On Artin algebras arising from Morita contexts

We study Morita rings \Lambda_{(\phi,\psi)}=\bigl({smallmatrix} A &_AN_B_BM_A & B {smallmatrix}\bigr) in the context of Artin algebras from various perspectives. First we study covariant finite, contravariant finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms $\phi$ and $\psi$ are zero. Further we give bounds for the global dimension of a Morita ring $\Lambda_{(0,0)}$, regarded as an Artin algebra, in terms of the global dimensions of $A$ and $B$ in the case when both $\phi$ and $\psi$ are zero. We illustrate our bounds with some examples. Finally we investigate when a Morita ring is a Gorenstein Artin algebra and then we determine all the Gorenstein-projective modules over the Morita ring with $A=N=M=B=\Lambda$, where $\Lambda$ is an Artin algebra.Comment: 29 pages, revised versio

Realisation functors in tilting theory

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an injective cogenerator. For this purpose we develop a theory of (non-compact, or large) tilting and cotilting objects that generalises the preceding notions in the literature. Within the scope of derived Morita theory for rings we show that, under some assumptions, the realisation functor is a derived tensor product. This fact allows us to approach a problem by Rickard on the shape of derived equivalences. Finally, we apply the techniques of this new derived Morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t-structures glueing to a tilting or a cotilting t-structure. As a further application, we answer a question by Xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras

Change of rings and singularity categories

We investigate the behavior of singularity categories and stable categories of Gorenstein projective modules along a morphism of rings. The natural context to approach the problem is via change of rings, that is, the classical adjoint triple between the module categories. In particular, we identify conditions on the change of rings to induce functors between the two singularity categories or the two stable categories of Gorenstein projective modules. Moreover, we study this problem at the level of `big singularity categories' in the sense of Krause. Along the way we establish an explicit construction of a right adjoint functor between certain homotopy categories. This is achieved by introducing the notion of 0-cocompact objects in triangulated categories and proving a dual version of Bousfield's localization lemma. We provide applications and examples illustrating our main results.Comment: v2: 40 pages, minor changes in Section 6, including a shift in the definition of a 0-cocompact objec

FaceRNET: a Facial Expression Intensity Estimation Network

This paper presents our approach for Facial Expression Intensity Estimation from videos. It includes two components: i) a representation extractor network that extracts various emotion descriptors (valence-arousal, action units and basic expressions) from each videoframe; ii) a RNN that captures temporal information in the data, followed by a mask layer which enables handling varying input video lengths through dynamic routing. This approach has been tested on the Hume-Reaction dataset yielding excellent results