Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities

We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOP572 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Time inhomogeneous Markov chains with wave-like behavior

Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.Comment: Published in at http://dx.doi.org/10.1214/09-AAP661 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect II: Dispersive waves

Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order in the ratio of depth to wavelength. The dislocation of the incident wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short wavelengths the scattering is qualitatively similar to the nondispersive case. At moderate wavelengths, however, there are two markedly different scattering regimes according to wether the capillary length is smaller or larger than $\sqrt{3}$ times depth. The dislocation is characterized by a parameter that depends both on phase and group velocity. The validity range of the calculation is the same as in the shallow water case: wavelengths small compared to vortex radius, and low Mach number. The implications of these limitations are carefully considered.Comment: 30 pages, 11 figure

The Effect of Goal Setting, Motivation, and Fitness Trackers on Daily Step Counts

Purpose: Wearable devices for tracking health and fitness-related activities are thought to motivate individuals to participate in regular exercise. It has been suggested that personal activity trackers can empower individuals to create and keep fitness goals. Therefore, this research was conducted to examine whether using a fitness tracking device in combination with working towards a given goal, self-reporting daily steps, and receiving motivational emails would increase physical activity. Methods: 44 participants (13 males, 31 females) were recruited and randomized into either an experimental (goal setting) or control group (n=22 per group). Participants reported step counts every day for four weeks using an online form. After the first week of data collection, daily step count averages were calculated and goals were given to participants in the experimental group, by adding 500 steps to their daily average. Participants were notified of this goal and sent motivational emails each week, while participants in the control group were not given a specific goal or motivation. Results: Week one step count averages were similar between groups (8460.9 ± 3329.8 steps for the control group and 8783.6 ± 4317.6 steps for the experimental group). Step counts declined in both groups across the three-week period. The week three average was 7731.8 ± 4231.5 steps for the control group and 7642.1 ± 4208.9 steps for the experimental group. Despite email encouragement in the experimental group, only 40.9 percent met their given goal in week one. By the third week, only 27.3 percent of participants in the experimental group met their goal, missing this goal by an average of 1595.88 ± 3294 steps. Participants reported that the use of these devices encouraged them to participate in physical activity (44.8 percent of the control group and 63.7 percent of the experimental group) despite the declining step count trend observed. 69.6 percent of the control group and 72.7 percent of the experimental group reported that they would continue to wear a fitness tracking device outside of the study. Conclusion: There was no significant difference between experimental and control groups with their adherence to the program and step count levels throughout each week. Both groups on average did not reach the widely accepted recommendation of 10,000 steps per day. Interestingly, the majority of participants reported that they still plan to use a fitness tracking device in the future and consider them to be a piece of motivational technology

Applications of the overlap formalism to super Yang-Mills theories

We show that the idea to use the overlap formalism to formulate 4D N=1 super Yang-Mills theory on the lattice without fine-tuning can be applied to 3D N=1 case as well. Another application we propose is a regularization of the IIB matrix model, which is large N reduced model of 10D N=1 super Yang-Mills theory.Comment: 3 pages, LaTeX with espcrc2.sty. Talk presented at Lattice97, Edinburgh, 22-26 July 1997, to appear in Nucl. Phys. B (Proc.Suppl.

Uniform bounds on complexity and transfer of global properties of Nash functions

We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of many properties of Nash functions and a good behaviour under real closed field extension (e.g. primary decomposition). As a distinguished application, we derive the solution of the extension and global equations problems over arbitrary real closed fields, in particular over the field of real algebraic numbers. This last fact and a technique of change of base are used to prove that the Artin-Mazur description holds for abstract Nash functions on the real spectrum of any commutative ring, and solve extension and global equations in that abstract setting. To complete the view, we prove the idempotency of the real spectrum and an abstract version of the separation problem. We also discuss the conditions for the rings of abstract Nash functions to be noetherian

Four-strand hamstring tendon autograft for ACL reconstruction in patients aged 50years or older

SummaryIntroductionReconstruction of the anterior cruciate ligament using a four-strand hamstring tendon autograft in symptomatic patients aged 50years or older is an accepted treatment option.HypotesisFour-strand hamstring tendon autograft although not universally utilized in patients who are at least 50years old is an efficient procedure to control knee instability.Material and methodsIn this retrospective, we analyzed the clinical outcomes of 18patients treated from September 1998 to September 2003. Criteria for inclusion were the following: age above 50years at surgery, chronic anterior laxity associated or not with meniscal damage; one or more episodes of knee instability and no prior ligament surgery on the involved knee. A same operative technique (arthroscopic single-bundle four-strand hamstring reconstruction, blind femoral tunnel, through anteromedial portals), a same fixation type (absorbable interference screws in femur and tibia) and a same rehabilitation protocol were used for all these knees. The IKDC 93scores were determined pre- and postoperatively combined with anteroposterior and lateral views, single leg stance, 30° flexion stance, and passive Lachman test (Telos) postoperatively.ResultsAt mean 30month-follow-up (range 12–59months), there were no graft failure and no loss of extension for any of these knees. Three patients complained of hypoesthesia in the medial saphenous nerve territory and one patient experienced posterior knee pain. All patients graded their knee as normal or nearly normal, all were satisfied or very satisfied with their operation. None of the patients reported instability. The Lachman-Trillat test was noted “firm end point” in 14knees and “delayed firm end point” in four. The pivot-shift test was negative in 16knees and mild positive in two. The mean residual differential laxity was 3.1mm (0 to +6mm) for the passive Lachman test. At last follow-up, the overall IKDC score was 7A, 7B, 3C, and 1 D. Patients with preserved meniscus (nine patients) reported a lesser degree of pain and a better residual laxity control compared with patients who had undergone a meniscectomy.ConclusionAge over 50years is not a contraindication to select a hamstring tendon autograft for ACL reconstruction. This surgery can restore knee stability but does not modify the pain pattern in patients, who had a medial meniscectomy prior to the ACL reconstruction.Level of evidence: level IV, therapeutic study

Continuum Gauge Fields from Lattice Gauge Fields

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the $U(1)$ theory in two dimensions, where it leads to simple results.Comment: 16 pages, HLRZ 92-3