid dynamics and wind tunnel testing. This alternate method of developing dynamic airship models will reduce time and cost. Results are compared to other stable airship dynamic models to validate the methods. Future work will address a lateral airship model using the same methods.
Tang, Yuanyuan; Sinha, Debajyoti; Pati, Debdeep; Lipsitz, Stuart; Lipshultz, Steven
Unlike majority of current statistical models and methods focusing on mean response for highly skewed longitudinal data, we present a novel model for such data accommodating a partially linear median regression function, a skewed error distribution and within subject association structures. We provide theoretical justifications for our methods including asymptotic properties of the posterior and associated semiparametric Bayesian estimators. We also provide simulation studies to investigate the finite sample properties of our methods. Several advantages of our method compared with existing methods are demonstrated via analysis of a cardiotoxicity study of children of HIV-infected mothers. PMID:25792623
Kowalczyk, Piotr; Glendinning, Paul; Brown, Martin; Medrano-Cerda, Gustavo; Dallali, Houman; Shapiro, Jonathan
We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then investigate. Stable periodic motions (limit cycles) about an upright position are found. The existence of these limit cycles is studied as a function of system parameters. The exploration of the parameter space leads to the detection of multi-stability and homoclinic bifurcations. PMID:21697168
Dehghani, Mehdi; Mardaani, Maryam; Monemzadeh, Majid; Nejad, Salman Abarghouei
Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyperplane and hypersphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one directly. In contrast, the first class system related to the free particle on the hypersphere is derived with the help of the infinite Batalin-Fradkin-Tyutin (BFT) embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hypersphere is a nontrivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At the end, we find an open algebra for three first class objects of the embedded nonlinear system.
Gupta, Vikrant; Juniper, Matthew
In this paper, we consider the growth of large scale coherent structures in turbulent flows by performing linear stability analysis around a mean flow. Turbulent flows are characterized by fine-scale stochastic perturbations. The momentum transfer caused by these perturbations affects the development of larger structures. Therefore, in a linear stability analysis, it is important to include the perturbations' influence. One way to do this is to include a turbulence model in the stability analysis. This is done in the literature by using eddy viscosity models (EVMs), which are first order turbulence models. We extend this approach by using second order turbulence models, in this case explicit algebraic Reynolds stress models (EARSMs). EARSMs are more versatile than EVMs, in that they can be applied to a wider range of flows, and could also be more accurate. We verify our EARSM-based analysis by applying it to a channel flow and then comparing the results with those from an EVM-based analysis. We then apply the EARSM-based stability analysis to swirling pipe flows and Taylor-Couette flows, which demonstrates the main benefit of EARSM-based analysis. This project is supported by EPSRC and Rolls-Royce through a Dorothy Hodgkin Research Fellowship.
Jurling, Alden S.; Content, David A.
In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.
A model-based approach that integrates known portion of the cardiovascular system and unknown portion through a parameter estimation to predict evolution of the mean arterial pressure is considered. The unknown portion corresponds to the neural portion that acts like a controller that takes corrective actions to regulate the arterial blood pressure at a constant level. The input to the neural part is the arterial pressure and output is the sympathetic nerve activity. In this model, heart rate is considered a proxy for sympathetic nerve activity. The neural portion is modeled as a linear discrete-time system with random coefficients. The performance of the model is tested on a case study of acute hypotensive episodes (AHEs) on PhysioNet data. TPRs and FPRs improve as more data becomes available during estimation period. PMID:22254409
Belgard, Maria R.; Min, Leo Yoon-Gee
An operations research method to optimize the teaching-learning process is introduced in this paper. In particular, a linear programing model is proposed which, unlike dynamic or control theory models, allows the computer to react to the responses of a learner in seconds or less. To satisfy the assumptions of linearity, the seemingly complicated…
Wagner, Helene H
The linear regression model, with its numerous extensions including multivariate ordination, is fundamental to quantitative research in many disciplines. However, spatial or temporal structure in the data may invalidate the regression assumption of independent residuals. Spatial structure at any spatial scale can be modeled flexibly based on a set of uncorrelated component patterns (e.g., Moran's eigenvector maps, MEM) that is derived from the spatial relationships between sampling locations as defined in a spatial weight matrix. Spatial filtering thus addresses spatial autocorrelation in the residuals by adding such component patterns (spatial eigenvectors) as predictors to the regression model. However, space is not an ecologically meaningful predictor, and commonly used tests for selecting significant component patterns do not take into account the specific nature of these variables. This paper proposes "spatial component regression" (SCR) as a new way of integrating the linear regression model with Moran's eigenvector maps. In its unconditioned form, SCR decomposes the relationship between response and predictors by component patterns, whereas conditioned SCR provides an alternative method of spatial filtering, taking into account the statistical properties of component patterns in the design of statistical hypothesis tests. Application to the well-known multivariate mite data set illustrates how SCR may be used to condition for significant residual spatial structure and to identify additional predictors associated with residual spatial structure. Finally, I argue that all variance is spatially structured, hence spatial independence is best characterized by a lack of excess variance at any spatial scale, i.e., spatial white noise. PMID:24400490
Mills, J E; Field, C A; Dupuis, D J
Longitudinal data modeling is complicated by the necessity to deal appropriately with the correlation between observations made on the same individual. Building on an earlier nonrobust version proposed by Heagerty (1999, Biometrics 55, 688-698), our robust marginally specified generalized linear mixed model (ROBMS-GLMM) provides an effective method for dealing with such data. This model is one of the first to allow both population-averaged and individual-specific inference. As well, it adopts the flexibility and interpretability of generalized linear mixed models for introducing dependence but builds a regression structure for the marginal mean, allowing valid application with time-dependent (exogenous) and time-independent covariates. These new estimators are obtained as solutions of a robustified likelihood equation involving Huber's least favorable distribution and a collection of weights. Huber's least favorable distribution produces estimates that are resistant to certain deviations from the random effects distributional assumptions. Innovative weighting strategies enable the ROBMS-GLMM to perform well when faced with outlying observations both in the response and covariates. We illustrate the methodology with an analysis of a prospective longitudinal study of laryngoscopic endotracheal intubation, a skill that numerous health-care professionals are expected to acquire. The principal goal of our research is to achieve robust inference in longitudinal analyses. PMID:12495126
Guven, Aytac; Kisi, Ozgur
This study compares the accuracy of linear genetic programming (LGP), fuzzy genetic (FG), adaptive neuro-fuzzy inference system (ANFIS), artificial neural networks (ANN) and Stephens-Stewart (SS) methods in modeling pan evaporations. Monthly climatic data including solar radiation, air temperature, relative humidity, wind speed and pan evaporation from Antalya and Mersin stations, in Turkey are used in the study. The study composed of two parts. First part of the study focuses the comparison of LGP models with those of the FG, ANFIS, ANN and SS models in estimating pan evaporations of Antalya and Mersin stations, separately. From the comparison results, the LGP models are found to be better than the other models. Comparison of LGP models with the other models in estimating pan evaporations of the Mersin Station by using both stations' inputs is focused in the second part of the study. The results indicate that the LGP models better accuracy than the FG, ANFIS, ANN and SS models. It is seen that the pan evaporations can be successfully estimated by the LGP method.
Cheong, Yuk Fai; Kamata, Akihito
In this article, we discuss and illustrate two centering and anchoring options available in differential item functioning (DIF) detection studies based on the hierarchical generalized linear and generalized linear mixed modeling frameworks. We compared and contrasted the assumptions of the two options, and examined the properties of their DIF…
The contribution deals with application of the hybrid RANS/LES model for calculation of flow around the circular cylinder. Used hybrid RANS/LES model is based on transport equation for the kinetic energy which is shared in both RANS and LES modes. The linear and the nonlinear closure formulas are described in the paper. Numerical results are compared with the experimental data. Results show that the nonlinear model predicts development of the wake behind the cylinder better than the linear model.
Tommasi, C.; May, C.
The DKL-optimality criterion has been recently proposed for the dual problem of model discrimination and parameter estimation, for the case of two rival models. A sequential version of the DKL-optimality criterion is herein proposed in order to discriminate and efficiently estimate more than two nested non-linear models. Our sequential method is inspired by the procedure of Biswas and Chaudhuri (2002), which is however useful only in the set up of nested linear models.
Yang, Runhua; Cohn, Stephen E.; da Silva, Arlindo; Joiner, Joanna; Houser, Paul R.
In this study, a tangent linear eigenanalysis is applied to the Mosaic land surface model (LSM) [, 1992] to examine the impacts of the model internal dynamics and physics on the land surface state variability. The tangent linear model (TLM) of the Mosaic LSM is derived numerically for two sets of basic states and two tile types of land condition, grass and bare soil. An additional TLM, for the soil moisture subsystem of this LSM, is derived analytically for the same cases to obtain explicit expressions for the eigenvalues. An eigenvalue of the TLM determines a characteristic timescale, and the corresponding eigenvector, or mode, describes a particular coupling among the perturbed states. The results show that (1) errors in initial conditions tend to decay with e-folding times given by the characteristic timescales; (2) the LSM exhibits a wide range of internal variability, modes mainly representing surface temperature and surface moisture perturbations exhibit short timescales, whereas modes mainly representing deep soil temperature perturbations and moisture transfer throughout the entire soil column exhibit much longer timescales; (3) the modes of soil moisture tend to be weakly coupled with other perturbed variables, and the mode representing the deep soil temperature perturbation has a consistent e-folding time across the experiments; (4) the key parameters include soil moisture, soil layer depth, and soil hydraulic parameters. The results agree qualitatively with previous findings. However, tangent linear eigenanalysis provides a new approach to the quantitative substantiation of those findings. Also, it reveals the evolution and the coupling of the perturbed land states that are useful for the development of land surface data assimilation schemes. One must be careful when generalizing the quantitative results since they are obtained with respect to two specific basic states and two simple land conditions. Also, the methodology employed here does not apply
Juang, Jer-Nan; Phan, Minh
This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.
Chechelnitsky, Michael Y.
Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large
Holben, Brent N.; Shimabukuro, Yosio E.
A linear mixing model was applied to coarse spatial resolution data from the NOAA Advanced Very High Resolution Radiometer. The reflective component of the 3.55 - 3.93 microns channel was extracted and used with the two reflective channels 0.58 - 0.68 microns and 0.725 - 1.1 microns to run a Constraine Least Squares model to generate vegetation, soil, and shade fraction images for an area in the Western region of Brazil. The Landsat Thematic Mapper data covering the Emas National park region was used for estimating the spectral response of the mixture components and for evaluating the mixing model results. The fraction images were compared with an unsupervised classification derived from Landsat TM data acquired on the same day. The relationship between the fraction images and normalized difference vegetation index images show the potential of the unmixing techniques when using coarse resolution data for global studies.
Thornquist, Heidi K.; Mei, Ting; Keiter, Eric Richard; Bond, Brad
Model order reduction (MOR) techniques have been used to facilitate the analysis of dynamical systems for many years. Although existing model reduction techniques are capable of providing huge speedups in the frequency domain analysis (i.e. AC response) of linear systems, such speedups are often not obtained when performing transient analysis on the systems, particularly when coupled with other circuit components. Reduced system size, which is the ostensible goal of MOR methods, is often insufficient to improve transient simulation speed on realistic circuit problems. It can be shown that making the correct reduced order model (ROM) implementation choices is crucial to the practical application of MOR methods. In this report we investigate methods for accelerating the simulation of circuits containing ROM blocks using the circuit simulator Xyce.
Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984
Harris, Kelley; Sheehan, Sara; Kamm, John A.; Song, Yun S.
In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population. PMID:25340178
Santini, Alberto; Alsing Friberg, Henrik; Ropke, Stefan
This article studies the quay crane scheduling problem with non-crossing constraints, which is an operational problem that arises in container terminals. An enhancement to a mixed integer programming model for the problem is proposed and a new class of valid inequalities is introduced. Computational results show the effectiveness of these enhancements in solving the problem to optimality.
Maran, P.; Sornakumar, T.; Sundararajan, T.
A heat and fluid flow model has been developed to solve the gas tungsten arc (GTA) linear welding problem for austenitic stainless steel. The moving heat source problem associated with the electrode traverse has been simplified into an equivalent two-dimensional (2-D) transient problem. The torch residence time has been calculated from the arc diameter and torch speed. The mathematical formulation considers buoyancy, electromagnetic induction, and surface tension forces. The governing equations have been solved by the finite volume method. The temperature and velocity fields have been determined. The theoretical predictions for weld bead geometry are in good agreement with experimental measurements.
Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro
We apply the Markov-random-field model to linear seismic tomography and propose a method to estimate the hyperparameters for the smoothness and the magnitude of the noise. Optimal hyperparameters can be determined analytically by minimizing the free energy function, which is defined by marginalizing the evaluation function. In synthetic inversion tests under various settings, the assumed velocity structures are successfully reconstructed, which shows the effectiveness and robustness of the proposed method. The proposed mathematical framework can be applied to inversion problems in various fields in the natural sciences. PMID:25375468
Dutta-Bergman, Mohan Jyoti
The recent growth of research in message tailoring has opened up new avenues for researchers to use personality variables for message delivery. This article builds on research on idiocentrism and self-monitoring to propose a framework for message appeal construction. Based on a scheme for appeal categorization borrowed from commercial marketing, the article suggests that low and high idiocentrics differ from each other in the way they respond to appeal types. Similarly, significant differences are demonstrated between low and high self-monitors in the realm of their response to message appeals. A linear interaction model is proposed to document the combined effects of self-monitoring and idiocentrism. PMID:12553779
Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen
To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities. PMID:22370050
Wittenburg, Dörte; Guiard, Volker; Liese, Friedrich; Reinsch, Norbert
Summary Quantitative trait loci (QTLs) may affect not only the mean of a trait but also its variability. A special aspect is the variability between multiple measured traits of genotyped animals, such as the within-litter variance of piglet birth weights. The sample variance of repeated measurements is assigned as an observation for every genotyped individual. It is shown that the conditional distribution of the non-normally distributed trait can be approximated by a gamma distribution. To detect QTL effects in the daughter design, a generalized linear model with the identity link function is applied. Suitable test statistics are constructed to test the null hypothesis H0: No QTL with effect on the within-litter variance is segregating versus HA: There is a QTL with effect on the variability of birth weight within litter. Furthermore, estimates of the QTL effect and the QTL position are introduced and discussed. The efficiency of the presented tests is compared with a test based on weighted regression. The error probability of the first type as well as the power of QTL detection are discussed and compared for the different tests. PMID:18208630
Laine, Marko; Kyrölä, Erkki
We describe a hierarchical statistical state space model for ozone profile time series. The time series are from satellite measurements by the SAGE II and GOMOS instruments spanning years 1984-2012. The original data sets are combined and gridded monthly using 10 degree latitude bands, and covering 20-60 km with 1 km vertical spacing. Model components include level, trend, seasonal effect with solar activity, and quasi biennial oscillations as proxy variables. A typical feature of an atmospheric time series is that they are not stationary but exhibit both slowly varying and abrupt changes in the distributional properties. These are caused by external forcing such as changes in the solar activity or volcanic eruptions. Further, the data sampling is often nonuniform, there are data gaps, and the uncertainty of the observations can vary. When observations are combined from various sources there will be instrument and retrieval method related biases. The differences in sampling lead also to uncertainties. Standard classical ARIMA type of statistical time series methods are mostly useless for atmospheric data. A more general approach makes use of dynamical linear models and Kalman filter type of sequential algorithms. These state space models assume a linear relationship between the unknown state of the system and the observations and for the process evolution of the hidden states. They are still flexible enough to model both smooth trends and sudden changes. The above mentioned methodological challenges are discussed, together with analysis of change points in trends related to recovery of stratospheric ozone. This work is part of the ESA SPIN and ozone CCI projects.
Yang, H. Q.; West, Jeff
Propellant tank slosh dynamics are typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control (GN&C) analysis. For a partially-filled smooth wall propellant tank, the critical damping based on classical empirical correlation is as low as 0.05%. Due to this low value of damping, propellant slosh is potential sources of disturbance critical to the stability of launch and space vehicles. It is postulated that the commonly quoted slosh damping is valid only under the linear regime where the slosh amplitude is small. With the increase of slosh amplitude, the critical damping value should also increase. If this nonlinearity can be verified and validated, the slosh stability margin can be significantly improved, and the level of conservatism maintained in the GN&C analysis can be lessened. The purpose of this study is to explore and to quantify the dependence of slosh damping with slosh amplitude. Accurately predicting the extremely low damping value of a smooth wall tank is very challenging for any Computational Fluid Dynamics (CFD) tool. One must resolve thin boundary layers near the wall and limit numerical damping to minimum. This computational study demonstrates that with proper grid resolution, CFD can indeed accurately predict the low damping physics from smooth walls under the linear regime. Comparisons of extracted damping values with experimental data for different tank sizes show very good agreements. Numerical simulations confirm that slosh damping is indeed a function of slosh amplitude. When slosh amplitude is low, the damping ratio is essentially constant, which is consistent with the empirical correlation. Once the amplitude reaches a critical value, the damping ratio becomes a linearly increasing function of the slosh amplitude. A follow-on experiment validated the developed nonlinear damping relationship. This discovery can
Knutti, Reto; Rugenstein, Maria A A
The term 'feedback' is used ubiquitously in climate research, but implies varied meanings in different contexts. From a specific process that locally affects a quantity, to a formal framework that attempts to determine a global response to a forcing, researchers use this term to separate, simplify and quantify parts of the complex Earth system. We combine new model results with a historical and educational perspective to organize existing ideas around feedbacks and linear models. Our results suggest that the state- and forcing-dependency of feedbacks are probably not appreciated enough, and not considered appropriately in many studies. A non-constant feedback parameter likely explains some of the differences in estimates of equilibrium climate sensitivity from different methods and types of data. Clarifying the value and applicability of the linear forcing feedback framework and a better quantification of feedbacks on various timescales and spatial scales remains a high priority in order to better understand past and predict future changes in the climate system. PMID:26438287
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
In this paper, we study the pointwise (in the space variable) behavior of the linearized Fokker-Planck-Boltzmann model for nonsmooth initial perturbations. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as the long-wave expansion in the spectrum of the Fourier modes for the space variable, and it has polynomial time decay rate. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. The Mixture Lemma plays an important role in constructing the kinetic-like waves, this lemma was originally introduced by Liu-Yu (Commun Pure Appl Math 57:1543-1608, 2004) for Boltzmann equation, but the Fokker-Planck term in this paper creates some technical difficulties.
Holben, Brent N.; Shimabukuro, Yosio E.
A linear mixing model typically applied to high resolution data such as Airborne Visible/Infrared Imaging Spectrometer, Thematic Mapper, and Multispectral Scanner System is applied to the NOAA Advanced Very High Resolution Radiometer coarse resolution satellite data. The reflective portion extracted from the middle IR channel 3 (3.55 - 3.93 microns) is used with channels 1 (0.58 - 0.68 microns) and 2 (0.725 - 1.1 microns) to run the Constrained Least Squares model to generate fraction images for an area in the west central region of Brazil. The derived fraction images are compared with an unsupervised classification and the fraction images derived from Landsat TM data acquired in the same day. In addition, the relationship betweeen these fraction images and the well known NDVI images are presented. The results show the great potential of the unmixing techniques for applying to coarse resolution data for global studies.
Wang, John T.
The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.
Sasso, M.; Palmieri, G.; Amodio, D.
Appropriate knowledge of viscoelastic properties of polymers and elastomers is of fundamental importance for a correct modelization and analysis of structures where such materials are present, especially when dealing with dynamic and vibration problems. In this paper experimental results of a series of compression and tension tests on specimens of styrene-butadiene rubber and polypropylene plastic are presented; tests consist of creep and relaxation tests, as well as cyclic loading at different frequencies. Experimental data are then used to calibrate some linear viscoelastic models; besides the classical approach based on a combination in series or parallel of standard mechanical elements as springs and dashpots, particular emphasis is given to the application of models whose constitutive equations are based on differential equations of fractional order (Fractional Derivative Model). The two approaches are compared analyzing their capability to reproduce all the experimental data for given materials; also, the main computational issues related with these models are addressed, and the advantage of using a limited number of parameters is demonstrated.
Chivukula, R. Sekhar; Simmons, Elizabeth H.; He, H.-J.; Kurachi, Masafumi; Tanabashi, Masaharu
We calculate the form of the corrections to the electroweak interactions in the class of Higgsless models which can be deconstructed to a chain of SU(2) gauge groups adjacent to a chain of U(1) gauge groups, and with the fermions coupled to any single SU(2) group and to any single U(1) group along the chain. The primary advantage of our technique is that the size of corrections to electroweak processes can be directly related to the spectrum of vector bosons ('KK modes'). In Higgsless models, this spectrum is constrained by unitarity. Our methods also allow for arbitrary background 5D geometry, spatially dependent gauge-couplings, and brane kinetic energy terms. We find that, due to the size of corrections to electroweak processes in any unitary theory, Higgsless models with localized fermions are disfavored by precision electroweak data. Although we stress our results as they apply to continuum Higgsless 5D models, they apply to any linear moose model including those with only a few extra vector bosons. Our calculations of electroweak corrections also apply directly to the electroweak gauge sector of 5D theories with a bulk scalar Higgs boson; the constraints arising from unitarity do not apply in this case.
Li, Yi; Dicker, Lee; Zhao, Sihai Dave
The Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. To our knowledge, most work involving the Dantzig selector has been performed with fully-observed response variables. This paper proposes a new class of adaptive Dantzig variable selectors for linear regression models when the response variable is subject to right censoring. This is motivated by a clinical study to identify genes predictive of event-free survival in newly diagnosed multiple myeloma patients. Under some mild conditions, we establish the theoretical properties of our procedures, including consistency in model selection (i.e. the right subset model will be identified with a probability tending to 1) and the optimal efficiency of estimation (i.e. the asymptotic distribution of the estimates is the same as that when the true subset model is known a priori). The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply our new methods to the aforementioned myeloma clinical trial and identify important predictive genes. PMID:24478569
Benhalla, Abdelhay; Houssou, Mohamed; Charif, Moussa
This paper deals with the linearization of the full activated sludge model No 1 (ASM1) in the scope of interaction analysis. For consistency, the linearization procedure is developed and validated within the BSM1 simulation benchmark framework. It is based on reaction rate approximation by linear combinations of states. The linear rate models are identified and incorporated in the mass balance equations, yielding a linear locally equivalent to the ASM1 model. Linear models for anoxic and aerated compartments are proposed. It is observed that the presented models track very closely the nonlinear ASM1 responses to various influent data. The key feature of this linearization strategy is that the gotten linear version of the ASM1 model is linear time invariant (LTI) and that it conserves the states biological interpretation and the original ASM1 dimension. It allows, therefore, application of interaction analysis methods and makes it possible to determine motivated control configurations for the ASM1 model. PMID:20131068
Halpin, Peter F.; Maraun, Michael D.
A method for selecting between K-dimensional linear factor models and (K + 1)-class latent profile models is proposed. In particular, it is shown that the conditional covariances of observed variables are constant under factor models but nonlinear functions of the conditioning variable under latent profile models. The performance of a convenient…
Rugenstein, M.; Knutti, R.
The term "feedback" is used ubiquitously in climate research, but implies varied meanings in different contexts. From a specific process that locally affects a quantity, to a formal framework that attempts to determine a global response to a forcing, researchers use this term to separate, simplify, and quantify parts of the complex Earth system. We combine large (>120 member) ensemble GCM and EMIC step forcing simulations over a broad range of forcing levels with a historical and educational perspective to organize existing ideas around feedbacks and linear forcing-feedback models. With a new method overcoming internal variability and initial condition problems we quantify the non-constancy of the climate feedback parameter. Our results suggest a strong state- and forcing-dependency of feedbacks, which is not considered appropriately in many studies. A non-constant feedback factor likely explains some of the differences in estimates of equilibrium climate sensitivity from different methods and types of data. We discuss implications for the definition of the forcing term and its various adjustments. Clarifying the value and applicability of the linear forcing feedback framework and a better quantification of feedbacks on various timescales and spatial scales remains a high priority in order to better understand past and predict future changes in the climate system.
Wiedermann, Wolfgang; von Eye, Alexander
Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed. PMID:26609741
Teitsworth, Stephen; Ghanta, Akhil; Neu, John
Understanding the spatio-temporal structure of most probable fluctuation pathways to rarely occurring states is a central problem in the study of noise-driven, non-equilibrium dynamical systems. When the underlying system does not possess detailed balance, the optimal fluctuation pathway to a particular state and relaxation pathway from that state may combine to form a loop-like structure in the system phase space which we call a fluctuation loop. Here, we study fluctuation loops in a linear circuit model consisting of coupled RC elements, where each element is driven by its own noise source and, generally, the effective noise strengths of different elements are not equal. Using a stochastic Hamiltonian approach, we determine the optimal fluctuation pathways, and construct corresponding fluctuation loops. Analytical results agree closely with suitably averaged simulation results based on the associated Langevin equation. To better characterize fluctuation loops, we study the time-dependent area tensor that is swept out by individual stochastic trajectories in the system phase space. At long times, the area tensor scales linearly with time, with a coefficient that precisely vanishes when the system satisfies detailed balance.
Asante, Kwabena O.; Arlan, Guleid A.; Pervez, Md Shahriar; Rowland, James
In many river basins around the world, inaccessibility of flow data is a major obstacle to water resource studies and operational monitoring. This paper describes a geospatial streamflow modeling system which is parameterized with global terrain, soils and land cover data and run operationally with satellite‐derived precipitation and evapotranspiration datasets. Simple linear methods transfer water through the subsurface, overland and river flow phases, and the resulting flows are expressed in terms of standard deviations from mean annual flow. In sample applications, the modeling system was used to simulate flow variations in the Congo, Niger, Nile, Zambezi, Orange and Lake Chad basins between 1998 and 2005, and the resulting flows were compared with mean monthly values from the open‐access Global River Discharge Database. While the uncalibrated model cannot predict the absolute magnitude of flow, it can quantify flow anomalies in terms of relative departures from mean flow. Most of the severe flood events identified in the flow anomalies were independently verified by the Dartmouth Flood Observatory (DFO) and the Emergency Disaster Database (EM‐DAT). Despite its limitations, the modeling system is valuable for rapid characterization of the relative magnitude of flood hazards and seasonal flow changes in data sparse settings.
Figura, Simon; Livingstone, David M; Kipfer, Rolf
Although temperature is an important determinant of many biogeochemical processes in groundwater, very few studies have attempted to forecast the response of groundwater temperature to future climate warming. Using a composite linear regression model based on the lagged relationship between historical groundwater and regional air temperature data, empirical forecasts were made of groundwater temperature in several aquifers in Switzerland up to the end of the current century. The model was fed with regional air temperature projections calculated for greenhouse-gas emissions scenarios A2, A1B, and RCP3PD. Model evaluation revealed that the approach taken is adequate only when the data used to calibrate the models are sufficiently long and contain sufficient variability. These conditions were satisfied for three aquifers, all fed by riverbank infiltration. The forecasts suggest that with respect to the reference period 1980 to 2009, groundwater temperature in these aquifers will most likely increase by 1.1 to 3.8 K by the end of the current century, depending on the greenhouse-gas emissions scenario employed. PMID:25412761
Silva, Eliana Costa e.; Correia, Aldina; Lopes, Isabel Cristina
The maximum likelihood method is usually chosen to estimate the regression parameters of Generalized Linear Models (GLM) and also for hypothesis testing and goodness of fit tests. The classical method for estimating GLM parameters is the Fisher scores. In this work we propose to compute the estimates of the parameters with two alternative methods: a derivative-based optimization method, namely the BFGS method which is one of the most popular of the quasi-Newton algorithms, and the PSwarm derivative-free optimization method that combines features of a pattern search optimization method with a global Particle Swarm scheme. As a case study we use a dataset of biological parameters (phytoplankton) and chemical and environmental parameters of the water column of a Portuguese reservoir. The results show that, for this dataset, BFGS and PSwarm methods provided a better fit, than Fisher scores method, and can be good alternatives for finding the estimates for the parameters of a GLM.
Liang, Min; Marcotte, Denis; Shamsipour, Pejman
A fast and efficient method to simulate multivariate fields with non-linear models of coregionalization (N-LMC) is described. The method generalizes FFTMA to the multivariate simulation of the N-LMC with symmetric cross-covariances, hence the name GFFTMA. It allows us for example to use an exponential model as the direct covariance for the main variable, a Cauchy model for the secondary variable and a K-Bessel model for the cross-covariance. Each covariance and cross-covariance are Fast Fourier Transformed (FFT) to get the discrete spectral densities. Then the spectral matrix is eigen-decomposed at each frequency separately to provide the square root matrix and to enforce positive-definiteness in cases where small negative eigenvalues are found. Finally the simulated spectrum is obtained as multiplication of the root matrix and the white noise coefficients. The method is particularly fast for covariances having derivatives at the origin and/or for covariances with long range. Hence, two-variables' 2D fields of 100 million pixels with all-Gaussian or all-cubic covariances and cross-covariance are both simulated in less than 200 s. The CPU-time increases only as N log(N) (N, the number of points to simulate). Additional realizations are obtained at a low marginal cost as the eigen-decomposition step needs to be done only once for the first realization. The main limitation of the approach is its rather stringent memory requirement. Synthetic examples illustrate the simulations of N-LMC with two and three variables for different combinations of the seven available models. It shows that the theoretical models are all well reproduced. An illustrative case-study on overburden thickness simulation is provided where the secondary information consists of a latent Gaussian variable identifying the geological domain.
Stadler, Michael; Marnay, Chris; Mendes, Goncalo; Kloess, Maximillian; Cardoso, Goncalo; Mégel, Olivier; Siddiqui, Afzal
Connecting electric storage technologies to smartgrids will have substantial implications in building energy systems. Local storage will enable demand response. Mobile storage devices in electric vehicles (EVs) are in direct competition with conventional stationary sources at the building. EVs will change the financial as well as environmental attractiveness of on-site generation (e.g. PV, or fuel cells). In order to examine the impact of EVs on building energy costs and CO2 emissions in 2020, a distributed-energy-resources adoption problem is formulated as a mixed-integer linear program with minimization of annual building energy costs or CO2 emissions. The mixed-integer linear program is applied to a set of 139 different commercial buildings in California and example results as well as the aggregated economic and environmental benefits are reported. The research shows that considering second life of EV batteries might be very beneficial for commercial buildings.
Azar, Ofer H.
The article analyzes a linear-city model where the consumer distribution can be asymmetric, which is important because in real markets this distribution is often asymmetric. The model yields equilibrium price differences, even though the firms’ costs are equal and their locations are symmetric (at the two endpoints of the city). The equilibrium price difference is proportional to the transportation cost parameter and does not depend on the good's cost. The firms' markups are also proportional to the transportation cost. The two firms’ prices will be equal in equilibrium if and only if half of the consumers are located to the left of the city’s midpoint, even if other characteristics of the consumer distribution are highly asymmetric. An extension analyzes what happens when the firms have different costs and how the two sources of asymmetry – the consumer distribution and the cost per unit – interact together. The model can be useful as a tool for further development by other researchers interested in applying this simple yet flexible framework for the analysis of various topics. PMID:26034984
Andrews, Sheldon; Teichmann, Marek; Kry, Paul G
We present a method for the simulation of compliant, articulated structures using a plausible approximate model that focuses on modeling endpoint interaction. We approximate the structure's behavior about a reference configuration, resulting in a first order reduced compliant system, or FORK (-1) S. Several levels of approximation are available depending on which parts and surfaces we would like to have interactive contact forces, allowing various levels of detail to be selected. Our approach is fast and computation of the full structure's state may be parallelized. Furthermore, we present a method for reducing error by combining multiple FORK (-1)S models at different linearization points, through twist blending and matrix interpolation. Our approach is suitable for stiff, articulate grippers, such as those used in robotic simulation, or physics-based characters under static proportional derivative control. We demonstrate that simulations with our method can deal with kinematic chains and loops with non-uniform stiffness across joints, and that it produces plausible effects due to stiffness, damping, and inertia. PMID:26829238
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog α( n) (for some constant α) which is optimal complexity for such problems.