Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a perfect matching or not and (2) a unique perfect matching or not, are in the logspace complexity class \SPL. Since \SPL\ is contained in the logspace counting classes \oplus\L (in fact in \modk\ for all $k\geq 2$), \CeqL, and \PL, our upper bound places the above-mentioned matching problems in these counting classes as well. We also show that the search version, computing a perfect matching, for this class of graphs is in \FL^{\SPL}. Our results extend the same upper bounds for these problems over bipartite planar graphs known earlier. As our main technical result, we design a logspace computable and polynomially bounded weight function which isolates a minimum weight perfect matching in bipartite graphs embedded on surfaces of constant genus. We use results from algebraic topology for proving the correctness of the weight function.Comment: 23 pages, 13 figure

Equipartition of Current in Parallel Conductors on Cooling Through the Superconducting Transition

Our experiments show that for two or more pieces of a wire, of different lengths in general, combined in parallel and connected to a dc source, the current ratio evolves towards unity as the combination is cooled to the superconducting transition temperature Tc, and remains pinned at that value below it. This re-distribution of the total current towards equipartition without external fine tuning is a surprise. It can be physically understood in terms of a mechanism that involves the flux-flow resistance associated with the transport current in a wire of type-II superconducting material. It is the fact that the flux-flow resistance increases with current that drives the current division towards equipartition.Comment: Revised version of J.Phys. Condens.Matter; vol. 18(2006) L143-L147 14 pages including 3 figures; provided an explanation in terms of the physical mechanism of flux flow induced resistance that is proportional to the impressed current. We are adding a simple, physically robust derivation of our equipartition without taking resort to the minimum dissipation principl

THRUST GENERATION BY ION PROPULSION TECHNOLOGY

Electric propulsion system proven to be a suitable and efficient alternative for conventional propulsion systems .Ion thrusters is one of the electric propulsion systems. It has very high specific impulse generation (Isp) and consumes very low amount of fuel. Ion thrusters can easily compete with chemical rockets propulsion, even if the thrust produce is very low compares to chemical propulsion. Ion propulsion system can be used for various space missions like orbit station keeping for geostationary satellite, orbit and altitude controlling, multi-goal missions. Ion thrusters are more compatible for deep space missions as they are tested for endurance test where as chemical proportion is highly unsuitable for deep space mission

Equipartition of current in parallel conductors on cooling through the superconducting transition

Our experiments show that for two or more pieces of a wire, of different lengths in general, combined in parallel and connected to a dc source, the current ratio evolves towards unity as the combination is cooled to the superconducting transition temperature Tc, and remains pinned at that value below it. This redistribution of the total current towards equipartition without external fine-tuning is a surprise. It can be physically understood in terms of a mechanism that involves the flux-flow resistance associated with the transport current in a wire of type-II superconducting material. It is a fact that the flux-flow resistance increases with the current that drives the current division towards equipartition

Primary total knee replacement using dished polyethylene with resected posterior cruciate ligament

Background: The choice between preserving, sacrificing or substituting the posterior cruciate ligament (PCL) is always a controversial topic in total knee replacement (TKR). Dished polyethylene insert with PCL resection enables correction of the commonly present fixed flexion and varus deformities. Additionally, the risk of premature wear of polyethylene is less because of the confirming articular geometry between the femoral and tibial component.Methods: This is a retrospective study in which we studied 120 knees in 95 consecutive patients undergoing primary TKR by the senior author at our institute. We used TKR system with dished metal backed polyethylene tibial component. PCL resection was performed in all cases. Pre-operative and post-operative functional assessment were done using knee society clinical scores and Western Ontario and McMaster universities osteoarthritis index (WOMAC). All radiographs were assessed using the knee society Roentgenographic scoring system (KSRES). Statistical analysis was performed using paired student t tests. Survivorship was determined using Kaplan-Meier survivorship curves. Results: Mean follow-up was 8 years. Range of motion increased from 75 degrees to 110 degrees.  The knee society pain score increased from 30 to 94. The knee society function score increased from 35 to 75. WOMAC score increased in terms of pain, stiffness and physical function.Conclusions: We conclude that deep dish bearing is a viable option in presence of deficient PCL and provides adequate stability and functional outcome. We need a larger sample size, multicentre trial and longer follow-up to see for complication rate, revision rate and survival

Use of human perivascular stem cells for bone regeneration

Human perivascular stem cells (PSCs) can be isolated in sufficient numbers from multiple tissues for purposes of skeletal tissue engineering(1-3). PSCs are a FACS-sorted population of 'pericytes' (CD146+CD34-CD45-) and 'adventitial cells' (CD146-CD34+CD45-), each of which we have previously reported to have properties of mesenchymal stem cells. PSCs, like MSCs, are able to undergo osteogenic differentiation, as well as secrete pro-osteogenic cytokines(1,2). In the present protocol, we demonstrate the osteogenicity of PSCs in several animal models including a muscle pouch implantation in SCID (severe combined immunodeficient) mice, a SCID mouse calvarial defect and a femoral segmental defect (FSD) in athymic rats. The thigh muscle pouch model is used to assess ectopic bone formation. Calvarial defects are centered on the parietal bone and are standardly 4 mm in diameter (critically sized)(8). FSDs are bicortical and are stabilized with a polyethylene bar and K-wires(4). The FSD described is also a critical size defect, which does not significantly heal on its own(4). In contrast, if stem cells or growth factors are added to the defect site, significant bone regeneration can be appreciated. The overall goal of PSC xenografting is to demonstrate the osteogenic capability of this cell type in both ectopic and orthotopic bone regeneration models

Human Perivascular Stem Cells Show Enhanced Osteogenesis and Vasculogenesis with Nel-Like Molecule I Protein

An ideal mesenchymal stem cell (MSC) source for bone tissue engineering has yet to be identified. Such an MSC population would be easily harvested in abundance, with minimal morbidity and with high purity. Our laboratories have identified perivascular stem cells (PSCs) as a candidate cell source. PSCs are readily isolatable through fluorescent-activated cell sorting from adipose tissue and have been previously shown to be indistinguishable from MSCs in the phenotype and differentiation potential. PSCs consist of two distinct cell populations: (1) pericytes (CD146+, CD34−, and CD45−), which surround capillaries and microvessels, and (2) adventitial cells (CD146−, CD34+, and CD45−), found within the tunica adventitia of large arteries and veins. We previously demonstrated the osteogenic potential of pericytes by examining pericytes derived from the human fetal pancreas, and illustrated their in vivo trophic and angiogenic effects. In the present study, we used an intramuscular ectopic bone model to develop the translational potential of our original findings using PSCs (as a combination of pericytes and adventitial cells) from human white adipose tissue. We evaluated human PSC (hPSC)-mediated bone formation and vascularization in vivo. We also examined the effects of hPSCs when combined with the novel craniosynostosis-associated protein, Nel-like molecule I (NELL-1). Implants consisting of the demineralized bone matrix putty combined with NELL-1 (3 μg/μL), hPSC (2.5×10(5) cells), or hPSC+NELL-1, were inserted in the bicep femoris of SCID mice. Bone growth was evaluated using microcomputed tomography, histology, and immunohistochemistry over 4 weeks. Results demonstrated the osteogenic potential of hPSCs and the additive effect of hPSC+NELL-1 on bone formation and vasculogenesis. Comparable osteogenesis was observed with NELL-1 as compared to the more commonly used bone morphogenetic protein-2. Next, hPSCs induced greater implant vascularization than the unsorted stromal vascular fraction from patient-matched samples. Finally, we observed an additive effect on implant vascularization with hPSC+NELL-1 by histomorphometry and immunohistochemistry, accompanied by in vitro elaboration of vasculogenic growth factors. These findings hold significant implications for the cell/protein combination therapy hPSC+NELL-1 in the development of strategies for vascularized bone regeneration