Finite-dimensional Lie subalgebras of algebras with continuous inversion

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute modulo the Jacobson radical.Comment: 9 pages; to appear in the journal Studia Mathematic

Wannier-Function based Scattering-Matrix Formalism for Photonic Crystal Circuitry

In this dissertation, I develop and investigate in detail a scattering-matrix approach for the efficient treatment of Photonic Crystal circuits and demonstrate its applicability to large-scale 2D circuits. The approach relies on the efficient calculation of the scattering matrices of basic functional elements using an expansion of fields into photonic Wannier functions, which represent a basis ideally suited to describe localized fields within defect structures in Photonic Crystals

Combining data-driven MT systems for improved sign language translation

In this paper, we investigate the feasibility of combining two data-driven machine translation (MT) systems for the translation of sign languages (SLs). We take the MT systems of two prominent data-driven research groups, the MaTrEx system developed at DCU and the Statistical Machine Translation (SMT) system developed at RWTH Aachen University, and apply their respective approaches to the task of translating Irish Sign Language and German Sign Language into English and German. In a set of experiments supported by automatic evaluation results, we show that there is a definite value to the prospective merging of MaTrEx’s Example-Based MT chunks and distortion limit increase with RWTH’s constraint reordering

Hand in hand: automatic sign Language to English translation

In this paper, we describe the first data-driven automatic sign-language-to- speech translation system. While both sign language (SL) recognition and translation techniques exist, both use an intermediate notation system not directly intelligible for untrained users. We combine a SL recognizing framework with a state-of-the-art phrase-based machine translation (MT) system, using corpora of both American Sign Language and Irish Sign Language data. In a set of experiments we show the overall results and also illustrate the importance of including a vision-based knowledge source in the development of a complete SL translation system

Emergence of the mitochondrial reticulum from fission and fusion dynamics

Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging