A note on quasi-Gorenstein rings

In this paper, after giving a criterion for a Noetherian local ring to be quasi-Gorenstein, we obtain some sufficient conditions for a quasi- Gorenstein ring to be Gorenstein. In the course, we provide a slight generalization of a theorem of Evans and Griffith.Comment: To appear in Arch. Mat

On rationality of nonnegative matrix factorization

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether every rational matrix M has an NMF with minimal d whose factors W and H are also rational. We answer this question negatively, by exhibiting a matrix M for which W and H require irrational entries. As an application of this result, we show that state minimization of labeled Markov chains can require the introduction of irrational transition probabilities. We complement these irrationality results with an NP- complete version of NMF for which rational numbers suffice

Comprehensive thermodynamic and operational optimization of a solar-assisted LiBr/water absorption refrigeration system

Absorption cooling systems have been investigated for many years due to their ability to use low-grade heat instead of electricity as the energy source. The aim of this work is to advance the performance of a single-effect Lithium bromide/water absorption cooling system. Taking the generator and evaporator temperatures as variables, the system is optimized to maximize exergetic and energetic efficiencies at different operational conditions using a multi-objective–multi-variable Genetic Algorithm. The Group Method of Data Handling neural network approach is adopted to derive correlations between the design variables and operational parameters. Finally, the system is coupled to evacuated tube solar collectors and compared to a similar system. The results reflect a maximum improvement in energetic and exergetic efficiencies of about 9.1% and 3.0%, respectively. This translates into savings of 187 dollars for every square meter of solar collector at present time. This improvement is achieved by decreasing the mean temperature of the generator by 6.2 °C and increasing the mean temperature of the evaporator by 1.6 °C. In the case of applying low-grade heat such as solar energy, it brings about both an improvement in the thermodynamic performances and a reduction in the generator temperature

Modeling sustainability : Population, inequality, consumption, and bidirectional coupling of the Earth and human systems

Over the last two centuries, the impact of the Human System has grown dramatically, becoming strongly dominant within the Earth System in many different ways. Consumption, inequality, and population have increased extremely fast, especially since about 1950, threatening to overwhelm the many critical functions and ecosystems of the Earth System. Changes in the Earth System, in turn, have important feedback effects on the Human System, with costly and potentially serious consequences. However, current models do not incorporate these critical feedbacks. We argue that in order to understand the dynamics of either system, Earth SystemModels must be coupled with Human SystemModels through bidirectional couplings representing the positive, negative, and delayed feedbacks that exist in the real systems. In particular, key Human System variables, such as demographics, inequality, economic growth, and migration, are not coupled with the Earth System but are instead driven by exogenous estimates, such as United Nations population projections.This makes current models likely to miss important feedbacks in the real Earth-Human system, especially those that may result in unexpected or counterintuitive outcomes, and thus requiring different policy interventions from current models.The importance and imminence of sustainability challenges, the dominant role of the Human System in the Earth System, and the essential roles the Earth System plays for the Human System, all call for collaboration of natural scientists, social scientists, and engineers in multidisciplinary research and modeling to develop coupled Earth-Human system models for devising effective science-based policies and measures to benefit current and future generations

Identification of biomolecule mass transport and binding rate parameters in living cells by inverse modeling

BACKGROUND: Quantification of in-vivo biomolecule mass transport and reaction rate parameters from experimental data obtained by Fluorescence Recovery after Photobleaching (FRAP) is becoming more important. METHODS AND RESULTS: The Osborne-Moré extended version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the Fluorescence Recovery after Photobleaching (FRAP) protocol, and the numerical solution of a set of two partial differential equations governing macromolecule mass transport and reaction in living cells, to inversely estimate optimized values of the molecular diffusion coefficient and binding rate parameters of GFP-tagged glucocorticoid receptor. The results indicate that the FRAP protocol provides enough information to estimate one parameter uniquely using a nonlinear optimization technique. Coupling FRAP experimental data with the inverse modeling strategy, one can also uniquely estimate the individual values of the binding rate coefficients if the molecular diffusion coefficient is known. One can also simultaneously estimate the dissociation rate parameter and molecular diffusion coefficient given the pseudo-association rate parameter is known. However, the protocol provides insufficient information for unique simultaneous estimation of three parameters (diffusion coefficient and binding rate parameters) owing to the high intercorrelation between the molecular diffusion coefficient and pseudo-association rate parameter. Attempts to estimate macromolecule mass transport and binding rate parameters simultaneously from FRAP data result in misleading conclusions regarding concentrations of free macromolecule and bound complex inside the cell, average binding time per vacant site, average time for diffusion of macromolecules from one site to the next, and slow or rapid mobility of biomolecules in cells. CONCLUSION: To obtain unique values for molecular diffusion coefficient and binding rate parameters from FRAP data, we propose conducting two FRAP experiments on the same class of macromolecule and cell. One experiment should be used to measure the molecular diffusion coefficient independently of binding in an effective diffusion regime and the other should be conducted in a reaction dominant or reaction-diffusion regime to quantify binding rate parameters. The method described in this paper is likely to be widely used to estimate in-vivo biomolecule mass transport and binding rate parameters