Multidimensional Setting Research Articles

Multidimensional control systems: case studies in design and evaluation

Multidimensional control systems have been the subject of much productive research over more than three decades. In contrast to standard control systems, there has been much less reported on applications where the multidimensional setting is the only possible setting for design or produces implementations that perform to at least the same level. This paper addresses the latter area where case studies focusing on control law design and evaluation, including experimental results in one case, are reported. These demonstrate that movement towards the actual deployment of multidimensional control systems is increasing.

Convergence in variation and a characterization of the absolute continuity

We study approximation results for a family of Mellin integral operators of the form where is a family of kernels, , , and f is a function of bounded variation on . The starting point of this study is motivated by the important applications that approximation properties of certain families of integral operators have in image reconstruction and in other fields. In order to treat such problems, to work in BV -spaces in the multidimensional setting of becomes crucial: for this reason we use a multidimensional concept of variation in the sense of Tonelli, adapted from the classical definition to the present setting of equipped with the Haar measure. Using such definition of variation, we obtain a convergence result proving that , as , whenever f is an absolutely continuous function; moreover we also study the problem of the rate of approximation. In case of regular kernels, we finally prove a characterization of the absolute continuity in terms of the convergence in variation by means of the Mellin-type operators .

A Characterization of Absolute Continuity by means of Mellin Integral Operators

In the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical BV -spaces, both in the one-dimensional and in the multidimensional setting.

An experimental analysis of multidimensional cheap talk

We design experimental games that capture the logic of Battaglini's (2002) construction of fully revealing equilibrium in multidimensional cheap talk. Two senders transmit information to a receiver over a 2×2 state space. Despite overall misaligned interests, full revelation is achieved in equilibrium by having the senders truthfully reveal along distinct dimensions. Our experimental findings confirm that more information can be extracted with two senders in a multidimensional setting. The extent to which information is transmitted depends on whether dimensional interests are aligned between a sender and the receiver, the sizes of the message spaces, and the specification of out-of-equilibrium beliefs. While inducing interest alignment on the relevant dimensions and restricting the message spaces facilitated equilibrium play and information transmission, having a fully revealing equilibrium that is supported by implausible beliefs reduced the instances in which the equilibrium was played.

Mechanisms for Scheduling with Single-Bit Private Values

We study the problem of designing truthful mechanisms for makespan minimization in scheduling. In particular, we consider randomized mechanisms for a restriction of the general multi-dimensional domain (i.e., unrelated machines). In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information. Some of the impossibility results for deterministic mechanisms carry over our setting as well. We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms.

Delegating Resource Allocation: Multidimensional Information vs. Decisions

This paper studies the problem of how to delegate the allocation of finite resources across multiple categories to an agent who has better information on their benefits. It focuses on a tractable, natural class of delegation policies that impose a floor or cap on the allocation to each category, a generalization of Holmstrom’s (1977) “interval controls” to multidimensional settings. The paper characterizes the optimal policies and shows that they can impose distorting limits on categories which cause no conflict of interest with the agent, so as to curb how the conflict in other categories affects his overall allocation. Such limits are more likely to be optimal when the conflict is weaker and the agent also has specific information on categories causing no conflict. These solutions to the trade-off between rules and discretion differ substantively from those in settings with unidimensional decisions or information. The paper discusses applications to delegation within firms, the design of fiscal constitutions and policies, and individual commitment problems.

Scaling Multidimensional Inference for Structured Gaussian Processes.

Exact Gaussian process (GP) regression has O(N(3)) runtime for data size N, making it intractable for large N . Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several data sets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.

Gas Storage Valuation Under Multi-Factor Levy Processes

This paper builds upon the work of Kiely et al. [2015] to provide a storage valuation methodology which is capable of utilizing both market and historical information. We begin by extending the Mean Reverting Variance Gamma process to an arbitrary number of dimensions and by way of specific examples show how the traditional Principal Component Analysis based view of gas forward curve dynamics can be incorporated into a primarily market based valuation. We discuss the calibration of such models to the monthly delivery swaption market through a modi cation of the market implied moments technique of Guillaume and Schoutens [2013]. We go on to present details of the Fourier Transform based valuation methodology in a multidimensional setting and fi nally present empirical valuation results for a stylized storage deal under different specif cations of a two factor model of the forward curve.

Modeling Driver Behavior in Work and Nonwork Zones

A new multidimensional framework for modeling car following on the basis of statistical evaluation of driver behavior in work and non-work zones is presented. The models developed as part of this multidimensional framework use psychophysical concepts for car following that are close in character to the Wiedemann model used in popular traffic simulation software such as VISSIM. The authors hypothesized that with an instrumented research vehicle (IRV) in a living laboratory (LL) along a roadway, the parameters of models developed from the multidimensional framework could be derived statistically and calibrated for driver behavior in work zones. This hypothesis was validated with data collected from a group of 64 random participants who drove the IRV through an LL set up along a work zone on I-95 near Washington, D.C. For this validation, the IRV was equipped with sensors, including radar, and an onboard data collection system to record the vehicle performance. One of the limitations of current car-following models is that they account for only one overall behavioral condition. This study demonstrated that there are four different categories of car-following behavior models, each with different parameter distributions: the four categories are divided by traffic condition (congested versus non congested) and by roadway condition (work versus nonwork zone). Calibrated threshold values for each of these four categories are presented. Furthermore, this new framework for modeling car-following behavior is described in a multidimensional setting and can be used to enhance vehicle behavior in microsimulation models.

Use of Psychotropics and Drug-Drug Interactions in Oncology: Reflections from a Study in a Portuguese Psycho-Oncology Unit

Introduction: Psychopharmacological treatment is an important tool of the multidimensional approach in oncologic setting but cancer patient´s susceptibility to drug-drug interactions may pose them at risk. Objective: To describe the use of psychotropic in patients referred to a psycho-oncology unit and to point out potential and clinical relevant drug-drug interactions in this context. Methods: Descriptive study of a sample of patients referred for the first time to the Psycho-Oncology Unit of Coimbra University Hospital Centre, between April and December 2013. A retrospective collection of the sociodemographic, clinical and prescription data was made by consulting clinical processes. Results: From the sample of 110 patients, 51,8% of the patients were already taking some psychotropic drug and 91,9% were on antineoplastic medication at the time of the psycho-oncology appointment. Among the psychotropic medication, almost all were benzodiazepines and antidepressants. Psychotropic can cause potential interactions with antineoplastic medication administered in cancer patients. Some pharmacological agents have more potential to cause drug-drug interactions. Conclusions: Prescription of psychotropic medication by the oncological team is common and cancer patients usually take several drugs at the same time. This study outlines the importance of promoting scientific research on drug-drug interactions in psycho-oncology and a closer collaboration between oncology and psychiatry in order to reduce the risk of drug-drug Interactions, to increase its awareness and to adequately prescribe a psychopharmacologic treatment for each patient.

How Does May’s Law Work in Multi-dimensional Competition? Intra-party Opinion Structure in Catalonia

AbstractThis article explores how multi-dimensional competition party systems shape the intraparty opinion structure in political parties. The aim is to extend and test May’s law of ideological curvilinear disparity to multi-dimensional settings. The data are based on the case of Catalonia, a party system characterized by the relevant presence of non-state wide parties, where political competition is based on two main dimensions: the left right axis and the subjective national identity one. The paper shows that while the Catalan parties do fit with May’s law in the left-right axis, this is not the case in the national identity one. In addition, it further illustrates how the interaction between both axes affects party competition and internal opinion differences between leaders, activists and voters. The results attest the complexity of the intraparty opinion structures in multidimensional competition systems.

The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case

We consider two-phase flow problems in porous media with overshooting waves. If higher-order effects are neglected, such problems are governed by a hyperbolic conservation law with a nonconvex flux function as the macroscale model. It is well known that there can be multiple weak solutions. To ensure uniqueness, we use on the microscale either a kinetic relation or in a second approach an extended system, taking rate-dependent capillary pressure effects into account. We present a new multidimensional mass-conserving numerical method to solve the macroscale model. The method belongs to the class of heterogeneous multiscale methods in the sense of E and Engquist [Commun. Math. Sci., 1 (2003), pp. 87--132] and is $L^{\infty}$-stable. A key part of the approximation is a novel numerical flux function for the multidimensional setting, which captures undercompressive waves and generalizes the one-dimensional approach of Boutin et al. [Interfaces Free Bound., 10 (2008), pp. 399--421]. Furthermore, we improve the overall computational complexity, using a data-based approach. Finally, we validate the numerical method and test it on several infiltration problems.

Multidimensional Affluence in Income and Wealth in the Eurozone: A Cross-Country Comparison Using the HFCS

This paper applies multidimensional affluence measures to a new dataset on income and wealth in 15 Eurozone countries. We start our analysis by examining the income and wealth distributions separately for each country, and extend it to a multidimensional setting by considering the joint distribution of income and wealth. The results indicate that, with the exception of Cyprus, France, Italy and Slovenia, less than 10% of households are affluent in both income and net wealth. Investigating the joint distributions of income and net wealth confirms that France demonstrates a more homogenous distribution of richness among affluent households compared to other countries in the sample. Portugal demonstrates a higher concentration of richness in the hands of a few compared to the majority of other countries in the sample. The degree of countries' affluence rankings differs with respect to the measures of multidimensional affluence considered.

Predicting majority rule: Evaluating the uncovered set and the strong point

This paper compares two solution concepts for majority rule decision-making in multi-dimensional settings: the uncovered set and the strong point. Our goal is to determine which of these solution concepts is the appropriate generalization of the median voter theorem to more complex (and more realistic) multi-dimensional majority-rule settings. By making this comparison, we also contribute to the debate about the degree of sophisticated decision-making exhibited by experimental subjects and their real-world counterparts. Using data from eleven previously-published majority rule experiments and analytic techniques drawn from geography, our analysis confirms expectations that the uncovered set provides accurate predictions of majority-rule decision-making; and, moreover, that the strong point provides little added insight, either as a solution concept on its own, or as a predictor of where outcomes lie inside the uncovered set.

Quickest detection of a hidden target and extremal surfaces

Let $Z=(Z_{t})_{t\ge0}$ be a regular diffusion process started at $0$, let $\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\tau_{\ell}=\inf\{t\ge0\vert Z_{t}=\ell\}$ be the first entry time of $Z$ at the level $\ell$. We show that the quickest detection problem \[\inf_{\tau}[\mathsf{P}(\tau<\tau_{\ell})+c\mathsf{E}(\tau -\tau_{\ell})^{+}]\] is equivalent to the (three-dimensional) optimal stopping problem \[\sup_{\tau}\mathsf{E}[R_{\tau}-\int_{0}^{\tau}c(R_{t})\,dt],\] where $R=S-I$ is the range process of $X=2F(Z)-1$ (i.e., the difference between the running maximum and the running minimum of $X$ ) and $c(r)=cr$ with $c>0$. Solving the latter problem we find that the following stopping time is optimal: \[\tau_{*}=\inf \{t\ge0\vert f_{*}(I_{t},S_{t})\le X_{t}\le g_{*}(I_{t},S_{t})\},\] where the surfaces $f_{*}$ and $g_{*}$ can be characterised as extremal solutions to a couple of first-order nonlinear PDEs expressed in terms of the infinitesimal characteristics of $X$ and $c$. This is done by extending the arguments associated with the maximality principle [Ann. Probab. 26 (1998) 1614–1640] to the three-dimensional setting of the present problem and disclosing the general structure of the solution that is valid in all particular cases. The key arguments developed in the proof should be applicable in similar multi-dimensional settings.

Queues and Risk Models with Simultaneous Arrivals

We focus on a particular connection between queueing and risk models in a multidimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue), we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline of how the two-dimensional risk model with a general two-dimensional claim size distribution (hence, without ordering of claim sizes) is related to a known Riemann boundary-value problem.

Queues and Risk Models with Simultaneous Arrivals

We focus on a particular connection between queueing and risk models in a multidimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue), we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline of how the two-dimensional risk model with a general two-dimensional claim size distribution (hence, without ordering of claim sizes) is related to a known Riemann boundary-value problem.

How to pick your staff? Using data envelopment analysis

Purpose– This purpose of this paper is to present a tool for facilitating personnel selection when multiple heterogeneous human resource managers use multiple criteria. Two problems result from such a situation. First, when multiple criteria are applied, it is unusual for one candidate to dominate the other candidates in all areas, which requires assigning weights to the different criteria to be able to rank the candidates. Second, in a heterogeneous selection committee, finding weights that accurately reflect the individual preferences of all members is difficult.Design/methodology/approach– To deal with the multidimensional setting of selecting personnel, this paper introduces data envelopment analysis with assurance region (DEA-AR) to determine individually optimal weights for each applicant.Findings– DEA-AR leads to a score for each applicant that can serve as a signal for productivity and, thus, for evaluating the candidate. Based on linear programming, DEA-AR not only aggregates multiple dimensions into a single score but also incorporates managers’ preferences. In addition, the procedure is transparent and fair. It seems to be highly appropriate for selecting personnel. Based on a simulated dataset of applicants, the use of DEA-AR for selecting personnel is illustrated and discussed.Originality/value– DEA-AR provides a tool for supporting personnel selection or pre-selection. This model is based on a mechanical procedure and considers managers’ ideas about weights.

A Non-Stationary Model of Dividend Distribution in A Stochastic Interest-Rate Setting

In this paper the solutions to several variants of the so-called dividend-distribution problem in a multi-dimensional setting are studied. In a nutshell, the manager of a firm must balance the retention of earnings (so as to ward off bankruptcy and earn interest) and the distribution of dividends (so as to please the shareholders). A dynamic-programming approach is used, where the state variables are the current levels of cash reserves and of the stochastic short-rate, as well as time. This results in a family of Hamilton-Jacobi-Bellman variational inequalities whose solutions must be approximated numerically. To do so, a finite-element approximation and a time-marching scheme are employed.

Nonparametric estimation of general multivariate tail dependence and applications to financial time series

In order to analyse the entire tail dependence structure among random variables in a multidimensional setting, we present and study several nonparametric estimators of general tail dependence functions. These estimators measure tail dependence in different orthants, complementing the commonly studied positive (lower and upper) tail dependence. This approach is in line with the parametric analysis of general tail dependence. Under this unifying approach the different dependencies are analysed using the associated copulas. We generalise estimators of the lower and upper tail dependence coefficient to the general multivariate tail dependence function and study their statistical properties. Tail dependence measures come as a response to the incapability of the correlation coefficient as an extreme dependence measure. We run a Monte Carlo simulation study to assess the performance of the nonparametric estimators. We also employ selected estimators in two empirical applications to detect and measure the general multivariate non-positive tail dependence in financial data, which popular parametric copula models commonly applied in the financial literature fail to capture.