Persistence of the Jordan center in Random Growing Trees

The Jordan center of a graph is defined as a vertex whose maximum distance to other nodes in the graph is minimal, and it finds applications in facility location and source detection problems. We study properties of the Jordan Center in the case of random growing trees. In particular, we consider a regular tree graph on which an infection starts from a root node and then spreads along the edges of the graph according to various random spread models. For the Independent Cascade (IC) model and the discrete Susceptible Infected (SI) model, both of which are discrete time models, we show that as the infected subgraph grows with time, the Jordan center persists on a single vertex after a finite number of timesteps. Finally, we also study the continuous time version of the SI model and bound the maximum distance between the Jordan center and the root node at any time.Comment: 28 pages, 14 figure

SH3 AND MULTIPLE ANKYRIN REPEAT DOMAIN 3 (SHANK3) AFFECTS THE EXPRESSION OF HYPERPOLARIZATION-ACTIVATED CYCLIC NUCLEOTIDE-GATED (HCN) CHANNELS IN MOUSE MODELS OF AUTISM

SH3 and multiple ankyrin repeat domains 3 (SHANK3) is a multidomain scaffold protein that is highly augmented in the postsynaptic density (PSD) of excitatory glutamatergic synapses within the central and peripheral nervous systems. SHANK3 links neurotransmitter receptors, ion channels, and other critical membrane proteins to intracellular cytoskeleton and signal transduction pathways. Mutations in SHANK3 are linked with a number neuropsychiatric disorders including autism spectrum disorders (ASDs). Intellectual disability, impaired memory and learning, and epilepsy are some of the deficits commonly associated with ASDs that result from mutations in SHANK3. Interestingly, these symptoms show some clinical overlap with presentations of human neurological disorders involving hyperpolarization-activated cyclin nucleotide-gated (HCN) channels. In fact, it has recently been demonstrated in human neurons that SHANK3 haploinsufficiency causes Ih-channel dysfunction, and that SHANK3 has a physical interaction with HCN channels via its ANKYRIN repeat domain. These insights suggest that SHANK3 may play important roles in HCN channel expression and function, and put forward the idea that HCN channelopathies may actually encourage some of the symptoms observed in patients with SHANK-deficiency related ASDs. In this study, we provide preliminary data that suggests the ANK domain of SHANK3 interacts with COOH portion of HCN1. We also exploited the differences between two mouse models of autism to show that a subset of SHANK3 isoforms may be involved in the proper expression and function of HCN channels. We found that HCN2 expression is significantly decreased in a mouse model lacking all major isoforms of SHANK3 (exons 13-16 deleted; Δ13-16), while HCN2 expression is unaltered in a mouse model only lacking SHANK3a and SHANK3b (exons 4-9 deleted; Δ4-9). Surprisingly, we also found that HCN4 expression is altered in SHANK3Δ13-16, but not SHANK3Δ4-9. Taken together, our results show HCN channelopathy as a major downstream carrier of SHANK3 deficiency

Comparison of fetal outcome in spontaneous versus induced labor in postdated pregnancy: a study in a tertiary care centre

Background: Pregnancy lasting beyond 40 weeks is a known complication of normal delivery. Various studies have found incidence between 2-14%. Post-dated pregnancy carries specific hazards to both mother and fetus. While mothers are faced with problems like increased incidences of induced labour, instrumental delivery and LSCS with associated morbidities, fetuses are faced with morbidities ranging from IUGR to macrosomia. Authors tried to study fetal outcome in post-dated pregnancy present study. The objective is to compare fetal outcome in spontaneous versus induced labour in post-dated pregnancy.Methods: This is a prospective cross-sectional study done at a tertiary care hospital in obstetrics and gynecology in duration of 18 months. After screening according to inclusion criteria, all patients who were admitted in labour wards are selected and two groups were created according to clinical examination. First group consists of patients with spontaneous onset of labour and second group consists of patients with induction of labour. In each group USG, NST and BPP were performed, and labor monitored according to standard partograph. Fetal outcomes in both groups were studied.Results: Fetal outcomes were nearly same in both groups, induced and spontaneous onset of labour, except a few like thick meconium which was common in spontaneous onset group while rate of LSCS was more in induced group.Conclusions: Women with uncomplicated pregnancies should be offered induction of labour, while women with any complicating factors LSCS should be considered

A clinical study of maternal outcome in post dated pregnancy in a tertiary care hospital

Background: Pregnancy lasting beyond 40 weeks is a known complication of normal delivery. Studies have found incidence between 2-14%. Post-dated pregnancy carries specific hazards to both mother and fetus. While mothers are faced with problems like increased incidences of induced labour, instrumental delivery and LSCS with associated morbidities, fetuses are faced with morbidities ranging from IUGR to macrosomia. We here tried to study maternal outcome in post-dated pregnancy. The objective is to study maternal outcome in post-dated pregnancy and to compare maternal outcome in spontaneous versus induced labour in post-dated pregnancy.Methods: This study was done at a tertiary care hospital in obstetrics and gynecology department for duration of 18 months. After screening according to inclusion criteria, all patients who were admitted in labour wards were grouped in two groups according to clinical examination. First group consists of patients with spontaneous onset of labour and second group consists of patients with induction of labour. In each group same protocol for fetal monitoring were performed, and labor monitored according to standard partograph. Maternal outcomes in both groups were studied.Results: Maternal outcomes were nearly same in both groups; induced and spontaneous onset of labour, except rate of LSCS, Which was more in induced group though not statistically significant.Conclusions: Women with uncomplicated post dated pregnancies with good bishop score should be allowed spontaneous labour and those with poor bishop should be offered induction of labour, while women with any complicating factors LSCS should be considered

A Spectral Approach to Polytope Diameter

We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for integer polytopes in terms of the length of the description of the polytope (in bits) and the minimum angle between facets of its polar. The second is a smoothed analysis bound: given an appropriately normalized polytope, we add small Gaussian noise to each constraint. We consider a natural geometric measure on the vertices of the perturbed polytope (corresponding to the mean curvature measure of its polar) and show that with high probability there exists a "giant component" of vertices, with measure $1-o(1)$ and polynomial diameter. Both bounds rely on spectral gaps -- of a certain Schr\"odinger operator in the first case, and a certain continuous time Markov chain in the second -- which arise from the log-concavity of the volume of a simple polytope in terms of its slack variables.Comment: Replaced the proof of Theorem 2.2 with a reference, added acknowledgments. 28p

A study on outcome of various K-wire fixations in paediatric supracondylar humerus fractures

Background: The ideal pin geometry for treatment of paediatric supracondylar humerus fracture is still debated. Various studies have been carried out comparing medial-lateral pinning (MLP) and lateral only pinning (LOP), but none have compared all three individually i.e. MLP, lateral divergent pinning and Lateral Trans olecranon fossa four cortex purchase pinning (TOF-FCP). This study aims to compare the cosmetic and functional outcome of these three pinning methods.Methods: 54 children with supracondylar humerus (Gartland type 2 or 3) meeting inclusion criteria were treated operatively and followed up till 6 months postoperatively. At 6 months the cosmetic and functional outcomes were assessed using the modified Flynn criteria.Results: All fractures united within 3 to 6 weeks duration. The mean duration of fracture union was 4.05 weeks. Functional outcome was satisfactory (i.e. excellent or good) at 6 months according to Flynn criteria in 95% of cases in cross pinning, 100% cases in TOF-FCP construct and 89% cases in lateral entry divergent pinning. cosmetic outcome was satisfactory (i.e. excellent or good) at 6 months according to Flynn criteria in 95% of cases in cross pinning, 100% cases in TOF-FCP construct and 89% cases in lateral entry divergent.Conclusions: Functional and cosmetic outcome of all three pinning geometries after operative intervention of paediatric supracondylar humerus fracture is similar in expert hands. The incidence of complications with TOF-FCP construct is less amongst the lateral only pinning