Partition-based formulations for mixed-integer optimization of trained ReLU neural networks

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions via disjunctive programming. At one extreme, one partition per input recovers the convex hull of a node, i.e., the tightest possible formulation for each node. For fewer partitions, we develop smaller relaxations that approximate the convex hull, and show that they outperform existing formulations. Specifically, we propose strategies for partitioning variables based on theoretical motivations and validate these strategies using extensive computational experiments. Furthermore, the proposed scheme complements known algorithmic approaches, e.g., optimization-based bound tightening captures dependencies within a partition

Error bounds for monomial convexification in polynomial optimization

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

Interleukin-1beta Promoter (−31T/C and −511C/T) Polymorphisms in Major Recurrent Depression

To elucidate a genetic predisposition to major depressive disorder, we investigated two polymorphisms (−31T/C and −511C/T) in the interleukin-1beta promoter region in patients who suffered from major recurrent depression. The aim of the current work was to compare alleles and genotype layout between patients with major recurrent depression and healthy people. We would like to indicate such combination of genotypes which corresponds with major recurrent depression. Correlations between genotypes for analyzed polymorphisms and number of episodes, number of points in Hamilton Depression Rating Scale, and age of onset were investigated as well. The study group consisted of 94 patients diagnosed with major recurrent depression. The control group included 206 healthy individuals. Both groups involved representatives of Caucasian population. Genotyping of polymorphisms was performed by using PCR-RFLP technique. A specific haplotype, composed of the C allele at −31 and the T allele at −511, has a tendency to have a statistically significant difference (p = 0.064) between patients and control group. Correspondence analysis revealed that genotype T/T at −31 and genotype C/C at −511 are associated with major recurrent depression. No association was found between genotypes for studied polymorphic sites and number of episodes, number of points in Hamilton Depression Rating Scale, and age of onset

Drug information resources used by nurse practitioners and collaborating physicians at the point of care in Nova Scotia, Canada: a survey and review of the literature

BACKGROUND: Keeping current with drug therapy information is challenging for health care practitioners. Technologies are often implemented to facilitate access to current and credible drug information sources. In the Canadian province of Nova Scotia, legislation was passed in 2002 to allow nurse practitioners (NPs) to practice collaboratively with physician partners. The purpose of this study was to determine the current utilization patterns of information technologies by these groups of practitioners. METHODS: Nurse practitioners and their collaborating physician partners in Nova Scotia were sent a survey in February 2005 to determine the frequency of use, usefulness, accessibility, credibility, and current/timeliness of personal digital assistant (PDA), computer, and print drug information resources. Two surveys were developed (one for PDA users and one for computer users) and revised based on a literature search, stakeholder consultation, and pilot-testing results. A second distribution to nonresponders occurred two weeks following the first. Data were entered and analysed with SPSS. RESULTS: Twenty-seven (14 NPs and 13 physicians) of 36 (75%) recipients responded. 22% (6) returned personal digital assistant (PDA) surveys. Respondents reported print, health professionals, and online/electronic resources as the most to least preferred means to access drug information, respectively. 37% and 35% of respondents reported using "both print and electronic but print more than electronic" and "print only", respectively, to search monograph-related drug information queries whereas 4% reported using "PDA only". Analysis of respondent ratings for all resources in the categories print, health professionals and other, and online/electronic resources, indicated that the Compendium of Pharmaceuticals and Specialties and pharmacists ranked highly for frequency of use, usefulness, accessibility, credibility, and current/timeliness by both groups of practitioners. Respondents' preferences and resource ratings were consistent with self-reported methods for conducting drug information queries. Few differences existed between NP and physician rankings of resources. CONCLUSION: The use of computers and PDAs remains limited, which is also consistent with preferred and frequent use of print resources. Education for these practitioners regarding available electronic drug information resources may facilitate future computer and PDA use. Further research is needed to determine methods to increase computer and PDA use and whether these technologies affect prescribing and patient outcomes

The severity of pandemic H1N1 influenza in the United States, from April to July 2009: A Bayesian analysis

Background: Accurate measures of the severity of pandemic (H1N1) 2009 influenza (pH1N1) are needed to assess the likely impact of an anticipated resurgence in the autumn in the Northern Hemisphere. Severity has been difficult to measure because jurisdictions with large numbers of deaths and other severe outcomes have had too many cases to assess the total number with confidence. Also, detection of severe cases may be more likely, resulting in overestimation of the severity of an average case. We sought to estimate the probabilities that symptomatic infection would lead to hospitalization, ICU admission, and death by combining data from multiple sources. Methods and Findings: We used complementary data from two US cities: Milwaukee attempted to identify cases of medically attended infection whether or not they required hospitalization, while New York City focused on the identification of hospitalizations, intensive care admission or mechanical ventilation (hereafter, ICU), and deaths. New York data were used to estimate numerators for ICU and death, and two sources of data - medically attended cases in Milwaukee or self-reported influenza-like illness (ILI) in New York - were used to estimate ratios of symptomatic cases to hospitalizations. Combining these data with estimates of the fraction detected for each level of severity, we estimated the proportion of symptomatic patients who died (symptomatic case-fatality ratio, sCFR), required ICU (sCIR), and required hospitalization (sCHR), overall and by age category. Evidence, prior information, and associated uncertainty were analyzed in a Bayesian evidence synthesis framework. Using medically attended cases and estimates of the proportion of symptomatic cases medically attended, we estimated an sCFR of 0.048% (95% credible interval [CI] 0.026%-0.096%), sCIR of 0.239% (0.134%-0.458%), and sCHR of 1.44% (0.83%-2.64%). Using self-reported ILI, we obtained estimates approximately 7-96lower. sCFR and sCIR appear to be highest in persons aged 18 y and older, and lowest in children aged 5-17 y. sCHR appears to be lowest in persons aged 5-17; our data were too sparse to allow us to determine the group in which it was the highest. Conclusions: These estimates suggest that an autumn-winter pandemic wave of pH1N1 with comparable severity per case could lead to a number of deaths in the range from considerably below that associated with seasonal influenza to slightly higher, but with the greatest impact in children aged 0-4 and adults 18-64. These estimates of impact depend on assumptions about total incidence of infection and would be larger if incidence of symptomatic infection were higher or shifted toward adults, if viral virulence increased, or if suboptimal treatment resulted from stress on the health care system; numbers would decrease if the total proportion of the population symptomatically infected were lower than assumed.published_or_final_versio

The influence of a Healthy Welcoming Environment on participation in club sport by adolescent girls: a longitudinal study

Background: This study investigated the perceived influence of a Healthy Welcoming Environment (HWE) on participation in sports clubs among adolescent girls, and how these perceptions changed longitudinally. HWE was defined in terms of a set of health promotion policies advocated by a health promotion foundation as the basis of sport club health promotion practice to promote structural reform in state sporting organisations and their affiliated associations and clubs. These included sports injury prevention, smoke-free, responsible serving of alcohol, sun protection, healthy eating, and welcoming and inclusive environments. Methods: Year 7 and 11 female students from metropolitan (n = 17) and non-metropolitan secondary schools (n = 14) in Australia were invited to participate in three annual surveys. These surveys collected information about current or past membership of a sports club and the influence of HWEs on their decision to participate (or not) in a sports club. Results: Year 7 (n = 328; 74.5%) and Year 11 (n = 112; 25.5%) female students completed all three waves (19.6% response rate; 82.7 and 74.0% retention rate). Most agreed that characteristics of HWEs were a positive influence on their participation in sports clubs, except those relating to alcohol and Sunsmart. Welcoming factors had consistent high agreement among respondents. Alcohol and friendliness factors of the club were regarded as being positively influential by higher percentages of non-metropolitan than metropolitan respondents. Conclusions: Welcoming factors were the most positive influences on decisions to participate in sports clubs. These factors may be important in reducing barriers to sport participation. Strategies supporting the social environment within sports clubs should be prioritised

Long-Term Cold Acclimation Extends Survival Time at 0°C and Modifies the Metabolomic Profiles of the Larvae of the Fruit Fly Drosophila melanogaster

Drosophila melanogaster is a chill-susceptible insect. Previous studies on this fly focused on acute direct chilling injury during cold shock and showed that lower lethal temperature (LLT, approximately -5°C) exhibits relatively low plasticity and that acclimations, both rapid cold hardening (RCH) and long-term cold acclimation, shift the LLT by only a few degrees at the maximum.We found that long-term cold acclimation considerably improved cold tolerance in fully grown third-instar larvae of D. melanogaster. A comparison of the larvae acclimated at constant 25°C with those acclimated at constant 15°C followed by constant 6°C for 2 d (15°C→6°C) showed that long-term cold acclimation extended the lethal time for 50% of the population (Lt(50)) during exposure to constant 0°C as much as 630-fold (from 0.137 h to 86.658 h). Such marked physiological plasticity in Lt(50) (in contrast to LLT) suggested that chronic indirect chilling injury at 0°C differs from that caused by cold shock. Long-term cold acclimation modified the metabolomic profiles of the larvae. Accumulations of proline (up to 17.7 mM) and trehalose (up to 36.5 mM) were the two most prominent responses. In addition, restructuring of the glycerophospholipid composition of biological membranes was observed. The relative proportion of glycerophosphoethanolamines (especially those with linoleic acid at the sn-2 position) increased at the expense of glycerophosphocholines.Third-instar larvae of D. melanogaster improved their cold tolerance in response to long-term cold acclimation and showed metabolic potential for the accumulation of proline and trehalose and for membrane restructuring