Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge

What is the most effective management of acute fractures of the base of the fifth metatarsal?

For acute Jones' fractures in recreationally active patients, early intramedullary screw fixation results in lower failure rates and shorter times to both clinical union and return to sports than non-weightbearing short leg casting (strength of recommendation [SOR]: A, based on 2 randomized controlled trials (RCT)]. Non- weightbearing short leg casting achieves union in 56% to 100% of patients but can require prolonged casting (SOR: B, based on 2 prospective cohorts and multiple retrospective, follow-up studies). Stress fractures were not included in this review. For avulsion fractures of the fifth metatarsal tuberosity, a soft Jones' dressing allows earlier return to pre-injury levels of activity than rigid short leg casting (SOR: B, based on a lower-quality RCT)

Executive functioning in preschool children: Performance on A-Not-B and other delayed response format tasks

The A-not-B (AB) task has been hypothesized to measure executive/frontal lobe function; however, the developmental and measurement characteristics of this task have not been investigated. The present study examined performance on AB and comparison tasks adapted from developmental and neuroscience literature in 117 1.9-5.5 yr old preschool children. Age significantly predicted performance on AB, Delayed Alternation, Spatial Reversal, Color Reversal, and Self-Control tasks. A 4-factor analytic model best fit task performance data. AB task indices loaded on 2 factors with measures from the Self-Control and Delayed Alternation tasks, respectively. AB indices did not load with those from the reversal tasks despite similarities in task administration and presumed cognitive demand (working memory). These results indicate that AB is sensitive to individual differences in age-related performance in preschool children and suggest that AB performance is related to both working memory and inhibition processes in this age range

Majority Dynamics and Aggregation of Information in Social Networks

Consider n individuals who, by popular vote, choose among q >= 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n tends to infinity. Our interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is "majority dynamics", in which each voter adopts the most popular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of "efficient aggregation of information": in which cases is the better alternative chosen with probability approaching one as n tends to infinity? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the limit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.Comment: 22 page

Clustering and the hyperbolic geometry of complex networks

Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was proposed recently by Krioukov et al. as a mathematical model of complex networks, under the fundamental assumption that hyperbolic geometry underlies the structure of these networks. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show how the global clustering coefficient can be tuned by these parameters and we give an explicit formula for this function.Comment: 51 pages, 1 figur

A 15-Year Analysis of Early and Late Autologous Hematopoietic Stem Cell Transplant in Relapsed, Aggressive, Transformed, and Nontransformed Follicular Lymphoma

AbstractAutologous stem cell transplant (ASCT) has been shown to be an effective treatment for follicular lymphoma (FL). We explored our experience in ASCT for FL among all patients treated over a 15-year period from diagnosis through their entire treatment history including relapse post ASCT. All patients who underwent an unpurged ASCT for relapsed, advanced FL between June 1990 and December 2000 were analyzed. After salvage therapy they received melphalan/etoposide/total body irradiation, BCNU, etoposide, cytarabine, melphalan (BEAM), or cyclophosphamide BCNU etoposide (CBV) as conditioning for the ASCT. One hundred thirty-eight patients with a median age of 48 years and a median follow-up of 7.6 years were analyzed. The majority were of the subtype grade 1, nontransformed (FL-NT), having had 1 prior chemotherapy. The progression-free (PFS) and overall survival (OS) of the FL-NT at 10 years were 46% and 57%, respectively, and at 5 years for the transformed (FL-T) were 25% and 56%, respectively, of which only the PFS was significantly different (P = .007). The median OS from diagnosis was 16 years for the FL-NT. ASCT positively altered the trend of shorter remissions with subsequent chemotherapies, and there was no difference in OS between those who had 1, 2, or >2 chemotherapies prior to ASCT. Salvage therapy for relapse post ASCT was effective (OS >1 year) in a third of patients. Unpurged ASCT is an effective tool in the treatment of relapsed, aggressive FL-NT and FL-T, is superior to retreatment with standard chemotherapy, is effective at various stages of treatment, is likely to have a beneficial influence on the natural history of this disease, and the disease is amenable to salvage therapy post-ASCT relapse

Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c