On Reduction Systems Equivalent to the Non-associative Lambek Calculus with the Empty String

The article concludes a series of results on cut-rule axiomatizabilityof the Lambek calculus. It is proved that the non-associativeproduct-free Lambek calculus with the empty string (NL₀) isnot finitely axiomatizable if the only rule of inference admittedis Lambek's cut rule. The proof makes use of the (infinitely)cut-rule axiomatized calculus NC designed by the author exactlyfor that purpose.     

Segmentation of microscope images of living cells

This paper describes a segmentation method combining a texture based technique with a contour based method. The technique is designed to enable the study of cell behaviour over time by segmenting brightfield microscope image sequences. The technique was tested on artificial images, based on images of living cells and on real sequences acquired from microscope observations of neutrophils and lymphocytes as well as on a sequence of MRI images. The results of the segmentation are compared with the results of the watershed and snake segmentation methods. The results show that the method is both effective and practical.

The structure of subword graphs and suffix trees of Fibonacci words

We use automata-theoretic approach to analyze properties of Fibonacci words. The directed acyclic subword graph (dawg) is a useful deterministic automaton accepting all suffixes of the word. We show that dawg's of Fibonacci words have particularly simple structure. Our main result is a unifying framework for a large collection of relatively simple properties of Fibonacci words. The simple structure of dawgs of Fibonacci words gives in many cases simplified alternative proofs and new interpretation of several well-known properties of Fibonacci words. In particular, the structure of lengths of paths corresponds to a number-theoretic characterization of occurrences of any subword. Using the structural properties of dawg's it can be easily shown that for a string w$w$ we can check if w$w$ is a subword of a Fibonacci word in time O(|w|)$\mathrm{O}(|w|)$ and O(1)$\mathrm{O}(1)$ space. Compact dawg's of Fibonacci words show a very regular structure of their suffix trees and show how the suffix tree for the Fibonacci word grows (extending the leaves in a very simple way) into the suffix tree for the next Fibonacci word.     

Structural and spectroscopic characteristics of synthetic hydrohaematite

In order to investigate the identity of water-containing haematite, a method of preparation has been elaborated which leads to samples of hydrohaematite which are structurally pure and free of amorphous iron hydroxide. Differential thermal analysis by a lack of endothermic effect at 423 to 473 K on the DTA-curves and by a steady fall of the TG curves up to 1150 K revealed that water in the preparations must be tightly held in the lattice of haematite. Measurements of intensities of X-ray reflections of the (1 0 4) and (0 2 4) planes in relation to the (1 1 3) plane confirmed Fe³⁺-deficiency in the haematite cationic sublattice brought about by the presence of OH^– ions in the anionic sublattice. The infrared spectrum of hydrohaematite, in addition to six bands from Fe-O variations, exhibits three bands from hydroxyl groups. The effect of silicates on the pattern of the infrared spectra of natural and synthetic hydrohaematites and the discrepancies in the infrared spectra of haematites published to date are discussed.     

Progressive Virtual Beam Lights

A recent technique that forms virtual ray lights (VRLs) from path segments in media, reduces the artifacts common to VPL approaches in participating media, however, distracting singularities still remain. We present Virtual Beam Lights (VBLs), a progressive many‐lights algorithm for rendering complex indirect transport paths in, from, and to media. VBLs are efficient and can handle heterogeneous media, anisotropic scattering, and moderately glossy surfaces, while provably converging to ground truth. We inflate ray lights into beam lights with finite thicknesses to eliminate the remaining singularities. Furthermore, we devise several practical schemes for importance sampling the various transport contributions between camera rays, light rays, and surface points. VBLs produce artifact‐free images faster than VRLs, especially when glossy surfaces and/or anisotropic phase functions are present. Lastly, we employ a progressive thickness reduction scheme for VBLs in order to render results that converge to ground truth.     

Grid-Controlled Lightpaths for High Performance Grid Applications

Grid applications call for high performance networking support. One attractive solution is to deploy Grids over optical networks. However, resource management in optical domains is traditionally very rigid and cannot successfully meet the requirements of Grid applications, such as flexible provisioning and configuration. In this paper, we present a customizable resource management solution for optical networks where users can create lightpaths on demand and manage their own network resources. Thanks to a Grid-centric system architecture, lightpath resources can be shared among users and easily integrated with data and computation Grids.     

Using Convex Sets for Exploratory Data Analysis and Visualization

In this paper a new, abstract method for analysis and visualization of multidimensional data sets in pattern recognition problems is introduced. It can be used to determine the properties of an unknown, complex data set and to assist in finding the most appropriate recognition algorithm. Additionally, it can be employed to design layers of a feedforward artificial neural network or to visualize the higher-dimensional problems in 2-D and 3-D without losing relevant data set information. The method is derived from the convex set theory and works by considering convex subsets within the data and analyzing their respective positions in the original dimension. Its ability to describe certain set features that cannot be explicitly projected into lower dimensions sets it apart from many other visualization techniques. Two classical multidimensional problems are analyzed and the results show the usefulness of the presented method and underline its strengths and weaknesses.     

A comparison of two MLEM2 rule induction algorithms extended to probabilistic approximations

A probabilistic approximation is a generalization of the standard idea of lower and upper approximations, defined for equivalence relations. Recently probabilistic approximations were additionally generalized to an arbitrary binary relation so that probabilistic approximations may be applied for incomplete data. We discuss two ways to induce rules from incomplete data using probabilistic approximations, by applying true MLEM2 algorithm and an emulated MLEM2 algorithm. In this paper we report novel research on a comparison of both approaches: new results of experiments on incomplete data with three interpretations of missing attribute values. Our results show that both approaches do not differ much.     

Risk assessment for a video surveillance system based on Fuzzy Cognitive Maps

For various IT systems security is considered a key quality factor. In particular, it might be crucial for video surveillance systems, as their goal is to provide continuous protection of critical infrastructure and other facilities. Risk assessment is an important activity in security management; it aims at identifying assets, threats and vulnerabilities, analysis of implemented countermeasures and their effectiveness in mitigating risks. This paper discusses an application of a new risk assessment method, in which risk calculation is based on Fuzzy Cognitive Maps (FCMs) to a complex automated video surveillance system. FCMs are used to capture dependencies between assets and FCM based reasoning is applied to aggregate risks assigned to lower-level assets (e.g. cameras, hardware, software modules, communications, people) to such high level assets as services, maintained data and processes. Lessons learned indicate, that the proposed method is an efficient and low-cost approach, giving instantaneous feedback and enabling reasoning on effectiveness of security system.