Signless Laplacian spectral radius and fractional matchings in graphs

A {\it fractional matching} of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ so that $\sum_{e\in \Gamma(v)}f(e)\leq 1$ for each $v\in V(G)$, where $\Gamma(v)$ is the set of edges incident to $v$. The {\it fractional matching number} of $G$, written $\alpha'_{*}(G)$, is the maximum of $\sum_{e\in E(G)}f(e)$ over all fractional matchings $f$. In this paper, we propose the relations between the fractional matching number and the signless Laplacian spectral radius of a graph. As applications, we also give sufficient spectral conditions for existence of a fractional perfect matching in a graph in terms of the signless Laplacian spectral radius of the graph and its complement

Pairing symmetry of heavy fermion superconductivity in the two-dimensional Kondo-Heisenberg lattice model

In the two-dimensional Kondo-Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion superconductivity. We find that the pairing symmetry \textit{strongly} depends on the Fermi surface (FS) structure in the normal metallic state. When $J_{H}/J_{K}$ is very small, the FS is a small hole-like circle around the corner of the Brillouin zone, and the s-wave pairing symmetry has a lower ground state energy. For the intermediate coupling values of $J_{H}/J_{K}$, the extended s-wave pairing symmetry gives the favored ground state. However, when $J_{H}/J_{K}$ is larger than a critical value, the FS transforms into four small hole pockets crossing the boundary of the magnetic Brillouin zone, and the d-wave pairing symmetry becomes more favorable. In that regime, the resulting superconducting state is characterized by either nodal d-wave or nodeless d-wave state, depending on the conduction electron filling factor as well. A continuous phase transition exists between these two states. This result may be related to the phase transition of the nodal d-wave state to a fully gapped state, which is recently observed in Yb doped CeCoIn$_{5}$.Comment: 5 pages, 5 figures; published versio

Weak ferromagnetism with the Kondo screening effect in the Kondo lattice systems

We carefully consider the interplay between ferromagnetism and the Kondo screening effect in the conventional Kondo lattice systems at finite temperatures. Within an effective mean-field theory for small conduction electron densities, a complete phase diagram has been determined. In the ferromagnetic ordered phase, there is a characteristic temperature scale to indicate the presence of the Kondo screening effect. We further find two distinct ferromagnetic long-range ordered phases coexisting with the Kondo screening effect: spin fully polarized and partially polarized states. A continuous phase transition exists to separate the partially polarized ferromagnetic ordered phase from the paramagnetic heavy Fermi liquid phase. These results may be used to explain the weak ferromagnetism observed recently in the Kondo lattice materials.Comment: 6 pages, 6 figures; published versio

Solar system constraints on asymptotically flat IR modified Horava gravity through light deflection

In this paper, we study the motion of photons around a Kehagias-Sfetsos (KS) black hole and obtain constraints on IR modified Ho$\check{r}$ava gravity without cosmological constant ($\sim \Lambda_{W}$). An analytic formula for the light deflection angle is obtained. For a propagating photon, the deflection angle $\delta \phi$ increases with large values of the Ho$\check{r}$ava gravity parameter $\omega$. Under the UV limit $\omega \longrightarrow \infty$, deflection angle reduces to the result of usual Schwarzschild case, $4GM/R$. It is also found that with increasing scale of astronomical observation system the Ho$\check{r}$ava-Lifshitz gravity should satisfy $|\omega M^2|>1.1725 \times10^{-16}$ with 12% precision for Earth system, $|\omega M^2| > 8.27649 \times 10^{-17}$ with 17% precision for Jupiter system and $|\omega M^2| > 8.27650\times 10^{-15}$ with 0.17% precision for solar system.Comment: 13 pages, 2 figures; References added; To appear in Gen. Rel. Gra

Phase evolution of the two-dimensional Kondo lattice model near half-filling

Within a mean-field approximation, the ground state and finite temperature phase diagrams of the two-dimensional Kondo lattice model have been carefully studied as functions of the Kondo coupling $J$ and the conduction electron concentration $n_{c}$. In addition to the conventional hybridization between local moments and itinerant electrons, a staggered hybridization is proposed to characterize the interplay between the antiferromagnetism and the Kondo screening effect. As a result, a heavy fermion antiferromagnetic phase is obtained and separated from the pure antiferromagnetic ordered phase by a first-order Lifshitz phase transition, while a continuous phase transition exists between the heavy fermion antiferromagnetic phase and the Kondo paramagnetic phase. We have developed a efficient theory to calculate these phase boundaries. As $n_{c}$ decreases from the half-filling, the region of the heavy fermion antiferromagnetic phase shrinks and finally disappears at a critical point $n_{c}^{*}=0.8228$, leaving a first-order critical line between the pure antiferromagnetic phase and the Kondo paramagnetic phase for $n_{c}<n_{c}^{* }$. At half-filling limit, a finite temperature phase diagram is also determined on the Kondo coupling and temperature ($J$-$T$) plane. Notably, as the temperature is increased, the region of the heavy fermion antiferromagnetic phase is reduced continuously, and finally converges to a single point, together with the pure antiferromagnetic phase and the Kondo paramagnetic phase. The phase diagrams with such triple point may account for the observed phase transitions in related heavy fermion materials.Comment: 9 pages, 9 figure

What I See Is What You See: Joint Attention Learning for First and Third Person Video Co-analysis

In recent years, more and more videos are captured from the first-person viewpoint by wearable cameras. Such first-person video provides additional information besides the traditional third-person video, and thus has a wide range of applications. However, techniques for analyzing the first-person video can be fundamentally different from those for the third-person video, and it is even more difficult to explore the shared information from both viewpoints. In this paper, we propose a novel method for first- and third-person video co-analysis. At the core of our method is the notion of "joint attention", indicating the learnable representation that corresponds to the shared attention regions in different viewpoints and thus links the two viewpoints. To this end, we develop a multi-branch deep network with a triplet loss to extract the joint attention from the first- and third-person videos via self-supervised learning. We evaluate our method on the public dataset with cross-viewpoint video matching tasks. Our method outperforms the state-of-the-art both qualitatively and quantitatively. We also demonstrate how the learned joint attention can benefit various applications through a set of additional experiments

On Optimizing Energy Efficiency in Multi-Radio Multi-Channel Wireless Networks

Multi-radio multi-channel (MR-MC) networks contribute significant enhancement in the network throughput by exploiting multiple radio interfaces and non-overlapping channels. While throughput optimization is one of the main targets in allocating resource in MR-MC networks, recently, the network energy efficiency is becoming a more and more important concern. Although turning on more radios and exploiting more channels for communication is always beneficial to network capacity, they may not be necessarily desirable from an energy efficiency perspective. The relationship between these two often conflicting objectives has not been well-studied in many existing works. In this paper, we investigate the problem of optimizing energy efficiency under full capacity operation in MR-MC networks and analyze the optimal choices of numbers of radios and channels. We provide detailed problem formulation and solution procedures. In particular, for homogeneous commodity networks, we derive a theoretical upper bound of the optimal energy efficiency and analyze the conditions under which such optimality can be achieved. Numerical results demonstrate that the achieved optimal energy efficiency is close to the theoretical upper bound.Comment: 6 pages, 5 figures, Accepted to Globecom 201

ILCR: Item-based Latent Factors for Sparse Collaborative Retrieval

Interactions between search and recommendation have recently attracted significant attention, and several studies have shown that many potential applications involve with a joint problem of producing recommendations to users with respect to a given query, termed $Collaborative$ $Retrieval$ (CR). Successful algorithms designed for CR should be potentially flexible at dealing with the sparsity challenges since the setup of collaborative retrieval associates with a given $query$ $\times$ $user$ $\times$ $item$ tensor instead of traditional $user$ $\times$ $item$ matrix. Recently, several works are proposed to study CR task from users' perspective. In this paper, we aim to sufficiently explore the sophisticated relationship of each $query$ $\times$ $user$ $\times$ $item$ triple from items' perspective. By integrating item-based collaborative information for this joint task, we present an alternative factorized model that could better evaluate the ranks of those items with sparse information for the given query-user pair. In addition, we suggest to employ a recently proposed scalable ranking learning algorithm, namely BPR, to optimize the state-of-the-art approach, $Latent$ $Collaborative$ $Retrieval$ model, instead of the original learning algorithm. The experimental results on two real-world datasets, (i.e. \emph{Last.fm}, \emph{Yelp}), demonstrate the efficiency and effectiveness of our proposed approach.Comment: 10 pages, conferenc

Coarse-to-Fine Classification via Parametric and Nonparametric Models for Computer-Aided Diagnosis

Classification is one of the core problems in Computer-Aided Diagnosis (CAD), targeting for early cancer detection using 3D medical imaging interpretation. High detection sensitivity with desirably low false positive (FP) rate is critical for a CAD system to be accepted as a valuable or even indispensable tool in radiologists' workflow. Given various spurious imagery noises which cause observation uncertainties, this remains a very challenging task. In this paper, we propose a novel, two-tiered coarse-to-fine (CTF) classification cascade framework to tackle this problem. We first obtain classification-critical data samples (e.g., samples on the decision boundary) extracted from the holistic data distributions using a robust parametric model (e.g., \cite{Raykar08}); then we build a graph-embedding based nonparametric classifier on sampled data, which can more accurately preserve or formulate the complex classification boundary. These two steps can also be considered as effective "sample pruning" and "feature pursuing + $k$NN/template matching", respectively. Our approach is validated comprehensively in colorectal polyp detection and lung nodule detection CAD systems, as the top two deadly cancers, using hospital scale, multi-site clinical datasets. The results show that our method achieves overall better classification/detection performance than existing state-of-the-art algorithms using single-layer classifiers, such as the support vector machine variants \cite{Wang08}, boosting \cite{Slabaugh10}, logistic regression \cite{Ravesteijn10}, relevance vector machine \cite{Raykar08}, $k$-nearest neighbor \cite{Murphy09} or spectral projections on graph \cite{Cai08}

Investigating different structures of the Z_{b}(10610) and Z_{b}(10650)

The recently observed narrow resonance $Z_{b}(10610)$ is examined with the assumptions both as a $B^{*}\bar{B}$ molecular state and a $[bd][\bar{b}\bar{u}]$ tetraquark state with quantum numbers $I^{G}J^{P}=1^{+}1^{+}$. Possible interpolating currents are constructed to describe the $Z_{b}(10650)$ as an axial-vector $B^{*}\bar{B}^{*}$ molecular state or a $[bd][\bar{b}\bar{u}]$ tetraquark state. Using QCD sum rules (QCDSR), we consider contributions up to dimension six in the operator product expansion (OPE) at the leading order in $\alpha_{s}$. The mass is obtained as $(10.44\pm0.23) GeV$ for molecular state and $(10.50\pm0.19) GeV$ for tetraquark state, both of which coincide with the $Z_{b}(10610)$. The results $m_{B^{*}\bar{B}^{*}}=(10.45\pm0.31) GeV$ and $m_{[bd][\bar{b}\bar{u}]}=(10.48\pm0.33) GeV$ are consistent with the $Z_{b}(10650)$.Comment: 17 pages, 9 figure