Search results for "Graph theory"
showing 10 items of 784 documents
The rank of random regular digraphs of constant degree
2018
Abstract Let d be a (large) integer. Given n ≥ 2 d , let A n be the adjacency matrix of a random directed d -regular graph on n vertices, with the uniform distribution. We show that the rank of A n is at least n − 1 with probability going to one as n grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of A n .
Immune networks: multitasking capabilities near saturation
2013
Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with $N_T$ T-lymphocytes can manage a number $N_B!=!\order(N_T^\delta)$ of B-lymphocytes simultaneously, with $\delta!<!1$. Here we study this model in the extensive load regime $N_B!=!\alpha N_T$, with also a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivit…
Decomposable multiphase entropic descriptor
2013
To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase splitting' of the adapted descriptor. As a result, each of the phase descriptors (PDs) describes the spatial inhomogeneity attributed to each phase-component. Obviously, their sum equals to the value of the overall spatial inhomogeneity. We apply this approach to three-phase synthetic patterns. The black and grey components are aggregated or clustered while the white phase is the background one. The examples show how the valuable microstuctural information related…
Immune networks: Multi-tasking capabilities at medium load
2013
Associative network models featuring multi-tasking properties have been introduced recently and studied in the low load regime, where the number $P$ of simultaneously retrievable patterns scales with the number $N$ of nodes as $P\sim \log N$. In addition to their relevance in artificial intelligence, these models are increasingly important in immunology, where stored patterns represent strategies to fight pathogens and nodes represent lymphocyte clones. They allow us to understand the crucial ability of the immune system to respond simultaneously to multiple distinct antigen invasions. Here we develop further the statistical mechanical analysis of such systems, by studying the medium load r…
Entropic measure of spatial disorder for systems of finite-sized objects
2000
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference configuration of the objects. When applied to a given binary image it provides the quantitatively correct results in comparison to its point object version. On examples of simple cluster configurations, two-dimensional Sierpinski carpets and population of interacting particles, the behaviour of S_Delta is compared with the normalized information entropy H' introduced by Van Siclen [Phys. Rev. E 56, (1997) 5211]. For the latter example, the additional middle-scale fe…
Block–Savits Characterization and Star Ordering of Exponential Mixtures
2008
Block and Savits (1980) established a characterization of life distributions using the Laplace transform. In this article, we remark that one of the necessary conditions to be IFRA distribution is equivalent to the star ordering of exponential mixtures. It leads to the definition of two new classes of life distributions, called LIFR and LIFRA, and their dual classes: LDFR and LDFRA. It occurs that these classes have many useful aging properties and preserve known reliability operations. Properties of the classes are studied and relations with known classes are established.
Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs
2011
We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erd\"{o}s-R\'{e}ny graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with re…
Star-shaped conjugated compounds forming nematic discotic systems
2004
Abstract Star-shaped compounds, having a benzene ( 9a,b ) or a 1,3,5-triazine ( 11a,b ) core and stilbenoid arms were prepared. Hexyloxy chains, attached in the middle of the arms, provide nematic discotic phases ND, which are unusual for such systems. The position of the sidechains prevents the micro-segregation, which is valid for star-shaped discs of columnar phases. The stilbenoid character of 9a,b and 11a,b guarantees a high light sensitivity. Apart from the statistical CC bond formation by irradiation in solution or in the LC phases, a topochemically controlled chemo-, regio- and stereoselective photocyclodimerization 11a → 12 was found in the crystalline state. The structure determin…
Selecting industrial robots for milling applications using AHP
2017
Abstract Industrial robots are usually used for pick-and-place applications, which require only point-to-point motion control. However, the recent developments, both in robot technology and in Computer Automated Machining (CAM) software, allow the use of these equipment in applications which require continuous path control, such as multi-axis milling processes. However, the producers do not offer robots specifically developed for this kind of application, thus the user has to choose the most appropriate robot for this goal from a wide range of general purpose robot types. This research work proposes a method based upon Analytic Hierarchy Process (AHP) for selecting the industrial robot for …
Reflections towards a generative theory of musical parallelism
2010
Parallelism plays a core role in Lerdahl and Jackendoff's (1983) GTTM, as it rules the emergence of motivic, metrical, grouping and even formal structures. Due to the high amount of detail and complexity characterising associational structures, neither explicit model nor systematic methodology of parallelism-based structural inference has been included into the GTTM. This paper develops a methodological and computational answer to this problem founded on a computational modelling of pattern extraction operations. The paper focuses in particular on the methodological interest of the pattern mining formalism, and in particular its application to the formalisation of grouping and metrical str…