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1323816 documents, page 1 of 132382

Kitaev model for mirror bicrossproduct Hopf algebras and its tensor network representation

Girelli, Florian; Osei, Prince K.; Osumanu, Abdulmajid (2017)
Kitaev's model [1,2] is usually defined in terms of the Drinfeld double. We propose a new version defined in terms of the mirror bicrossproduct quantum group [3]. By some aspects, even though the bicrossproduct quantum group is more complicated than the Drinfeld double, the construction of the new model is actually simpler and relies on the use of a covariant system. We also provide the definition of the ground state of the new Hamiltonian in terms of a tensor network representation.

Cocenters of $p$-adic groups, III: Elliptic and rigid cocenters

Ciubotaru, Dan; He, Xuhua (2017)
In this paper, we show that the elliptic cocenter of the Hecke algebra of a connected reductive group over a nonarchimedean local field is contained in the rigid cocenter. As applications, we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-$l$ representations.

Maximum scattered $\mathbb{F}_q$-linear sets of $\mathrm{PG}(1,q^4)$

Csajbók, Bence; Zanella, Corrado (2017)
There are two known families of maximum scattered $\mathbb{F}_q$-linear sets in $PG(1,q^t)$: the linear sets of pseudoregulus type and for $t\geq 4$ the scattered linear sets found by Lunardon and Polverino. For $t=4$ we show that these are the only maximum scattered $\mathbb{F}_q$-linear sets and we describe the orbits of these linear sets under the groups $PGL(2,q^4)$ and $P\Gamma L(2,q^4)$.

Solutions of Quadratic First-Order ODEs applied to Computer Vision Problems

Casillas-Perez, David; Pizarro, Daniel (2017)
The article proves the existence of a maximum of two possible solutions to the initial value problem composed by the planar-perspective equation and an initial condition. This initial value problem has a geometric interpretation. Solutions are curves than pass trough the initial condition which is a point of the plane.

Penalized pairwise pseudo likelihood for variable selection with nonignorable missing data

Zhao, Jiwei; Yang, Yang; Ning, Yang (2017)
The regularization approach for variable selection was well developed for a completely observed data set in the past two decades. In the presence of missing values, this approach needs to be tailored to different missing data mechanisms. In this paper, we focus on a flexible and generally applicable missing data mechanism, which contains both ignorable and nonignorable missing data mechanism assumptions. We show how the regularization approach for variable selection can be adapted to the situ...

Network Analysis of Particles and Grains

Papadopoulos, Lia; Porter, Mason A.; Daniels, Karen E.; Bassett, Danielle S. (2017)
The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, statistical, and ...

CNNs are Globally Optimal Given Multi-Layer Support

Huang, Chen; Kong, Chen; Lucey, Simon (2017)
Stochastic Gradient Descent (SGD) is the central workhorse for training modern CNNs. Although giving impressive empirical performance it can be slow to converge. In this paper we explore a novel strategy for training a CNN using an alternation strategy that offers substantial speedups during training. We make the following contributions: (i) replace the ReLU non-linearity within a CNN with positive hard-thresholding, (ii) reinterpret this non-linearity as a binary state vector making the enti...

Pruned non-local means

Ghosh, Sanjay; Mandal, Amit K.; Chaudhury, Kunal N. (2017)
In Non-Local Means (NLM), each pixel is denoised by performing a weighted averaging of its neighboring pixels, where the weights are computed using image patches. We demonstrate that the denoising performance of NLM can be improved by pruning the neighboring pixels, namely, by rejecting neighboring pixels whose weights are below a certain threshold $\lambda$. While pruning can potentially reduce pixel averaging in uniform-intensity regions, we demonstrate that there is generally an overall im...

Topological nodal points in two coupled SSH chains

Li, Ci.; Lin, Sen.; Zhang, Gang.; Song, Zhi. (2017)
We study two coupled Su-Schrieffer-Heeger (SSH) chains system, which is shown to contain rich quantum phases associated with topological invariants protected by symmetries. In the weak coupling region, the system supports two non-trivial topological insulating phases, characterized by winding number N = +1 or -1, and two types of edge states. The boundary between the two topological phases arises from two band closing points, which exhibit topological characteristics in one-dimensional k spac...

On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals

Dexter, Nick; Tran, Hoang; Webster, Clayton (2017)
We consider the problem of reconstructing a set of sparse vectors sharing a common sparsity pattern from incomplete measurements. To take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty $\ell_{2,1}$. This paper discusses the computation of the solutions of linear inverse problems with such relaxation by forward-backward splitting algorithm. We establish new strong convergence results for the algo...