Weakly Supervised Local-Global Relation Network for Facial Expression Recognition

To extract crucial local features and enhance the complementary relation between local and global features, this paper proposes a Weakly Supervised Local-Global Relation Network (WS-LGRN), which uses the attention mechanism to deal with part location and feature fusion problems. Firstly, the Attention Map Generator quickly finds the local regions-of-interest under the supervision of image-level labels. Secondly, bilinear attention pooling is employed to generate and refine local features. Thirdly, Relational Reasoning Unit is designed to model the relation among all features before making classification. The weighted fusion mechanism in the Relational Reasoning Unit makes the model benefit from the complementary advantages between different features. In addition, contrastive losses are introduced for local and global features to increase the inter-class dispersion and intra-class compactness at different granularities. Experiments on lab-controlled and real-world facial expression dataset show that WS-LGRN achieves state-of-the-art performance, which demonstrates its superiority in FER.

Sentimental Globalism

This chapter argues that neo-abolitionism uses sentimentalism to dehistoricize contemporary atrocities, viewing them as revivals of a superseded Atlantic past. Modern slave narratives, explicitly written to abolish modern slavery across the globe (ranging across Sudan, Haiti, and Sierra Leone, promoted by various neo-abolitionist organizations), enshrine the language of sentimentalism as the most effective weapon in the human rights arsenal, defining a global relation between us and them solely as a matter of sentiment. Survivors outline an idyllic childhood, abduction and captivity, a life of servitude, until the moment of humanitarian rescue and a new life in America. Reading Francis Bok’s memoir Escape from Slavery (2003) alongside Dave Eggers’s neoliberal novel What Is the What (2006), I trace how the formal exchanges among subject, author, and amanuensis generate a seemingly new way for Americans to imagine themselves as global citizens, constituting themselves as global via their humanitarian empathy for the African victim of atrocity.

The unified transform for mixed boundary condition problems in unbounded domains

This paper implements the unified transform to problems in unbounded domains with solutions having corner singularities. Consequently, a wide variety of mixed boundary condition problems can be solved without the need for the Wiener–Hopf technique. Such problems arise frequently in acoustic scattering or in the calculation of electric fields in geometries involving finite and/or multiple plates. The new approach constructs a global relation that relates known boundary data, such as the scattered normal velocity on a rigid plate, to unknown boundary values, such as the jump in pressure upstream of the plate. By approximating the known data and the unknown boundary values by suitable functions and evaluating the global relation at collocation points, one can accurately obtain the expansion coefficients of the unknown boundary values. The method is illustrated for the modified Helmholtz and Helmholtz equations. In each case, comparisons between the traditional Wiener–Hopf approach, other spectral or boundary methods and the unified transform approach are discussed.

A study of computational and algorithmic methods for solving partial differential equations based on the unified transform method

Στην παρούσα διδακτορική διατριβή αναπτύχθηκαν αριθμητικές τεχνικές για την επίλυση γραμμικών, ελλειπτικών μερικών διαφορικών εξισώσεων (Μ.Δ.Ε.) με βάση τη μέθοδο του ενοποιημένου μετασχηματισμού (ή μέθοδος του Φωκά). Συγκεκριμένα, προτάθηκε προσυντονισμένο σχήμα για την αριθμητική επίλυση της γενικευμένης απεικόνισης Dirichlet-to-Neumann (DtN). Επίσης, αναπτύχθηκαν μέθοδοι επαναληπτικού χωρικού βηματισμού με βάση ανοιχτές μεθόδους χρονικής ολοκλήρωσης για την επίλυση της Μ.Δ.Ε. στο εσωτερικό του υπολογιστικού χωρίου. Ακόμα, προτάθηκε τεχνική εκτίμησης σφάλματος με χρήση της εξίσωσης global relation. Εν συνεχεία, προτάθηκε κλάση συμπαγών μεθόδων χωρικού βηματισμού για την επίλυση της Μ.Δ.Ε. στο εσωτερικό υπολογιστικού χωρίου, όπου γίνεται χρήση είτε ανοιχτών είτε κλειστών μεθόδων χρονικής ολοκλήρωσης. Επιπρόσθετα, προτάθηκε κλάση παράλληλων τεχνικών ενοποιημένου μετασχηματισμού με βάση τη μέθοδο διαχωρισμού του χωρίου.

Extending the unified transform: curvilinear polygons and variable coefficient PDEs

We provide the first significant extension of the unified transform (also known as the Fokas method) applied to elliptic boundary value problems, namely, we extend the method to curvilinear polygons and partial differential equations (PDEs) with variable coefficients. This is used to solve the generalized Dirichlet-to-Neumann map. The central component of the unified transform is the coupling of certain integral transforms of the given boundary data and of the unknown boundary values. This has become known as the global relation and, in the case of constant coefficient PDEs, simply links the Fourier transforms of the Dirichlet and Neumann boundary values. We extend the global relation to PDEs with variable coefficients and to domains with curved boundaries. Furthermore, we provide a natural choice of global relations for separable PDEs. These generalizations are numerically implemented using a method based on Chebyshev interpolation for efficient and accurate computation of the integral transforms that appear in the global relation. Extensive numerical examples are provided, demonstrating that the method presented in this paper is both accurate and fast, yielding exponential convergence for sufficiently smooth solutions. Furthermore, the method is straightforward to use, involving just the construction of a simple linear system from the integral transforms, and does not require knowledge of Green’s functions of the PDE. Details on the implementation are discussed at length.