Evacuating Two Robots from a Disk: A Second Cut

We present an improved algorithm for the problem of evacuating two robots from the unit disk via an unknown exit on the boundary. Robots start at the center of the disk, move at unit speed, and can only communicate locally. Our algorithm improves previous results by Brandt et al. [CIAC'17] by introducing a second detour through the interior of the disk. This allows for an improved evacuation time of $5.6234$. The best known lower bound of $5.255$ was shown by Czyzowicz et al. [CIAC'15].Comment: 19 pages, 5 figures. This is the full version of the paper with the same title accepted in the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO'19

Model of Enterpreneurship and Social-cultural and Market Orientation of Small Business Owners in Poland

In the development of SMEs in Poland crucial meaning is legislation, steadily adapted to EU regulations, especially to the European Charter for Small Enterprises. Research conducted in Poland by many authors provide data for doing so, to confirm the hypothesis that among small businesses a vital role in shaping their work situation did not continue to play the market mechanisms and orientations, but mainly socio-cultural factors.W rozwoju MŚP w Polsce podstawowe znaczenie mają również uregulowania prawne, systematycznie dostosowywane do regulacji unijnych, zwłaszcza zaś do Europejskiej Karty Małych Przedsiębiorstw. Badania prowadzone w Polsce przez wielu autorów dostarczają danych ku temu, by potwierdzić tezę, że wśród drobnych przedsiębiorców decydującą rolę w kształtowaniu ich sytuacji pracy odgrywają nadal nie mechanizmy i orientacje rynkowe, ale przede wszystkim czynniki społeczno-kulturowe

Knowledge-Driven Agile Sensor-Mission Assignment

In this paper, we show how knowledge representation and reasoning techniques can support sensor-mission assignment, proceeding from a high-level specification of information requirements, to the allocation of assets such as sensors and platforms. In our previous work, we showed how assets can be matched to mission tasks by formalising the military missions and means framework in terms of an ontology, and using this ontology to drive a matchmaking process derived from the area of semantic Web services. The work reported here extends the earlier approach in two important ways: (1) by providing a richer and more realistic way for a user to specify their information requirements, and (2) by using the results of the semantic matchmaking process to define the search space for efficient asset allocation algorithms. We accomplish (1) by means of a rule-based representation of the NIIRS approach to relating sensed data to the tasks that data may support. We illustrate (2)by showing how the output of our matching process can drive a well-known efficient combinatorial auction algorithm (CASS). Finally, we summarise the status of our illustration-of-concept application, SAM (Sensor Assignment to Missions), and discuss various roles such an application can play in supporting sensormission assignment

Asynchronous rendezvous with different maps

© Springer Nature Switzerland AG 2019. This paper provides a study on the rendezvous problem in which two anonymous mobile entities referred to as robots rA and rB are asked to meet at an arbitrary node of a graph G = (V,E). As opposed to more standard assumptions robots may not be able to visit the entire graph G. Namely, each robot has its own map which is a connected subgraph of G. Such mobility restrictions may be dictated by the topological properties combined with the intrinsic characteristics of robots preventing them from visiting certain edges in E. We consider four different variants of the rendezvous problem introduced in [Farrugia et al. SOFSEM’15] which reflect on restricted maneuverability and navigation ability of rA and rB in G. In the latter, the focus is on models in which robots’ actions are synchronised. The authors prove that one of the maps must be a subgraph of the other. I.e., without this assumption (or some extra knowledge) the rendezvous problem does not have a feasible solution. In this paper, while we keep the containment assumption, we focus on asynchronous robots and the relevant bounds in the four considered variants. We provide some impossibility results and almost tight lower and upper bounds when the solutions are possible

Industrial applications of lipases in the synthesis of high added-value chemicals – 85 years of lipase-based enzymatic catalysis. Part 1

Lipases (EC 3.1.1.3; triacylglycerol acylhydrolases) are the most commonly used enzymes in biotransformations of organic compounds. In living organisms lipases catalyze hydrolysis of higher fatty acid esters of glycerol, thus fulfill an essential function in metabolism of lipids (e.g. fats and oils) and lipoproteins. This year marks 125 years since J.R. Green has identified and described the first lipase isolated from germinated castor-oil beans (Ricinus communis L.) in the form of an extract showing hydrolytic properties. Plants, as well as bacteria are able to produce lipases what was reported in 1901 by Dutch scientist ‒ Christiaan Eijkman. Lipases are also produced by fungi, yeasts, and various organs of higher organisms. A strong foundation, which had a huge impact on the development of global lipase-mediated biotransformations was the discovery made in 1935 and described in Biochemistry Journal and Biochemische Zeitschrift by Polish biochemist- -enzymologist Ernest Alexander Sym (1893-1950) that these enzymes retain almost full catalytic activity even in nearly anhydrous organic solvents. This was exactly fifty years before Russian chemist Alexander Klibanov in 1985 described a lipase- -catalyzed reaction carried out in organic solvents. Since that moment, lipases have became extremely popular in both academic and industrial usage, nowadays being the most important among all biocatalysts used in biochemical processes carried out on an industrial scale. The purpose of this article is to provide a brief characterization of the two most widely used in industrial biotransformations lipases ‒ lipase B from Candida antarctica (CAL-B) and lipase from Burkholderia cepacia (BCL) ‒ and familiarize the readers with the issues of biotechnological processes catalyzed by them. The specifics of a range of industrial applications based on lipase catalysis, including the chemical, pharmaceutical, cosmetic and food industries are also discussed. Keywords

Industrial applications of lipases in the synthesis of high added-value chemicals – 85 years of lipase-based enzymatic catalysis. Part 2

Biotransformations are processes, in which chemical reactions are catalyzed by isolated enzymes or whole cells containing them. Among the biocatalysts, lipases are the most commonly used chiral selectors that exhibit high chemo-, regio-, and stereo-selectivity toward wide spectrum of organic compounds of xenobiothic nature. Moreover, lipases are very stable and active in organic solvents, as well as in neat solvents or in supercritical fluids in the absence of added water. Biotransformations by using lipases can be carried out at high substrate concentrations, at ambient temperature and neutral pH, without need for addition of cofactors, application of high pressures, extremely harsh reaction conditions or complex chemical apparatus. In addition, processes based on efficient biocatalytic technologies has proven to be beneficial for the chemical industry, as the lipases are able to catalyze reactions, which are not easily conducted by classical methods or in other cases allow reactions, which can replace several chemical steps. The above mentioned features of lipase-based biotransformations often cause significant improvement in energy efficiency (savings), and lead to a reduction in waste generation thereby making manufacturing processes even more economically attractive and environmentally acceptable. Since the mid-1980s the use of biotransformations with lipases in industry for the production of high added-value compounds, including pharmaceuticals, vitamins, cosmetics, fragrances and flavors, diagnostic preparations and therapeutics, high-tonnage preparation of agrochemicals, modified foods, nutraceuticals, detergents, polymers, advanced materials and biofuels has steadily increased. In this part of the review article on industrial applications of lipases, next group of popularly utilized enzymes relevant for the production of high added-value chemicals are described. It was also shown on several examples that enzymatic catalysis can significantly simplify manufacturing processes of complex structures being green and economical alternative for conventional chemical-based processes. Keywords

Colourings of (k - r, k)-trees

Trees are generalized to a special kind of higher dimensional complexes known as (j, k)-trees ([L.W. Beineke, R.E. Pippert, On the structure of (m,n)-trees, Proc. 8th S-E Conf. Combinatorics, Graph Theory and Computing, 1977, 75-80]), and which are a natural extension of k-trees for j = k—1. The aim of this paper is to study (k — r, k)-trees ([H.P. Patil, Studies on k-trees and some related topics, PhD Thesis, University of Warsaw, Poland, 1984]), which are a generalization of k-trees (or usual trees when k = 1). We obtain the chromatic polynomial of (k — r, k)-trees and show that any two (k — r, k)-trees of the same order are chromatically equivalent. However, if r ≠ 1 in any (k — r, k)-tree G, then it is shown that there exists another chromatically equivalent graph H, which is not a (k — r, k)-tree. Further, the vertex-partition number and generalized total colourings of (k — r, k)-trees are obtained. We formulate a conjecture about the chromatic index of (k — r, k)-trees, and verify this conjecture in a number of cases. Finally, we obtain a result of [M. Borowiecki, W. Chojnacki, Chromatic index of k-trees, Discuss. Math. 9 (1988), 55-58] as a corollary in which k-trees of Class 2 are characterized

Colourings of (k-r,k)-trees

Trees are generalized to a special kind of higher dimensional complexes known as $(j,k)$-trees ([L. W. Beineke, R. E. Pippert, On the structure of $(m,n)$-trees, Proc. 8th S-E Conf. Combinatorics, Graph Theory and Computing, 1977, 75-80]), and which are a natural extension of $k$-trees for $j=k-1$. The aim of this paper is to study$(k-r,k)$-trees ([H. P. Patil, Studies on $k$-trees and some related topics, PhD Thesis, University of Warsaw, Poland, 1984]), which are a generalization of $k$-trees (or usual trees when $k=1$). We obtain the chromatic polynomial of $(k-r,k)$-trees and show that any two $(k-r,k)$-trees of the same order are chromatically equivalent. However, if $r\neq 1$ in any $(k-r,k)$-tree $G$, then it is shown that there exists another chromatically equivalent graph $H$, which is not a $(k-r,k)$-tree. Further, the vertex-partition number and generalized total colourings of $(k-r,k)$-trees are obtained. We formulate a conjecture about the chromatic index of $(k-r,k)$-trees, and verify this conjecture in a number of cases. Finally, we obtain a result of [M. Borowiecki, W. Chojnacki, Chromatic index of $k$-trees, Discuss. Math. 9 (1988), 55-58] as a corollary in which $k$-trees of Class 2 are characterized