2-Modules and the Representation of 2-Rings

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring \cR, we prove that its modules form a 2-Abelian category.Comment: 78 pages, 99 figure

Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)

In this paper, we will define the derived 2-functor by projective resolution of any symmetric 2-group, and give some related properties of the derived 2-functor.Comment: 30 pages, 50 figures. This is the third paper of the series of our works on higher dimensional homological algebra. In the coming papers, we define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod). In this version, we correct some errors in last version, add more results, such as 2-chain homotopy, its related results, et

Higher Dimensional Homology Algebra II:Projectivity

In this paper, we will prove that the 2-category (2-SGp) of symmetric 2-groups and 2-category (\cR-2-Mod) of \cR-2-modules(\cite{5}) have enough projective objects, respectively.Comment: 10 pages, 4 figures. This is the second paper of the series works on higher dimensional homology algebra. The first paper is "2-Modules and the Representation of 2-Rings\cite{4}". In the coming papers, we shall give the definition of injective object in the 2-category (\cR-2-Mod), prove that this 2-category has enough injective objects and develop the (co)homology theory of i

Higher Dimensional Homology Algebra IV:Projective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the projective resolution of any \cR-2-module, define the derived 2-functor and give some related properties of the derived 2-functor.Comment: 17pages, 32 figures, This is the fourth paper of the series of our works on higher dimensional homological algebra. In the coming papers, we shall define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod), and give some relations of left derived 2-functors and right derived 2-functor

A Price Driven Hazard Approach to User Retention

Customer loyalty is crucial for internet services since retaining users of a service to ensure the staying time of the service is of significance for increasing revenue. It demands the retention of customers to be high enough to meet the needs for yielding profit for the internet servers. Besides, the growing of rich purchasing interaction feedback helps in uncovering the inner mechanism of purchasing intent of the customers. In this work, we exploit the rich interaction data of user to build a customers retention evaluation model focusing on the return time of a user to a product. Three aspects, namely the consilience between user and product, the sensitivity of the user to price and the external influence the user might receive, are promoted to effect the purchase intents, which are jointly modeled by a probability model based on Cox's proportional hazard approach. The hazard based model provides benefits in the dynamics in user retention and it can conveniently incorporate covariates in the model. Extensive experiments on real world purchasing data have demonstrated the superiority of the proposed model over state-of-the-art algorithms.Comment: 11 page

Higher Dimensional Homology Algebra V:Injective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the injective resolution of any \cR-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in (\cR-2-Mod).Comment: 29 pages, 57 figures. This paper is the fifth paper of the series of our works on higher dimensional homology algebra. In our coming papers, we shall define \cExt 2-functor and spectral sequence in an abelian 2-category, try to give the relation between \cExt 2-functor and the extension of 2-module

Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.Comment: 1 figures, Quantum Information Processing 201

Broadband Circular Polarizers Constructed by Helix-like Chiral Metamaterials

In this paper, a kind of helix-like chiral metamaterial, which can be realized with multiple conventional lithography or electron beam lithographic techniques, is proposed to achieve broadband bianisotropic optical response analogous to helical metamaterial. On the basis of twisted metamaterial, via tailoring the relative orientation within the lattice, the anisotropy of arc is converted into magneto-electric coupling of closely spaced arc pairs, which leads to a broad bianisotropic optical response. By connecting the adjacent upper and lower arcs, the coupling of metasurface pairs is transformed to the coupling of the three-dimensional inclusions, and provides a much broader and higher bianisotropic optical response. For only a four-layer helix-like metamaterial, the maximum extinction ratio can reach 19.7. The operation band is in the wavelength range from 4.69 {\mu}m to 8.98 {\mu}m with an average extinction ratio of 6.9. And the transmittance for selective polarization is above 0.8 in the entire operation band. Such a structure is promising for integratable and scalable broadband circular polarizers, especially has great potential to act as broadband circular micropolarizers in the field of the full-stokes division of focal plane polarimeters

Self-normalized Cram\'er Type Moderate Deviations under Dependence

We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider two types of self-normalization: the big-block-small-block scheme and the interlacing or equal-block scheme. Simulation study shows that the latter can have a better finite-sample performance. Our result is applied to multiple testing and construction of simultaneous confidence intervals for high-dimensional time series mean vectors

New localization mechanism of fermions on braneworlds

It is known that by introducing the Yukawa coupling between the fermion and the background scalar field, a bulk spin-half fermion can be localized on general Randall-Sundrum braneworlds generated by a kinklike background scalar. However, this localization mechanism does not work anymore for Randall-Sundrum braneworlds generated by a scalar whose configuration is an even function of the extra dimension. In this paper, we present a new localization mechanism for spin-half fermions for such a class of braneworld models, in which extra dimension has the topology $S^1/Z_2$. By two examples, it is shown that the new localization mechanism produces interesting results. In the first model with the brane generated by two scalars, the zero mode of the left-handed fermion is localized on the brane and there is a mass gap between the fermion zero mode and excited KK modes. In the second model with the brane generated by a dilaton scalar, the zero mode of the left- or right-chiral fermion can be localized on the brane and there is no mass gap.Comment: 8 pages, 2 figure