Bi-objective multi-resource scheduling problem for emergency relief operations

Abstract

Resource scheduling for emergency relief operations is complex as it has many constraints. However, an effective allocation and sequencing of resources are crucial for the minimization of the completion times in emergency relief operations. Despite the importance of such decisions, only a few mathematical models of emergency relief operations have been studied. This article presents a bi-objective mixed integer programming (MIP) that helps to minimize both the total weighted time of completion of the demand points and the makespan of the total emergency relief operation. A two-phase method is developed to solve the bi-objective MIP problem. Additionally, a case study of hospital network in the Melbourne metropolitan area is used to evaluate the model. The results indicate that the model can successfully support the decisions required in the optimal resource scheduling of emergency relief operations.     

Split Hamiltonian Monte Carlo

We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by “splitting” the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is possible is when the log density of the distribution of interest (the potential energy function) can be written as the log of a Gaussian density, which is a quadratic function, plus a slowly-varying function. Hamiltonian dynamics for quadratic energy functions can be analytically solved. With the splitting technique, only the slowly-varying part of the energy needs to be handled numerically, and this can be done with a larger stepsize (and hence fewer steps) than would be necessary with a direct simulation of the dynamics. Another context where splitting helps is when the most important terms of the potential energy function and its gradient can be evaluated quickly, with only a slowly-varying part requiring costly computations. With splitting, the quick portion can be handled with a small stepsize, while the costly portion uses a larger stepsize. We show that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the posterior distribution is small.     

Association between serum levels of testosterone and biomarkers of subclinical atherosclerosis

Objective: To investigate the association between serum levels of testosterone and biomarkers of subclinical atherosclerosis based on data from 119 middle-aged men of the general population.

Methods: Testosterone, Apolipoprotein A-1 (ApoA-1), Apolipoprotein B (ApoB), Apolipoprotein B-to-Apolipoprotein A-1 ratio (ApoB-to-ApoA-1), high-sensitive C-reactive protein (hsCRP), and fibrinogen levels were measured. Data were also gathered based on age, BMI, waist circumference, smoking, alcohol consumption, and family history of cardiovascular diseases. Men were classified into two groups based on testosterone levels: hypogonadal (testosterone ≤12?nmol/L) and eugonadal men (testosterone >12?nmol/L).

Results: When compared to eugonadal, the hypogonadal men were significantly older (56?years vs. 55?years, p?=?.03), had greater BMI (28?kg/cm² vs. 26?kg/cm², p?=?.01), and higher waist circumference (104?cm vs. 100?cm, p?=?.01). Moreover, ApoB, ApoB-to-ApoA-1 ratio, and hsCRP were significantly higher in hypogonadal men compared to eugonadal men (1.1?g/L vs. 1.0?g/L, p?=?.03), (0.8 vs. 0.7, p?=?.03), (3.3?mg/L vs. 2.0?mg/L, p?=?.01), respectively. On the other hand, ApoA-1 and fibrinogen levels did not differ significantly between groups (p?>?.05). In an adjusted multivariate regression analysis model, only ApoB showed a significant negative association with testosterone levels (β?=??0.01; 95% CI?=??0.02, ?1.50; p?=?.04).

Conclusion: Testosterone levels showed an inverse relation to ApoB, a biomarker implicated in subclinical atherosclerosis. These findings support the hypothesis that low testosterone levels play a role in atherosclerosis.     

Hamiltonian Monte Carlo acceleration using surrogate functions with random bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.     

CROSSING TEHRAN AVENUE

The online city magazine TehranAvenue.com (TA) occupies the transnational crossroad of digital and urban space. It thus provides an important case study of how urban studies, postcolonial theory and critical cyber studies can be combined fruitfully to explain the potentialities and limits of digital and social networks in transnational Middle Eastern contexts. The article explores metaphors of the Internet as city, theories of transnational urban space and recent studies of the Internet and its politico-cultural uses in Iran to establish a theoretical method that can explain the simultaneity of local and transnational in digital and urban spaces. Qualitative data (email and telephone interviews with TA's founder, editor and contributors), combined with content analysis of the site, supports the claim that the city as metaphor and metonym can account for the intersection between contemporary North African and Middle Eastern digital spaces and national and diasporic urban spaces. The digital city – or blogabad – expands physical urban space into transnational networks. But there are important limits to the transnational reach of mediated social networking practices. In fact, the located identifications of web users are often much more important than the global reach of the technologies they use.     

A solution to an open problem on lower against number in graphs

In Wang (Appl Anal Discret Math 4:207–218, 2010) the problem of finding a sharp lower bound on lower against number of a general graph is mentioned as an open question. We solve the problem by establishing a tight lower bound on lower against number of a general graph in terms of order and maximum degree.     

Monitoring Multi-Attribute Processes Based on NORTA Inverse Transformed Vectors

Although multivariate statistical process control has been receiving a well-deserved attention in the literature, little work has been done to deal with multi-attribute processes. While by the NORTA algorithm one can generate an arbitrary multi-dimensional random vector by transforming a multi-dimensional standard normal vector, in this article, using inverse transformation method, we initially transform a multi-attribute random vector so that the marginal probability distributions associated with the transformed random variables are approximately normal. Then, we estimate the covariance matrix of the transformed vector via simulation. Finally, we apply the well-known T ² control chart to the transformed vector. We use some simulation experiments to illustrate the proposed method and to compare its performance with that of the deleted-Y method. The results show that the proposed method works better than the deleted-Y method in terms of the out-of-control average run length criterion.     

Three New Multivariate Process Capability Indices

Different multivariate process capability indices are developed by researchers to evaluate process capability when vectors of quality characteristics are considered in a study. This article presents three indices referred to as NCpM, MCpM, and NMC _PM in order to evaluate process capability in multivariate environment. The performance of the proposed indices is investigated numerically. Simulation results indicate that the proposed indices have descended estimation error and improved performance compared to the existing ones. These results can be important to researchers and practitioners who are interested in evaluating process capability in multivariate domain.     

Evaluation of different statistical methods using SAS software: an in silico approach for analysis of real-time PCR data

Real-time polymerase chain reaction (PCR) is reliable quantitative technique in gene expression studies. The statistical analysis of real-time PCR data is quite crucial for results analysis and explanation. The statistical procedures of analyzing real-time PCR data try to determine the slope of regression line and calculate the reaction efficiency. Applications of mathematical functions have been used to calculate the target gene relative to the reference gene(s). Moreover, these statistical techniques compare C_t (threshold cycle) numbers between control and treatments group. There are many different procedures in SAS for real-time PCR data evaluation. In this study, the efficiency of calibrated model and delta delta C_t model have been statistically tested and explained. Several methods were tested to compare control with treatment means of C_t. The methods tested included t-test (parametric test), Wilcoxon test (non-parametric test) and multiple regression. Results showed that applied methods led to similar results and no significant difference was observed between results of gene expression measurement by the relative method.