The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction

We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein-Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.Comment: This paper has been corrected from a previous version. Author Austin McDaniel has been added. Lemma 2 has been rewritten, Lemma 3 added, previous version's Lemma 3 moved to Lemma 4. 20 pages, 1 figur

Engineering sensorial delay to control phototaxis and emergent collective behaviors

Collective motions emerging from the interaction of autonomous mobile individuals play a key role in many phenomena, from the growth of bacterial colonies to the coordination of robotic swarms. For these collective behaviours to take hold, the individuals must be able to emit, sense and react to signals. When dealing with simple organisms and robots, these signals are necessarily very elementary, e.g. a cell might signal its presence by releasing chemicals and a robot by shining light. An additional challenge arises because the motion of the individuals is often noisy, e.g. the orientation of cells can be altered by Brownian motion and that of robots by an uneven terrain. Therefore, the emphasis is on achieving complex and tunable behaviors from simple autonomous agents communicating with each other in robust ways. Here, we show that the delay between sensing and reacting to a signal can determine the individual and collective long-term behavior of autonomous agents whose motion is intrinsically noisy. We experimentally demonstrate that the collective behaviour of a group of phototactic robots capable of emitting a radially decaying light field can be tuned from segregation to aggregation and clustering by controlling the delay with which they change their propulsion speed in response to the light intensity they measure. We track this transition to the underlying dynamics of this system, in particular, to the ratio between the robots' sensorial delay time and the characteristic time of the robots' random reorientation. Supported by numerics, we discuss how the same mechanism can be applied to control active agents, e.g. airborne drones, moving in a three-dimensional space.Comment: 8 pages, 5 figure

Characterizing Participation and Perceived Engagement Benefits in an Integrated Digital Behavioral Health Recovery Community for Women: A Cross-Sectional Survey

Background: Research suggests that digital recovery support services (D-RSSs) may help support individual recovery and augment the availability of in-person supports. Previous studies highlight the use of D-RSSs in supporting individuals in recovery from substance use but have yet to examine the use of D-RSSs in supporting a combination of behavioral health disorders, including substance use, mental health, and trauma. Similarly, few studies on D-RSSs have evaluated gender-specific supports or integrated communities, which may be helpful to women and individuals recovering from behavioral health disorders. Objective: The goal of this study was to evaluate the SHE RECOVERS (SR) recovery community, with the following 3 aims: (1) to characterize the women who engage in SR (including demographics and recovery-related characteristics), (2) describe the ways and frequency in which participants engage with SR, and (3) examine the perception of benefit derived from engagement with SR. Methods: This study used a cross-sectional survey to examine the characteristics of SR participants. Analysis of variance and chi-square tests, as well as univariate logistic regressions, were used to explore each aim. Results: Participants (N=729, mean age 46.83 years; 685/729, 94% Caucasian) reported being in recovery from a variety of conditions, although the most frequent nonexclusive disorder was substance use (86.40%, n=630). Participants had an average length in recovery (LIR) of 6.14 years (SD 7.87), with most having between 1 and 5 years (n=300). The most frequently reported recovery pathway was abstinence-based 12-step mutual aid (38.40%). Participants reported positive perceptions of benefit from SR participation, which did not vary by LIR or recovery pathway. Participants also had high rates of agreement, with SR having a positive impact on their lives, although this too did vary by recovery length and recovery pathway. Participants with 1 to 5 years of recovery used SR to connect with other women in recovery at higher rates, whereas those with less than 1 year used SR to ask for resources at higher rates, and those with 5 or more years used SR to provide support at higher rates. Lifetime engagement with specific supports of SR was also associated with LIR and recovery pathway. Conclusions: Gender-specific and integrated D-RSSs are feasible and beneficial from the perspective of participants. D-RSSs also appear to provide support to a range of recovery typologies and pathways in an effective manner and may be a vital tool for expanding recovery supports for those lacking in access and availability because of geography, social determinants, or other barriers

Salesforce.com

Innovation! One of the most innovative companies, and also one of the best companies to work for, is losing money. This case traces the meteoric rise of the number one customer relationship management service provider against huge rivals such as Microsoft and Oracle. Detail regarding their highly innovative Scrum system is provided, along with detail regarding their marketing approach. How can Salesforce.com regain profitability while continuing to grow in a highly competitive industry

H3K36 Methylation Regulates Nutrient Stress Response in Saccharomyces cerevisiae by Enforcing Transcriptional Fidelity

Set2-mediated histone methylation at H3K36 regulates diverse activities, including DNA repair, mRNA splicing, and suppression of inappropriate (cryptic) transcription. Although failure of Set2 to suppress cryptic transcription has been linked to decreased lifespan, the extent to which cryptic transcription influences other cellular functions is poorly understood. Here, we uncover a role for H3K36 methylation in the regulation of the nutrient stress response pathway. We found that the transcriptional response to nutrient stress was dysregulated in SET2-deleted (set2Δ) cells and was correlated with genome-wide bi-directional cryptic transcription that originated from within gene bodies. Antisense transcripts arising from these cryptic events extended into the promoters of the genes from which they arose and were associated with decreased sense transcription under nutrient stress conditions. These results suggest that Set2-enforced transcriptional fidelity is critical to the proper regulation of inducible and highly regulated transcription programs

The relative influence of neighbourhood incivilities, cognitive social capital, club membership and individual characteristics on positive mental health

Previous research indicates that residents׳ perceptions of their neighbourhoods can have an adverse influence on their health and wellbeing over and above the influence of structural disadvantage. Contrary to most prior research, this study employed an indicator of positive wellbeing and assessed the impact of individual characteristics, perceived social and environmental incivilities, indicators of cognitive and structural social capital, and perceived safety. Analyses of data from a large regional UK representative study (n=8237; 69.64% response rate) found the most influential determinants of wellbeing were physical health problems, age, SES and cognitive social capital. Smaller, significant effects were also found for environmental and social incivilities, and for perceived safety. The effect of cognitive social capital was moderated by age, with a stronger effect found among those aged 65 years and over than among younger participants. Findings indicate that the promotion of positive mental health within communities may be facilitated by efforts to foster a greater sense of belonging among residents, and that older adults may benefit most from such efforts