Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical knot cobordisms. To do so, we give an alternate formulation for the Manturov definition of Khovanov homology for virtual knots and links with arbitrary coefficients. This approach uses cut loci on the knot diagram to induce a conjugation operator in the Frobenius algebra. We then discuss the implications of the maps induced in the aforementioned theory to the universal Frobenius algebra for virtual knots. Next we show how one can apply the Karoubi envelope approach of Bar-Natan and Morrison on abstract link diagrams with cross cuts to construct the canonical generators of the Khovanov-Lee homology. Using these canonical generators we derive a generalization of the Rasmussen invariant for virtual knot cobordisms and furthermore generalize Rasmussen's result on the slice genus for positive knots to the case of positive virtual knots. It should also be noted that this generalization of the Rasmussen invariant provides an easy to compute obstruction to knot cobordisms in $S_g \times I \times I$ in the sense of Turaev

Mapping the potential within a nanoscale undoped GaAs region using a scanning electron microscope

Semiconductor dopant profiling using secondary electron imaging in a scanning electron microscope (SEM) has been developed in recent years. In this paper, we show that the mechanism behind it also allows mapping of the electric potential of undoped regions. By using an unbiased GaAs/AlGaAs heterostructure, this article demonstrates the direct observation of the electrostatic potential variation inside a 90nm wide undoped GaAs channel surrounded by ionized dopants. The secondary electron emission intensities are compared with two-dimensional numerical solutions of the electric potential.Comment: 7 pages, 3 figure

Matrix proof method in annotated paraconsistent logic

The matrix connection method (MCM) is an alternative procedure for theorem proving than the usual resolution technique. We already have used the MCM for finding models in a real-time knowledge-based system generator. In this paper, we adapt the MCM to the particular case of sorne annotated propositional paraconsistent logics. Further developments related to these ideas are also outlined.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

3D tomography of cells in micro-channels

We combine confocal imaging, microfluidics and image analysis to record 3D-images of cells in flow. This enables us to recover the full 3D representation of several hundred living cells per minute. Whereas 3D confocal imaging has thus far been limited to steady specimen, we overcome this restriction and present a method to access the 3D shape of moving objects. The key of our principle is a tilted arrangement of the micro-channel with respect to the focal plane of the microscope. This forces cells to traverse the focal plane in an inclined manner. As a consequence, individual layers of passing cells are recorded which can then be assembled to obtain the volumetric representation. The full 3D information allows for a detailed comparisons with theoretical and numerical predictions unfeasible with e.g.\ 2D imaging. Our technique is exemplified by studying flowing red blood cells in a micro-channel reflecting the conditions prevailing in the microvasculature. We observe two very different types of shapes: `croissants' and `slippers'. Additionally, we perform 3D numerical simulations of our experiment to confirm the observations. Since 3D confocal imaging of cells in flow has not yet been realized, we see high potential in the field of flow cytometry where cell classification thus far mostly relies on 1D scattering and fluorescence signals

Synchronized single electron emission from dynamical quantum dots

We study synchronized quantized charge pumping through several dynamical quantum dots (QDs) driven by a single time modulated gate signal. We show that the main obstacle for synchronization being the lack of uniformity can be overcome by operating the QDs in the decay cascade regime. We discuss the mechanism responsible for lifting the stringent uniformity requirements. This enhanced functionality of dynamical QDs might find applications in nanoelectronics and quantum metrology.Comment: 4 pages, 3 figures, submitted to AP

Comparison of Clustering Algorithms for the Identification of Topics on Twitter

Topic Identification in Social Networks has become an important task when dealing with event detection, particularly when global communities are affected. In order to attack this problem, text processing techniques and machine learning algorithms have been extensively used. In this paper we compare four clustering algorithms – k-means, k-medoids, DBSCAN and NMF (Non-negative Matrix Factorization) – in order to detect topics related to textual messages obtained from Twitter. The algorithms were applied to a database initially composed by tweets having hashtags related to the recent Nepal earthquake as initial context. Obtained results suggest that the NMF clustering algorithm presents superior results, providing simpler clusters that are also easier to interpret. &nbsp