Set Of Possible Solutions Research Articles

Consistency of the posterior distribution in generalized linear inverse problems

For ill-posed inverse problems, a regularized solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set of possible solutions, as other posterior estimates can be used as a solution to the inverse problem, such as the posterior mean which can be easier to compute in practice. In this paper we prove consistency of Bayesian solutions of an ill-posed linear inverse problem in the Ky Fan metric for a general class of likelihoods and prior distributions in a finite-dimensional setting. This result can be applied to study infinite dimensional problems by letting the dimension of the unknown parameter grow to infinity which can be viewed as discretization on a grid or spectral approximation of an infinite dimensional problem. The likelihood and the prior distribution are assumed to be in an exponential form that includes distributions from the exponential family, and to be differentiable. The prior distribution can be non-conjugate or improper. The observations can be dependent, and no assumption of finite moments of observations, such as expected value or the variance, is necessary thus allowing for possibly non-regular likelihoods. If the variance exists, it may be heteroscedastic, namely, it may depend on the unknown function. We observe quite a surprising phenomenon when applying our result to the spectral approximation framework where it is possible to achieve the parametric rate of convergence, i.e. the problem becomes self-regularized. We also consider a particular case of the unknown parameter being on the boundary of the parameter set, and show that the rate of convergence in this case is faster than for an interior point parameter.

Optimal Locations and Sizes of Static Var Compensators Using NSGA II

This paper presents an approach to find optimal locations and sizes of static var compensators (SVCs) in transmission systems. The approach comprises two main parts. In the first part, a mixed continuous-discrete multi-objective optimisation problem is formulated in which SVCs locations and sizes are the variables. The second part develops an optimisation method based on NSGA II (non-dominated sorting genetic algorithm) to solve the problem. The outcome will be a set of possible solutions from which the most desirable, based on any nominated criteria, can be selected in a systematic manner. The proposed approach has been successfully tested on IEEE 14-bus system tofind the optimal locations and sizes of SVC devices. The obtained results show that with the allocation of SVC devices determined by the proposed method, system security expressed in terms of power flows and voltages in steady-state operation is maintained with an increased margin in both normal state and critical contingencies.

A New Optimization Algorithm For Combinatorial Problems

Combinatorial optimization problems are those problems that have a finite set of possible solutions. The best way to solve a combinatorial optimization problem is to check all the feasible solutions in the search space. However, checking all the feasible solutions is not always possible, especially when the search space is large. Thus, many meta-heuristic algorithms have been devised and modified to solve these problems. The meta-heuristic approaches are not guaranteed to find the optimal solution since they evaluate only a subset of the feasible solutions, but they try to explore different areas in the search space in a smart way to get a near-optimal solution in less cost and time. In this paper, we propose a new meta-heuristic algorithm that can be used for solving combinatorial optimization problems. The method introduced in this paper is named the Global Neighborhood Algorithm (GNA). The algorithm is principally based on a balance between both the global and local search. A set of random solutions are first generated from the global search space, and then the best solution will give the optimal value. After that, the algorithm will iterate, and in each iteration there will be two sets of generated solutions; one from the global search space and the other set of solutions will be generated from the neighborhood of the best solution. Throughout the paper, the algorithm will be delineated with examples. In the final phase of the research, the results of GNA will be discussed and compared with the results of Genetic Algorithm (GA) as an example of another optimization method.

Optimal locations and sizes of static var compensators using NSGA II

This paper presents an approach to find optimal locations and sizes of static var compensators (SVCs) in transmission systems. The approach comprises two main parts. In the first part, a mixed continuous-discrete multi-objective optimisation problem is formulated in which SVCs locations and sizes are the variables. The second part develops an optimisation method based on NSGA II (non-dominated sorting genetic algorithm) to solve the problem. The outcome will be a set of possible solutions from which the most desirable, based on any nominated criteria, can be selected in a systematic manner. The proposed approach has been successfully tested on IEEE 14-bus system to find the optimal locations and sizes of SVC devices. The obtained results show that with the allocation of SVC devices determined by the proposed method, system security expressed in terms of power flows and voltages in steady-state operation is maintained with an increased margin in both normal state and critical contingencies.

Generating Approximate Solutions to the TTP using a Linear Distance Relaxation

In some domestic professional sports leagues, the home stadiums are located in cities connected by a common train line running in one direction. For these instances, we can incorporate this geographical information to determine optimal or nearly-optimal solutions to the n-team Traveling Tournament Problem (TTP), an NP-hard sports scheduling problem whose solution is a double round-robin tournament schedule that minimizes the sum total of distances traveled by all n teams. We introduce the Linear Distance Traveling Tournament Problem (LD-TTP), and solve it for n=4 and n=6, generating the complete set of possible solutions through elementary combinatorial techniques. For larger n, we propose a novel "expander construction" that generates an approximate solution to the LD-TTP. For n congruent to 4 modulo 6, we show that our expander construction produces a feasible double round-robin tournament schedule whose total distance is guaranteed to be no worse than 4/3 times the optimal solution, regardless of where the n teams are located. This 4/3-approximation for the LD-TTP is stronger than the currently best-known ratio of 5/3 + epsilon for the general TTP. We conclude the paper by applying this linear distance relaxation to general (non-linear) n-team TTP instances, where we develop fast approximate solutions by simply "assuming" the n teams lie on a straight line and solving the modified problem. We show that this technique surprisingly generates the distance-optimal tournament on all benchmark sets on 6 teams, as well as close-to-optimal schedules for larger n, even when the teams are located around a circle or positioned in three-dimensional space.

Investigation of fine and coarse aerosol contributions to the total aerosol light scattering: Shape effects and concentration profiling by Raman lidar measurements

Remote sensing techniques, such as sun-photometry (columnar integrated aerosol parameters) and Raman lidar (profile aerosol parameters), are used in inversion models to yield information about particle size distribution (PSD), concentration, and average refractive index (RI). Ground-based AERONET network uses sun-photometric measurements to retrieve columnar effective particle size distribution and refractive index values, as well as other radiative properties such as absorption optical depth, albedo, and asymmetry parameter, which do not have a strong dependence on particle shape. Raman lidar measurements, on the other hand, yield shape-dependent quantities like particle depolarization, backscattering and lidar ratio at several wavelengths. In order to evaluate what light scattering parameters can be used to infer information regarding particle shape and concentration, a set of computer simulations was carried out. AERONET-inverted particle data (PSD, RI, concentration) have been used as input. Simulated data are obtained from ALFA, a light-scattering database, using the kernel approximation scheme. As expected, the effect of fine mode particle shape on near-infrared (1064nm) was found to be negligible; on the other hand, even a small amount of nonsphericity in small particles has a marked effect on depolarization ratio values. Data from a 2007 lidar campaign were then used to evaluate the validity of our approach on a real measurement campaign. Results show that our method can yield some information about layer profiling, such as the concentration of fine mode particles. Such information comes not as a best-fit solution but in the form of a compatible set of possible solutions, which could be narrowed by the use of closure relations.

A new light-based solution to the Hamiltonian path problem

The exponential running time for algorithms designed to solve NP-complete problems in conventional computers, mostly, makes it almost impossible solving large instances of such problems in reasonable time. Unconventional computers may be the answer to this problem. In this paper we use light to solve a Hamiltonian path problem in polynomial time. At first, the solution space of the problem is generated and then invalid solutions are eliminated from it. Our approach is based on filters which remove paths that are not Hamiltonian from the set of possible solutions. We perform polynomial preprocessing steps to produce the filters and find Hamiltonian paths of a graph based on the rays of light passing through them. Finally we report the design of filters and use light to solve the Hamiltonian path problem.

On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme

Dealing with Pythagorean Hodograph quintic Hermite interpolation in the space, we deepen the analysis of the so-called CC criterion proposed in Farouki et al. (2008) for fixing the two free angular parameters characterizing the set of possible solutions, which remarkably influence the shape of the chosen interpolant. Such criterion is easy to implement, guarantees the reproduction of the standard cubic Hermite interpolant when it is a PH curve and usually allows the selection of interpolants with good shape. Here we first rigorously prove that the PH interpolant it selects doesnʼt depend on the unit pure vector chosen for representing its hodograph in quaternion form. Then we evaluate the corresponding interpolation scheme from a theoretical point of view, proving with the help of symbolic computation that it has fourth approximation order. A selection of experiments related to the spline implementation of the method confirms our analysis.

A coopetitive model for the green economy

The paper proposes a coopetitive model for the Green Economy. It addresses the issue of the climate change policy and the creation and diffusion of low-carbon technologies. In the present paper the complex construct of coopetition is applied at macroeconomic level. The model, based on Game Theory, enables us to offer a set of possible solutions in a coopetitive context, allowing to find a Pareto solution in a win–win scenario. The model, which is based on the assumption that each country produces a level of output which is determined in a non-cooperative game of Cournot-type and that considers at the same time a coopetitive strategy regarding the low technologies, will suggest a solution that shows the convenience for each country to participate actively to a program of low carbon technologies within a coopetitive framework to address a policy of climate change, thus aiming at balancing the environmental imbalances.

Metadata and Tools for Integration and Preservation of Cultural Heritage 3D Information

In this paper we investigate many of the various storage, portability and interoperability issues arising among archaeologists and cultural heritage people when dealing with 3D technologies. On the one side, the available digital repositories look often unable to guarantee affordable features in the management of 3D models and their metadata; on the other side the nature of most of the available data format for 3D encoding seem to be not satisfactory for the necessary portability required nowadays by 3D information across different systems. We propose a set of possible solutions to show how integration can be achieved through the use of well known and wide accepted standards for data encoding and data storage. Using a set of 3D models acquired during various archaeological campaigns and a number of open source tools, we have implemented a straightforward encoding process to generate meaningful semantic data and metadata. We will also present the interoperability process carried out to integrate the encoded 3D models and the geographic features produced by the archaeologists. Finally we will report the preliminary (rather encouraging) development of a semantic enabled and persistent digital repository, where 3D models (but also any kind of digital data and metadata) can easily be stored, retrieved and shared with the content of other digital archives.

Electrolyte Stability in a Nanochannel with Charge Regulation

The stability of an electrolyte confined in one dimension between two solid surfaces is analyzed theoretically in the case where overlapping double layers produce nontrivial interactions. Within the Poisson-Boltzmann-Nernst-Planck description of the electrostatic interaction and transport of electrical charges, the presence of Stern layers can enrich the set of possible solutions. Our analytical and numerical study of the stability properties of the trivial state of this system identified an instability to a new antisymmetric state. This state is stable for a range of gap widths that depends on the Debye and Stern lengths, but for smaller gap widths, where the Stern layers overlap, a second transition takes place and the stable nontrivial solution diverges. The origin of this divergence is explained and its properties analyzed using asymptotic techniques which are in good agreement with numerical results. The relevance of our results to confined electrolytes at nanometer scales is discussed in the context of energy storage in nanometric systems.

Self-consistency and search for collective effects in semiclassical pairing theory

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-$\Delta$ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.

Chance-constrained multi-objective programming for optimal multi-layer aquifer remediation design

Groundwater remediation works are expensive, complex in nature, and generally involve uncertain design parameters and multiple conflicting objectives. Reduction in remediation cost is, normally, the primary objective of optimal remediation designs. Remediation time has significant influence on remediation cost. The main contributions of this study are: development of a chance-constrained multi-objective programming (CCMOP) model, exploration of the significance of flexible remediation time on optimal remediation designs, and exploration of some basic characteristics of multi-objective optimization algorithms. The developed methodology excludes inferior yet optimal solutions from the set of possible solutions, identifies the ranges in which non-inferior solutions lie, and prevents one from making inferior decisions. It provides insightful information about the problem and simplifies the decision making process considerably. The results suggest that by avoiding the use of faulty remediation times, highly significant amounts of remediation cost could be saved. The CCMOP is an effective uncertainty and reliability prediction technique.

An Efficient Algorithm for Haplotype Inference on Pedigrees with Recombinations and Mutations

Haplotype Inference (HI) is a computational challenge of crucial importance in a range of genetic studies. Pedigrees allow to infer haplotypes from genotypes more accurately than population data, since Mendelian inheritance restricts the set of possible solutions. In this work, we define a new HI problem on pedigrees, called MINIMUM-CHANGE HAPLOTYPE CONFIGURATION (MCHC) problem, that allows two types of genetic variation events: recombinations and mutations. Our new formulation extends the MINIMUM-RECOMBINANT HAPLOTYPE CONFIGURATION (MRHC) problem, that has been proposed in the literature to overcome the limitations of classic statistical haplotyping methods. Our contribution is twofold. First, we prove that the MCHC problem is APX-hard under several restrictions. Second, we propose an efficient and accurate heuristic algorithm for MCHC based on an L-reduction to a well-known coding problem. Our heuristic can also be used to solve the original MRHC problem and can take advantage of additional knowledge about the input genotypes. Moreover, the L-reduction proves for the first time that MCHC and MRHC are O(nm/(log nm))-approximable on general pedigrees, where n is the pedigree size and m is the genotype length. Finally, we present an extensive experimental evaluation and comparison of our heuristic algorithm with several other state-of-the-art methods for HI on pedigrees.

The Effectiveness of Genetic Algorithm in Solving Simultaneous Equations

There are several known conventional algorithms for solving system of linear equations, which are based on some theoretical principles. Finding solution to these set of equations through the evolutionary process of genetic algorithm is a new and developing research area of interest. The Genetic Algorithm approach follows the concept of solution evolution by stochastically developing generations of solutions population using a definite fitness function to determine the best fit solution to the problem. In this study, we experimented with a new non-conventional approach, based on biological evolution, to solving system of simultaneous linear equations. We discussed the origin of Genetic Algorithm and explore its applicability in solving system of simultaneous equations. We used Genetic Algorithm, on one hand, and Gaussian elimination method, on the other hand, to solve seven different systems of simultaneous linear equations. We then compared the results obtained from the two methods. It was observed that the Genetic Algorithm was very effective in discovering all possible sets of solutions that are applicable to any given system of simultaneous linear equations. Conventional numerical methods, such as Gaussian elimination method, produced a single set of solutions for a particular system of simultaneous linear equations, but GA was able to produce more than one set of solutions for certain systems of equations. For example, during our experiments with GA equation solver, one particular set of equations produced three different sets of perfect solutions, which perfectly fit into the equations. General Terms Genetic Algorithms

Solving linear constraints over real and rational fields

Practical methods are proposed to solve linear constraints over real and rational fields with quantifiers. Secondary problems are observed together with the set of possible solutions in the context of automatic software model verification.

A tabu search approach for assigning node Bs to switches in UMTS networks

This paper proposes a mathematical model for assigning Node Bs to switches in UMTS networks, as well as an implementation of the tabu search metaheuristic for solving such a problem. In this model, the overall problem is divided into two assignment sub-problems: the assignment of a set of Node Bs to a set of radio network controllers (RNCs), and the assignment of those RNC concurrently to a set of voice switches (MSCs: Mobile Switching Centers) and a set of data switches (SGSNs: Serving GPRS Support Nodes). In order to solve the overall assignment problem, the proposed implementation defines a number of moves which enable to efficiently explore the set of possible solutions. Computational results enable to identify the parameters that are able to reduce the costs of the obtained solutions, as such costs are relatively close to the estimated lower bounds and found in reasonable computational time.

Comparison of cardiac activation models using 3D MCG data

Event Abstract Back to Event Comparison of cardiac activation models using 3D MCG data Massimo D. Melis1* and Yoshinori Uchikawa1 1 Tokyo Denki University, Japan In the study of the inverse problem in biomagnetism, the measured signals are used to localize the source that generates a given magnetic field distribution. The problem has no unique solution, since the same magnetic field map (MFM) can be generated by an infinite number of possible source configurations. To restrict the set of possible solutions, physiological information can be used. In magnetocardiography (MCG), the knowledge of the heart functionality may help in making a suitable choice to model the current source in the human heart. A possible choice for the current model is a single dipole, with varying position, orientation and amplitude inside the heart volume, the so-called source space. An alternative solution can be a multiple dipole model, characterized by a limited number of dipoles, with varying positions and orientations, or a limited range of variability for the position inside the source space. A more general description of the wavefront propagation can be provided by a distributed sources model, which considers an elevated number of dipolar sources, located in fixed positions inside the heart volume region, having varying amplitudes and directions, to model the current flow during the heart cycle. A single dipole model is a suitable one only for short segments of the MCG signals, whereas a distributed model allows estimating the current density in the source space. In this study the source localizations of MCG signals were performed using different source models on the same data sets, to evaluate whether the differences in the source models descriptions can be minimized in the MCG data sets, or in some of them. The analyses are repeated on normal subjects and WPW patients, using normal components data and vector components data of the measured MFMs, to study the effect of the information provided by the additional tangential components. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: MCG: Instrumentation, Modeling, Basic and Clinical Studies Citation: Melis MD and Uchikawa Y (2010). Comparison of cardiac activation models using 3D MCG data. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00341 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 07 Apr 2010; Published Online: 07 Apr 2010. * Correspondence: Massimo D Melis, Tokyo Denki University, Tokyo, Japan, mdemelis@hotmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Massimo D Melis Yoshinori Uchikawa Google Massimo D Melis Yoshinori Uchikawa Google Scholar Massimo D Melis Yoshinori Uchikawa PubMed Massimo D Melis Yoshinori Uchikawa Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

SMART SYSTEMS ARCHITECTING: COMPUTATIONAL INTELLIGENCE APPLIED TO TRADE SPACE EXPLORATION AND SYSTEM DESIGN

The design trade space of a complex system is vast, and overlooking potential architecture alternatives can have an adverse impact on the final outcome. This paper presents a Smart Systems Architecting (SSA) approach for generating and assessing architecture alternatives. Computationally intelligent techniques such as Evolutionary Algorithms (EA) are used to explore the design trade space for candidate architectures. A novel fuzzy architecture assessment approach is presented to quantitatively evaluate the set of possible solutions based on the decision-maker's preferences even in the presence of incomplete, subjective and ambiguous information. The broad applicability of Smart Systems Architecting is demonstrated by three specific approaches to fuzzy evolutionary search at different levels of design ambiguity.

Quantifying Food Web Flows Using Linear Inverse Models

The quantitative mapping of food web flows based on empirical data is a crucial yet difficult task in ecology. The difficulty arises from the under-sampling of food webs, because most data sets are incomplete and uncertain. In this article, we review methods to quantify food web flows based on empirical data using linear inverse models (LIM). The food web in a LIM is described as a linear function of its flows, which are estimated from empirical data by inverse modeling. The under-sampling of food webs implies that infinitely many different solutions exist that are consistent with a given data set. The existing approaches to food web LIM select a single solution from this infinite set by invoking additional assumptions: either a specific selection criterion that has no solid ecological basis is used or the data set is artificially upgraded by assigning fixed values to, for example, physiological parameters. Here, we advance a likelihood approach (LA) that follows a different solution philosophy. Rather than singling out one particular solution, the LA generates a large set of possible solutions from which the marginal probability density function (mPDF) of each flow and correlations between flows can be derived. The LA is exemplified with an example model of a soil food web and is made available in the open-source R-software. Moreover, we show how stoichiometric data, stable isotope signatures, and fatty acid compositions can be included in the LIM to alleviate the under-sampling problem. Overall, LIM prove to be a powerful tool in food web research, which can bridge the gap between empirical data and the analysis of food web structures.