Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Refinement and Pilot Testing Social Networks for Encouraging Healthy Behaviors: The Social Pounds Off Digitally (Social POD) Study

Currently about 71% of adults in the US are considered overweight or obese. Overweight and obesity are associated with higher risk of developing many chronic diseases; however, health risks associated with overweight and obesity can be reduced by as little as a 3% to 5% reduction in weight. Mobile health (mHealth) has shown promise as a way to deliver weight loss interventions, yet maintaining participant engagement over time has been a challenge. The purpose of this study was to develop, refine, and pilot test the Social Pounds Off Digitally (POD) Android app for personalized health monitoring and interaction; revise the Social POD app based on participant feedback; and conduct a multi-site randomized clinical trial to pilot test the second iteration of the Social POD app. Overweight and obese adults with Android smartphones (BMI 25-49.9 kg/m2; N=9) were recruited for a two-month weight loss pilot intervention and iterative usability testing of the Social POD app. The app prompted participants via notification to track daily weight, diet, and PA behaviors. Participants received the content of the behavioral weight loss intervention via podcast. In order to re-engage infrequent users, the app prompted frequent app users to select one of three messages to send to infrequent users targeting one of three behavioral theory constructs: 1) social support, 2) self-efficacy, or 3) negative outcome expectations. Body weight and dietary intake (two 24-hr recalls) were assessed at baseline and two months. All participants attended one of two focus groups to provide feedback on use of the app. Based on the usability testing, the Social POD app was refined and a point-based incentive system was incorporated into the app and used in a larger randomized controlled trial. Overweight and obese adults (N=51, mean BMI=34.7 ± 6.0, 38% black) in Charleston and Columbia, SC who owned an Android phone or tablet were recruited to participate in a 12-week behavioral weight loss intervention delivered via mobile app and podcast. All participants received the behavioral content of the weight loss intervention via twice weekly podcasts and were randomized to download and use either a standard calorie tracking app (Fat Secret) or the Social POD app. Main outcomes included kilograms lost at 12-weeks and secondary outcomes included change in psychosocial variable scores from pre- to post-test, association between points earned and percent weight loss at 12-weeks, and reengagement based on message-type received. Following the usability testing participants lost a mean of -0.94 kg (±2.22 kg, p=0.24) and consumed significantly fewer kcals post-intervention (1570±508 kcal/day) as compared to baseline (2384±993 kcal/day, p=0.01). Mean number of app entries was 77.2 ± 73.8 per person with a range of 2 to 219. Messages selected and sent to infrequent users targeting social support were sent most frequently (n=32, 46%), followed by self-efficacy (n=29, 40%), and negative outcome expectations (n=10, 14%). Themes from the focus groups included functionality issues, revisions to the messaging system, and the addition of a point system with rewards for achieving goals. Participant attrition for the RCT was 12% (n=3 experimental and n=3 comparison). Experimental group participants lost significantly more weight (-5.3kg, CI: vi i -7.5, -3.0) than comparison group participants (-2.23kg, CI: -3.6, -1.0; p=0.02) and had a greater reduction in BMI (p=0.02). These outcomes were significant for both intentionto- treat (using baseline observation carried forward) and complete case. While there were significant differences in final positive outcome expectations scores between groups [4.56 experimental, 3.57 comparison (scale range from 1 to 7, maximum); p=0.04], other secondary outcomes (e.g., caloric intake and social support) were not significantly different by group assignment while controlling for baseline values. Among experimental group participants only, total points earned significantly predicted percent weight loss (B=-0.02, p=0.01). In addition, higher scores for the conscientiousness personality trait was significantly associated with total points earned (B=9.07, p=0.03), but other personality characteristics and demographics were not. Messages most frequently sent to infrequent users of the Social POD app were social support (n=119), followed by outcome expectations (n=99), and then messages targeting self-efficacy (n=97). There was a significant difference between the type of message received and re-engagement among infrequent users (p=0.03) with self-efficacy messages prompting the most engagement (n=7), followed by outcome expectation messages (n=5) and social support messages (n=1). In conclusion, use of the Social POD app led to greater weight loss than a standard diet-tracking app (Fat Secret). This mobile health intervention has the potential to be widely disseminated to reduce the risk of chronic disease associated with overweight and obesity

Hippocampal Infusion of Zeta Inhibitory Peptide Impairs Recent, but Not Remote, Recognition Memory in Rats.

Spatial memory in rodents can be erased following the infusion of zeta inhibitory peptide (ZIP) into the dorsal hippocampus via indwelling guide cannulas. It is believed that ZIP impairs spatial memory by reversing established late-phase long-term potentiation (LTP). However, it is unclear whether other forms of hippocampus-dependent memory, such as recognition memory, are also supported by hippocampal LTP. In the current study, we tested recognition memory in rats following hippocampal ZIP infusion. In order to combat the limited targeting of infusions via cannula, we implemented a stereotaxic approach for infusing ZIP throughout the dorsal, intermediate, and ventral hippocampus. Rats infused with ZIP 3-7 days after training on the novel object recognition task exhibited impaired object recognition memory compared to control rats (those infused with aCSF). In contrast, rats infused with ZIP 1 month after training performed similar to control rats. The ability to form new memories after ZIP infusions remained intact. We suggest that enhanced recognition memory for recent events is supported by hippocampal LTP, which can be reversed by hippocampal ZIP infusion

Hippocampal Global Remapping Can Occur without Input from the Medial Entorhinal Cortex.

The high storage capacity of the episodic memory system relies on distinct representations for events that are separated in time and space. The spatial component of these computations includes the formation of independent maps by hippocampal place cells across environments, referred to as global remapping. Such remapping is thought to emerge by the switching of input patterns from specialized spatially selective cells in medial entorhinal cortex (mEC), such as grid and border cells. Although it has been shown that acute manipulations of mEC firing patterns are sufficient for inducing hippocampal remapping, it remains unknown whether specialized spatial mEC inputs are necessary for the reorganization of hippocampal spatial representations. Here, we examined remapping in rats without mEC input to the hippocampus and found that highly distinct spatial maps emerged rapidly in every individual rat. Our data suggest that hippocampal spatial computations do not depend on inputs from specialized cell types in mEC

Regulation of de Novo Synthesis of Cytochrome P-450 17Α in Mouse LeydigCell Cultures a

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73047/1/j.1749-6632.1987.tb25049.x.pd