Fewer Number Of Variables Research Articles

Optimization of train schedule with uncertain maintenance plans in high-speed railways: A stochastic programming approach

In high-speed railways, unexpected disturbances on maintenance activities may cause serious delays of the scheduled trains and greatly affect the service quality for traveling passengers. In contrast to most existing studies that focused on deterministic maintenance activities, this paper develops a two-stage stochastic programming approach to address the optimization of train schedules under uncertain maintenance plans. Specifically, in the first stage, we aim to determine the departure times of trains from the origin station, since this information needs to be public to passengers in advanced. The objective function is to minimize the expected travel time of trains under uncertain duration time of maintenance activities. In the second stage, given the specific information of maintenance activities, we generate the train schedule by adjusting the stop patterns, train orders and the assignment of tracks at key stations. Due to the computational difficulties arising from the large number of discrete decision variables, we particularly develop a dual decomposition based solution approach to solve the two-stage stochastic model. Our approach decomposes the original problem into a set of scenario-dependent subproblems with much fewer number of variables, which greatly improves the computational efficiency. Finally, we conduct several sets of real-world instances based on the Beijing–Guangzhou high-speed railway corridor to verify the effectiveness of the proposed model and solution approach. The results demonstrate that our approach evidently outperforms state-of-art solvers (Gurobi), especially for large-scale instances that Gurobi cannot even return feasible solutions.

Mathematical Oncology to Cancer Systems Medicine: Translation from Academic Pursuit to Individualized Therapy with MORA

Aim & Objective: This article is aimed to understand the gradual development of cancer systems medicine and how this provides a better therapeutic strategy (in terms of drug selection, dose and duration) and patients care. Hence, this study is focused to understand the need and the evolving nature of the analytical models for the assessment of the outcome of different cancer therapeutics. Background: Presently, cancer is viewed from a quantitative standpoint; hence, several analytical models on different cancers have developed. From the information of cancer development to therapeutic advantage, mathematical oncology has contributed significantly. With a fewer number of variables, models in this area have successfully synchronized the model output with real-life dynamical data. However, with the availability of large scale data for different cancers, systems biology has gained importance. It provides biomedical insights among a large number of variables. And to get information for clinically relevant variables especially, the controlling variable(s), cancer systems medicine is suggested. Methods: In this article, we have reviewed the gradual development of the field from mathematical oncology to cancer systems biology to cancer systems medicine. An intensive search with PubMed, IEEE Xplorer and Google for cancer model, analytical model and cancer systems biology was made and the latest developments have been noted. Results: Gradual development of cancer systems biology entails the importance of the development of models towards a unified model of cancer treatment. For this, the model should be flexible so that different types of cancer and/or its therapy can be included within the same model. With the existing knowledge, relevant variables are included in the same model, followed by simulation studies that will enrich the knowledge base further. Such a deductive approach in the modelling and simulations efforts can help to tackle the adversity of individual cancer cases in future. This approach is indeed important to encompass the fourth industrial revolution in health sector. Conclusion: Towards the development of a unified modelling effort, a multi-scale modelling approach could be suitable; so that different researchers across the globe can add their contribution to enrich the same model. Moreover, with this, the identification of controlling variables may be possible. Towards this goal, middle-out rationalist approach (MORA) is working on analytical models for cancer treatment.

Société de Biomécanique Young Investigator Award 2021: Numerical investigation of the time-dependent stress–strain mechanical behaviour of skeletal muscle tissue in the context of pressure ulcer prevention

BackgroundPressure-induced tissue strain is one major pathway for Pressure Ulcer development and, especially, Deep Tissue Injury. Biomechanical investigation of the time-dependent stress–strain mechanical behaviour of skeletal muscle tissue is therefore essential. In the literature, a viscoelastic formulation is generally assumed for the experimental characterization of skeletal muscles, with the limitation that the underlying physical mechanisms that give rise to the time dependent stress–strain behaviour are not known. The objective of this study is to explore the capability of poroelasticity to reproduce the apparent viscoelastic behaviour of passive muscle tissue under confined compression. MethodsExperimental stress-relaxation response of 31 cylindrical porcine samples tested under fast and slow confined compression by Vaidya and collaborators were used. An axisymmetric Finite Element model was developed in ABAQUS and, for each sample a one-to-one inverse analysis was performed to calibrate the specimen-specific constitutive parameters, namely, the drained Young's modulus, the void ratio, hydraulic permeability, the Poisson's ratio, the solid grain's and fluid's bulk moduli. FindingsThe peak stress and consolidation were recovered for most of the samples (N=25) by the poroelastic model (normalised root-mean-square error ≤0.03 for fast and slow confined compression conditions). InterpretationThe strength of the proposed model is its fewer number of variables (N=6 for the proposed poroelastic model versus N=18 for the viscohyperelastic model proposed by Vaidya and collaborators). The incorporation of poroelasticity to clinical models of Pessure Ulcer formation could lead to more precise and mechanistic explorations of soft tissue injury risk factors.

Relapse Prediction Model for Immune-Mediated Thrombotic Thrombocytopenic Purpura

Background: Immune mediated thrombotic thrombocytopenic purpura (iTTP) is defined by thrombocytopenia and microangiopathic hemolytic anemia caused by severely deficient ADAMTS13 activity (<10%). After resolution of their initial episode, patients remain at risk for relapse. Relapse is most common during the first year, but can occur at any point in their lives. In asymptomatic patients, severely deficient ADAMTS13 activity in remission has been shown to be a risk factor for relapses and can guide consideration of preemptive therapy with Rituximab. However, severely deficient ADAMTS13 activity alone does not uniformly lead to relapse, and patients with non-deficient ADAMTS13 activity in remission may still relapse in the following months. The aim of this study was to develop a multivariable model to identify patients at high risk of relapse, using other biomarkers known to have a role in the pathophysiology of iTTP. Patients/Methods: This analysis utilized samples from patients enrolled in the Ohio State University TMA registry beginning in 2003 until 2014. Patients were followed every 3 months to monitor for relapse and for the development of long-term complications. Clinical data (CBC, chemistry, LDH, ADAMTS13 biomarkers) were obtained on each visit to confirm remission in addition to research samples. Clinical and demographic data in addition to biomarkers of complement activation that were performed on banked samples were used to develop a model to quantify the risk for relapse in the following 3 months. A Lasso logistic regression model (Tibshirani et al 1996) with relapse in the following 3 months as the response variable using the R package glmnet (https://cran.r-project.org/web/packages/glmnet/index.html) was used to identify those variables most predictive of relapse from the 17 studied (Table 1). The data from all subjects were split into training data (75%) and testing data (25%) to develop and subsequently test the performance of the model. The final predictors were then standardized to develop the final model and the program to predict the risk of relapse (%) in the following 3 months. Results: Data from a total of 131 patient encounters from 42 patients in a clinical remission were included in the study to develop the statistical model (Table 2). 31(75.6%) were White and 10 (24.4%) were African American. The average age was 42 (18-69), and 31 (75.6%) were women. The median number of encounters from each patient was 2 (range, 1 to 10). From these 131 encounters, 39 relapses occurred in 20 patients over the next 3 months following their clinic visit. The 39 relapse encounters were compared to the 92 encounters where no relapse occurred to develop the model. The performance of both the 11-factor and 6-factor models are shown in Table 3. Given the comparable data in terms of the AUC, sensitivity and specificity to the 11-factor model to predict relapse, the 6-factor model was judged to be more practical given the fewer number of variables. Both the 11-factor and 6-factor models performed better than the ADAMTS13 activity alone. In this model, the presence of ULVWF multimers, increased levels of LDH, complement activation as measured by C3a (log transformed), a lower ADAMTS13 activity (log transformed), ADAMTS13 antigen (log transformed), and younger age increased the risk for relapse. These variables would be entered into the model with the result being read out as a percent risk for relapse in the following 3 months as described in the hypothetical examples in Table 4. Conclusion: Utilizing a model that includes a combination of biomarkers in asymptomatic patients in remission from iTTP provides more accurate identification of patients at increased risk of relapse in the next 3 months, when compared to using the ADAMTS13 activity alone. This model would allow physicians to initiate preemptive therapy with rituximab to patients at the greatest risk for relapse, and potentially avoiding therapy in patients whose risk may be lower than what would be predicted by the ADAMTS13 activity alone. Disclosures Cataland: Ablynx/Sanofi: Consultancy, Research Funding; Alexion: Consultancy, Research Funding.

The Error Linear Complexity Spectrum as a Cryptographic Criterion of Boolean Functions

The error linear complexity spectrum constitutes a well-known cryptographic criterion for sequences, indicating how the linear complexity of the sequence decreases as the number of bits allowed to be modified per period increases. In this paper, via defining an association between $2^{n}$ -periodic binary sequences and Boolean functions on $n$ variables, it is shown that the error linear complexity spectrum also provides useful cryptographic information for the corresponding Boolean function $f$ - namely, it yields an upper bound on the minimum Hamming distance between $f$ and the set of functions depending on fewer number of variables. Therefore, the prominent Lauder-Paterson algorithm for computing the error linear complexity spectrum of a sequence may also be used for efficiently determining approximations of a Boolean function that depend on fewer number of variables. Moreover, it is also shown that, through this approach, low-degree approximations of a Boolean function can be also obtained in an efficient way.

Sex estimation of femur using simulated metapopulation database: A preliminary investigation

Accurate and reliable methods of sex estimation are essential in forensic practice. In the literature, both the population based and non-population specific standards are existing. In the present work, the summary statistics of 3 femoral standard measurements (joints and length diameters) were collected from 13 published studies of modern populations. The metric data of each population were regenerated using truncated normal distribution approach. A simulated metapopulation database was constructed using the combined metric data of 2275 femur bones. Despite interpopulation differences, the calculation of stable non-population specific discriminant functions (DF) was possible using the most discriminatory variables selected by stepwise analysis.The functions were tested on raw data of 6 populations which were obtained from authentic sources. The pooled DFs produced lower but comparable accuracies to the population specific functions using fewer number of variables. The total allocation accuracies of the temporally distant Terry collection did reach better than 90% in both American whites and blacks while in the contemporary Turkish and Hispanic samples were more than 85%. In Asian populations, the total accuracies ranged from 69.7% to 84.9%. Nevertheless, raising the posterior probability threshold to 0.95 increased the total allocation accuracies above 95% in all populations using the pooled populations function of femur joints diameters. This function permitted the classification of one third to more than half of the total sample size in each population which suggest a considerable practical value in estimating sex of unknown individuals without a priori recognition of population affinity.

Use of higher-order Legendre polynomials for multilayered plate elements with node-dependent kinematics

In the present work, higher-order Legendre polynomials are adopted as shape functions of p-version plate finite elements (FEs) and used in combination with node-dependent kinematics (NDK) to construct computationally efficient global–local FE models for the analysis of multilayered plates. The use of higher-order Legendre polynomials enables the elements to accommodate the complex structural deformations with a fewer number of variables in the FE model. Derived from Carrera Unified Formulation (CUF), NDK can integrate plate kinematics based on Equivalent Single Layer (ESL) models and Layer-wise (LW) models to obtain global–local models using no ad hoc coupling. The combination of Legendre-type shape functions and NDK shows excellent rates of convergence, which can lead to FE models with high accuracy in the refined local area with a reduction in the computational efforts. The capabilities of the proposed approach are investigated through various numerical examples by comparing the solution accuracy versus the computational expenses.

Improved HSDT accounting for effect of thickness stretching in advanced composite plates

In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

Modeling Surface Soil Moisture from Microwave Remote Sensing Data in Solani River Catchment, Uttarakhand, India

The spatiotemporal variation of surface soil moisture is a key subject variable need to be assessed accurately since it plays a crucial role in partitioning of rainfall into runoff and infiltration. Active microwave remote sensing has offered prominent potential towards accurate estimation of surface soil moisture. Present study utilizes ERS-2 SAR image for estimating surface soil moisture by incorporating the effect of topography, vegetation and surface roughness over three land cover types namely; sugarcane, wheat and barren land through Multiple Linear Regression (MLR) approach. Five independent variables considered for MLR analysis include backscatter coefficient (σ0 ), local incidence angle (αi), surface roughness height (hs), Leaf Area Index (LAI) and Plant Water Content (PWC), respectively. Results indicate retrieval of soil moisture within ± 20% accuracy for all the three land cover types with higher accuracy for barren land (i.e. R2 ~ 0.78 and RMSE = 1.31) as compared to the other two land cover types (i.e. sugarcane; R2 ~ 0.67 and RMSE = 3.60 and wheat; R2 ~ 0.72 and RMSE = 1.94). The present study reveals the effectiveness of MLR approach in the retrieval of surface soil moisture using fewer numbers of variables.

An Integer Programming Model for a Complex University Timetabling Problem: A Case Study

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

Somatic mutation detection using ensemble of flexible neural tree model

The advances on next-generation sequencing technology (NGS) have enabled researchers to detect somatic mutations. Much effect has been devoted to improve accuracy of discovering somatic mutations from tumour/normal NGS data. In this study, flexible neural tree model (FNT) is proposed to detect somatic mutations in tumour-normal paired sequencing data. To improve the classification accuracy further, a new classification ensemble approach based on Radial Basis Function (RBF) neural networks as nonlinear combination function is proposed. The proposed method is applied to real biological dataset from exome capture data and the whole genome shotgun data. Results show that the obtained FNT model has a fewer number of variables with reduced number of input features and with significant improvement in the detection accuracy using the proposed ensemble learning method. Our method also selects 10 import features for somatic mutation detection, which could be used to analyze NGS mutations further.

Evaluation of data discretization methods to derive platform independent isoform expression signatures for multi-class tumor subtyping.

BackgroundMany supervised learning algorithms have been applied in deriving gene signatures for patient stratification from gene expression data. However, transferring the multi-gene signatures from one analytical platform to another without loss of classification accuracy is a major challenge. Here, we compared three unsupervised data discretization methods--Equal-width binning, Equal-frequency binning, and k-means clustering--in accurately classifying the four known subtypes of glioblastoma multiforme (GBM) when the classification algorithms were trained on the isoform-level gene expression profiles from exon-array platform and tested on the corresponding profiles from RNA-seq data.ResultsWe applied an integrated machine learning framework that involves three sequential steps; feature selection, data discretization, and classification. For models trained and tested on exon-array data, the addition of data discretization step led to robust and accurate predictive models with fewer number of variables in the final models. For models trained on exon-array data and tested on RNA-seq data, the addition of data discretization step dramatically improved the classification accuracies with Equal-frequency binning showing the highest improvement with more than 90% accuracies for all the models with features chosen by Random Forest based feature selection. Overall, SVM classifier coupled with Equal-frequency binning achieved the best accuracy (> 95%). Without data discretization, however, only 73.6% accuracy was achieved at most.ConclusionsThe classification algorithms, trained and tested on data from the same platform, yielded similar accuracies in predicting the four GBM subgroups. However, when dealing with cross-platform data, from exon-array to RNA-seq, the classifiers yielded stable models with highest classification accuracies on data transformed by Equal frequency binning. The approach presented here is generally applicable to other cancer types for classification and identification of molecular subgroups by integrating data across different gene expression platforms.

Quantum dynamics in classical thermal baths

A particular type of open quantum system dynamics is achieved by embedding a quantum system in a classical thermal bath. Such a bath can be represented in terms of the non-Hamiltonian evolution of few variables by means of the so-called Nosè–Hoover Power thermostat. The classical dynamics of the thermostat is integrated by means of time-reversible measure-preserving algorithms. In this work we show that the Nosè–Hoover Power thermostat, when applied to the dissipative evolution of a quantum spin, provides numerical results which agree with those obtained using Nosè–Hoover chains. However, since a fewer number of variables are needed to achieve the correct sampling of the canonical distribution at equilibrium, the Nosè–Hoover Power thermostat promises to be better suited for the simulation of low dimensional open quantum system on discrete grids.

Higher Serum Free Triiodothyronine Levels within the Normal Range Are Associated with Metabolic Syndrome Components in Type 2 Diabetic Subjects with Euthyroidism

Associations of thyroid hormones with visceral obesity and insulin resistance in obese subjects with euthyroidism have been reported. However, there are no such reports in subjects with type 2 diabetes. The purpose of our study is to observe a relationship between thyroid hormones and components of metabolic syndrome (MetS) in type 2 diabetic subjects with euthyroidism defined by normal thyroid stimulating hormone (TSH) and free thyroxine (FT4) levels. Subjects were 301 Japanese patients with type 2 diabetes. Serum TSH, FT4, free triiodothyronine (FT3), and variables related to MetS were measured. MetS was defined by the Japanese criteria and the criteria of the National Cholesterol Education Program modified for Asians. We found that serum FT3 levels were significantly and positively associated with BMI, visceral fat area, systolic and diastolic blood pressure, estimated glomerular filtration rate, serum triglyceride, and urine C peptide as a marker of insulin production, whereas negatively with age and HbA1c. In contrast, fewer numbers of variables were associated with serum TSH and FT4 levels. By a multiple regression analysis, FT3 level was independently associated with components of MetS such as visceral fat area, systolic blood pressure, and fasting blood glucose levels. On the other hand, the presence of these MetS components was independently associated with FT3 levels and urine C peptide. In conclusion, these results suggest a significant relationship between serum FT3 levels and components of MetS in type 2 diabetic subjects with euthyroidism, and imply a role of FT3 in MetS in type 2 diabetes.

A Hybrid Approach to Model Hysteretic Behavior of PZT Stack Actuators

In order to model the hysteretic behavior of piezoceramic actuators, a hybrid model is developed by combining the Preisach concepts with a neural network mapping function. Preisach concepts are utilized in producing a data set for generalization and calculating the final displacements for actuators having nonlocal memory. Although generalization is typically handled by interpolation functions in a traditional Preisach model, these functions can lead to significant errors unless there are sufficient data points around critical regions. In the hybrid model, the generalization of all first-order reversal curves is provided by a single neural network. Since the neural network is essentially a nonlinear mapping function, its functionality is implemented with a fewer number of variables than the Preisach model. In order to account for errors caused by frequency dependency and large input variations, an on-line training technique is also developed. Various comparisons between the outputs of the hybrid model and those of an actual actuator are presented.

THE FLEXIBLE TOLERANCE METHOD FOR ESTIMATING HYDROLOGIC PARAMETERS IN THE ROOT ZONE

: In this study, a constrained minimization method, the flexible tolerance method, was used to solve the optimization problems for determining hydrologic parameters in the root zone: water uptake rate, spatial root distribution, infiltration rate, and evaporation. Synthetic soil moisture data were first generated using the Richards' equation and its associated initial and boundary conditions, and these data were then used for the inverse analyses. The results of inverse simulation indicate the following. If the soil moisture data contain no noise, the rate of estimated water uptake and spatial root distribution parameters are equal to the true values without using constraints. If there is noise in the observed data, constraints must be used to improve the quality of the estimate results. In the estimation of rainfall infiltration and surface evaporation, interpolation methods should be used to reduce the number of unknowns. A fewer number of variables can improve the quality of inversely estimated parameters. Simultaneous estimation of spatial root distribution and water uptake rate or estimation of evaporation and water uptake rate is possible. The method was used to estimate the water uptake rate, spatial root distribution, infiltration rate, and evaporation using long-term soil moisture data collected from Nebraska's Sand Hills.

Small Cities Matter, Too: The Impacts of an Airport and Local Infrastructure on Housing Prices in a Small Urban City

Cities with small populations tend not to receive as much attention in housing hedonic studies as do large metropolitan areas despite their similar economic development goals (quality of life improvements for their citizens, etc.). However, small cities, with their relatively smaller number of amenities and features, tend to have fewer numbers of variables that operate to determine house prices. Therefore, hedonic prices can be estimated adequately for a single neighborhood in a small city with publicly available data, particularly for local officials who do not have the time or financial resources to complete detailed studies of their cities. In this study, a general model is estimated that uncovers the impacts of airport‐related noise, local recreational amenities, public transportation services, and schools on housing prices in a small city in metropolitan Atlanta, Georgia, USA. The implications and usefulness of this approach to local economic developers and city planners will be discussed.

Large Scale Kernel Regression via Linear Programming

The problem of tolerant data fitting by a nonlinear surface, induced by a kernel-based support vector machine is formulated as a linear program with fewer number of variables than that of other linear programming formulations. A generalization of the linear programming chunking algorithm for arbitrary kernels is implemented for solving problems with very large datasets wherein chunking is performed on both data points and problem variables. The proposed approach tolerates a small error, which is adjusted parametrically, while fitting the given data. This leads to improved fitting of noisy data (over ordinary least error solutions) as demonstrated computationally. Comparative numerical results indicate an average time reduction as high as 26.0% over other formulations, with a maximal time reduction of 79.7%. Additionally, linear programs with as many as 16,000 data points and more than a billion nonzero matrix elements are solved.

Best trigonometric and bilinear approximations of functions of several variables from the classes Bp,?r� I

Approximations are studied of the classes Bp,θr of periodic functions of several variables with the help of trigonometric polynomials with a given number of harmonics. The results obtained are used to establish order estimates of the approximation of functions of the form f(x−y), f(x) e Bp,θr, by combinations of products of functions of a fewer number of variables.

On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables

We present a simple method for finding the values of the best approximation of a function of n variables of a given class by means of sums of two functions of a fewer number of variables; we establish close upper and lower bounds for the value of the best approximation to the functionf(x1, ..., xn), having the mixed derivativef x1 ... xn, by means of sums of a function of n−1 variables.