Local time of diffusion with stochastic resetting

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the presence of an absorbing boundary. Given a Brownian trajectory that evolved for $t$ units of time, the local time is simply defined as the total time the trajectory spent in a small vicinity of its initial position. However, as Brownian trajectories are stochastic --- the local time itself is a random variable which fluctuates round and about its mean value. In the past, the statistics of these fluctuations has been quantified in detail; but not in the presence of resetting which biases the particle to spend more time near its starting point. Here, we extend past results to include the possibility of stochastic resetting with, and without, the presence of an absorbing boundary and/or drift. We obtain exact results for the moments and distribution of the local time and these reveal that its statistics usually admits a simple form in the long-time limit. And yet, while fluctuations in the absence of stochastic resetting are typically non-Gaussian --- resetting gives rise to Gaussian fluctuations. The analytical findings presented herein are in excellent agreement with numerical simulations.Comment: 23 pages, 10 figure

Comparison of open reduction and internal fixation by lateral extensile approach versus minimal invasive percutaneous fixation (Essex Lopresti) for the management of Sanders type 2 and 3 calcaneum fractures: a prospective, two-arm, parallel group study

Background: Calcaneum is one of the most common tarsal bone to get fractured accounting for around 50-60% of all tarsal fractures. Due to lack of Indian studies comparing the outcomes of fracture calcaneus managed by operative methods of open reduction internal fixation (ORIF) versus the percutaneous minimal invasive approach (Essex Lopresti); we decided to conduct one such study. Methods: Adult patients with intra-articular Sander type 2 and 3 calcaneum fractures, managed by ORIF or Essex Lopresti were enrolled. The clinical outcomes (VAS score for pain, range of motion), radiological outcomes (Bohler’s and Crucial angle of Gissane) and functional outcomes (American orthopedic foot and ankle society (AOFAS) and Maryland foot score) were assessed at 6th month and 1-year post intervention and compared. Results: 117 patients managed with percutaneous fixation (n=63) or ORIF (n=54) were enrolled. Mean age of patients was 42.63±7.93 years. Mean VAS score was statistically comparable in both operative groups at 6th month and 1 year (p>0.05). Mean dorsiflexion and eversion angles were significantly higher in plating group at 6th month (p<0.05) while other movements were comparable in both the groups. Mean Bohler’s angle, Gissane’s angle, AOFAS and Maryland scores were found to be comparable in both groups (p>0.05) on follow-up. Both groups showed similar complications trend. Conclusions: Percutaneous fixation and plating methods were found to be comparable for calcaneus fracture management based on clinical, functional and radiological outcomes with similar complication rates

Assessment of the safety and efficacy of intravenous versus topical tranexamic acid in patients undergoing primary total hip and knee arthroplasty surgeries with respect to decreasing peri-operative blood loss and blood transfusion rates: a prospective and comparative study

Background: Synthetic antifibrinolytic agent like tranexamic acid has been increasingly used in Arthroplasty surgeries to decrease the peri-operative blood loss. The current study was undertaken to compare the efficacy between the intravenous and Topical route of TXA in deceasing the blood loss and transfusion rate in patients undergoing primary total hip and knee arthroplasty (THR and TKR) surgeries. Methods: A total of 120 patients were enrolled in the study with 60 each undergoing THR and TKR surgeries with 30 each given TXA in IV and Topical routes. Outcomes were assessed in terms of mean 24 hours drain output, mean blood loss, mean drop in hemoglobin blood transfusion rate. Results: The mean drain output was more in the IV group in both THR and TKR patients (p>0.05). The mean blood loss was more in the Topical group in both THR and TKR patients (p>0.05). The mean drop in hemoglobin was more in the Topical group, with the difference being significant in the THR patients (p<0.05) and being insignificant in TKR patients (p>0.05). In IV group 9 patients (15%) and in Topical group 25 patients (41.67%) needed blood transfusions, the difference being statistically significant. Conclusions: Both IV and Topical routes of TXA are equally effective in decreasing the peri-operative blood loss and transfusion rates in patients undergoing primary arthroplasty surgeries, with IV route having slightly upper hand as compared to the Topical route.

India, Germany and Europe: a Spatial Perspective at SDG 3 on Good Health and Well-Being

Responding to crucial challenges in urban and rural development led the United Nations decide on the New Urban Agenda as well as the 2030 Agenda and the Sustainable Development Goals (SDGs). In order to understand the spatial patterns, which SDGs produce, a national and supranational spatial perspective is taken on SDG 3 “Good health and Well-Being”. Progress in health concomitantly affects several pathways of development in a country. Persistent improvements in the life expectancy at birth ascertain significant progress towards health care in any country. The development in the respective health system is validated by improving health-related indicators, such as institutional deliveries, infant and child mortality rates, full immunisation and nutrition. Sub-goal 3.7 addresses the universal access to sexual and reproductive health care services, including family planning, information and education. Adolescent pregnancy leading to teenage parenthood is an obviously global concern affecting low- and high-income countries in the same way. Alternating maps illustrate the spatial perspective on SDG 3 in India, Germany and Europe by taking manifold national as well as supranational views wherever feasible

India, Germany and Europe: a Spatial Perspective at SDG 4 on Quality Education

Responding to crucial challenges in urban and rural development led the United Nations decide on the New Urban Agenda as well as the 2030 Agenda and the Sustainable Development Goals (SDGs). In order to understand the spatial patterns, which SDGs produce, a national and supranational spatial perspective is taken on SDG 4 "Quality Education". SDG 4 highlights the human right on education and requests institutions to ensure inclusive and equal access to education for all. In many countries, one can note gender differences related to schooling at all levels or at graduation. Education in general and the education of females in particular influences largely the social and economic development of countries, ranging from health and birth control to a higher economic output of enterprises lead by mixed teams. The chapters visualise the spatial analysis of SDG 4, respectively on school graduates, female school graduates and scholar exclusion. Alternating maps illustrate the spatial perspective on SDG 4 in India, Germany and Europe by taking manifold national as well as supranational views wherever feasible