The paper describes a modification of genetic local search consisting in changing local search space topology. The modification may be interpreted as an extension of the idea of distance preserving crossover used in some efficient implementations of genetic local search. In the presented approach, local optimization performed after recombination does not change elements that were common to both parents. A two phases local optimization is also considered. In the second phase, local optimization is allowed to change all elements. The proposed approach is applied to travelling salesperson problem. Results of experiments reported in the paper prove that this kind of modification of the local search space topology significantly improves performance of genetic local search.
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We present an approach for segmentation of 3D voxel data based on algebraic topology. The framework leads to a single pass algorithm for constructing symbolic descriptions of volumertic data. Unlike previous algorithms segmentation is not limited to sxtracting isosurfaces, i.e. 2D manifolds, enabling the processing of image sequences. Due to the anchoring on algebraic topology, the correctioness of the algorithm can be proven.
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We ascribe the solar magnetic activity to the interplay between the plasma flow and the magnetic field. Observations by SOHO, Hinode and upcoming SDO are discussed. We then discuss the understanding and modeling of solar magnetic activity based on mathematical topological concepts. We present predictions using neural networks. Further we describe the outcome of the cycle 24 prediction panel. Finally, recommendations are given for making improved predictions.
The article is an attempt to introduce relationships between hermeneutics, pedagogy and psychoanalysis. The essential issue under consideration is the interpretation of topological figures as a particular tool allowing to perceive hermeneutics from the subject’s clinic perspective. The key importance for pedagogy here is the indication that both hermeneutics and psychoanalysis have a cognitive value recognising the subject in categories which exceed the traditional subject narratives, formulated from the perspective of the hermeneutic circle.
The article is an attempt to introduce relationships between hermeneutics, pedagogy and psychoanalysis. The essential issue under consideration is the interpretation of topological figures as a particular tool allowing to perceive hermeneutics from the subject’s clinic perspective. The key importance for pedagogy here is the indication that both hermeneutics and psychoanalysis have a cognitive value recognising the subject in categories which exceed the traditional subject narratives, formulated from the perspective of the hermeneutic circle.
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In this paper we investigate the use of general topological spaces in connection with a generalised variant of membrane systems. We provide an approach which produces a fine grain description of local operations occurring simultaneously in sets of compartments of the system by restricting the interactions between objects. This restriction is given by open sets of a topology and multisets of objects associated with them, which dynamically change during the functioning of the system and which together define a notion of vicinity for the objects taking part in the interactions.
As part of the solution of problem optimization of large-scale facilities carried out formalization of the system description of large-scale monitoring, defined the composition and the relationship subsets of elements, relationships, topologies and properties. Formulated the mathematical model and the task of reengineering topological structures of centralized three-tier system of largescale monitoring based on indices of cost and efficiency. The proposed mathematical model explicitly set relations between costs for the reengineering and time processing messages in the system from its structure and topology. The analysis of the objective function revealed that envelopes their local extrema are one-extreme (relative to the number of nodes in the system). Considering this, proposed a method of directed inspection of local extrema, which allow to find best solutions in terms of the minimum additional cost. Selection of the single solution from a set of effective proposed to carry out the method of hierarchy analysis or cardinalist approach aided by the additive function of general utility. The values of the weighting coefficients of the utility functions is carried out by an expert or based on comparator identification. Practical application these results allows reduce the time of obtaining solutions and more accurate solving of large dimension problem.
Geographical Information Systems (GIS) has revolutionised the process of collecting and processing data, therefore, more and more data recorded in an analogue form are transformed into the digital format. However, the process of generating vector models poses a risk of appearing defects of different types. A methodology of correcting common geometric and topological errors that appear in the manual vectorization of a raster model was presented in the paper. The research material was the vector layer including the digitized version of several dozens of drawings of spatial development plans. The paper also presents a procedure for creating a vector model of spatial data with attention paid to potential sources of errors which could be incurred at the stage of its creation as well as indicates methods for their prevention. The tools and plug-ins for evaluation and revision of geometric and topological correctness of a vector model implemented in QGIS software were mainly used in the survey. Elaborated algorithms are aimed at acceleration of data processing to allow their usage during that process. Indeed, proper conducting of spatial analyses needs to administer a data set which is free of errors. Only then, is it possible to obtain proper results and draw appropriate conclusions.
PL
Systemy Informacji Geograficznej (ang. GIS – Geographical Information System) zrewolucjonizowały proces gromadzenia i przetwarzania informacji, w efekcie czego coraz więcej danych zapisanych w postaci analogowej transformuje się do postaci cyfrowej. Proces generowania modeli wektorowych obarczony jest jednak ryzykiem pojawienia się różnego rodzaju wadliwości. W pracy przedstawiono metodykę korekty popularnych błędów geometrycznych i topologicznych powstałych głównie podczas ręcznej wektoryzacji modelu rastrowego. Materiał badawczy stanowiła warstwa wektorowa zawierająca zdigitalizowaną wersję kilkudziesięciu rysunków miejscowych planów zagospodarowania przestrzennego. Artykuł przedstawia także procedurę tworzenia wektorowego modelu danych przestrzennych, zwracając uwagę na potencjalne źródła błędów mogących powstać na etapie jego tworzenia oraz wskazuje metody służące zapobieganiu im. W badaniu wykorzystano głównie zaimplementowane w oprogramowanie QGIS narzędzia i wtyczki oceny oraz korekty poprawności geometrycznej i topologicznej modelu wektorowego. Opracowane algorytmy mają na celu przyspieszenie procesu uzdatniania danych oraz umożliwienie ich wykorzystania w procesie przetwarzania. Prawidłowe wykonanie analiz przestrzennych wymaga bowiem dysponowania zbiorem danych wolnym od błędów. Tylko wówczas możliwe jest otrzymanie prawidłowych wyników i wyciągnięcie stosownych wniosków.
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In the paper there are considered the topologies defined in real linear spaces: the core topology, the topology generated by the family of directionally continuous functions, and the topology defined by Klee in [7]. The notion of the last one is extended to infinite dimensional case by means of the finite topology investigated by Kakutani and Klee [5]. Some properties of the finite topology are proved. The main result says that every one of considered topologies contain essentially the next one in the order listed above.
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This review study analyses Martin Nitsche’s monograph devoted to Heidegger’s Contributions to philosophy (Beiträge zur Philosophie), primarily addressing the question of whether Nitsche succeeds in displaying the phenomenological character of the Contributions. It identifies a key step in Nitsche’s interpretation; that is, Heidegger’s shift from emphasising the specific entity of Dasein to emphasising the distinctive “phenomenological” or “relational field”, which is understood as an “ontological locality”. The study focuses on the question of whether it is possible, subsequent to this shift, to preserve the phenomenological character of (Heidegger’s) thought, and it arrives at a negative conclusion in this regard: Heidegger does not offer a phenomenological description - nay, he presents a conceptual, or perhaps even narrative, structure, in which he lays claim to the possibility of speaking from a principled position of (the experienced) “enowning”.
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We present here a new interpretation of topological concepts based on communication. The context that allows us to see this is that of basic pairs, the most elementary structures that allow to present topology. In particular, we prove that the subsets which can be communicated faithfully between the sides of a basic pair are exactly open subsets and closed subsets. We also prove that a relation between two sets of points can be communicated faithfully if and only if it is continuous or open. Finally we introduce new notions of point and of continuous function which are communicable.
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Rough set theory is an important tool to deal with vagueness and granularity in information systems. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough set approximations is based on equivalence relations and has been extended to relation-based generalized rough set approximations. In this paper, properties of relation-based generalized rough set approximations are examined, and topological properties of relation-based generalized rough set approximations presents. Necessary and sufficient conditions for the relation-based generalized upper (lower) approximation operators to be topological closure (interior) operators are proposed.
Arbitrary and random motion of mobile ad hoc network nodes while communicating results in frequent topology changes and multiple disconnections of links. This dynamic environment challenges the routing of data from the source to the destination and imposes the need for prediction models to track these changes, and then determine future topology of the network. The prediction of network mobility into the future will reduce the frequency of location updates for geographical routing protocols. Moreover it will reduce route request delay and the frequency of route updates in topology based protocols. This paper proposes a predictive model called polynomial regression trajectory estimation. This model is based on the regular behavior of nodes and uses polynomial regression to allow each mobile node to estimate its future locations as a function of time. The estimated locations will be disseminated to the network so that nodes can use them to estimate the future topologies of the entire network. The efficiency of the proposed model has been evaluated by MATLAB simulation.
In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.
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We prove a large deviations principle (LDP) for partial sums U-processes indexed by the half line. The LDP can be formulated on a suitable subset of the set of all absolutely continuous paths. We endow the space with a topology, which is stronger than the usual topology of uniform convergence on compact intervals. An LDP for the maximum of the sample path of the U-processes is obtained as a particular application.
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The process of biological membrane fusion can be analysed by topological methods. Mathematical analysis of the fusion process of vesicles indicated two significant facts: the formation of an inner, transient structure (hexagonal phase - HII) and a translocation of some lipids within the membrane. This shift had a vector character and only occurred from the outer to the inner layer. Model membrane composed of phosphatidylcholine (PC), phosphatidylethanolamine (PE) and phosphatidylserine (PS) was studied. 31P- and 1H-NMR methods were used to describe the process of fusion. 31P-NMR spectra of multilamellar vesicles (MLV) were taken at various temperatures and concentrations of Ca2+ ions (natural fusiogenic agent). A 31P-NMR spectrum with the characteristic shape of the HII phase was obtained for the molar Ca2+/PS ratio of 2.0. During the study, 1H-NMR and 31P-NMR spectra for small unilamellar vesicle (SUV), which were dependent on time (concentration of Pr3+ ions was constant), were also recorded. The presence of the paramagnetic Pr3+ ions permits observation of separate signals from the hydrophilic part of the inner and outer lipid bilayers. The obtained results suggest that in the process of fusion translocation of phospholipid molecules takes place from the outer to the inner layer of the vesicle and size of the vesicles increase. The NMR study has showed that the intermediate state of the fusion process caused by Ca2+ ions is the HII phase. The experimental results obtained are in agreement with the topological model as well.
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This paper studies quasi-discrete closure spaces and fuzzy closure spaces. We show that any topological closure cT induced by a closure c is the smallest extension from a closure space to a topological closure space in both crisp and fuzzy environment, in addition, a characterization of the continuous mappings in quasi-discrete closure spaces is obtained. We propose the concept of quasi-discrete fuzzy closure spaces in the context of fuzzy sets and establish a one to one correspondence between quasi-discrete fuzzy closure spaces and reflexive fuzzy relations. We also discuss the relationship between topological closure cT and closure c in quasi-discrete fuzzy closure spaces and show that the process from closure c to topological closure cT can be realized via the process from a reflexive fuzzy relation to its transitive closure.
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The notion of some connectedness is introduced and it is compared with usual connected sets. Subsets of a topological space that are called i-connected have been introduced by J. Knop & M. Wróbel in [2] in 2006 The reason of introducing this notion is based upon the fact that a subset of the space R with nonempty interior is i-connected if and only if it is connected.
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This paper outlines a review of application of ShuffleNet and its variations as logical topologies in lightwave networks and tries to consolidate the results reported so far. ShuffleNet, a very popular interconnection structure, proposed by Acampora as a logical topology in multihop optical networks has been generalized later with a view to obtaining a network topology for optimal throughput. Bilayered ShuffleNet has been designed to reduce the diameter and average hop distance compared to ShuffleNet. But, absence of any simple bidirectional self-routing scheme in Bilayered ShuffleNet led to design SW-Banyan network, an isornorphic equivalent of the ShuffleNet offering a convenient layout. Bi-directional ShuffleNet facilitates lesser hopping distance between any source-destination pair compared to ShuffleNet. Multistar Implementation of expandable ShuffleNet and GEMNet have been developed to insert flexibility in the structure of ShuffleNet.
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