Social reference: Aggregating online usage of scientific literature in CiteULike for clustering academic resources

Citation-based methods have been widely studied and employed for clustering academic resources and mapping science. Although effective, these methods suffer from citation delay. In this study, we extend reference and citation analysis to a broader notion from social perspective. We coin the term "social reference" to refer to the references of literatures in social academic web environment. We propose clustering methods using social reference information from CiteULike. We experiment for journal clustering and author clustering using social reference and compare with citation-based methods. Our experiments indicate: first, social reference implies connections among literatures which are as effective as citation in clustering academic resources; second, in practical settings, social reference-based clustering methods are not as effective as citation-based ones due to the sparseness of social reference data, but they can outperform in clustering new resources that have few citation. © 2011 Authors

The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality

The $(2+1)$-d U(1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a $(2+1)$-d \RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.Comment: 4.5 pages, 6 figure

Crystalline Confinement

We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The $(2+1)$-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi-stranded strings between charge-anti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate $SO(2)$ global symmetry. The low-energy physics is described by a $(2+1)$-d $\mathbb{R}P(1)$ effective field theory, perturbed by a dangerously irrelevant $SO(2)$ breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.Comment: Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements

We consider a large quantum system with spins $\frac{1}{2}$ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution of a 2-d Heisenberg antiferromagnet, which is driven to a disordered phase, either by sporadic measurements or by continuous monitoring described by Lindblad evolution.Comment: 5 pages, 7 figure

Expanded mixed multiscale finite element methods and their applications for flows in porous media

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity and Lagrange multipliers. We use multiscale basis functions for the both velocity and gradient of pressure. In the expanded mixed MsFEM framework, we consider both cases of separable-scale and non-separable spatial scales. We specifically analyze the methods in three categories: periodic separable scales, $G$- convergence separable scales, and continuum scales. When there is no scale separation, using some global information can improve accuracy for the expanded mixed MsFEMs. We present rigorous convergence analysis for expanded mixed MsFEMs. The analysis includes both conforming and nonconforming expanded mixed MsFEM. Numerical results are presented for various multiscale models and flows in porous media with shales to illustrate the efficiency of the expanded mixed MsFEMs.Comment: 33 page

Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

Factors of sums and alternating sums involving binomial coefficients and powers of integers

We study divisibility properties of certain sums and alternating sums involving binomial coefficients and powers of integers. For example, we prove that for all positive integers $n_1,..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, there holds {align*} \sum_{k=0}^{n_1}\epsilon^k (2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod (n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any nonnegative integer $r$ and positive integer $s$ such that $r+s$ is odd, $$\sum_{k=0}^{n}\epsilon ^k (2k+1)^{r}({2n\choose n-k}-{2n\choose n-k-1})^{s} \equiv 0 \mod{{2n\choose n}},$$ where $\epsilon=\pm 1$.Comment: 14 pages, to appear in Int. J. Number Theor