We propose new approach to numerical study of quantum spin systems. Our method is based on a fact that one can use any set of states for the path integral as long as it is complete. We apply our method to one-dimensional quantum spin system with next-to-nearest neighbor interactions. We found remarkable improvement in negative sign problem.

Facebook is the most popular social networking site, with more than 500 million active members. With its ability to easily manage multi-user social networks synchronously, it provides a fertile foundation to promote e-mentoring among the current generation of technologyand Facebook-astute students. This study reviews Network of Practice (NoP) theories to provide insights to a mentoring structur...

Background: Pre-operative nociceptive thresholds are able to predict patients susceptible to developing post-operative chronic pain. Thresholds are dependent on stimulus properties (i.e. pulsewidth (PW), number of pulses (NoP), and inter-pulse interval (IPI)) and are related to different mechanisms in the nociceptive system. Measuring multiple thresholds enables a detailed observation of periph...

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are...

In this paper, we study some functional inequalities (such as Poincaré inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy inequalities) for reversible nearest-neighbor Markov processes on a connected finite graph by means of (random) path method. We provide estimates of the involved c...

In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.

A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P . In 1988 H. Broersma stated a result implying that every n-vertex kconnected graph G such that σ(k+2)(G) ≥ n− 2k − 1 contains a dominating path. We show that every n-vertex k-connected graph with σ2(G) ≥ 2n k+2 + f(k) contains a dominating path of length at most O(|T |), where T is a minimum do...

Mixed layer (ML) gross (GOP) and net (NOP) oxygen production rates based on in situ mass balances of triple oxygen isotopes (TOI) and O2/Ar are influenced by vertical transport from below, a term traditionally difficult to constrain. Here we present a new approach to estimate vertical eddy diffusivity (Kz) based on density gradients in the upper thermocline and wind speed-based rates of turbule...

Building a topology-aware peer-to-peer overlay network can bring many advantages, such as providing locality-aware connectivity and reducing routing path length. While its benefits on performance have been recognized, an uneven overlay zone distribution has emerged. Recent work has shown that topology-aware neighbor selection during construction can aggravate the unbalance of zone distribution ...

The research for this report was produced under the auspices of the IFS Savings Consortium, to whom the authors are grateful for financial assistance and many useful discussions and comments in the series of seminars over the last four years. The members of the IFS Savings Consortium are: Acknowledgements The research in this report was funded by the IFS Savings Consortium and co-funded by the ...