Multi-point correlations for two dimensional coalescing random walks

This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\mathbb{Z}^2$, started from the initial condition with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation functions of the model decay, for any $N \geq 2$, as $$\rho_N (x_1,\ldots,x_N;t) = \frac{c_0(x_1,\ldots,x_N)}{\pi^N} (\log t)^{N-{N \choose 2}} t^{-N} \left(1 + O\left( \frac{1}{\log^{\frac12-\delta}\!t} \right) \right)$$ as $t \to\infty$. This generalises the results for $N=1$ due to Bramson and Griffeath and confirms a prediction in the physics literature for $N>1$. An analogous statement holds for instantaneously annihilating random walks. The key tools are the known asymptotic $\rho_1(t) \sim \log t/\pi t$ due to Bramson and Griffeath, and the non-collision probability $p_{NC}(t)$, that no pair of a finite collection of $N$ two dimensional simple random walks meets by time $t$, whose asymptotic $p_{NC}(t) \sim c_0 (\log t)^{-{N \choose 2}}$ was found by Cox, Merle and Perkins. This paper re-derives the asymptotics both for $\rho_1(t)$ and $p_{NC}(t)$ by proving that these quantities satisfy {\it effective rate equations}, that is approximate differential equations at large times. This approach can be regarded as a generalisation of the Smoluchowski theory of renormalised rate equations to multi-point statistics.Comment: 26 page

The effects of mood status and competitive anxiety in elite basketball players

Interest has developed in studying the relationship between pre-competitive mood and anxiety with athletic performance (eg. Beedie, Terry & Lane, 2000; Morgan, Ellickson, O'Connor & Bradley, 1992). The most commonly used instrument for measuring mood states in sport psychology is the Profile of Mood States (POMS). A weak to moderate relationship exists between pre-competitive mood and the performance of similarly skilled athletes (Cox, 2002). The current study examined the relationship between pre-game mood status (POMS), competitive-anxiety (SCAT), task-ego orientation (TEOSQ) and game statistics during the season of an elite basketball competition

Preparation, Perception, and Professional Wisdom: Driving Forces in Novice Teachers' Implementation of Evidence-Based Practices for Students with Autism

Special educators are the primary implementers of evidence-based practices (EBPs) for school-aged students with autism. Twenty-eight strategies and interventions have been categorized as evidence-based with demonstrated efficacy for children and youth with autism (Steinbrenner et al., 2020). However, the research-to-practice gap persists, with inconsistent training and implementation of these practices to meet the needs of students in authentic school settings (Hsiao & Sorensen Petersen, 2019; Knight et al., 2019). Due to the recency of the EBP movement in education, novice special educators transitioning from preparation programs into their first years in the profession are well-positioned to increase EBP implementation. Teachers’ knowledge and beliefs about EBPs begin to form early in their careers and exert influence over their teaching practice. Discerning the elements of training, context, and perceptions that impact the implementation of EBPs can support the translation of these practices from controlled research settings into everyday classrooms. A cross-sectional online survey of 137 novice special educators in North and South Carolina gathered self-reports of their knowledge, perceptions of social validity (i.e., acceptability and feasibility), and frequency of use of 12 EBPs for students with autism. Follow-up interviews were conducted with a purposive subsample of ten teachers to explain and expand upon the quantitative data. Overall, teachers’ knowledge, perceptions, and use of EBPs were closely linked. Positive behavior supports and visual schedules emerged as the most accepted and implemented practices. The use of EBPs was primarily driven by teachers’ knowledge of the practice and judgment of its social validity. Completing a pre-service research methods course was the only training element associated with more frequent use of EBPs, underscoring the importance of preparing teachers as informed consumers of research. The thematic analysis revealed how teachers evaluated practices through a broad conceptualization of social validity, including assessing an EBP’s alignment with students’ needs and goals, its feasibility, its generalizability across students and settings, and its compatibility with professional values. Taken together, the results have implications for improving pre-service and in-service training of special educators, particularly by developing the professional wisdom they need to implement EBPs most effectively.Doctor of Philosoph

Qualifying 4D Deforming Surfaces by Registered Differential Features

Institute of Perception, Action and BehaviourRecent advances in 4D data acquisition systems in the field of Computer Vision have opened up many exciting new possibilities for the interpretation of complex moving surfaces. However, a fundamental problem is that this has also led to a huge increase in the volume of data to be handled. Attempting to make sense of this wealth of information is then a core issue to be addressed if such data can be applied to more complex tasks. Similar problems have been historically encountered in the analysis of 3D static surfaces, leading to the extraction of higher-level features based on analysis of the differential geometry.Our central hypothesis is that there exists a compact set of similarly useful descriptors for the analysis of dynamic 4D surfaces. The primary advantages in considering localised changes are that they provide a naturally useful set of invariant characteristics. We seek a constrained set of terms - a vocabulary - for describing all types of deformation. By using this, we show how to describe what the surface is doing more effectively; and thereby enable better characterisation, and consequently more effective visualisation and comparison.This thesis investigates this claim. We adopt a bottom-up approach of the problem, in which we acquire raw data from a newly constructed commercial 4D data capture system developed by our industrial partners. A crucial first step resolves the temporal non-linear registration between instances of the captured surface. We employ a combined optical/range flow to guide a conformation over a sequence. By extending the use of aligned colour information alongside the depth data we improve this estimation in the case of local surface motion ambiguities. By employing a KLT/thin-plate-spline method we also seek to preserve global deformation for regions with no estimate.We then extend aspects of differential geometry theory for existing static surface analysis to the temporal domain. Our initial formulation considers the possible intrinsic transitions from the set of shapes defined by the variations in the magnitudes of the principal curvatures. This gives rise to a total of 15 basic types of deformation. The change in the combined magnitudes also gives an indication of the extent of change. We then extend this to surface characteristics associated with expanding, rotating and shearing; to derive a full set of differential features.Our experimental results include qualitative assessment of deformations for short episodic registered sequences of both synthetic and real data. The higher-level distinctions extracted are furthermore a useful first step for parsimonious feature extraction, which we then proceed to demonstrate can be used as a basis for further analysis. We ultimately evaluate this approach by considering shape transition features occurring within the human face, and the applicability for identification and expression analysis tasks

Coalescing random walks and universality in two dimensions

We study infinite systems of coalescing nearest neighbour random walks on the integer lattice, Z 2 . We are interested in the decay of the probability that the origin is occupied as time increases. This is a well known result for the case that the random walks coalesce instantaneuously and was first proved by Bramson and Griffeath in [2]. We rederive this result and strengthen it by providing an error bound by using the methods employed by van den Berg and Kesten in [27], where they worked in dimensions greater than 2. We further study coalescing random walks that do not coalesce immediately on collision, but can occupy the same site for an exponential (rate λ ∈ (0, ∞)) random time before coalescing, in this was they have a chance to walk away before coalescing. We derive the analogous asymptotic for the decay of the probability of the occupation of the origin and find that, in two dimensions, this decay is independent of the coalescence rate λ in the leading order and agrees with the decay for the instantaneuously coalescing walks

Low Earth orbit thermal control coatings exposure flight tests: A comparison of U.S. and Russian results

Both the United States (US) and Russia have conducted a variety of space environment effects on materials (SEEM) flight experiments in recent years. A prime US example was the Long Duration Exposure Facility (LDEF), which spent 5 years and 9 months in low Earth orbit (LEO) from April 1984 to January 1990. A key Russian experiment was the Removable Cassette Container experiment, (RCC-1), flown on the Mir Orbital Station from 11 January 1990 to 26 April 1991. This paper evaluates the thermal control coating materials data generated by these two missions by comparing: environmental exposure conditions, functionality and chemistry of thermal control coating materials, and pre- and post-flight analysis of absorptance, emittance, and mass loss due to atomic oxygen erosion. It will be seen that there are noticeable differences in the US and Russian space environment measurements and models, which complicates comparisons of environments. The results of both flight experiments confirm that zinc oxide and zinc oxide orthotitanate white thermal control paints in metasilicate binders (Z93, YB71, TP-co-2, TP-co-11, and TP-co-12), are the most stable upon exposure to the space environment. It is also seen that Russian flight materials experience broadens to the use of silicone and acrylic resin binders while the US relies more heavily on polyurethane

Efficacy of Leukemia Inhibitory Factor as a Therapeutic for Permanent Large Vessel Stroke Differs among Aged Male and Female Rats

Preclinical studies using rodent models of stroke have had difficulty in translating their results to human patients. One possible factor behind this inability is the lack of studies utilizing aged rodents of both sexes. Previously, this lab showed that leukemia inhibitory factor (LIF) promoted recovery after stroke through antioxidant enzyme upregulation. This study examined whether LIF promotes neuroprotection in aged rats of both sexes. LIF did not reduce tissue damage in aged animals, but LIF-treated female rats showed partial motor skill recovery. The LIF receptor (LIFR) showed membrane localization in young male and aged rats of both sexes after stroke. Although LIF increased neuronal LIFR expression in vitro, it did not increase LIFR in the aged brain. Levels of LIFR protein in brain tissue were significantly downregulated between young males and aged males/females at 72 h after stroke. These results demonstrated that low LIFR expression reduces the neuroprotective efficacy of LIF in aged rodents of both sexes. Furthermore, the ability of LIF to promote motor improvement is dependent upon sex in aged rodents

Measurement of the Cotton-Mouton effect in nitrogen, oxygen, carbon dioxide, argon, and krypton with the Q & A apparatus

Experiments for vacuum birefringence and vacuum dichroism have been set up with high-finesse high magnetic experimental apparatuses, which seem to be ideal for small gaseous Cotton-Mouton effect (CME) measurements. PVLAS Collaboration has measured CMEs in krypton, xenon and neon at the wavelength of 1064 nm. In this Letter, we report on our measurement of CMEs in nitrogen, oxygen, carbon dioxide, argon, and krypton at the same wavelength in a magnetic field B = 2.3 T at pressure P = 0.5-300 Torr and temperature T = 295-298 K. Our results agree with the PVLAS results in the common cases.Comment: 8 pages, 2 tables, 5 figures, submitted to Chemical Physics Letters. Some modifications are made in the revision according to the referee's comments: Donotations in equations are unified. Error in quoting numbers in 2 places in Table 2 is corrected. Uncertainty in modulation depth is included in the total systematic error. References are order re-arrange