Existence and stability of multiple solutions to the gap equation

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in describing a broad range of hadron physics observables. We apply the homotopy continuation method to each of our four exemplars and thereby find all solutions that exist within the interesting domains of light current-quark masses and interaction strengths; and simultaneously provide an explanation of the nature and number of the solutions, many of which may be associated with dynamical chiral symmetry breaking. Introducing a stability criterion based on the scalar and pseudoscalar susceptibilities we demonstrate, however, that for any nonzero current-quark mass only the regular Nambu solution of the gap equation is stable against perturbations. This guarantees that the existence of multiple solutions to the gap equation cannot complicate the description of phenomena in hadron physics.Comment: 14 pages, 15 figure

Robust virtual unrolling of historical parchment XMT images

We develop a framework to virtually unroll fragile historical parchment scrolls, which cannot be physically unfolded via a sequence of X-ray tomographic slices, thus providing easy access to those parchments whose contents have remained hidden for centuries. The first step is to produce a topologically correct segmentation, which is challenging as the parchment layers vary significantly in thickness, contain substantial interior textures and can often stick together in places. For this purpose, our method starts with linking the broken layers in a slice using the topological structure propagated from its previous processed slice. To ensure topological correctness, we identify fused regions by detecting junction sections, and then match them using global optimization efficiently solved by the blossom algorithm, taking into account the shape energy of curves separating fused layers. The fused layers are then separated using as-parallel-as-possible curves connecting junction section pairs. To flatten the segmented parchment, pixels in different frames need to be put into alignment. This is achieved via a dynamic programming-based global optimization, which minimizes the total matching distances and penalizes stretches. Eventually, the text of the parchment is revealed by ink projection. We demonstrate the effectiveness of our approach using challenging real-world data sets, including the water damaged fifteenth century Bressingham scroll

Beyond Social Exchange: Career Adaptability Linking Work Stressors and Counterproductive Work Behavior

Drawing upon career construction theory (Savickas, 2002, 2013) and the job demand-control-support model (JDCS; Johnson and Hall, 1988; Van der Doef and Maes, 1999), the present study aims to explore the adaptability resources mechanism of the relationship between work stressors and counterproductive work behavior (CWB). Two-wave data were collected from 305 employees working in the operation department of an e-commerce company. The results showed that career adaptability mediated the relationship between work stressors and CWB against both coworkers (CWB-I) and the organization (CWB-O), going above, and beyond the mediation effect of job satisfaction (i.e., an indicator of a social exchange path). Also, the association between career adaptability and CWB-O was stronger among employees who perceived a low (vs. high) level of organizational support. This study sheds light on how work stressors are related to CWBs indirectly through career adaptability. The findings also offer practical advice for organizations to prevent CWBs by developing employees’ adaptability

Depth-aware neural style transfer

Neural style transfer has recently received significant attention and demonstrated amazing results. An efficient solution proposed by Johnson et al. trains feed-forward convolutional neural networks by defining and optimizing perceptual loss functions. Such methods are typically based on high-level features extracted from pre-trained neural networks, where the loss functions contain two components: style loss and content loss. However, such pre-trained networks are originally designed for object recognition, and hence the high-level features often focus on the primary target and neglect other details. As a result, when input images contain multiple objects potentially at different depths, the resulting images are often unsatisfactory because image layout is destroyed and the boundary between the foreground and background as well as different objects becomes obscured. We observe that the depth map effectively reflects the spatial distribution in an image and preserving the depth map of the content image after stylization helps produce an image that preserves its semantic content. In this paper, we introduce a novel approach for neural style transfer that integrates depth preservation as additional loss, preserving overall image layout while performing style transfer

Distributed Robust Multi-Cell Coordinated Beamforming with Imperfect CSI: An ADMM Approach

Multi-cell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the inter-cell interference, has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method that can obtain the worst-case robust beamforming solutions in a decentralized fashion, with only local CSI used at each BS and little backhaul signaling for message exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method in the centralized form, based on the semidefinite relaxation (SDR) technique. To obtain the robust beamforming solution in a decentralized fashion, we further propose a distributed robust MCBF algorithm, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution and its better bandwidth efficiency in backhaul signaling over the existing dual decomposition based algorithms. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm