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Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization problems via minimizing the$$\ell _{p}$$${\ell }_p$quasi-norm, where$$0$0<p<1$. An iterative two-block algorithm for minimizing the$$\ell _{p}$$${\ell }_p$quasi-norm subject to convex constraints is proposed. The proposed algorithm requires solving for the roots of a scalar degree polynomial as opposed to applying a soft thresholding operator in the case of$$\ell _{1}$$${\ell }_1$norm minimization. The algorithm’s merit relies on its ability to solve the$$\ell _{p}$$${\ell }_p$quasi-norm minimization subject to any convex constraints set. For the specific case of constraints defined by differentiable functions with Lipschitz continuous gradient, a second, faster algorithm is proposed. Using a proximal gradient step, we mitigate the convex projection step and hence enhance the algorithm’s speed while proving its convergence. We present various applications where the proposed algorithm excels, namely, sparse signal reconstruction, system identification, and matrix completion. The results demonstrate the significant gains obtained by the proposed algorithm compared to other$$\ell _{p}$$${\ell }_p$quasi-norm based methods presented in previous literature.

 

The COVID-19 pandemic adversely impacted physical activity, but little is known about how contextual changes following the pandemic declaration impacted either the dynamics of people’s physical activity or their responses to micro-interventions for promoting physical activity.

This paper explored the effect of the COVID-19 pandemic on the dynamics of physical activity responses to digital message interventions.

Insufficiently-active young adults (18–29 years; N = 22) were recruited from November 2019 to January 2020 and wore a Fitbit smartwatch for 6 months. They received 0–6 messages/day via smartphone app notifications, timed and selected at random from three content libraries (Move More, Sit Less, and Inspirational Quotes). System identification techniques from control systems engineering were used to identify person-specific dynamical models of physical activity in response to messages before and after the pandemic declaration on March 13, 2020.

Daily step counts decreased significantly following the pandemic declaration on weekdays (Cohen’s d = -1.40) but not on weekends (d = -0.26). The mean overall speed of the response describing physical activity (dominant pole magnitude) did not change significantly on either weekdays (d = -0.18) or weekends (d = -0.21). In contrast, there was limited rank-order consistency in specific features of intervention responses from before to after the pandemic declaration.

Generalizing models of behavioral dynamics across dramatically different environmental contexts (and participants) may lead to flawed decision rules for just-in-time physical activity interventions. Periodic model-based adaptations to person-specific decision rules (i.e., continuous tuning interventions) for digital messages are recommended when contexts change.

 

Abstract Background This scoping review summarized research on (a) seasonal differences in physical activity and sedentary behavior, and (b) specific weather indices associated with those behaviors. Methods PubMed, CINAHL, and SPORTDiscus were searched to identify relevant studies. After identifying and screening 1459 articles, data were extracted from 110 articles with 118,189 participants from 30 countries (almost exclusively high-income countries) on five continents. Results Both physical activity volume and moderate-to-vigorous physical activity (MVPA) were greater in summer than winter. Sedentary behavior was greater in winter than either spring or summer, and insufficient evidence existed to draw conclusions about seasonal differences in light physical activity. Physical activity volume and MVPA duration were positively associated with both the photoperiod and temperature, and negatively associated with precipitation. Sedentary behavior was negatively associated with photoperiod and positively associated with precipitation. Insufficient evidence existed to draw conclusions about light physical activity and specific weather indices. Many weather indices have been neglected in this literature (e.g., air quality, barometric pressure, cloud coverage, humidity, snow, visibility, windchill). Conclusions The natural environment can influence health by facilitating or inhibiting physical activity. Behavioral interventions should be sensitive to potential weather impacts. Extreme weather conditions brought about by climate change may compromise health-enhancing physical activity in the short term and, over longer periods of time, stimulate human migration in search of more suitable environmental niches. 

Self-reports indicate that stress increases the risk for smoking; however, intensive data from sensors can provide a more nuanced understanding of stress in the moments leading up to and following smoking events. Identifying personalized dynamical models of stress-smoking responses can improve characterizations of smoking responses following stress, but techniques used to identify these models require intensive longitudinal data. This study leveraged advances in wearable sensing technology and digital markers of stress and smoking to identify person-specific models of stress and smoking system dynamics by considering stress immediately before, during, and after smoking events. Adult smokers (n = 45) wore the AutoSense chestband (respiration-inductive plethysmograph, electrocardiogram, accelerometer) with MotionSense (accelerometers, gyroscopes) on each wrist for three days prior to a quit attempt. The odds of minute-level smoking events were regressed on minute-level stress probabilities to identify person-specific dynamic models of smoking responses to stress. Simulated pulse responses to a continuous stress episode revealed a consistent pattern of increased odds of smoking either shortly after the beginning of the simulated stress episode or with a delay, for all participants. This pattern is followed by a dramatic reduction in the probability of smoking thereafter, for about half of the participants (49%). Sensor-detected stress probabilities indicate a vulnerability for smoking that may be used as a tailoring variable for just-in-time interventions to support quit attempts.