A Splitting Equilibration Algorithm for the Computation of Large-Scale Constrained Matrix Problems; Theoretical Analysis and Applications

In this paper we introduce a general parallelizable computational method for solving a wide spectrum of constrained matrix problems. The constrained matrix problem is a core problem in numerous applications in economics. These include the estimation of input/output tables, trade tables, and social/national accounts, and the projection of migration flows over space and time. The constrained matrix problem, so named by Bacharach, is to compute the best possible estimate X of an unknown matrix, given some information to constrain the solution set, and requiring either that the matrix X be a minimum distance from a given matrix, or that X be a functional form of another matrix. In real-world applications, the matrix X is often very large (several hundred to several thousand rows and columns), with the resulting constrained matrix problem larger still (with the number of variables on the order of the square of the number of rows/columns; typically, in the hundreds of thousands to millions). In the classical setting, the row and column totals are known and fixed, and the individual entries nonnegative. However, in certain applications, the row and column totals need not be known a priori, but must be estimated, as well. Furthermore, additional objective and subjective inputs are often incorporated within the model to better represent the application at hand. It is the solution of this broad class of large-scale constrained matrix problems in a timely fashion that we address in this paper. The constrained matrix problem has become a standard modelling tool among researchers and practitioners in economics. Therefore, the need for a unifying, robust, and efficient computational procedure for solving constrained matrix problems is of importance. Here we introduce a.n algorithm, the splitting equilibration algorithm, for computing the entire class of constrained matrix problems. This algorithm is not only theoretically justiflid, hilt l'n fi,1 vl Pnitsf htnh thP lilnlprxing s-trlrtilre of thpCp !arop-Cspe mrnhlem nn the advantages offered by state-of-the-art computer architectures, while simultaneously enhancing the modelling flexibility. In particular, we utilize some recent results from variational inequality theory, to construct a splitting equilibration algorithm which splits the spectrum of constrained matrix problems into series of row/column equilibrium subproblems. Each such constructed subproblem, due to its special structure, can, in turn, be solved simultaneously via exact equilibration in closed form. Thus each subproblem can be allocated to a distinct processor. \We also present numerical results when the splitting equilibration algorithm is implemented in a serial, and then in a parallel environment. The algorithm is tested against another much-cited algorithm and applied to input/output tables, social accounting matrices, and migration tables. The computational results illustrate the efficacy of this approach

What is infidelity? Perceptions based on biological sex and personality

The study examines perceptions of infidelity, paying particular attention to how these perceptions differ based on biological sex and personality traits, specifically agency and communion and their unmitigated counterparts. The study utilizes a sample of 125 male and 233 female college students. In addition to the personality measures, participants completed a 19-item checklist that assessed their perceptions of specific items that could potentially be construed as infidelity. It was hypothesized that females would construe more items as infidelity than would males. It was also predicted that unmitigated communion and communion would be positively correlated with these perceptions and that unmitigated agency would be negatively correlated with these perceptions. No correlation was predicted between agency and infidelity. All hypotheses were supported. Implications and suggestions for future research are discussed

Biomarkers Enhance Discrimination and Prognosis of Type 2 Myocardial Infarction

Background: The observed incidence of type 2 myocardial infarction (T2MI) is expected to increase with the implementation of increasingly sensitive cardiac troponin (cTn) assays. However, it remains to be determined how to diagnose, risk stratify and treat patients with T2MI. We aimed to discriminate and risk-stratify T2MI using biomarkers. Methods: Patients presenting to the Emergency Department with chest pain, enrolled in the CHOPIN study, were retrospectively analyzed. Two cardiologists adjudicated type 1 MI (T1MI) and T2MI. The prognostic ability of several biomarkers alone or in combination to discriminate T2MI from T1MI was investigated using receiver operating characteristic (ROC) curve analysis. The biomarkers analyzed were cTnI, copeptin, mid-regional pro-atrial natriuretic peptide (MRproANP), C-terminal pro-endothelin-1 (CT-proET1), mid-regional pro-adrenomedullin (MRproADM) and procalcitonin. Prognostic utility of these biomarkers for all-cause mortality and major adverse cardiovascular event (MACE: a composite of acute MI, unstable angina pectoris, reinfarction, heart failure, and stroke) at 180-day follow-up was also investigated. Results: Among the 2071 patients, T1MI and T2MI were adjudicated in 94 and 176 patients, respectively. Patients with T1MI had higher levels of baseline cTnI, while those with T2MI had higher baseline levels of MR-proANP, CT-proET1, MR-proADM, and procalcitonin. The area under the ROC curve (AUC) for the diagnosis of T2MI was higher for CT-proET1, MRproADM and MR-proANP (0.765, 0.750, and 0.733, respectively) than for cTnI (0.631). Combining all biomarkers resulted in a similar accuracy to a model using clinical variables and cTnI (0.854 versus 0.884, p = 0.294). Addition of biomarkers to the clinical model yielded the highest AUC (0.917). Other biomarkers, but not cTnI, were associated with mortality and MACE at 180-day among all patients, with no interaction between the diagnosis of T1MI or T2MI. Conclusions: Assessment of biomarkers reflecting pathophysiologic processes occurring with T2MI might help differentiate it from T1MI. Additionally, all biomarkers measured, except cTnI, were significant predictors of prognosis, regardless of type of MI

A parallel network equilibration algorithm for a class of constrained matrix problems

In this paper we propose a network equilibration algorithm for the solution of a class of constrained matrix problems with transportation-type constraints. The algorithm decomposes the problem into two series of supply and demand network equilibrium problems with special structure which can then be solved exactly and in parallel. The theoretical results obtained include the proof of convergence, the rate of convergence, and computational complexity analysis, and are obtained by interpreting the algorithm as a dual method. Computational results on datasets illustrate the theory and the efficiency of this approach

Progressive equilibration algorithms: the case of linear transaction costs

In this paper we consider the solution of large-scale market equilibrium problems with linear transaction costs which can be formulated as strictly convex quadratic programming problems, subject to supply and demand constraints. In particular, we introduce two new classes of progressive equilibration algorithms, which retain the simplicity of the original cyclic ones in that at each step either the supply or demand market equilibrium subproblem can be solved explicitly in closed form. However, rather than equilibrating the markets in cyclic manner, the next market to be equilibrated is selected in a more strategic fashion. We then provide qualitative results for the entire family of progressive equilibration algorithms, i.e., the rate of convergence and computational complexity. We discuss implementation issues and give computational results for large-scale examples in order to illustrate and give insights into the theoretical analysis. Furthermore, we show that one of the new classes of algorithms, the lsquogood-enoughrsquo one, is computationally the most efficient. Theoretical results are important in that the relative efficiency of different algorithms need no longer be language, machine, or programmer dependent. Instead, the theory can guide both practitioners and researchers in ensuring that their implementation of these algorithms is, indeed, good. Since an equivalent quadratic programming problem arises in a certain class of constrained matrix problems, our results can be applied there, as well. Finally, since more general asymmetric multicommodity market equilibrium problems can be solved as series of the type of problems considered here, the result$ are also applicable to such equilibrium problems

Predicting safe sex practices from gender-related interpersonal variables

This study investigated whether safe sex practices, including condom use and partner communication, may be predicted from the interpersonal traits of agency, unmitigated agency, communion, and unmitigated communion. Participants were 375 college students (77% women, 23% men), who completed an online questionnaire assessing the variables of interest. Hierarchical regression analyses revealed that high-agency individuals employed greater safe sex practices (p = .001) and had greater communication with their partners about safe sex (p < .001) than low-agency individuals, whereas high-unmitigated agency individuals employed fewer safe sex practices (p = .009) and used condoms less often (p = .017) than low-unmitigated agency individuals. Furthermore, high-communion individuals had better partner communication about safe sex (p = .013) than low-communion individuals. These findings are consistent with past research showing the positive impact of agency and communion, as well as negative impact of unmitigated agency, on risky health behaviors