Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003

Staying physically active after spinal cord injury:a qualitative exploration of barriers and facilitators to exercise participation

<p>Abstract</p> <p>Background</p> <p>While enhancing physical activity has been an essential goal of public health officials, people with physical impairments such as spinal cord injury (SCI) are more likely to live a sedentary lifestyle. Exercise has been shown to decrease the risk for many of the secondary conditions associated with SCI, including osteoporosis, cardiovascular disease, pressure ulcers, urinary tract infections, diabetes and arthritis, yet this population is rarely a target for health promotion efforts. This paper examines the self-reported exercise experiences of people with SCI using a qualitative-exploratory design.</p> <p>Methods</p> <p>We enrolled 26 individuals with SCI (15 self-described 'exercisers' and 11 'non-exercisers') from a non-random pool of survey responders. Semi-structured phone interviews were conducted to record participants' experiences with exercise pre/post injury, barriers and facilitators to being active and perceived health impact.</p> <p>Results</p> <p>Regardless of exercise status, all participants reported physical activity prior to injury and expressed interest in becoming active or maintaining an active lifestyle. Participants identified a range of both motivational and socio-environmental factors that were either facilitating or constraining of such a lifestyle. Non-exercisers identified barriers to exercise, including a perceived low return on physical investment, lack of accessible facilities, unaffordable equipment, no personal assistance and fear of injury. Exercisers identified facilitators, including personal motivation, independence, availability of accessible facilities and personal assistants, fear of health complications, and weight management. Exercisers associated a greater range of specific health benefits with being active than non-exercisers.</p> <p>Conclusion</p> <p>Despite motivation and interest in being exercise active, people with SCI face many obstacles. Removal of barriers coupled with promotion of facilitating factors, is vital for enhancing opportunities for physical activity and reducing the risk of costly secondary conditions in this population.</p