Common Special Cases Research Articles

A comparison of alternative models for solving a non-linear single plant Hydro Unit Commitment problem

A wide range of real world optimization problems involves continuous decisions and non-linearities. Each non-linear component of such problems can be modeled either linearly or non-linearly, considering or not additional integer variables. This results into different modeling choices that can drastically impact the solution time and quality. In this paper, we evaluate representative modeling alternatives, including common models from the literature as well as new models featuring less common functions. The single plant Hydro Unit Commitment problem (1-HUC) is the considered non-linear use case. Among the non-linearities of the 1-HUC, we focus on those involved in the power production, more precisely the head effect and the turbines efficiency. The power is defined as a two-dimensional non-convex and non-concave function of the water flow and head decision variables, the latter being itself a one-dimensional concave function of the turbined volume. We consider both the general problem and a common special case, assuming that the water head is fixed. Several available solvers are used for each non-linear model and the best virtual solver is retained to focus on the model capabilities rather than on the solver performance. Based on the numerical experiments, three models stand out as the most efficient in terms of computational time, solution quality and feasibility, sometimes in a counter-intuitive manner. For each of these models, a solver is highlighted as the most adequate.

МОДЕЛИРОВАНИЕ И СРАВНЕНИЕ РЕЗУЛЬТАТОВ ТОЧНОГО АНАЛИТИЧЕСКОГО РЕШЕНИЯ КРАЕВОЙ ЗАДАЧИ ТЕЧЕНИЯ В ТОНКОМ СЛОЕ С ЭКСПЕРИМЕНТАЛЬНЫМИ ДАННЫМИ

Many technological processes of metal forming include deformation of an elongated workpiece by approaching tools, the contact surfaces of which have shallow grooved cavities. A common special case are stamps or part of their contact surfaces, which are planes: sites for draft and some types of harvesting streams. The article is devoted to mathematical modeling of the flow of a thin metal layer over rough surfaces. The article presents the results of an analytical study of the boundary value problem of the viscoplastic flow of a thin layer of metal located between thin rough plates moving towards each other. Exact solutions based on the classical formulation in the framework of an "ideal fluid" and "viscoplastic fluid" are given. A real experiment is described for assessing the effect of shear stresses averaged over the layer thickness on the kinematics of the flow of a plastic layer. In order to assess the effect of shear stresses averaged over the layer thickness on the flow kinematics, and, in particular, near fixed boundaries, experiments were carried out and the results on settlement between converging rigid plates of a thin plastic sample bounded by fixed walls and initially having the shape of a rectangle in plan are analyzed. . The fixed walls of the tool are located along the long sides of the rectangle. Experimental regularities have been established. Spreading of samples occurs as expected, i.e., along straight streamlines parallel to the long side of the rectangle, or along the rays of a circular sector. It was found that the longitudinal displacements near the immovable walls noticeably lag behind the displacements far from the boundary, and the maximum displacements are observed on the line of symmetry of the sample with respect to the immovable walls. This fact indicates the presence of nonzero shear stresses and (velocities) of deformations in the considered flows of a thin plastic layer. Comparison of the obtained experimental and analytical simulation results allows us to evaluate the correctness of the chosen mathematical model, which can be used to describe the flows.

Effect of Train-Driving Simulator Practice in the European Rail Traffic Management System: An Experimental Study

Many European train drivers face major changes in their work with the introduction of the new train-protection system, the European Rail Traffic Management System (ERTMS), as information retrieval shifts from outside to in-cab, and a new rulebook is introduced. Therefore, many train drivers have to be educated in a short time, to make the transition safe and efficient. The purpose was to find out how a successful ERTMS practice can be designed in a physically low-fidelity but highly functional train-driving simulator. An experimental design was used, with 16 drivers divided into two groups: one group practiced in a simulator, and the other in reality. Standard training methodology was used, and the learning outcome was assessed by both measuring driving errors and via instructor evaluation of a simulator test. The drivers also filled in a questionnaire to capture how different factors, such as repeated practice, experience, and self-estimated confidence, correlate with performance. Results show that the simulator group committed significantly fewer driving errors and received significantly higher scores from the instructor. In addition, the simulator group's better performance is mostly caused by the possibility of repeated training of different special cases. The findings also imply that several of the more common special cases on the ERTMS can hardly be provoked in real train driving. Furthermore, this work strengthens the theory that novices can hardly estimate their own ability. Therefore, we argue that this type of low-fidelity simulator is well suited for research purposes, for practicing special cases, and for train operation companies to assess drivers’ skills.

Testing and relaxing the exclusion restriction in the control function approach

The control function approach which employs an instrumental variable excluded from the outcome equation is a very common solution to deal with the problem of endogeneity in nonseparable models. Exclusion restrictions, however, are frequently controversial. We first argue that, in a nonparametric triangular structure typical of the control function literature, one can actually test this exclusion restriction provided the instrument satisfies a local irrelevance condition. Second, we investigate identification without such exclusion restrictions, i.e., if the “instrument” that is independent of the unobservables in the outcome equation also directly affects the outcome variable. In particular, we show that identification of average causal effects can be achieved in the two most common special cases of the general nonseparable model: linear random coefficients models and single index models.

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation performance that is based on quantized data. In order to maintain physical constraints and simultaneously bring substantial performance gain, in this work we consider systems with mixed-resolution, 1-bit quantized and continuous-valued, data. First, we describe the linear minimum mean-squared error (LMMSE) estimator and its associated mean-squared error (MSE) for the general mixed-resolution model. However, the MSE of the LMMSE requires matrix inversion in which the number of measurements defines the matrix dimensions and thus, is not a tractable tool for optimization and system design. Therefore, we present the linear Gaussian orthonormal (LGO) measurement model and derive a closed-form analytic expression for the MSE of the LMMSE estimator under this model. In addition, we present two common special cases of the LGO model: 1) scalar parameter estimation and 2) channel estimation in mixed-ADC multiple-input multiple-output (MIMO) communication systems. We then solve the resource allocation optimization problem of the LGO model with the proposed tractable form of the MSE as an objective function and under a power constraint using a one-dimensional search. Moreover, we present the concept of dithering for mixed-resolution models and optimize the dithering noise as part of the resource allocation optimization problem for two dithering schemes: 1) adding noise only to the quantized measurements and 2) adding noise to both measurement types. Finally, we present simulations that demonstrate the advantages of using mixed-resolution measurements and the possible improvement introduced with dithering and resource allocation.

Block Forests: random forests for blocks of clinical and omics covariate data

BackgroundIn the last years more and more multi-omics data are becoming available, that is, data featuring measurements of several types of omics data for each patient. Using multi-omics data as covariate data in outcome prediction is both promising and challenging due to the complex structure of such data. Random forest is a prediction method known for its ability to render complex dependency patterns between the outcome and the covariates. Against this background we developed five candidate random forest variants tailored to multi-omics covariate data. These variants modify the split point selection of random forest to incorporate the block structure of multi-omics data and can be applied to any outcome type for which a random forest variant exists, such as categorical, continuous and survival outcomes. Using 20 publicly available multi-omics data sets with survival outcome we compared the prediction performances of the block forest variants with alternatives. We also considered the common special case of having clinical covariates and measurements of a single omics data type available.ResultsWe identify one variant termed “block forest” that outperformed all other approaches in the comparison study. In particular, it performed significantly better than standard random survival forest (adjusted p-value: 0.027). The two best performing variants have in common that the block choice is randomized in the split point selection procedure. In the case of having clinical covariates and a single omics data type available, the improvements of the variants over random survival forest were larger than in the case of the multi-omics data. The degrees of improvements over random survival forest varied strongly across data sets. Moreover, considering all clinical covariates mandatorily improved the performance. This result should however be interpreted with caution, because the level of predictive information contained in clinical covariates depends on the specific application.ConclusionsThe new prediction method block forest for multi-omics data can significantly improve the prediction performance of random forest and outperformed alternatives in the comparison. Block forest is particularly effective for the special case of using clinical covariates in combination with measurements of a single omics data type.

Digital Module 05: Diagnostic Measurement—The G‐DINA Framework https://ncme.elevate.commpartners.com

AbstractIn this ITEMS module, we introduce the generalized deterministic inputs, noisy “and” gate (G‐DINA) model, which is a general framework for specifying, estimating, and evaluating a wide variety of cognitive diagnosis models. The module contains a nontechnical introduction to diagnostic measurement, an introductory overview of the G‐DINA model, as well as common special cases, and a review of model‐data fit evaluation practices within this framework. We use the flexible GDINA R package, which is available for free within the R environment and provides a user‐friendly graphical interface in addition to the code‐driven layer. The digital module also contains videos of worked examples, solutions to data activity questions, curated resources, a glossary, and quizzes with diagnostic feedback.

A Behavioral Dynamic Nonlinear Model for Time-Interleaved ADC Based on Volterra Series

The non-ideal circuit implementations cause a significant degradation in the performance of the time-interleaved analog-to-digital converter (TIADC) system. In this paper, a behavioral model for the TIADC based on Volterra series is proposed to model the dynamic nonlinearities in TIADC. The time-domain and frequency-domain expressions of the behavioral model based on hybrid Volterra series are derived first. Then, the discrete-time equivalent model is proposed by transforming the hybrid TIADC system to a discrete time one based on discrete-time Volterra series only. The derivations give a theoretical foundation to use discrete-time Volterra series to model the mixed-domain TIADC system, which makes it possible to make full use of the related existing derivations, conclusions, and methodologies on discrete-time Volterra series. We also summarize some common special cases of Volterra series to provide practical guidelines for ADC and TIADC practitioners. We present the main features of these models and their relationship with the Volterra series. The simulation and experimental results show the effectiveness of the proposed model.

A Ratio-Based Efficiency Measurement for Ranking Multi-Stage Production Systems in DEA

Conventional data envelopment analysis (DEA) models are used to measure efficiency score of production systems when they are considered as black boxes and their internal relationship is ignored. This paper deals with a common special case of network systems which is called multi-stage production system and can be generalized to many organizations. A multi stage production system has some stages in which the outputs of each stage are used as the inputs of the next stage to produce the final outputs of the system. Most of the approaches handling multi-stage systems in DEA evaluate efficiency measure of a production system considering the interrelationship between its stages; however, they do not present their ranking or impact of each stage in ranking of a special multi-stage system through comparison with the others. In this paper, considering the series internal structure of the multi-stage systems and their efficiency measure, we propose some new ratio-based DEA models to determine the best and the worst rank of the multi-stage systems over all sets of feasible weights. In order to improve the performance of the whole system, the proposed models are used to recognize the stages with the most important role in the system’s inefficiency. Some numerical examples are presented to illustrate the approach.

A generalized approach to modeling absorption and photocurrent in solar cells with light scattering structures

The spatial dependence of absorption in optical structures is important for determining the performance of optoelectronic devices, such as solar cells and photodetectors. When random scattering structures are introduced, the absorption can be difficult to calculate without direct simulation or broad simplifying assumptions. Here we present a theoretical framework for calculating the absorption in individual layers of arbitrary stratified media composed of any combination of coherent thin-films and/or incoherent thick slabs in the presence of randomizing scattering structures. This model allows for accurate predictions of generated carriers in photovoltaic systems. We discuss how these equations may be implemented to describe several common special cases as well as a few complex, non-traditional structures to show the wide range of applicability. Finally, we perform experiments on two multilayer structures with interlaced scattering layers to demonstrate utility and accuracy of the technique.

Energy-Efficiency Analysis of Analog and Digital Compressive Sensing in Wireless Sensors

Compressive sensing (CS) is a signal acquisition strategy that, based on the assumption of sparsity, promises to relax the design constraints of signal acquisition systems with respect to conventional strategies. In this paper, we contrast signal acquisition systems for low-rate applications based on analog CS encoding with systems based on digital CS encoding. We consider the complete signal chain from acquisition to reconstruction, with particular attention to the effects of quantization, and show that the two schemes differ significantly in encoder precision, measurement resolution, compression ratio, and reconstruction quality. Further, we develop first-order power estimation models to asses the relative energy-efficiency of different CS and conventional signal acquisition systems. Our numerical evaluations suggest that when the power consumption of data storage/communication outweighs the power consumption of data acquisition and processing, analog CS systems can outperform their digital counterparts, despite their higher hardware complexity. Moreover, we provide evidence that the common special case of analog and digital encoding, known as non-uniform sampler, performs best under all conditions.

Consistent thinning of large geographical data for map visualization

Large-scale map visualization systems play an increasingly important role in presenting geographic datasets to end-users. Since these datasets can be extremely large, a map rendering system often needs to select a small fraction of the data to visualize them in a limited space. This article addresses the fundamental challenge of thinning : determining appropriate samples of data to be shown on specific geographical regions and zoom levels. Other than the sheer scale of the data, the thinning problem is challenging because of a number of other reasons: (1) data can consist of complex geographical shapes, (2) rendering of data needs to satisfy certain constraints, such as data being preserved across zoom levels and adjacent regions, and (3) after satisfying the constraints, an optimal solution needs to be chosen based on objectives such as maximality , fairness , and importance of data. This article formally defines and presents a complete solution to the thinning problem. First, we express the problem as an integer programming formulation that efficiently solves thinning for desired objectives. Second, we present more efficient solutions for maximality, based on DFS traversal of a spatial tree. Third, we consider the common special case of point datasets, and present an even more efficient randomized algorithm. Fourth, we show that contiguous regions are tractable for a general version of maximality for which arbitrary regions are intractable. Fifth, we examine the structure of our integer programming formulation and show that for point datasets, our program is integral. Finally, we have implemented all techniques from this article in Google Maps [Google 2005] visualizations of fusion tables [Gonzalez et al. 2010], and we describe a set of experiments that demonstrate the trade-offs among the algorithms.

Why the damped trend works

The damped trend method of exponential smoothing is a benchmark that has been difficult to beat in empirical studies of forecast accuracy. One explanation for this success is the flexibility of the method, which contains a variety of special cases that are automatically selected during the fitting process. That is, when the method is fitted, the optimal parameters usually define a special case rather than the method itself. For example, in the M3-competition time series, the parameters defined the damped trend method only about 43% of the time using local initial values for the method components. In the remaining series, a special case was selected, ranging from a random walk to a deterministic trend. The most common special case was a new method, simple exponential smoothing with a damped drift term.

Five convolution formulae of orthogonal polynomials

By means of the classical Lagrange expansion theorem, five convolution formulae are established for the orthogonal polynomials named after Laguerre, Jacobi, Meixner, Gegenbauer and Pollaczek, that contain the well-known Hagen–Rothe formula for binomial coefficients as common special case.

Quantum logic with weakly coupled qubits

There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.

Automatic hidden-web table interpretation, conceptualization, and semantic annotation

The longstanding problem of automatic table interpretation still eludes us. Its solution would not only be an aid to table processing applications such as large volume table conversion, but would also be an aid in solving related problems such as information extraction, semantic annotation, and semi-structured data management. In this paper, we offer a solution for the common special case in which so-called sibling pages are available. The sibling pages we consider are pages on the hidden web, commonly generated from underlying databases. Our system compares them to identify and connect nonvarying components (category labels) and varying components (data values). We tested our solution using more than 2000 tables in source pages from three different domains—car advertisements, molecular biology, and geopolitical information. Experimental results show that the system can successfully identify sibling tables, generate structure patterns, interpret tables using the generated patterns, and automatically adjust the structure patterns as it processes a sequence of hidden-web pages. For these activities, the system was able to achieve an overall F-measure of 94.5%. Further, given that we can automatically interpret tables, we next show that this leads immediately to a conceptualization of the data in these interpreted tables and thus also to a way to semantically annotate these interpreted tables with respect to the ontological conceptualization. Labels in nested table structures yield ontological concepts and interrelationships among these concepts, and associated data values become annotated information. We further show that semantically annotated data leads immediately to queriable data. Thus, the entire process, which is fully automatic, transform facts embedded within tables into facts accessible by standard query engines.

Backward bifurcations and multiple equilibria in epidemic models with structured immunity

Many disease pathogens stimulate immunity in their hosts, which then wanes over time. To better understand the impact of this immunity on epidemiological dynamics, we propose an epidemic model structured according to immunity level that can be applied in many different settings. Under biologically realistic hypotheses, we find that immunity alone never creates a backward bifurcation of the disease-free steady state. This does not rule out the possibility of multiple stable equilibria, but we provide two sufficient conditions for the uniqueness of the endemic equilibrium, and show that these conditions ensure uniqueness in several common special cases. Our results indicate that the within-host dynamics of immunity can, in principle, have important consequences for population-level dynamics, but also suggest that this would require strong non-monotone effects in the immune response to infection. Neutralizing antibody titer data for measles are used to demonstrate the biological application of our theory.

Steady-State Operating Policies for Plants with Multiple Reactions of Equal Overall Order

A simple methodology for determining optimal steady-state operating policies for plants with recycle has been developed by Ward et al. (Ward, J. D.; Mellichamp, D. A.; Doherty, M. F. Ind. Eng. Chem. Res. 2004, 43, 3957). Heuristics were developed to classify irreversible process chemistries into two groups, bounded and nonbounded. This classification has important implications for how to design a control system and operate a chemical plant that contains excess equipment capacity. In this paper, formal rules are developed and presented for classifying a common special case of process chemistries that have multiple undesired irreversible reactions with equal overall reaction order. This new classification procedure is essential for determining the optimal steady-state operating policy for process chemistries of multiple parallel or series/parallel reactions.

A Simple Local Sensitivity Analysis Tool for Nonignorable Coarsening: Application to Dependent Censoring

Right- and interval-censored data are common special cases of coarsened data (Heitjan and Rubin, 1991, Annals of Statistics19, 2244-2253). As with missing data, standard statistical methods that ignore the random nature of the coarsening mechanism may lead to incorrect inferences. We extend a simple sensitivity analysis tool, the index of local sensitivity to nonignorability (Troxel, Ma, and Heitjan, 2004, Statistica Sinica14, 1221-1237), to the evaluation of nonignorability of the coarsening process in the general coarse-data model. By converting this index into a simple graphical display one can easily assess the sensitivity of key inferences to nonignorable coarsening. We illustrate the validity of the method with a simulated example, and apply it to right-censored data from an observational study of cardiac transplantation and to interval-censored data on time to detectable viral load from a clinical trial in HIV disease.

Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels

This paper considers the problem of determining the achievable rates in multi-hop wireless mesh networks with orthogonal channels. We classify wireless networks with orthogonal channels into two types, half duplex and full duplex, and consider the problem of jointly routing the flows and scheduling transmissions to achieve a given rate vector. We develop tight necessary and sufficient conditions for the achievability of the rate vector. We develop efficient and easy to implement Fully Polynomial Time Approximation Schemes for solving the routing problem. The scheduling problem is a solved as a graph edge-coloring problem. We show that this approach guarantees that the solution obtained is within 50% of the optimal solution in the worst case (within 67% of the optimal solution in a common special case) and, in practice, is close to 90% of the optimal solution on the average. The approach that we use is quite flexible and can be extended to handle more sophisticated interference conditions, and routing with diversity requirements.