Facial Expression Restoration Based on Improved Graph Convolutional Networks

Facial expression analysis in the wild is challenging when the facial image is with low resolution or partial occlusion. Considering the correlations among different facial local regions under different facial expressions, this paper proposes a novel facial expression restoration method based on generative adversarial network by integrating an improved graph convolutional network (IGCN) and region relation modeling block (RRMB). Unlike conventional graph convolutional networks taking vectors as input features, IGCN can use tensors of face patches as inputs. It is better to retain the structure information of face patches. The proposed RRMB is designed to address facial generative tasks including inpainting and super-resolution with facial action units detection, which aims to restore facial expression as the ground-truth. Extensive experiments conducted on BP4D and DISFA benchmarks demonstrate the effectiveness of our proposed method through quantitative and qualitative evaluations.Comment: Accepted by MMM202

On the complexity of color-avoiding site and bond percolation

The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent but certain classes of vertices or edges share a mutual vulnerability. In this study, we consider a graph and we assign colors to the vertices or edges, where the color-classes correspond to the shared vulnerabilities. An important problem is to find robustly connected vertex sets: nodes that remain connected to each other by paths providing any type of error (i.e. erasing any vertices or edges of the given color). This is also known as color-avoiding percolation. In this paper, we study various possible modeling approaches of shared vulnerabilities, we analyze the computational complexity of finding the robustly (color-avoiding) connected components. We find that the presented approaches differ significantly regarding their complexity.Comment: 14 page

An Edgeworth expansion for finite population L-statistics

In this paper, we consider the one-term Edgeworth expansion for finite population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity of the expansion which are expressed in terms of the weight function that defines the statistics and moment conditions.Comment: 14 pages. Minor revisions. Some explanatory comments and a numerical example were added. Lith. Math. J. (to appear

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques

The tomato Prf complex is a molecular trap for bacterial effectors based on Pto transphosphorylation

The bacteria Pseudomonas syringae is a pathogen of many crop species and one of the model pathogens for studying plant and bacterial arms race coevolution. In the current model, plants perceive bacteria pathogens via plasma membrane receptors, and recognition leads to the activation of general defenses. In turn, bacteria inject proteins called effectors into the plant cell to prevent the activation of immune responses. AvrPto and AvrPtoB are two such proteins that inhibit multiple plant kinases. The tomato plant has reacted to these effectors by the evolution of a cytoplasmic resistance complex. This complex is compromised of two proteins, Prf and Pto kinase, and is capable of recognizing the effector proteins. How the Pto kinase is able to avoid inhibition by the effector proteins is currently unknown. Our data shows how the tomato plant utilizes dimerization of resistance proteins to gain advantage over the faster evolving bacterial pathogen. Here we illustrate that oligomerisation of Prf brings into proximity two Pto kinases allowing them to avoid inhibition by the effectors by transphosphorylation and to activate immune responses

Linear Estimation of Location and Scale Parameters Using Partial Maxima

Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.Comment: This article is devoted to the memory of my six-years-old, little daughter, Dionyssia, who leaved us on August 25, 2010, at Cephalonia isl. (26 pages, to appear in Metrika

Conjunctiva granuloma, a rare presentation of ocular leptospirosis presenting as conjunctiva granuloma : case series

Diagnosis of ocular leptospirosis is challenging and requires a high index of suspicion of previous leptospiral infection and good laboratory support. This case series focuses on two young females with unilateral conjunctiva granuloma. To the best of our knowledge, these are the first two cases of ocular leptospirosis with conjunctiva granuloma. The definitive diagnosis of ocular leptospirosis was based on laboratory studies in which conjunctival biopsies in these two cases showed positive leptospira DNA. Retrospectively, the history was suggestive as both patients had exposure to leptospira organism. In conclusion, a diagnosis of ocular leptospirosis requires a high clinical suspicion index supported by mandatory laboratory investigations

The All-Data-Based Evolutionary Hypothesis of Ciliated Protists with a Revised Classification of the Phylum Ciliophora (Eukaryota, Alveolata)

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