A note on the error estimate of the virtual element methods

This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary for the optimal order of the conforming VEM error estimate in the $H^1$-seminorm, are relaxed for that in a bilinear form-induced energy norm

Probing Higgs Width and Top Quark Yukawa Coupling from ttˉHt\bar{t}H and ttˉttˉt\bar{t}t\bar{t} Productions

We demonstrate that four top-quark production is a powerful tool to constrain the top Yukawa coupling. The constraint is robust in the sense that it does not rely on the Higgs boson decay. Taking into account the projection of the $t\bar{t}H$ production by the ATLAS collaobration, we obtain a bound on Higgs boson width, $\Gamma_H\leq 3.1~\Gamma_H^{\rm SM}$, at the 14 TeV LHC with an integrated luminosity of $300~{\rm fb}^{-1}$. Increasing the luminosity to $500~{\rm fb}^{-1}$ yields $\Gamma_H\leq 2.1~\Gamma_H^{\rm SM}$

Transfer Adversarial Hashing for Hamming Space Retrieval

Hashing is widely applied to large-scale image retrieval due to the storage and retrieval efficiency. Existing work on deep hashing assumes that the database in the target domain is identically distributed with the training set in the source domain. This paper relaxes this assumption to a transfer retrieval setting, which allows the database and the training set to come from different but relevant domains. However, the transfer retrieval setting will introduce two technical difficulties: first, the hash model trained on the source domain cannot work well on the target domain due to the large distribution gap; second, the domain gap makes it difficult to concentrate the database points to be within a small Hamming ball. As a consequence, transfer retrieval performance within Hamming Radius 2 degrades significantly in existing hashing methods. This paper presents Transfer Adversarial Hashing (TAH), a new hybrid deep architecture that incorporates a pairwise $t$-distribution cross-entropy loss to learn concentrated hash codes and an adversarial network to align the data distributions between the source and target domains. TAH can generate compact transfer hash codes for efficient image retrieval on both source and target domains. Comprehensive experiments validate that TAH yields state of the art Hamming space retrieval performance on standard datasets

A broad-band laser-driven double Fano system - photoelectron spectra

Fano profiles, with their asymmetric character, have many potential applications in technology. The design of Fano profiles into optical systems may create new nonlinear and switchable metamaterials, high-quality optical waveguides, ultrasensitive media for chemical or biosensing etc. In this paper, we consider an external field-driven double Fano model, in which, instead of one autoionizing state, there are two discrete states embedded in one continuum. We assume further that the external electromagnetic field can be decomposed into two parts: a deterministic (or coherent) part and a randomly fluctuating chaotic component, which is a \delta-correlated, Gaussian, Markov and stationary process (white noise). This assumption corresponds to the case of the real multimode laser operating without any correlation between the modes. We solve a set of coupled stochastic integro-differential equations involving the Fano model with two discrete levels. We derive an exact formula by determining the photoelectron spectrum and compare it with the results obtained in our previous papers

On dRGT massive gravity with degenerate reference metrics

In dRGT massive gravity, to get the equations of motion, the square root tensor is assumed to be invertible in the variation of the action. However, this condition can not be fulfilled when the reference metric is degenerate. This implies that the resulting equations of motion might be different from the case where the reference metric has full rank. In this paper, by generalizing the Moore-Penrose inverse to the symmetric tensor on Lorentz manifolds, we get the equations of motion of the theory with degenerate reference metric. It is found that the equations of motion are a little bit different from those in the non-degenerate cases. Based on the result of the equations of motion, for the $(2+n)$-dimensional solutions with the symmetry of $n$-dimensional maximally symmetric space, we prove a generalized Birkhoff theorem in the case where the degenerate reference metric has rank $n$, i.e., we show that the solutions must be Schwarzschild-type or Nariai-Bertotti-Robinson-type under the assumptions.Comment: v1, Latex, 29 pages, no figures; v2, references added, typos corrected, 30 page

Computer simulation of two-mode nonlinear quantum scissors

We present a simulation method allowing for modeling of quantum dynamics of nonlinear quantum scissors' (NQS) systems. We concentrate on the two-mode model involving two mutually interacting nonlinear quantum oscillators (Kerr nonlinear coupler) excited by a series of ultra-short external coherent pulses. We show that despite the simplicity of the method one can obtain non-trivial results. In particular, we discuss and compare two cases of kicked nonlinear coupler, showing that the quantum evolution of the system remains closed within a two-qubit Hilbert space and can lead to maximally entangled states generation

Black hole hair in higher dimensions

We study the property of matter in equilibrium with a static, spherically symmetric black hole in D-dimensional spacetime. It requires this kind of matter has an equation of state (\omega\equiv p_r/\rho=-1/(1+2kn), k,n\in \mathbb{N}), which seems to be independent of D. However, when we associate this with specific models, some interesting limits on space could be found: (i)(D=2+2kn) while the black hole is surrounded by cosmic strings; (ii)the black hole can be surrounded by linear dilaton field only in 4-dimensional spacetime. In both cases, D=4 is special.Comment: 8 page

Self-consistency in relativistic theory of infinite statistics fields

Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. Our previous work has built a relativistic quantum field theory which allows interactions involving infinite statistics particles. In this paper, a more detailed analysis of this theory is available. Topics discussed include cluster decomposition, CPT symmetry and renormalization.Comment: 7 page

Covariant versions of Margolus-Levitin Theorem

The Margolus-Levitin Theorem is a limitation on the minimal evolving time of a quantum system from its initial state to its orthogonal state. It also supplies a bound on the maximal operations or events can occur within a volume of spacetime. We compare Margolus-Levitin Theorem with other form of limitation on minimal evolving time, and present covariant versions of Margolus-Levitin Theorem in special and general relativity respectively. The relation among entropy bound, maximum information flow and computational limit are discussed, by applying the covariant versions of Margolus-Levitin Theorem.Comment: 11 pages, 1 figure, revte

Multi-Adversarial Domain Adaptation

Recent advances in deep domain adaptation reveal that adversarial learning can be embedded into deep networks to learn transferable features that reduce distribution discrepancy between the source and target domains. Existing domain adversarial adaptation methods based on single domain discriminator only align the source and target data distributions without exploiting the complex multimode structures. In this paper, we present a multi-adversarial domain adaptation (MADA) approach, which captures multimode structures to enable fine-grained alignment of different data distributions based on multiple domain discriminators. The adaptation can be achieved by stochastic gradient descent with the gradients computed by back-propagation in linear-time. Empirical evidence demonstrates that the proposed model outperforms state of the art methods on standard domain adaptation datasets.Comment: AAAI 2018 Oral. arXiv admin note: substantial text overlap with arXiv:1705.10667, arXiv:1707.0790