Dyson-Schwinger Equations with a Parameterized Metric

We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.Comment: 10 pages, 7 figures. To appear in Physical Review

The Effect of Flow and Motivation on Users’ Learning Outcomes in Second Life

This study aims to investigate the effect of the users’ immersion experience, motivation, and learning outcomes in Second Life. The data collected for this study occurred over a 2 month period. Participants were 113 students taking classes in Second Life at a university. Their ages ranged from 18-22 years, with 47 participants as male and 66 as female. From the analysis of the collected data, the immersion experience and motivation have effects on the learning outcomes in Second Life. The results revealed more one was immersed in Second Life, the motivation was improved, and thus, the learning outcomes were reinforced. These findings are also discussed in virtual learning and teaching design

Phase diagram and critical endpoint for strongly-interacting quarks

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (\mu^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at \mu=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.Comment: 4 pages, 3 figure

A method for constructing graphs with the same resistance spectrum

Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The resistance distance $R_G(x,y)$ between two vertices $x,y$ of $G$ is defined to be the effective resistance between the two vertices in the corresponding electrical network in which each edge of $G$ is replaced by a unit resistor. The resistance spectrum $\mathrm{RS}(G)$ of a graph $G$ is the multiset of the resistance distances of all pairs of vertices in the graph. This paper presents a method for constructing graphs with the same resistance spectrum. It is obtained that for any positive integer $k$, there exist at least $2^k$ graphs with the same resistance spectrum. Furthermore, it is shown that for $n \geq 10$, there are at least $2(n-9) p(n-9)$ pairs of graphs of order $n$ with the same resistance spectrum, where $p(n-9)$ is the number of partitions of the integer $n-9$

Robustness Verification of Tree-based Models

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches find the minimal adversarial perturbation by a mixed integer linear programming (MILP) problem, which takes exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles, the verification problem can be cast as a max-clique problem on a multi-partite graph with bounded boxicity. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we develop an efficient multi-level verification algorithm that can give tight lower bounds on the robustness of decision tree ensembles, while allowing iterative improvement and any-time termination. OnRF/GBDT models trained on 10 datasets, our algorithm is hundreds of times faster than the previous approach that requires solving MILPs, and is able to give tight robustness verification bounds on large GBDTs with hundreds of deep trees.Comment: Hongge Chen and Huan Zhang contributed equall

Crossing at a Red Light: Behavior of Cyclists at Urban Intersections

To investigate the relationship between cyclist violation and waiting duration, the red-light running behavior of nonmotorized vehicles is examined at signalized intersections. Violation waiting duration is collected by video cameras and it is assigned as censored and uncensored data to distinguish between normal crossing and red-light running. A proportional hazard-based duration model is introduced, and variables revealing personal characteristics and traffic conditions are used to describe the effects of internal and external factors. Empirical results show that the red-light running behavior of cyclist is time dependent. Cyclist’s violating behavior represents positive duration dependence, that the longer the waiting time elapsed, the more likely cyclists would end the wait soon. About 32% of cyclists are at high risk of violation and low waiting time to cross the intersections. About 15% of all the cyclists are generally nonrisk takers who can obey the traffic rules after waiting for 95 seconds. The human factors and external environment play an important role in cyclists’ violation behavior. Minimizing the effects of unfavorable condition in traffic planning and designing may be an effective measure to enhance traffic safety