The Supersymmetric Standard Models with a Pseudo-Dirac Gluino from Hybrid F−F- and D−D-Term Supersymmetry Breakings

We propose the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino from hybrid $F-$ and $D-$term supersymmetry (SUSY) breakings. Similar to the SSMs before the LHC, all the supersymmetric particles in the Minimal SSM (MSSM) obtain the SUSY breaking soft terms from the traditional gravity mediation and have masses within about 1 TeV except gluino. To evade the LHC SUSY search constraints, the gluino also has a heavy Dirac mass above 3 TeV from $D-$term SUSY breaking. Interestingly, such a heavy Dirac gluino mass will not induce the electroweak fine-tuning problem. We realize such SUSY breakings via an anomalous $U(1)_X$ gauge symmetry inspired from string models. To maintain the gauge coupling unification and increase the Higgs boson mass, we introduce extra vector-like particles. We study the viable parameter space which satisfies all the current experimental constraints, and present a concrete benchmark point. This kind of models not only preserves the merits of pre-LHC SSMs such as naturalness, dark matter, etc, but also solves the possible problems in the SSMs with Dirac gauginos due to the $F$-term gravity mediation.Comment: 6 pages,3 figures,revised versio

Tree-Based Integration of One-versus-Some (OVS) Classifiers for Multiclass Classification

Motivated by applications such as gene expression analysis, binary classification has achieved notable success. (e.g., cancer samples versus normal samples) When comes to multiclass classification, the extension is not straightforward. There has been two main directions on such extensions: 1) via a sequence of nested binary classifiers in a classification tree or 2) via classifier ensembles that integrate votes from all one-versus-all (OVA) classifiers or all all-pairs (AP) classifiers. In this article, we present a new way to combine both strategies in a multiclass classification

Towards Drinfeld-Sokolov reduction for quantum groups

In this paper we study the Poisson-Lie version of the Drinfeld-Sokolov reduction defined in q-alg/9704011, q-alg/9702016. Using the bialgebra structure related to the new Drinfeld realization of affine quantum groups we describe reduction in terms of constraints. This realization of reduction admits direct quantization. As a byproduct we obtain an explicit expression for the symplectic form associated to the twisted Heisenberg double and calculate the moment map for the twisted dressing action. For some class of infinite-dimensional Poisson Lie groups we also prove an analogue of the Ginzburg-Weinstein isomorphism.Comment: 30 pages, LaTeX 2

Trade-off Between Two Advertising Strategies: Coverage or Penetration

Advertising has always been an important way for companies to promote their products and carry out product publicity. With the advent of the information age and the convenience of the Internet, the spread and dissemination of advertising are becoming widespread. There are two different basic advertising strategies, namely expanding market coverage and increasing market penetration. Expanding market coverage is a common advertising strategy for company managers. Through this strategy, they focus on the size of the market. Increasing market penetration is another way to increase demand. Company managers focus on the current market, but gain and maintain greater penetration by improving the quality of products or services. The first (coverage) strategy can be seen as distributing flyers, advertising boards and mass acquisitions. The efforts of the second (penetration) strategy can be seen as improving product quality, service environment and positive reputation. Which one is more effective, coverage or penetration? Under what conditions is it better for the company manager? These problems have not been found in the literature. By establishing a two-stage model, this article discusses the optimal advertising levels of these two strategies. Specifically, this article compares the optimal profits of the two strategies in various market environments and finds more effective advertising strategies. Management insights are generated for decision-making of firm managers

On the anisotropies of the cosmological gravitational-wave background from pulsar timing array observations

Significant evidence for a stochastic gravitational-wave background has recently been reported by several Pulsar Timing Array observations. These studies have shown that, in addition to astrophysical explanations based on supermassive black hole binaries (SMBHBs), cosmological origins are considered equally important sources for these signals. To further explore these cosmological sources, in this study, we discuss the anisotropies in the cosmological gravitational wave background (CGWB) in a model-independent way. Taking the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 15-year dataset as a benchmark, we estimate the angular power spectra of the CGWB and their cross-correlations with cosmic microwave background (CMB) fluctuations and weak gravitational lensing. We find that the NANOGrav 15-year data implies suppressed Sachs-Wolf (SW) effects in the CGBW spectrum, leading to a marginally negative cross-correlation with the CMB at large scales. This procedure is applicable to signals introduced by different early universe processes and is potentially useful for identifying unique features about anisotropies of CGWB from future space-based interferometers and astrometric measurements.Comment: 22 pages, 4 figure