Discrete Support Research Articles

Projection predictive variable selection for discrete response families with finite support

AbstractThe projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity. Its projection problem is not easy to solve in general because it is based on the Kullback–Leibler divergence from a restricted posterior predictive distribution of the so-called reference model to the parameter-conditional predictive distribution of a candidate model. Previous work showed how this projection problem can be solved for response families employed in generalized linear models and how an approximate latent-space approach can be used for many other response families. Here, we present an exact projection method for all response families with discrete and finite support, called the augmented-data projection. A simulation study for an ordinal response family shows that the proposed method performs better than or similarly to the previously proposed approximate latent-space projection. The cost of the slightly better performance of the augmented-data projection is a substantial increase in runtime. Thus, if the augmented-data projection’s runtime is too high, we recommend the latent projection in the early phase of the model-building workflow and the augmented-data projection for final results. The ordinal response family from our simulation study is supported by both projection methods, but we also include a real-world cancer subtyping example with a nominal response family, a case that is not supported by the latent projection.

Gap distributions of Fourier quasicrystals with integer weights via Lee–Yang polynomials

Recent work of Kurasov and Sarnak provides a method for constructing one-dimensional Fourier quasicrystals (FQ) from the torus zero sets of a special class of multivariate polynomials called Lee–Yang polynomials. In particular, they provided a non-periodic FQ with unit coefficients and uniformly discrete support, answering an open question posed by Meyer. Their method was later shown to generate all one-dimensional Fourier quasicrystals with \mathbb{N} -valued coefficients ( \mathbb{N} -FQ). In this paper, we characterize which Lee–Yang polynomials give rise to non-periodic \mathbb{N} -FQs with unit coefficients and uniformly discrete support, and show that this property is generic among Lee–Yang polynomials. We also show that the infinite sequence of gaps between consecutive atoms of any \mathbb{N} -FQ has a well-defined distribution, which, under mild conditions, is absolutely continuous. This generalizes previously known results for the spectra of quantum graphs to arbitrary \N -FQs. Two extreme examples are presented: first, a sequence of \mathbb{N} -FQs whose gap distributions converge to a Poisson distribution. Second, a sequence of random Lee–Yang polynomials that results in random \mathbb{N} -FQs whose empirical gap distributions converge to that of a random unitary matrix (CUE).

Almost periodic distributions and crystalline measures

We study temperate distributions and measures with discrete support in Euclidean space and their Fourier transformswith special attention to almost periodic distributions. In particular, we prove that if distances between points of the support of a measure do not quickly approach 0 at infinity, then this measure is a Fourier quasicrystal (Theorem 1).
 We also introduce a new class of almost periodicity of distributions,close to the previous one, and study its properties.Actually, we introduce the concept of s-almost periodicity of temperate distributions. We establish the conditions for a measure $\mu$ to be s-almost periodic (Theorem 2), a connection between s-almost periodicityand usual almost periodicity of distributions (Theorem 3). We also prove that the Fourier transform of an almost periodic distribution with locally finite support is a measure (Theorem 4),and prove a necessary and sufficient condition on a locally finite set $E$ for each measure with support on $E$ to have s-almost periodic Fourier transform (Theorem 5).

Documentation of results and medication prescribing after combinatorial psychiatric pharmacogenetic testing: A case for discrete results

PurposeCombinatorial pharmacogenetic (PGx) panels intended to aid psychiatric prescribing are available to clinicians. Here, we evaluated the documentation of PGx panel results and subsequent prescribing patterns within a tertiary health care system. MethodsWe performed a query of psychiatry service note text in our electronic health record using 71 predefined PGx terms. Patients who underwent combinatorial PGx testing were identified, and documentation of test results was analyzed. Prescription data following testing were examined for the frequency of prescriptions influenced by genes on the panel along with the medical specialties involved. ResultsA total of 341 patients received combinatorial PGx testing, and documentation of results was found to be absent or incomplete for 198 patients (58%). The predominant method of documentation was through portable document formats uploaded to the electronic health record’s “Media” section. Among patients with at least 1 year of follow-up, a large majority (194/228, 85%) received orders for medications affected by the tested genes, including 132 of 228 (58%) patients receiving at least 1 non-psychiatric medication influenced by the test results. ConclusionResults from combinatorial PGx testing were poorly documented. Medications affected by these results were often prescribed after testing, highlighting the need for discrete results and clinical decision support.

On Eigenmeasures Under Fourier Transform

Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on mathbb {R}hspace{0.5pt}^d. In particular, we classify all periodic eigenmeasures on mathbb {R}hspace{0.5pt}, which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on mathbb {R}hspace{0.5pt} with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodic Meyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around 0.

A factor pricing model based on machine learning algorithm

We adopt Discrete Wavelet Transform (DWT) and Support Vector Regression (SVR) algorithm to predict stock returns and form a time-varying Machine Learning (ML) factor based on the predicted returns for improving the classical asset pricing in the Chinese stock market from 2000 to 2020. The results show that the sorted portfolios formed by the predicted return rates can obtain significant excess returns in the Chinese market. Furthermore, our research shows that incorporating the ML factor into the CH4 and FF5 model can improve the pricing power significantly. It indicates that the ML factor can complement the traditional pricing models. We also find the performance of factor models depend on macroeconomy and market sentiment, that is, the better the macroeconomic and stock market performance, the stronger the pricing power of the factor models in the Chinese market. Additionally, we explore whether ML factor falls under short-term, median-term, and long-term momentum and reversal factors, and our analysis demonstrates that the ML factor is more effective than momentum and reversal factors.

Dynamic Analysis of CRTS II Ballastless Track-Vehicle System Based on Moving Unit Method

On account of the influence of the discontinuity of CRTS II ballastless track slabs and the discrete support of track pads on the high-speed rail vehicle-ballastless track system, a vibration analysis calculation model of the ballastless track-vehicle coupling system was established on the basis of the moving unit method. The dynamic response of the system at different travel speeds and with and without consideration of the track plate discontinuities was investigated. The effect of the random process discontinuity on the dynamic response of the steel rails was analyzed by Fourier inverse transform on the high and low discontinuity spectra of ballastless rails on China’s high-speed rail. We also generated time domain samples of the track discontinuity corresponding to the three percentile spectra. The results show that the dynamic response of the track structure increases with the speed of the train under the condition of track unevenness, with the dynamic response of the steel rail being the most significant, while the dynamic response of the track slab and concrete foundation decreases step by step compared with that of the steel rail; the discontinuity of the track slab has a low impact on the vertical acceleration of the vehicle and does not affect the smoothness of the train; the magnitude of the dynamic response of the rail increases as the amplitude of the irregularities increases or the wavelength decreases. In the wavelength of 2~30 m, the maximum and as the wavelength of the discontinuity sample increases, the oscillation of the power response time curve decreases significantly and tends to be smooth.

Crash classification based on manner of collision: a comparative analysis

ABSTRACT Traffic crashes vary in the manner in which the collision occurs (collision type), and countermeasures to reduce crashes might vary significantly based on this collision type. The inherent complexity in their mechanism has motivated this study to identify significant factors influencing collision types, with the goal of better countermeasure deployment. The objective of this work is to compare the performances of statistical and machine learning (ML) models in classifying crashes based on collision type, and assess their generalizability and interpretability. Discrete choice models, Bayesian classifiers, tree-based algorithms, and support vector machines are among the data-driven methods considered for comparison. Results indicate that tree-based algorithms perform consistently well and offer a higher interpretability, with out-of-distribution robustness. However, while ML models provide a flexible framework for modeling large data volumes, statistical models provide additional interpretability on the effect of critical variables on crash mechanisms – which is relevant from a safety management standpoint.

Analysis of ECG-based arrhythmia detection system using machine learning

The 3D Discrete Wavelet Transform (DWT) and Support Vector Machine (SVM) are used in this study to analyze and characterize Electrocardiogram (ECG) signals. This technique consists of three stages: ECG signal preprocessing, feature extraction, and ECG signal order. The 3D wavelet transform is a signal preprocessing technique, de-noising, along with wavelet coefficient extraction.•SVM is used to categorize the ECG through each of the nine heartbeat types recognized by the various classifiers. For this work, around 6400 ECG beats were looked at over the China Physiological Signal Challenge (CPSC) 2018 arrhythmia dataset.•The best degree of exactness was acquired when level 4 rough constants with Symlet-8 (Sym8) channel were utilized for arrangement. Utilizing the ECG signals from CPSC 2018 data set, the SVM classifier has a normal precision of 99.02%, which is much better than complex support vector machine (CSVM) 98.5%, and weighted support vector machine (WSVM) 99%.•The suggested approach is far superior to others in terms of accuracy, and classification of several diseases of arrhythmia.

Temperate distributions with locally finite support and spectrum on Euclidean spaces

We prove that supports of a wide class of temperate distributions with uniformly discrete support and spectrum on Euclidean spaces are finite unions of translations of full-rank lattices. This result is a generalization of the corresponding theorem for Fourier quasicrystals, and its proof uses the technique of almost periodic distributions.

A Time-Domain Finite-Difference Method for Bending Waves on Infinite Beams on an Elastic Foundation

To model the vibration and structure-borne sound excitation and propagation of a railway rail, it can be modeled as an infinite beam on an elastic foundation. Existing analytical or numerical models are either formulated in the frequency domain or consider only finite beams in the time domain. Therefore, a time-domain approach for bending wave propagation on an effectively infinite beam on an elastic foundation is proposed. The approach makes use of an implicit finite-difference method that allows for varying properties of the beam and the foundation along the length of the beam. Strategies for an efficient discretization are discussed. The method is validated against existing analytical models for a single layer and two layers, as well as continuous and discrete support. The results show very good agreement, and it can be concluded that the proposed method can be seen as a versatile method for simulating the behavior of a beam on different kinds of elastic foundations.

Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributions

The privacy loss distribution (PLD) provides a tight characterization of the privacy loss of a mechanism in the context of differential privacy (DP). Recent work [18–20, 24] has shown that PLD-based accounting allows for tighter (ε, δ)-DP guarantees for many popular mechanisms compared to other known methods. A key question in PLD-based accounting is how to approximate any (potentially continuous) PLD with a PLD over any specified discrete support. We present a novel approach to this problem. Our approach supports both pessimistic estimation, which overestimates the hockey-stick divergence (i.e., δ) for any value of ε, and optimistic estimation, which underestimates the hockey-stick divergence. Moreover, we show that our pessimistic estimate is the best possible among all pessimistic estimates. Experimental evaluation shows that our approach can work with much larger discretization intervals while keeping a similar error bound compared to previous approaches and yet give a better approximation than an existing method [24].

The Modified Structural Quasi Score Estimator for Poisson Regression Parameters with Covariate Measurement Error

This article proposed the Modified Structural Quasi Score (MSQS) estimators for Poisson regression parameters when a covariate is subject to measurement error. We study the situation when the true covariate in the Poisson regression model is unobserved, and the surrogate for this covariate is related to the true covariate by the additive measurement error model. We assumed that true covariate as a random variable with unknown density function distribution and its observable values as surrogates, which also has Poisson distribution. We applied the Empirical Bayes Deconvolution (EBD) method for estimating the true covariate density with a finite discrete support set. To estimate Poisson regression parameters, we construct an MSQS estimating equation based on proper functions for the mean and variance of the Poisson distributed surrogate. The MSQS estimator for the Poisson regression parameter is the root of the quasi-score function based on the quasi-likelihood method. We did some simulation scenarios for assessing the MSQS estimator by assuming the true covariate comes from Gamma distribution as a conjugate before Poison distribution. We compute the standard error of the mean, standard deviation, and bias of the MSQS estimator for various sample sizes to examine the estimator's appropriateness. The simulation showed that a combination of the finite discrete support set of surrogates based on the range values and smaller-scale parameter of Gamma distribution yields smaller values of bias estimator and the estimated standard deviation.

Transfer matrix method for analyzing dynamic response of multi-span elastically supported SFT under moving load

This paper proposed a new theoretical model for analyzing the submerged floating tunnel(SFT) under moving load, whose boundary at two ends was regarded as elastic constraint, and the anchor cable was simplified as the discrete spring support. Besides, the tunnel joint was simulated as a flexural spring to connect two adjacent tube segments. The modes and natural frequencies of the model were solved by transfer matrix method, and the dynamic response of the SFT under moving load was investigated by the modal superposition method, which was verified by comparing with the results obtained by the general FEM software. The influence of boundary conditions, dissimilarity of cable stiffness and joint flexural stiffness on the dynamic response of the SFT was analyzed. The difference of the response between the beam on elastic supports (BOES) and the beam on elastic foundation (BOEF) was compared. The results showed that the boundary conditions had little influence on the vibration response of SFT's intermediate spans, but had great influence on the displacement and bending moment of the side span. Besides, even in the case when the frequency differentials of the BOES and the BOEF were small (1.84%), the displacements of the two models also had significant difference. The disparity of the cable stiffness and joint flexural stiffness had great influence on the distribution of displacement and bending moment of SFT.

An Efficient Numerical Model to Predict the Mechanical Response of a Railway Track in the Low-Frequency Range

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical baselines. Historically, computation rules for traffic conditions are based on simplified analytical works, which are considerably qualitative. They have evolved through feedback and experimental campaigns to comply with the track structure evolution. An efficient methodology based on numerical simulation is needed to evaluate railway vehicle admission to answer this issue. A perspective to update these computation rules is to evaluate the structural fatigue in the rail. That is to say, fatigue is caused by bending and shear stresses. The complexity of the railway system has led to an investigation at first of the vertical response of the railway track and quantifying its contribution to the rail’s stress response. In that sense, this paper investigates the vertical track response to a moving railway vehicle at low frequencies. For this purpose, a lightweight numerical model for the track, a multi-body model for the vehicle, and a random vertical track irregularity are proposed. More explicitly, the track model consists of a two-layer discrete support model in which the rail is considered as a beam and sleepers are point masses. The rail pads and ballast layer are modelled as spring/damper couples. Numerical results show a negligible effect of track inertia forces due to high track stiffness and damping. Nevertheless, this assumption is valid for normal rail stresses but not for ballast loading, especially in the case of sleeper voids or unsupported sleepers. Hence, the prediction of the mechanical stress state in the rail for fatigue issues is achieved through a static track model where the equivalent loading is obtained from a dynamic study of a simplified vehicle model. A statistical analysis shows that the variability of the vertical track irregularity does not influence the output variabilities like the maximum in time and space of the normal and shear stress.

Supporting Behavior Change in Sedentary Adults via Real-time Multidimensional Physical Activity Feedback: Mixed Methods Randomized Controlled Trial.

BackgroundIncreasing physical activity (PA) behavior remains a public health priority, and wearable technology is increasingly being used to support behavior change efforts. Using wearables to capture and provide comprehensive, visually persuasive, multidimensional feedback with real-time support may be a promising way of increasing PA in inactive individuals.ObjectiveThis study aims to explore whether a 6-week self-monitoring intervention using composite web-based multidimensional PA feedback with real-time daily feedback supports increased PA in adults.MethodsA 6-week, mixed methods, 2-armed exploratory randomized controlled trial with 6-week follow-up was used, whereby low to moderately active (PA level [PAL] <2.0) adults (mean age 51.3 years, SD 8.4 years; women 28/51, 55%) were randomly assigned to receive the self-monitoring intervention (36/51, 71%) or waiting list control (15/51, 29%). Assessment of PA across multiple health-harnessing PA dimensions (eg, PAL, weekly moderate to vigorous intensity PA, sedentary time, and steps), psychosocial cognitions (eg, behavioral regulation, barrier self-efficacy, and habit strength), and health were made at the prerandomization baseline at 6 and 12 weeks. An exploratory analysis of the mean difference and CIs was conducted using the analysis of covariance model. After the 12-week assessment, intervention participants were interviewed to explore their views on the program.ResultsThere were no notable differences in any PA outcome immediately after the intervention; however, at 12 weeks, moderate-to-large effects were observed with a mean difference in PAL of 0.09 (95% CI 0.02-0.15; effect size [Hedges g] 0.8), daily moderate-intensity PA of 24 (95% CI 0-45; Hedges g=0.6) minutes, weekly moderate-to-vigorous intensity PA of 195 (95% CI 58-331; Hedges g=0.8) minutes, and steps of 1545 (95% CI 581-2553; Hedges g=0.7). Descriptive analyses suggested that the differences in PA at 12 weeks were more pronounced in women and participants with lower baseline PA levels. Immediately after the intervention, there were favorable differences in autonomous motivation, controlled motivation, perceived competence for PA, and barrier self-efficacy, with the latter sustained at follow-up. Qualitative data implied that the intervention was highly informative for participants and that the real-time feedback element was particularly useful in providing tangible, day-to-day behavioral support.ConclusionsUsing wearable trackers to capture and present sophisticated multidimensional PA feedback combined with discrete real-time support may be a useful way of facilitating changes in behavior. Further investigation into the ways of optimizing the use of wearables in inactive participants and testing the efficacy of this approach via a robust study design is warranted.Trial RegistrationClinicalTrials.gov NCT02432924; https://clinicaltrials.gov/ct2/show/NCT02432924

A machine learning algorithm for classification of mental tasks

In this article, a contemporary tack of mental tasks on cognitive parts of humans is appraised using two different approaches such as wavelet transforms at a discrete time (DWT) and support vector machine (SVM). The put forth tack is instilled with the electroencephalogram (EEG) database acquired in real-time from CARE Hospital, Nagpur. Additional data is also acquired from a brain-computer interface (BCI). In the working model, signals from the database are wed out into different frequency sub-bands using DWT. Initially, updated statistical features are obtained from different frequency sub-bands. This type of representation defines the wavelet co-efficient which is introduced for reducing the measurement of data. Then, the projected method is realized using SVM for segregating both port and veracious hand movement. After segregation of EEG signals, results are achieved with an accuracy of 92% for BCI competition paradigm III and 97.89% for B-alert machine.

Distributionally Robust Chance Constrained Geometric Optimization

This paper discusses distributionally robust geometric programs with individual or joint chance constraints. Several groups of uncertainty sets are considered: uncertainty sets with first two order moments information; uncertainty sets with known first order or first two order moments information under nonnegative support; uncertainty sets constrained by the Kullback–Leibler divergence with a normal or discrete reference distribution; uncertainty sets constrained by the Wasserstein distance under discrete, full, or nonnegative real-space support; and joint uncertainty sets for the product of random variables. Under each group of uncertainty sets, we find deterministic reformulations of the distributionally robust geometric programs with individual or joint chance constraints. Convexity, solution methods, and relationships of the reformulation programs are discussed. Finally, numerical tests are carried out on a shape optimization problem.

Dynamic simulation of HTS maglev vehicle/track coupled based on discrete elastic support track model

High-Temperature Superconducting (HTS) Maglev has the potential to run at high speed with the advantages of stability. As a kind of track transportation vehicle, the performance of vehicle-track coupled vibration will affect the comfort and safety of vehicle operation. In this paper, the track structure is analysed and designed based on the dynamic response of vehicle-track coupling. The model of long pillow embedded ballastless track is used to simulate the discrete permanent magnet track supported by the fastener and elastic rubber pad under the fastener. Through the calculation of the coupling system of HTS maglev train, the vehicle dynamic performance under different fastener stiffness, different fastener distance and different speed is obtained. The dynamic performance of the vehicle is quantitatively evaluated by the maximum acceleration of the car body, fluctuation of suspension gap and the running stability of the vehicle. The vibration responses of vehicles and tracks under different working conditions are discussed, and reasonable design suggestions are given.

Uniqueness theorems for Fourier quasicrystals and temperate distributions with discrete support

It is proved that if some points of the supports of two Fourier quasicrystals approach each other while tending to infinity and the same is true for the masses at these points, then these quasicrystals coincide. A similar statement is obtained for a certain class of discrete temperate distributions.