Discrete Support Research Articles

Quantum models with spectrum generated by the flows of polynomial zeros

A class of purely bosonic models is characterized having the following properties in a Hilbert space of analytic functions: (i) wave function is the generating function for orthogonal polynomials of a discrete energy variable ϵ, (ii) any Hamiltonian has nondegenerate purely point spectrum that corresponds to infinite discrete support of measure in the orthogonality relation of the polynomials , (iii) the support is determined exclusively by the points of discontinuity of , (iv) the spectrum of can be numerically determined as fixed points of monotonic flows of the zeros of orthogonal polynomials , (v) one can compute practically an unlimited number of energy levels (e.g. in double precision). If a model of is exactly solvable, its spectrum can only assume one of four qualitatively different types. The results are applied to spin-boson quantum models that are, at least partially, diagonalizable and have at least single one-dimensional irreducible component in the spin subspace. Examples include the Rabi model and its various generalizations.

Fault location in loop distribution network using SVM technology

Abstract The purpose of this paper is to provide a hierarchical and active fault location method in neutral point non-effectively grounded loop distribution network. It analyzes the distribution of loop closing zero-sequence current with single-phase grounding (SPG) fault occurring in two different topologies. According to the variations characteristics of steady loop closing zero-sequence current, fault section can be determined. Then precise SPG fault position can be got using Discrete Wavelet Transform (DWT) and Support Vector Machine (SVM) technology. Even if the fault point cant be located at the first time, the method can still work by repeating the process till the accurate fault position is located. More than 115,200 study cases are simulated on the simulation platform built on PSCAD/EMTP. The results indicate that the proposed fault location method is effective and robust for neutral point non-effectively grounded loop distribution network.

Study on the safety of operating high-speed railway vehicles subjected to crosswinds

A coupled vehicle-track dynamic model is put forward for use in investigating the safety effects of crosswinds on the operation of a high-speed railway vehicle. In this model, the vehicle is modeled as a nonlinear multi-body system, and the ballasted track is modeled as a three-layer discrete elastic support system. The steady aerodynamic forces caused by crosswinds are modeled as ramp-shaped external forces being exerted on the vehicle body. This model was used in a numerical analysis of the dynamic response and dynamic derailment mechanisms of high-speed vehicles subjected to strong crosswinds. The effects of the crosswind speeds, crosswind attack angle, and vehicle speed on the operational safety of the vehicle were examined. The operational safety boundaries of a high-speed vehicle subjected to crosswinds were determined. The numerical results obtained indicate that crosswinds at attack angles of 75° to 90° with respect to the forward direction of the vehicle have a great influence on the safety of operating high-speed railway vehicles. The wheelset unloading limit, which determines the position of the warning boundary dividing the safe operating area and the warning area, is the most conservative, i.e., the safest, criterion to use in assessing the high-speed operational safety of vehicles in crosswinds.

A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs

Recent years have seen growing interest in coherent risk measures, especially in Conditional Value-at-Risk ($$\mathrm {CVaR}$$CVaR). Since $$\mathrm {CVaR}$$CVaR is a convex function, it is suitable as an objective for optimization problems when we desire to minimize risk. In the case that the underlying distribution has discrete support, this problem can be formulated as a linear programming (LP) problem. Over more general distributions, recent techniques, such as the sample average approximation method, allow to approximate the solution by solving a series of sampled problems, although the latter approach may require a large number of samples when the risk measures concentrate on the tail of the underlying distributions. In this paper we propose an automatic primal-dual aggregation scheme to exactly solve these special structured LPs with a very large number of scenarios. The algorithm aggregates scenarios and constraints in order to solve a smaller problem, which is automatically disaggregated using the information of its dual variables. We compare this algorithm with other common approaches found in related literature, such as an improved formulation of the full problem, cut-generation schemes and other problem-specific approaches available in commercial software. Extensive computational experiments are performed on portfolio and general LP instances.

Multi load-transmitting device based support layout optimization for large fuselage panels in digital assembly

A large fuselage panel is always connected to a full-scale shape-preserving bracket to enhance its stiffness in digital assembly processes and reduce assembly deformation induced by factors such as gravity. However, the full-scale shape-preserving bracket’s characteristics, such as large size and weight, usually result in a complex installation process and high maintenance costs. A method for optimizing a multi load-transmitting device based discrete support layout is presented in this paper. By constructing finite element model including the fuselage panel and LTDs, the panel’s strain energy under different support layout parameters is obtained according to the principle of mixed uniform design. Using the method of partial least squares regression, the mathematical relationship between the strain energy and the support layout parameters is established, which is then used to obtain the optimum multi LTD based support layout. Furthermore, by comparing the panel deformation under the optimum multi LTD based support with that under the full-scale shape-preserving bracket-based support, we conclude that the optimum multi LTD based support can not only suppress panel deformation effectively, but also keep the panel’s stiffness comparable to that under the full-scale shape-preserving bracket-based support.

Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings

This paper presents the results of a detailed investigation of the effects of rail corrugation on the dynamic behaviour of metro rail fastenings, obtained from extensive experiments conducted on site and from simulations of train–track dynamics. The results of tests conducted with a metro train operating on corrugated tracks are presented and discussed first. A three-dimensional (3D) model of the metro train and a slab track was developed using multi-body dynamics modelling and the finite element method to simulate the effect of rail corrugation on the dynamic behaviour of rail fastenings. In the model, the metro train is modelled as a multi-rigid body system, and the slab track is modelled as a discrete elastic support system consisting of two Timoshenko beams for the rails, a 3D solid finite element (FE) model for the slabs, periodic discrete viscoelastic elements for the rail fastenings that connect the rails to the slabs, and uniformly viscoelastic elements for the subgrade beneath the slabs. The proposed train–track model was used to investigate the effects of rail corrugation on the dynamic behaviour of the metro track system and fastenings. An FE model for the rail fastenings was also developed and was used to calculate the stresses in the clips, some of which rupture under the excitation of rail corrugation. The results of the field experiments and dynamics simulations provide an insight into the root causes of the fracture of the clips, and several remedies are suggested for mitigating strong vibrations and failure of metro rail fastening systems.

Centroids of Type-1 and Type-2 Fuzzy Sets When Membership Functions Have Spikes

Centroids are practically important in type-1 and type-2 fuzzy logic systems as a method of defuzzification and type reduction. However, computational problems arise when membership functions (MF) have singleton spikes. The novel thresholding aggregation operators that were described in our companion paper “ New Classes of Threshold Aggregation Functions Based Upon the Tsallis q-Exponential with Applications to Perceptual Computing” produce such MFs with spikes. Such spikes may occur when modeling concepts defined on a real-valued domain, and they are also formed in unions of fuzzy sets in which some have MFs with discrete support and others have support defined on an interval. This paper presents a modified definition of the centroid of a fuzzy set that avoids the computational problems associated with the usual definition and reduces to this definition when MFs are continuous and normal (i.e., of unit height) on some interval. We also present an enhanced Karnik-Mendel-type algorithm to compute the modified centroid of interval type-2 fuzzy sets whose MFs have spikes.

Bayes Hilbert Spaces

SummaryA Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be a Hilbert space, which can include probability and infinite measures, measures on the whole real line or discrete measures. It extends the ideas from the Hilbert space of densities on a finite support towards Hilbert spaces on general measure spaces. It is also a generalisation of the Euclidean structure of the simplex, the sample space of random compositions. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. A key tool is the centred‐log‐ratio transformation, a generalization of that used in compositional data analysis, which maps the Hilbert space of measures into a subspace of square‐integrable functions. As a consequence of this structure, distances between densities, orthonormal bases, and Fourier series representing measures become available. As an application, Fourier series of normal distributions and distances between them are derived, and an example related to grain size distributions is presented. The geometry of the sample space of random compositions, known as Aitchison geometry of the simplex, is obtained as a particular case of the Hilbert space when the measures have discrete and finite support.

Lattice-Based WOM Codes for Multilevel Flash Memories

We consider t-write codes for write-once memories with n cells that can store multiple levels. Assuming an underlying lattice-based construction and using the continuous approximation, we derive upper bounds on the worst-case sum-rate optimal and fixed-rate optimal n-cell t-write write-regions for the asymptotic case of continuous levels. These are achieved using hyperbolic shaping regions that have a gain of 1 bit/cell over cubic shaping regions. Motivated by these hyperbolic write-regions, we discuss construction and encoding of codebooks for cells with discrete support. We present a polynomial-time algorithm to assign messages to the codebooks and show that it achieves the optimal sum-rate for any given codebook when n = 2. Using this approach, we construct codes that achieve high sum-rate. We describe an alternative formulation of the message assignment problem for n≥ 3, a problem which remains open.

Lattices and Lotteries

We consider the consumer problem under uncertainty when the consumer can choose the quantity of a risk-free good and the lottery, or distribution, of a risky good from a set of distributions. These goods are imperfect substitutes in the consumer preferences, with additive preferences a special case. We develop sufficient conditions for the choice of the risky good to be monotone with respect to income, exploring different notions of monotonicity. The sufficient conditions are ordinal, independent of concavity, and do not require differentiability or continuity. Cardinal conditions and conditions from the single good case are not necessary and are not always sufficient. The sufficient conditions are formulated in appropriate value lattices. The framework is flexible and adaptable to handle different uncertainty applications. Examples demonstrate the sufficient conditions and different applications where available lotteries may be finite in number, may have discrete support, or may form a chain or a lattice.

Constructing Discrete Unbounded Distributions with Gaussian-Copula Dependence and Given Rank Correlation

A random vector X with given univariate marginals can be obtained by first applying the normal distribution function to each coordinate of a vector Z of correlated standard normals to produce a vector U of correlated uniforms over (0,1) and then transforming each coordinate of U by the relevant inverse marginal. One approach to fitting requires, separately for each pair of coordinates of X, the rank correlation, r(ρ), or the product-moment correlation, rL(ρ), where ρ is the correlation of the corresponding coordinates of Z, to equal some target r*. We prove the existence and uniqueness of a solution for any feasible target, without imposing restrictions on the marginals. For the case where r(ρ) cannot be computed exactly because of an infinite discrete support, the relevant infinite sums are approximated by truncation, and lower and upper bounds on the truncation errors are developed. With a function [Formula: see text] defined by the truncated sums, a bound on the error r(ρ*) − r* is given, where ρ* is a solution to [Formula: see text]. Based on this bound, an algorithm is proposed that determines truncation points so that the solution has any specified accuracy. The new truncation method has potential for significant work reduction relative to truncating heuristically, largely because as required accuracy decreases, so does the number of terms in the truncated sums. This is quantified with examples. The gain appears to increase with the heaviness of tails.

Geriatric Syndromes Predict Postdischarge Outcomes Among Older Emergency Department Patients: Findings From the interRAI Multinational Emergency Department Study

Identifying older emergency department (ED) patients with clinical features associated with adverse postdischarge outcomes may lead to improved clinical reasoning and better targeting for preventative interventions. Previous studies have used single-country samples to identify limited sets of determinants for a limited number of proxy outcomes. The objective of this study was to identify and compare geriatric syndromes that influence the probability of postdischarge outcomes among older ED patients from a multinational context. A multinational prospective cohort study of ED patients aged 75 years or older was conducted. A total of 13 ED sites from Australia, Belgium, Canada, Germany, Iceland, India, and Sweden participated. Patients who were expected to die within 24 hours or did not speak the native language were excluded. Of the 2,475 patients approached for inclusion, 2,282 (92.2%) were enrolled. Patients were assessed at ED admission with the interRAI ED Contact Assessment, a geriatric ED assessment. Outcomes were examined for patients admitted to a hospital ward (62.9%, n=1,436) or discharged to a community setting (34.0%, n=775) after an ED visit. Overall, 3% of patients were lost to follow-up. Hospital length of stay (LOS) and discharge to higher level of care was recorded for patients admitted to a hospital ward. Any ED or hospital use within 28 days of discharge was recorded for patients discharged to a community setting. Unadjusted and adjusted odds ratios (ORs) were used to describe determinants using standard and multilevel logistic regression. A multi-country model including living alone (OR=1.78, p≤0.01), informal caregiver distress (OR=1.69, p=0.02), deficits in ambulation (OR=1.94, p≤0.01), poor self-report (OR = 1.84, p≤0.01), and traumatic injury (OR=2.18, p≤0.01) best described older patients at risk of longer hospital lengths of stay. A model including recent ED visits (OR=2.10, p≤0.01), baseline functional impairment (OR=1.68, p≤0.01), and anhedonia (OR=1.73, p≤0.01) best described older patients at risk of proximate repeat hospital use. A sufficiently accurate and generalizable model to describe the risk of discharge to higher levels of care among admitted patients was not achieved. Despite markedly different health care systems, the probability of long hospital lengths of stay and repeat hospital use among older ED patients is detectable at the multinational level with moderate accuracy. This study demonstrates the potential utility of incorporating common geriatric clinical features in routine clinical examination and disposition planning for older patients in EDs.

Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

Artificial intelligence methodologies, as the core of discrete control and decision support systems, have been extensively applied in the industrial production sector. The resulting tools produce excellent results in certain cases; however, the NP-hard nature of many discrete control or decision making problems in the manufacturing area may require unaffordable computational resources, constrained by the limited available time required to obtain a solution. With the purpose of improving the efficiency of a control methodology for discrete systems, based on a simulation-based optimization and the Petri net (PN) model of the real discrete event dynamic system (DEDS), this paper presents a strategy, where a transformation applied to the model allows removing the redundant information to obtain a smaller model containing the same useful information. As a result, faster discrete optimizations can be implemented. This methodology is based on the use of a formalism belonging to the paradigm of the PN for describing DEDS, the disjunctive colored PN. Furthermore, the metaheuristic of genetic algorithms is applied to the search of the best solutions in the solution space. As an illustration of the methodology proposal, its performance is compared with the classic approach on a case study, obtaining faster the optimal solution.

Statistics of the sparse spectrum turbulent phase

A recently published sparse spectrum (SS) model of the phase front perturbations by atmospheric turbulence [J. Opt. Soc. Am. A 30, 479 (2013)] is based on the trigonometric series with discrete random support. The SS model enables fewer computational efforts, while preserving the wide range of scales typically associated with turbulence perturbations. We present an improved version of the SS model that accurately reproduces the power-law spectral density of the phase fluctuations in the arbitrary wide spectral band. We examine the higher-order statistics of the SS phase samples for four versions of the SS model. We also present the calculations of the long-exposure Strehl numbers and scintillation index for the different versions of the SS model. A nonoverlapping SS model with a log-uniform partition emerges as the most appropriate for the atmospheric turbulence representation.

Transcription factor-binding site identification and gene classification via fusion of the supervised-weighted discrete kernel clustering and support vector machine

The genetic regulatory mechanism heavily influences a substantial portion of biological functions and processes needed to sustain life. For a comprehensive mechanistic understanding of biological processes, it is important to identify the common transcription factor (TF) binding sites (TFBSs) from a set of promoter sequences of co-regulated genes and classify genes that are co-regulated by certain TFs, therefore to provide an insight into the mechanism that underlies the interaction among the co-regulated genes and complicate genetic regulation. We propose a new supervised-weighted discrete kernel clustering (SWDKC) classification method for the identification of TFBS and the classification of gene. Our SWDKC method gave smaller misclassification error rate than the other methods on both the simulated data and the real NF-κB data. We verify that the selected over-represented TFBSs serve informative TFBSs from a biological point of view.

Measures with uniformly discrete support and spectrum

We characterize the measures on R which have both their support and spectrum uniformly discrete. A similar result is obtained in Rn under a stronger discreteness restriction.

Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.

Dynamic analysis of a high-speed train operating on a curved track with failed fasteners

A high-speed train-track coupling dynamic model is used to investigate the dynamic behavior of a high-speed train operating on a curved track with failed fasteners. The model considers a high-speed train consisting of eight vehicles coupled with a ballasted track. The vehicle is modeled as a multi-body system, and the rail is modeled with a Timoshenko beam resting on the discrete sleepers. The vehicle model considers the effect of the end connections of the neighboring vehicles on the dynamic behavior. The track model takes into account the lateral, vertical, and torsional deformations of the rails and the effect of the discrete sleeper support on the coupling dynamics of the vehicles and the track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. The train model couples with the track model by using a Hertzian contact model for the wheel/rail normal force calculation, and the nonlinear creep theory by Shen et al, 1984 is used for wheel/rail tangent force calculation. In the analysis, a curved track of 7000-m radius with failed fasteners is selected, and the effects of train operational speed and the number of failed fasteners on the dynamic behaviors of the train and the track are investigated in detail. Furthermore, the wheel/rail forces and derailment coefficient and the wheelset loading reduction are analyzed when the high-speed train passes over the curved track with the different number of continuously failed fasteners at different operational speeds. Through the detailed numerical analysis, it is found that the high-speed train can operate normally on the curved track of 7000-m radius at the speeds of 200 km/h to 350 km/h.

A memetic approach to construct transductive discrete support vector machines

Transductive learning involves the construction and application of prediction models to classify a fixed set of decision objects into discrete groups. It is a special case of classification analysis with important applications in web-mining, corporate planning and other areas. This paper proposes a novel transductive classifier that is based on the philosophy of discrete support vector machines. We formalize the task to estimate the class labels of decision objects as a mixed integer program. A memetic algorithm is developed to solve the mathematical program and to construct a transductive support vector machine classifier, respectively. Empirical experiments on synthetic and real-world data evidence the effectiveness of the new approach and demonstrate that it identifies high quality solutions in short time. Furthermore, the results suggest that the class predictions following from the memetic algorithm are significantly more accurate than the predictions of a CPLEX-based reference classifier. Comparisons to other transductive and inductive classifiers provide further support for our approach and suggest that it performs competitive with respect to several benchmarks.

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle–track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli–Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.