Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $C_{d,p}(n)$ in their work on Boardman--Vogt tensor products of operads; they used homological algebra to prove a recursive formula and a functional equation. We express $C_{d,p}(n)$ as simple finite sums, and determine their growth rate and asymptotic behaviour. We give an elementary proof of the functional equation, using a bijection between hypercube decompositions and a family of full $p$-ary trees. Our results generalize the well-known correspondence between Catalan numbers and full binary trees

Janssen effect and the stability of quasi 2-D sandpiles

We present the results of three dimensional molecular dynamics study of global normal stresses in quasi two dimensional sandpiles formed by pouring mono dispersed cohesionless spherical grains into a vertical granular Hele-Shaw cell. We observe Janssen effect which is the phenomenon of pressure saturation at the bottom of the container. Simulation of cells with different thicknesses shows that the Janssen coefficient $\kappa$ is a function of the cell thickness. Dependence of global normal stresses as well as $\kappa$ on the friction coefficients between the grains ($\mu_p$) and with walls ($\mu_w$) are also studied. The results show that in the range of our simulations $\kappa$ usually increases with wall-grain friction coefficient. Meanwhile by increasing $\mu_p$ while the other system parameters are fixed, we witness a gradual increase in $\kappa$ to a parameter dependent maximal value

Survey of Inter-satellite Communication for Small Satellite Systems: Physical Layer to Network Layer View

Small satellite systems enable whole new class of missions for navigation, communications, remote sensing and scientific research for both civilian and military purposes. As individual spacecraft are limited by the size, mass and power constraints, mass-produced small satellites in large constellations or clusters could be useful in many science missions such as gravity mapping, tracking of forest fires, finding water resources, etc. Constellation of satellites provide improved spatial and temporal resolution of the target. Small satellite constellations contribute innovative applications by replacing a single asset with several very capable spacecraft which opens the door to new applications. With increasing levels of autonomy, there will be a need for remote communication networks to enable communication between spacecraft. These space based networks will need to configure and maintain dynamic routes, manage intermediate nodes, and reconfigure themselves to achieve mission objectives. Hence, inter-satellite communication is a key aspect when satellites fly in formation. In this paper, we present the various researches being conducted in the small satellite community for implementing inter-satellite communications based on the Open System Interconnection (OSI) model. This paper also reviews the various design parameters applicable to the first three layers of the OSI model, i.e., physical, data link and network layer. Based on the survey, we also present a comprehensive list of design parameters useful for achieving inter-satellite communications for multiple small satellite missions. Specific topics include proposed solutions for some of the challenges faced by small satellite systems, enabling operations using a network of small satellites, and some examples of small satellite missions involving formation flying aspects.Comment: 51 pages, 21 Figures, 11 Tables, accepted in IEEE Communications Surveys and Tutorial

Personal, family and societal educational needs assessment of individuals with spinal cord injury in Iran

Objectives: To explore individuals’ perception of the personal, family and societal educational needs following a spinal cord injury. Methods: Sixty-one patients who sustained a traumatic SCI between March 2015 and June 2016 referred to Brain and Spinal Cord Injury Research Center were included in a cross sectional study and completed an online survey containing open-and closed-ended questions, in Iran. Participants’ responses were analyzed i using a qualitative approach with a thematic analysis. Results: Following a thematic analysis of the patient’s perceived educational needs, 3 themes and 14 subthemes were identified. The 3 themes included personal, family, and societal educational perceived needs. Within personal educational needs, there were 7 subthemes which included personal independence and transportation, financial independence, life skills modification, knowledge about SCI, prevention of SCI complications, relationships and sexual function, and psychological adjustments. Among family educational needs, the 3 subthemes were caregiver skills and communication, first aid and emergency skills, and emotional and psychological support. For societal educational needs, the 4 subthemes described were social integration, interpersonal communication skills, SCI awareness and injury prevention, sympathize while avoiding pity. Conclusion: According to our findings, people with SCI have various needs that need to be addressed. Educational support should be a part of a comprehensive rehabilitation program and geared towards addressing the patients’ personal and family needs, while educating the community about SCI in order to allow for reintegration into society