Constraints on Little Higgs with Fully-Radiative Electroweak Symmetry Breaking

In a recent paper, we introduced a new Little Higgs model, which contains the gauge structure $SU(2)^3\times U(1)$, embedded in an approximate global $SO(5)\times SO(5)$ symmetry. After breaking to the standard model, $SU(2)_L \times U(1)_Y$, this produces two heavy $Z^\prime$ bosons and two heavy $W^{\prime\pm}$ bosons, along with a single Standard Model-like Higgs scalar. The unique feature of the model was that it was possible to obtain electroweak symmetry breaking and a light Higgs mass entirely from perturbative loop contributions to the Higgs effective potential. In this paper we consider the electroweak constraints on this model, including tree and loop contributions to the universal oblique and non-oblique parameters, tree-level corrections to the $ZWW$ vertex, and tree and loop level corrections to $Zb\bar{b}$. The most significant corrections are positive tree-level corrections to $\hat{S}$ and negative fermion-loop corrections to $\hat{T}$, which require that the scale for the global symmetry breaking be $\gtrsim2$ TeV, depending on the top-quark mixing parameter and the extra gauge couplings. In addition, the loop corrections to $Zb\bar{b}$ contain a divergence that must be absorbed into the coefficient of a new operator in the theory. The finite part of this $Zb\bar{b}$ correction, however, is negligible.Comment: 28 pages, 16 figures, RevTeX forma

Sieving by large integers and covering systems of congruences

An old question of Erdos asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) mod n for n in S whose union is all the integers. We prove that if $\sum_{n\in S} 1/n$ is bounded for such a covering of the integers, then the least member of S is also bounded, thus confirming a conjecture of Erdos and Selfridge. We also prove a conjecture of Erdos and Graham, that, for each fixed number K>1, the complement in the integers of any union of residue classes r(n) mod n, for distinct n in (N,KN], has density at least d_K for N sufficiently large. Here d_K is a positive number depending only on K. Either of these new results implies another conjecture of Erdos and Graham, that if S is a finite set of moduli greater than N, with a choice for residue classes r(n) mod n for n in S which covers the integers, then the largest member of S cannot be O(N). We further obtain stronger forms of these results and establish other information, including an improvement of a related theorem of Haight.Comment: v3. 28 pages. Minor corrections and notational improvements. Added reference to recent discovery by Gibson of a covering system with least modulus 25. To appear in J. Amer. Math. So

Yielding and hardening of flexible fiber packings during triaxial compression

This paper examines the mechanical response of flexible fiber packings subject to triaxial compression. Short fibers yield in a manner similar to typical granular materials in which the deviatoric stress remains nearly constant with increasing strain after reaching a peak value. Interestingly, long fibers exhibit a hardening behavior, where the stress increases rapidly with increasing strain at large strains and the packing density continuously increases. Phase diagrams for classifying the bulk mechanical response as yielding, hardening, or a transition regime are generated as a function of the fiber aspect ratio, fiber-fiber friction coefficient, and confining pressure. Large fiber aspect ratio, large fiber-fiber friction coefficient, and large confining pressure promote hardening behavior. The hardening packings can support much larger loads than the yielding packings contributing to the stability and consolidation of the granular structure, but larger internal axial forces occur within fibers.Comment: 14 pages, 4 figure

Adversarial Attack and Defense on Graph Data: A Survey

Deep neural networks (DNNs) have been widely applied to various applications including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to adversarial attacks. Though there are several works studying adversarial attack and defense strategies on domains such as images and natural language processing, it is still difficult to directly transfer the learned knowledge to graph structure data due to its representation challenges. Given the importance of graph analysis, an increasing number of works start to analyze the robustness of machine learning models on graph data. Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions. In addition, each work proposes its own mathematical formulation which makes the comparison among different methods difficult. Therefore, in this paper, we aim to survey existing adversarial learning strategies on graph data and first provide a unified formulation for adversarial learning on graph data which covers most adversarial learning studies on graph. Moreover, we also compare different attacks and defenses on graph data and discuss their corresponding contributions and limitations. In this work, we systemically organize the considered works based on the features of each topic. This survey not only serves as a reference for the research community, but also brings a clear image researchers outside this research domain. Besides, we also create an online resource and keep updating the relevant papers during the last two years. More details of the comparisons of various studies based on this survey are open-sourced at https://github.com/YingtongDou/graph-adversarial-learning-literature.Comment: In submission to Journal. For more open-source and up-to-date information, please check our Github repository: https://github.com/YingtongDou/graph-adversarial-learning-literatur

Searching for temporal patterns in the time series of publications of authors in a research specialty

In this paper we report results of our investigation of temporal patterns in the publication activity of authors in a research specialty. We base our analysis on Web of Science data for a field in the physical and chemical sciences from 1991‐2012. We determine the research groups in the field by clustering the co‐author network and generate our sample for this analysis by selecting the most productive author of each co‐author cluster to represent the activity of that group. Whereas a statistical time series analysis did not reveal any specific patterns, a time series clustering approach generated a grouping of time series that correlates with the structural network position (‘node role') of the respective authors in the clustered co‐author network. This work is part of a long‐term research project employing a mix of qualitative and network analytic methods to investigate field‐specific differences in collaborative patterns.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111080/1/meet14505101039.pd

Heritability of facial appearance

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