Independent Walks Research Articles

On a class of stochastic fractional heat equations

For the fractional heat equation ∂ ∂ t u ( t , x ) = − ( − Δ ) α 2 u ( t , x ) + u ( t , x ) W ˙ ( t , x ) \frac {\partial }{\partial t} u(t,x) = -(-\Delta )^{\frac {\alpha }{2}}u(t,x)+ u(t,x)\dot W(t,x) where the covariance function of the Gaussian noise W ˙ \dot W is defined by the heat kernel, we establish Feynman-Kac formulae for both Stratonovich and Skorohod solutions, along with their respective moments. In particular, we prove that d > 2 + α d>2+\alpha is a sufficient and necessary condition for the equation to have a unique square-integrable mild Skorohod solution. One motivation lies in the occurrence of this equation in the study of a random walk in random environment which is generated by a field of independent random walks starting from a Poisson field.

Designing movement space for elderly and disabled people in the construction law in selected countries.

Building law regulations determine designing the built environment recognising the needs of users of different ages and psychophysical abilities. Seniors and their spatial needs are covered there to a limited extent. The benchmark for design are wheelchair users. Their spatial requirements are greater in relation to independent walkers, including most older people. This makes it difficult to adapt the whole built environment to the needs of people with less mobility dysfunction. This can be considered in terms of spatial design and investment costs. The paper analyses the building regulations of 3 countries in terms of legal conditions to shape the architectural movement space of older people and disabled people. Analytical and comparative methods are used. Such research is becoming relevant and necessary. The analyses are conducted in the context of ageing populations. They are justified by statistical data on the age groups of Polish society. This is followed by design analyses of the legal requirements in the wheelchair movement space and proposals for alternatives, e.g., people walking with canes (case study). Their aim is to indicate methods to limit excessive communication spaces in buildings while maintaining functional values for all users. Research may show the possibility of greater diversification of regulations and alternatives to current laws. They are dedicated to participants in investment processes to shape accessible buildings. They can also be used in legislative work on amendments to the construction law. Changes in building regulations and a detailed approach to the mobility needs of older and disabled people (walking independently) are proposed. These decisions can provide benefits (spatial and economic savings). They fall into the "design for all" trend and sustainability of the built environment. These demands are based on no longer valid normative regulations. Med Pr Work Health Saf. 2024;75(3):189-197.

Early Postoperative Functional Recovery in Older Patients With Periprosthetic Femoral Fractures: Comparison Between Cemented and Cementless Stem Revisions

BackgroundEarly postoperative functional recovery is important in older patients with lower-extremity fractures to prevent disuse, and periprosthetic femoral fractures (PFFs) are no exception. This study aimed to compare the postoperative functional recovery in the early phase after revision for PFF with loose stems between cemented and cementless stems. MethodsEighteen patients with Unified Classification System type B2 PFF were included in this retrospective cohort study with a follow-up period of about 2 years. All patients underwent stem revision and were divided into 2 groups: the cemented stem group (n = 9) and the cementless stem group (n = 9). In postrevision, functional independence measure score, independent walk rate, activities of daily living recovery rate to the original level at 2 weeks postoperatively, the Beals and Tower classification for radiological status, and survival rate for readmission as endpoints were compared between the 2 groups. ResultsPatients in the cemented group recovered functional mobility earlier than in the cementless group, with higher postoperative functional independence measure functional subscale values (73 vs 50 points, P = .02), higher independent walk rate (89 vs 11%, P < .01), and more postoperative activities of daily living recovery (100% vs 44%, P = .03) at 2 weeks postoperatively. The Beals and Tower classification and survival rates were similar in both groups. ConclusionsRevision using a cemented stem for PFF in older patients was a useful surgical procedure in terms of early postoperative functional recovery. Cemented stem revision was comparable with cementless in bone union and safety at 2 years postoperatively.

Factors Associated With Ambulation Status and Survival One Year After Conservative Management of Hip Fracture.

Few studies have investigated the factors associated with ambulation and survival over one year. Therefore, this study aimed to examine the factors that influence ambulation and survival rates in elderly patients who have undergone conservative management for hip fractures. This retrospective study included 74 ambulatory individuals aged 65 years or older prior to their injuries. One-year mortality and ambulatory status were assessed. Statistical comparisons of background and medical characteristics between groups of independent and non-independent walkers, as well as between survivors and mortalities, were performed using the Pearson chi-squared, Fisher exact, and Mann-Whitney U tests. The numbers of older patients able to walk independently, those not able to walk independently, and those with mortality at one-year post-injury after conservative management of hip fractures were 13 (18.3%), 35 (49.3%), and 23 (32.4%), respectively. Independent walkers one year after conservative treatment for hip fracture were younger (p=0.04) and less likely to have cognitive impairment (p=0.04) than non-independent walkers. The proportion of individuals with cognitive impairment was found to be lower among survivors than among mortalities (p=0.0098). Cognitive decline may contribute to difficulties in walking independently and mortality at one year post-injury in this population.

Usefulness of the Kansas University Standing Balance Scale in inpatient rehabilitation: a retrospective validation study.

Adequate balance assessment is essential for designing rehabilitation programs and preventing falls. This study aimed to report the cross-cultural adaptation of the Korean version of the Kansas University Standing Balance Scale (KUSBS), investigate its concurrent and predictive validities, and examine aging-related differences. The adaptation was performed using a standard protocol. In this retrospective study, 1179 patients were included and classified into adult, young-old, old-old, and oldest-old groups. Furthermore, we compared the concurrent, discriminant, and predictive validities of the KUSBS and Berg Balance Scale (BBS). Nonparametric analysis was also conducted. The Spearman rho test revealed strong correlation coefficients between the KUSBS and BBS (r s > 0.7; P < 0.001). At admission, the relationship was strong in the adult, young-old, and old-old groups (r s = 0.931, 0.913, and 0.914, respectively; P < 0.001) but not the oldest-old group (r s = 0.790; P < 0.001). At discharge, the correlation coefficients were above 0.9 in all groups. Additionally, the relationship between the changes in both scales was moderate-to-strong (r s > 0.68; P < 0.001). The predictive validity for independent walking of the KUSBS was strong (r s = 0.791; P < 0.001) and significantly lower than that of the BBS (r s = 0.833; P < 0.001; Z = -3.001; P = 0.003). Furthermore, the cutoff value of the KUSBS at admission to predict independent ambulatory walkers at discharge was 3.5 in ordinal ranking in all age groups. The KUSBS is a reliable and effective tool for measuring balance in patients in inpatient rehabilitation.

Association of Serum Lactate Levels Measured in the Emergency Department with 30-Day Mortality in Older Patients with Unilateral Hip Fractures.

Hip fractures are frequent injuries in older patients and are associated with high mortality rates. This study assessed the association between serum lactate level and 30-day mortality in older patients with unilateral hip fractures and examined the prognostic value of this association on the clinical outcomes of these patients. This retrospective, single-center study included patients aged ≥65 years admitted to the emergency department due to low-energy trauma and diagnosed with unilateral hip fracture upon admission. The additional inclusion criteria were patients with independent ambulation or walker or cane assistance before the injury, with available data on serum lactate levels on venous blood gas analysis, and who underwent surgery. Among the 330 included patients, 30.9% experienced postoperative complications and 10.3% died within 30 days. Using a lactate cut-off value of 2 mmol/L to distinguish between living and deceased patients, the sensitivity and specificity were 41% and 88%, respectively. Multivariate logistic regression analysis revealed that high lactate and low albumin levels and male sex were associated with mortality. Identifying risk factors for mortality in geriatric patients with hip fractures is important. Male sex, low albumin levels, and particularly increased lactate levels were independent predictors of short-term mortality in these patients.

Complete integrability of the problem of full statistics of nonstationary mass transfer in the simple inclusion process.

The simple inclusion process (SIP) interpolates between two well-known lattice gas models: the independent random walkers and the Kipnis-Marchioro-Presutti model. Here we study large deviations of nonstationary mass transfer in the SIP at long times in one dimension. We suppose that N≫1 particles start from a single lattice site at the origin, and we are interested in the probability P(M,N,T) of observing M of the particles, 0≤M≤N, to the right of the origin at a specified time T≫1. At large times, the corresponding full probability distribution has a large-deviation behavior, -lnP(M,N,T)≃sqrt[T]s(M/N,N/sqrt[T]). We determine the rate function s exactly by uncovering and utilizing complete integrability, by the inverse scattering method, of the underlying equationsof the macroscopic fluctuation theory. We also analyze different asymptotic limits of the rate function s.

Quality of cementing in hemiarthroplasty for elderly neck of femur fractures does not affect short term functional outcomes.

Cemented hip hemiarthroplasty is a routine surgical option for elderly neck of femur (NOF) fractures. It is uncertain if quality of cementing has any effect on functional outcomes. The aim of this study was to determine if the quality of cementing would affect short term functional outcomes in elderly neck of femur fractures. Retrospective analysis of 637 single-centre cemented hip hemiarthroplasties from 2014 to 2021 was performed. Each post-operative radiograph was double-read by 2 authors (1 resident and 1 fellowship trained surgeon) to determine quality of cementing via the Barrack grading. Disagreements were reviewed by a third reader. Cement grades were grouped as Optimal (Barrack grade A-B), or Suboptimal (Barrack grade C-D). Functional outcomes were compared using mobility (community- or home-ambulant), assistance required for mobility, and Modified Barthel Index (MBI). Surgical parameters were compared between the groups. There were 429 Optimal and 208 Suboptimal cases of cementing performed. There was no difference in age, American Society of Anesthesiologists score, mobility, assistance required, and MBI score pre-operatively (p > 0.05). Patients in the "Suboptimal" cementing group had a higher Charlson Comorbidity Index (CCI) score (p < 0.001). At 1year post-operation, there was no significant difference between "Optimal" and "Suboptimal" cementing with regards to the proportion of community ambulators (30.2% vs. 25.7%, p = 0.252), walking independence (independent walkers (19.8% vs.17.3%), independent walkers with aids (41.3%vs.42.1%), walker with caregiver assistance (29.2%vs.33.7%), wheelchair-bound (9.6%vs.6.9%), p = 0.478), and distribution of MBI score (81.1%vs.82.2% achieving MBI > 60, p = 0.767). There was no significant difference in the proportion of patients with postoperative delirium (7.9% vs. 5.8, p = 0.324) or 1-year mortality rates (3.5% vs. 2.9%, p = 0.685). Except for stem design (12.2% tapered vs 20.1% collared; p = 0.011), no other surgical parameters were significantly different. The kappa value for inter-reader agreement was "substantial" at 0.727 (95% CI 0.682-0.772) (p < 0.001). Quality of cementing in cemented hip hemiarthroplasty for elderly NOF fractures does not affect the short-term functional outcomes. In low demand patients and patients at risk of BCIS, optimal cementing may not be necessary to achieve similar short-term functional outcomes. Further studies should be conducted to determine the effect of sub-optimal cementing on long-term functional outcomes.

First-passage time for many-particle diffusion in space-time random environments.

The first-passage time for a single diffusing particle has been studied extensively, but the first-passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently. We consider two models for many-particle diffusion-one treats each particle as independent simple random walkers while the other treats them as coupled to a common space-time random forcing field that biases particles nearby in space and time in similar ways. The first-passage time of a single diffusing particle under both models shows the same statistics and scaling behavior. However, for many-particle diffusions, the first-passage time among all particles (the extreme first-passage time) is very different between the two models, effected in the latter case by the randomness of the common forcing field. We develop an asymptotic (in the number of particles and location where first passage is being probed) theoretical framework to separate the impact of the random environment with that of the sampling trajectories within it. We identify a power law describing the impact of the environment on the variance of the extreme first-passage time. Through numerical simulations, we verify that the predictions from this asymptotic theory hold even for systems with widely varying numbers of particles, all the way down to 100 particles. This shows that measurements of the extreme first-passage time for many-particle diffusions provide an indirect measurement of the underlying environment in which the diffusion is occurring.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Funding Pattern Comparison Pre- and Post-Ayushman Bharat National Health Scheme (AB-PMJAY) in Active Females Undergoing TKA for Advanced Knee Arthritis with Clinical, QoL Analysis and AB-PMJAY Technical Data.

Patients visiting for Knee Arthroplasty have often been treated at neighborhood clinics and bonesetters. India floated world's largest publicly funded national health insurance program -AB-PMJAY covering Knee Arthroplasty. AB-PMJAY's data for Arthroplasty has not been published. A Prospective study from Jan 2016- Jan 2023 on females undergoing TKA. Age, DEXA Score, Walking Ability, KSS, 10MWT, SF36 Scores, Funding Pattern before and after AB-PMJAY, Time to Approval, Time to discharge, Time to Query reply and Rejection Rates were documented. 790 patients (91.86%) received treatment previously. 650 (78.54%) patients lived with family & 32 patients lost to follow-up. 37.67% & 62.32% patients had Grade. 3 & 4 osteoarthritis respectively. Commonest comorbidity was Vitamin D deficiency followed by Menopause and Hypertension. Post-treatment Vitamin D deficiency reduced from 68.59% to 2.17% at 3 months. Post-surgery, Functional Scores improved significantly at 1st and 6th month. VAS dropped significantly from 7.8 to 3.6 at 1st month follow up. At 6 months, 81.52% patients were independent outdoor walkers compared to 9.42% (baseline). Average hospital stay-54 hours and Return to work- 42 days. Central health scheme beneficiaries rose significantly from 12% (pre-PMJAY) to 42% (post-PMJAY). With AB-PMJAY, no rejection for surgical procedures, Time to surgery approval was 16 hours (mean) and Time to Discharge was 8 hours (mean). Time to reply was 6 hours (mean). Evident rise in patients getting TKA done through AB-PMJAY. TKA has become an affordable and achievable target for financially deprived patients, post regulation of knee implant prices & AB-PMJAY.

A multivariate extension of the Erdős–Taylor theorem

The Erdős–Taylor theorem (Acta Math Acad Sci Hungar, 1960) states that if LN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{L}_N$$\\end{document} is the local time at zero, up to time 2N, of a two-dimensional simple, symmetric random walk, then πlogNLN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ frac{\\pi }{\\log N} \\,\ extsf{L}_N$$\\end{document} converges in distribution to an exponential random variable with parameter one. This can be equivalently stated in terms of the total collision time of two independent simple random walks on the plane. More precisely, if LN(1,2)=∑n=1N1{Sn(1)=Sn(2)}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{L}_N^{(1,2)}=\\sum _{n=1}^N \\mathbb {1}_{\\{S_n^{(1)}= S_n^{(2)}\\}}$$\\end{document}, then πlogNLN(1,2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ frac{\\pi }{\\log N}\\, \ extsf{L}^{(1,2)}_N$$\\end{document} converges in distribution to an exponential random variable of parameter one. We prove that for every h⩾3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h \\geqslant 3$$\\end{document}, the family {πlogNLN(i,j)}1⩽i<j⩽h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\big \\{ \\frac{\\pi }{\\log N} \\,\ extsf{L}_N^{(i,j)} \\big \\}_{1\\leqslant i<j\\leqslant h}$$\\end{document}, of logarithmically rescaled, two-body collision local times between h independent simple, symmetric random walks on the plane converges jointly to a vector of independent exponential random variables with parameter one, thus providing a multivariate version of the Erdős–Taylor theorem. We also discuss connections to directed polymers in random environments.

ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

Abstract TMP32: Race and Ethnic Differences in Rehabilitation and Functional Recovery Post-Stroke Within the Florida Stroke Registry - Transitions of Care

Introduction: Historically, non-Hispanic black (NHB) and Hispanic stroke survivors have been discharged at a poorer functional level than non-Hispanic whites (NHW). The purpose of this study was to examine race and ethnic differences in rehabilitation prescription and participation at time of discharge (DC) and in modified Rankin Scale (mRS) at 30- and 90-days post-stroke. Methods: The Transitions of Stroke Care Disparities Study is designed to reduce disparities and optimize post-stroke care in hospital-to-home transitions. Survivors of ischemic stroke and intracerebral hemorrhage from a subset of 165 hospitals in the Florida Stroke Registry were included in the Get with the Guidelines-Stroke® (GWTG-S) database. Race and ethnicity, therapy prescription and participation, and mRS were extracted from GWTG-S, and by self-report at 30- and 90-days after DC. Race and ethnic differences were assessed in therapy prescription, participation, and mRS using binary logistic regression adjusted for age, sex, stroke severity (NIHSS), and DC walking ability. Results: In 1,129 stroke survivors (mean age 64y, 45% women, 55% NHW, 23% NHB, 22% Hispanic, 76% independent walkers at DC), 29% were prescribed inpatient and 50% outpatient rehabilitation at DC. Multivariable analysis showed NHW were significantly less likely to be prescribed inpatient therapy compared to NHB [OR 0.56, 95%CI (0.35-0.88)] or Hispanics [OR 0.50, 95%CI (0.31-0.80)]. Hispanic individuals [OR 1.69, 95%CI (1.20-2.38)] were significantly less likely to be prescribed outpatient therapy compared to NHW or NHB. No differences in therapy participation were seen between NHW and NHB [OR 1.16, 95%CI (0.69-1.97)] or Hispanics [OR 1.41, 95%CI (0.82-2.43)]. No differences in mRS were seen between NHW and NHB [30-days, OR 0.85, 95% CI (0.52-1.39); 90-days, OR 0.68, 95%CI (0.42-1.11)] or Hispanics [30-days, OR 0.63, 95% CI (0.37-1.10); 90-days, OR 0.61, 95%CI (0.36-1.03)]. Conclusions: Although there were significant race and ethnic differences in therapy prescription setting, no race and ethnic differences were seen in therapy participation or in mRS at either 30- or 90-days. Further research is warranted to examine race and ethnic differences in stroke recurrence and readmission rates.

Characterizing the Individuals Who Regain or Maintain Walking Ability after a Hip Fracture: Insights Into Physical Resilience

ObjectivesMaintaining walking ability is key to healthy aging. Hip fractures often lead to declined walking ability. This study investigated characteristics of individuals who regained walking ability after a hip fracture, an expression of physical resilience. DesignRegister-based cohort study. Setting and ParticipantsA total of 55,467 Swedish residents aged ≥60 years with a first hip fracture (71% women, mean age = 82.3 ± 8) included in the Swedish Hip Fracture Register. MethodsInformation about diseases, medications, and socioeconomic (SES) factors came from registers. Individuals were classified by prefracture walking ability (independent or assisted walking) and whether their walking ability 4 months post-fracture was maintained (physical resilience or nonresilience). Cluster analyses were conducted among individuals who maintained their walking ability to assess different physical resilience profiles. ResultsAt baseline, 38,493 individuals walked independently (69%), and 16,982 were assisted walkers. Half of the independent walkers maintained their walking ability 4 months post-fracture. Among them, 3 clusters were identified: a “Low SES, Low Disease” cluster (n = 8580, mean age 81.1 ± 7.5); a “High SES, Low Disease” cluster (n = 7778, mean age 76.7 ± 7.4); and a third “High SES, High Disease” cluster (n = 4320, mean age 77.7 ± 7.4).Sixty percent of the pre-assisted walkers maintained their level of assisted walking ability. Also among them, 3 clusters were identified: a “Low SES-Independent Living” cluster (n = 3077, mean age 85.5 ± 7.1); a second “Care Home” cluster (n = 2912, mean age 87.0 ± 6.5) with a high proportion with dementia diagnosis; and a last “High SES” cluster (n = 4044, mean age 83.0 ± 7.0) with the largest proportion of men. Conclusions and ImplicationsPhysical resilience is not characterized by one typical healthy profile, and it is possible to regain walking ability after a hip fracture despite unfavorable prerequisites in 1 domain. A favorable status in one domain may compensate for an unfavorable status in another, for example, a high disease burden in combination with high SES.

The 5-STS is a prognostic factor of sub-acute stroke patients who will not become community walkers at discharge from rehabilitation.

The recovery of community ambulation is a common concern among individuals after stroke. (1) To develop a potential readily applicable prognostic model able to correctly discriminate stroke patients who will not become independent community walkers at discharge; (2) To investigate the effects of early reassessment during the first month of treatment on the prediction accuracy of this model. This was a prospective cohort study. A consecutive sample of 80 patients at ≤60 days poststroke were assessed at baseline of outpatient physical rehabilitation and reassessed one month later. Non-functional community ambulation was measured. Seventy-four patients were followed until discharge. Of these, 47 patients were non-functional community walkers at discharge. A prediction model based on baseline performance in the five repetition sit-to-stand [5-STS] test was able to discriminate those patients of the sample (Area-under-curve = 0.956), and again with data from reassessment (AUC = 0.952). A time of 21 s at baseline was a highly prognostic cut-off point for discrimination (sensitivity = 87.2% and 85.1%). The combined use of baseline and reassessment data improved sensitivity (98.1%)CONCLUSION:Early findings of the 5-STS among stroke patients is an independent prognostic factor associated with independent community walking at discharge. It could discriminate individuals who will not become community walkers at discharge.

The Kuramoto model on dynamic random graphs

We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics are dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by N independent random walks on the underlying graph. We prove a synchronisation result for solutions starting from a phase-cohesive set independent of the speed of the random walkers, an averaging principle and a global synchronisation result with high probability for sufficiently fast processes. We also consider Kuramoto oscillators in a dynamical version of the random conductance model.

Infinite collision property for the three-dimensional uniform spanning tree

Let [Formula: see text] be the three-dimensional uniform spanning tree, whose probability law is denoted by [Formula: see text]. For [Formula: see text]-a.s. realization of [Formula: see text], the recurrence of the simple random walk on [Formula: see text] is proved in Benjamini et al. (2001) [I. Benjamini, R. Lyons, Y. Peres and O. Schramm, Uniform spanning forests, Ann. Probab. 29(1) (2001) 1–65] and it is also demonstrated in Hutchcroft and Peres (2015) [T. Hutchcroft and Y. Peres, Collisions of random walks in reversible random graphs, Electron. Commun. Probab. 20(63) (2015) 1–6] that two independent simple random walks on [Formula: see text] collide infinitely often. In this paper, we will give a quantitative estimate on the number of collisions of two independent simple random walks on [Formula: see text], which provides another proof of the infinite collision property of [Formula: see text].

Asymptotics of noncolliding q-exchangeable random walks

We consider a process of noncolliding q-exchangeable random walks on making steps 0 (‘straight’) and −1 (‘down’). A single random walk is called q-exchangeable if under an elementary transposition of the neighboring steps the probability of the trajectory is multiplied by a parameter . Our process of m noncolliding q-exchangeable random walks is obtained from the independent q-exchangeable walks via the Doob’s h-transform for a nonnegative eigenfunction h (expressed via the q-Vandermonde product) with the eigenvalue less than 1. The system of m walks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is the q-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncolliding q-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel of q-distributed random lozenge tilings of sawtooth polygons. In the limit as , with γ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel.

Using the Standing and Walking Assessment Tool at Discharge Predicts Community Outdoor Walking Capacity in Persons With Traumatic Spinal Cord Injury.

The Standing and Walking Assessment Tool (SWAT) standardizes the timing and content of walking assessments during inpatient rehabilitation by combining 12 stages ranging from lowest to highest function (0, 0.5, 1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C, and 4) with 5 standard measures: the Berg Balance Scale, the modified Timed "Up & Go" test, the Activities-specific Balance Confidence Scale, the modified 6-Minute Walk Test, and the 10-Meter Walk Test (10MWT). This study aimed to determine if the SWAT at rehabilitation discharge could predict outdoor walking capacity 1-year after discharge in people with traumatic spinal cord injury. This retrospective study used data obtained from the Rick Hansen Spinal Cord Injury Registry from 2014 to 2020. Community outdoor walking capacity was measured using the Spinal Cord Independence Measure III (SCIM III) outdoor mobility score obtained 12 (±4) months after discharge. Of 206 study participants, 90 were community nonwalkers (ie, SCIM III score 0-3), 41 were community walkers with aids (ie, SCIM III score 4-6), and 75 were independent community walkers (ie, SCIM III score 7-8). Bivariate, multivariable regression, and an area under the receiver operating characteristic curve analyses were performed. At rehabilitation discharge, 3 significant SWAT associations were confirmed: 0-3A with community nonwalkers, 3B/higher with community walkers with and without an aid, and 4 with independent community walkers. Moreover, at discharge, a higher (Berg Balance Scale, Activities-specific Balance Confidence Scale), faster (modified Timed "Up & Go," 10MWT), or further (10MWT) SWAT measure was significantly associated with independent community walking. Multivariable analysis indicated that all SWAT measures, except the 10MWT were significant predictors of independent community walking. Furthermore, the Activities-Specific Balance Confidence Scale had the highest area under the receiver operating characteristic score (0.91), demonstrating an excellent ability to distinguish community walkers with aids from independent community walkers. The SWAT stage and measures at discharge can predict community outdoor walking capacity in persons with traumatic spinal cord injury. Notably, a patient's confidence in performing activities plays an important part in achieving walking ability in the community. The discharge SWAT is useful to optimize discharge planning.