Mean-Field Spin Glass models from the Cavity--ROSt Perspective

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some of the ideas which have emerged in the mathematical study of its free energy. In particular, we highlight the perspective of the cavity dynamics, and the related variational principle. These are expressed in terms of Random Overlap Structures (ROSt), which are used to describe the possible states of the reservoir in the cavity step. The Parisi solution is presented as reflecting the ansatz that it suffices to restrict the variation to hierarchal structures which are discussed here in some detail. While the Parisi solution was proven to be correct, through recent works of F. Guerra and M. Talagrand, the reasons for the effectiveness of the Parisi ansatz still remain to be elucidated. We question whether this could be related to the quasi-stationarity of the special subclass of ROSts given by Ruelle's hierarchal `random probability cascades' (also known as GREM).Comment: Based on talks given at `Young Res. Symp.', Lisbon 2003, and `Math. Phys. of Spin Glasses', Cortona 200

Purposive discovery of operations

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements

An Extended Variational Principle for the SK Spin-Glass Model

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound, as well as the actual value, are obtained through an optimization procedure for which ultrametic/hierarchal structures form only a subset of the variational class. The validity of Parisi's ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex

Testing Modality Affects Performance on the Santa Barbara Solids Test

Spatial ability is associated with performance in science, technology, engineering, and mathematics (STEM) disciplines and has been used to predict the likelihood of success in these fields (Wai, Lubinski, & Benbow, 2009). Classically, spatial ability has been assessed by tests that measure general factors of spatial ability. However, these factors may be limited in that they were not developed with individual differences or cognitive theories in mind (Cohen & Hegarty, 2012). Although traditional measures of spatial ability give insight into a person’s general spatial processing, Cohen and Hegarty (2012) point out the need for theoretically motivated spatial ability tests that specifically relate to STEM performance. There are numerous spatial ability measures in use by researchers, yet there is a need for reliable and valid spatial ability measures that are directly applicable to STEM fields. One new measure of spatial ability developed theoretically with individual differences in mind is the Santa Barbara Solids Test (SBST; Cohen & Hegarty, 2012). In the SBST, participants must imagine what the bisection of three-dimensional forms will be when cut by a two-dimensional plane. This bisection can be horizontal, vertical, or oblique, and the shape can be a simple or complex three-dimensional form. The spatial skills involved in imagining a cross-section of a form have been linked with performance in STEM courses, such as anatomy (Rochford, 1985), biology (Russell-Gebbett, 1985), geology (Kali & Orion, 1996), geometry (Pittalis & Christou, 2010), engineering (Duesbury & O’Neil, 1996), and skills such as reading x-rays and MRIs (Hegarty, Keehner, Cohen, Montello, & Lippa, 2007). The SBST has been validated with undergraduate students with a range of spatial ability scores (Cohen & Hegarty, 2012), but additional studies of the SBST are needed to replicate and expand on the findings of this promising new measure. For example, it is important to determine the effects of testing modality on performance to highlight a potential confound in future spatial ability studies. Although computerized assessments are common and offer many conveniences (e.g., fast scoring, fewer resources) compared to other testing modalities (e.g., paper-based testing), participants may experience higher perceived workload in computer-based assessments (Mayes, Sims, & Koonce, 2001) or perform differently on the same test in another modality (c.f. Noyes & Garland, 2008). The current study (n = 241) compares the SBST with a traditional measure of spatial ability, the Paper Folding Test (PFT; Ekstrom, French, Harman, & Dermen, 1976), in two testing modalities: 1) computer-based, and 2) paper-based. Results showed there was a correlation between the spatial ability measures, indicating both were tapping the same underlying construct. There was not a difference in performance between testing modalities for the PFT. However, there was a difference in performance based on testing modality for the SBST such that participants in the paper-based condition performed better than those in the computerized condition. The implications of these results are that testing modality should be a consideration for future studies involving the SBST

Lateral Membrane Waves Constitute a Universal Dynamic Pattern of Motile Cells

We have monitored active movements of the cell circumference on specifically coated substrates for a variety of cells including mouse embryonic fibroblasts and T cells, as well as wing disk cells from fruit flies. Despite having different functions and being from multiple phyla, these cell types share a common spatiotemporal pattern in their normal membrane velocity; we show that protrusion and retraction events are organized in lateral waves along the cell membrane. These wave patterns indicate both spatial and temporal long-range periodic correlations of the actomyosin gel

WIP deficiency reveals a differential role for WIP and the actin cytoskeleton in T and B cell activation

Producción CientíficaWIP stabilizes actin filaments and is important for filopodium formation. To define the role of WIP in immunity, we generated WIP-deficient mice. WIP(minus sign/minus sign) mice have normal lymphocyte development, but their T cells fail to proliferate, secrete IL-2, increase their F-actin content, polarize and extend protrusions following T cell receptor ligation, and are deficient in conjugate formation with superantigen-presenting B cells and anti-CD3 bilayers. In contrast, WIP-deficient B lymphocytes have enhanced proliferation and CD69 expression following B cell receptor ligation and mount normal antibody responses to T-independent antigens. Both WIP-deficient T and B cells show a profound defect in their subcortical actin filament networks. These results suggest that WIP is important for immunologic synapse formation and T cell activation

Modifying effect of obesity on the association between sitting time and incident diabetes in post-menopausal women

Objective: To evaluate the association between self-reported daily sitting time and the incidence of type II diabetes in a cohort of postmenopausal women. Design and Methods Women (N = 88,829) without diagnosed diabetes reported the number of hours spent sitting over a typical day. Incident cases of diabetes were identified annually by self-reported initiation of using oral medications or insulin for diabetes over 14.4 years follow-up. Results: Each hour of sitting time was positively associated with increased risk of diabetes (Risk ratio (RR): 1.05; 95% confidence interval (CI): 1.02–1.08]. However, sitting time was only positively associated with incident diabetes in obese women. Obese women reporting sitting 8–11 (RR: 1.08; 95% CI 1.0–1.1), 12–15 (OR: 1.13; 95% CI 1.0–1.2), and ≥16 hours (OR: 1.25; 95% CI 1.0–1.5) hours per day had an increased risk of diabetes compared to women sitting ≤ 7 hours per day. These associations were adjusted for demographics, health conditions, behaviors (smoking, diet and alcohol intake) and family history of diabetes. Time performing moderate to vigorous intensity physical activity did not modify these associations. Conclusion: Time spent sitting was independently associated with increased risk of diabetes diagnosis among obese women— a population already at high risk of the disease

Change in Physical Activity after a Diabetes Diagnosis: Opportunity for Intervention

INTRODUCTION: Moderate intensity physical activity is recommended for individuals with diabetes to control glucose and prevent diabetes-related complications. The extent to which a diabetes diagnosis motivates patients to increase physical activity is unclear. This study used data from the Women\u27s Health Initiative Observational Study (baseline data collected from 1993-1998) to examine change in physical activity and sedentary behavior in women who reported a diabetes diagnosis compared to women who did not report diabetes over 7 years of follow-up (up to 2005). METHODS: Participants (n=84,300) were post-menopausal women who did not report diabetes at baseline [mean age=63.49; standard deviation (SD)=7.34; mean BMI=26.98 kg/m; SD=5.67]. Linear mixed model analyses were conducted adjusting for study year, age, race/ethnicity, BMI, education, family history of diabetes, physical functioning, pain, energy/fatigue, social functioning, depression, number of chronic diseases and vigorous exercise at age 18. Analyses were completed in August 2012. RESULTS: Participants who reported a diabetes diagnosis during follow-up were more likely to report increasing their total physical activity (p=0.002), walking (p CONCLUSION: A diabetes diagnosis may prompt patients to increase physical activity. Healthcare professionals should consider how best to capitalize on this opportunity to encourage increased physical activity and maintenance