Алгоритмы Решения Систем Линейных Диофантовых Уравнений в Дискретных Областях

Abstract.The algorithms for computation of minimal supported set of solutions for systems of linear Diophantine homogeneous equations over set of natural numbers and basis of systems of linear Diophantine homogeneous and inhomogeneous equations in ring and field of remainders on modulo of a number.

Partitions selection strategy for set of clustering solutions

Clustering is a difficult task: there is no single cluster definition and the data can have more than one underlying structure. Pareto-based multi-objective genetic algorithms (e.g., MOCK Multi-Objective Clustering with automatic K-determination and MOCLE-Multi-Objective Clustering Ensemble) were proposed to tackle these problems. However, the output of such algorithms can often contains a high number of partitions, becoming difficult for an expert to manually analyze all of them. In order to deal with this problem, we present two selection strategies, which are based on the corrected Rand, to choose a subset of solutions. To test them, they are applied to the set of solutions produced by MOCK and MOCLE in the context of several datasets. The study was also extended to select a reduced set of partitions from the initial population of MOCLE. These analysis show that both versions of selection strategy proposed are very effective. They can significantly reduce the number of solutions and, at the same time, keep the quality and the diversity of the partitions in the original set of solutions. (C) 2010 Elsevier B.V. All rights reserved.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

A minimal set of coordinates for describing humanoid shoulder motion

The kinematics of the anatomical shoulder are analysed and modelled as a parallel mechanism similar to a Stewart platform. A new method is proposed to describe the shoulder kinematics with minimal coordinates and solve the indeterminacy. The minimal coordinates are defined from bony landmarks and the scapulothoracic kinematic constraints. Independent from one another, they uniquely characterise the shoulder motion. A humanoid mechanism is then proposed with identical kinematic properties. It is then shown how minimal coordinates can be obtained for this mechanism and how the coordinates simplify both the motion-planning task and trajectory-tracking control. Lastly, the coordinates are also shown to have an application in the field of biomechanics where they can be used to model the scapulohumeral rhythm.

A minimal gene set for cellular life derived by comparison of complete bacterial genomes.

The recently sequenced genome of the parasitic bacterium Mycoplasma genitalium contains only 468 identified protein-coding genes that have been dubbed a minimal gene complement [Fraser, C.M., Gocayne, J.D., White, O., Adams, M.D., Clayton, R.A., et al. (1995) Science 270, 397-403]. Although the M. genitalium gene complement is indeed the smallest among known cellular life forms, there is no evidence that it is the minimal self-sufficient gene set. To derive such a set, we compared the 468 predicted M. genitalium protein sequences with the 1703 protein sequences encoded by the other completely sequenced small bacterial genome, that of Haemophilus influenzae. M. genitalium and H. influenzae belong to two ancient bacterial lineages, i.e., Gram-positive and Gram-negative bacteria, respectively. Therefore, the genes that are conserved in these two bacteria are almost certainly essential for cellular function. It is this category of genes that is most likely to approximate the minimal gene set. We found that 240 M. genitalium genes have orthologs among the genes of H. influenzae. This collection of genes falls short of comprising the minimal set as some enzymes responsible for intermediate steps in essential pathways are missing. The apparent reason for this is the phenomenon that we call nonorthologous gene displacement when the same function is fulfilled by nonorthologous proteins in two organisms. We identified 22 nonorthologous displacements and supplemented the set of orthologs with the respective M. genitalium genes. After examining the resulting list of 262 genes for possible functional redundancy and for the presence of apparently parasite-specific genes, 6 genes were removed. We suggest that the remaining 256 genes are close to the minimal gene set that is necessary and sufficient to sustain the existence of a modern-type cell. Most of the proteins encoded by the genes from the minimal set have eukaryotic or archaeal homologs but seven key proteins of DNA replication do not. We speculate that the last common ancestor of the three primary kingdoms had an RNA genome. Possibilities are explored to further reduce the minimal set to model a primitive cell that might have existed at a very early stage of life evolution.

Optimising and adapting the QoS of a dynamic set of inter-dependent tasks

Due to the growing complexity and adaptability requirements of real-time systems, which often exhibit unrestricted Quality of Service (QoS) inter-dependencies among supported services and user-imposed quality constraints, it is increasingly difficult to optimise the level of service of a dynamic task set within an useful and bounded time. This is even more difficult when intending to benefit from the full potential of an open distributed cooperating environment, where service characteristics are not known beforehand and tasks may be inter-dependent. This paper focuses on optimising a dynamic local set of inter-dependent tasks that can be executed at varying levels of QoS to achieve an efficient resource usage that is constantly adapted to the specific constraints of devices and users, nature of executing tasks and dynamically changing system conditions. Extensive simulations demonstrate that the proposed anytime algorithms are able to quickly find a good initial solution and effectively optimise the rate at which the quality of the current solution improves as the algorithms are given more time to run, with a minimum overhead when compared against their traditional versions.

Comparative gene finding in chicken indicates that we are closing in on the set of multi-exonic widely-expressed human genes

The recent availability of the chicken genome sequence poses the question of whether there are human protein-coding genes conserved in chicken that are currently not included in the human gene catalog. Here, we show, using comparative gene finding followed by experimental verification of exon pairs by RT–PCR, that the addition to the multi-exonic subset of this catalog could be as little as 0.2%, suggesting that we may be closing in on the human gene set. Our protocol, however, has two shortcomings: (i) the bioinformatic screening of the predicted genes, applied to filter out false positives, cannot handle intronless genes; and (ii) the experimental verification could fail to identify expression at a specific developmental time. This highlights the importance of developing methods that could provide a reliable estimate of the number of these two types of genes.

Minimal analytical characterisation of engineered nanomaterials need for hazard assessment in biological matrices

The safe and responsible development of engineered nanomaterials (ENM), nanotechnology-based materials and products, together with the definition of regulatory measures and implementation of "nano"-legislation in Europe require a widely supported scientific basis and sufficient high quality data upon which to base decisions. At the very core of such a scientific basis is a general agreement on key issues related to risk assessment of ENMs which encompass the key parameters to characterise ENMs, appropriate methods of analysis and best approach to express the effect of ENMs in widely accepted dose response toxicity tests. The following major conclusions were drawn: Due to high batch variability of ENMs characteristics of commercially available and to a lesser degree laboratory made ENMs it is not possible to make general statements regarding the toxicity resulting from exposure to ENMs. 1) Concomitant with using the OECD priority list of ENMs, other criteria for selection of ENMs like relevance for mechanistic (scientific) studies or risk assessment-based studies, widespread availability (and thus high expected volumes of use) or consumer concern (route of consumer exposure depending on application) could be helpful. The OECD priority list is focussing on validity of OECD tests. Therefore source material will be first in scope for testing. However for risk assessment it is much more relevant to have toxicity data from material as present in products/matrices to which men and environment are be exposed. 2) For most, if not all characteristics of ENMs, standardized methods analytical methods, though not necessarily validated, are available. Generally these methods are only able to determine one single characteristic and some of them can be rather expensive. Practically, it is currently not feasible to fully characterise ENMs. Many techniques that are available to measure the same nanomaterial characteristic produce contrasting results (e.g. reported sizes of ENMs). It was recommended that at least two complementary techniques should be employed to determine a metric of ENMs. The first great challenge is to prioritise metrics which are relevant in the assessment of biological dose response relations and to develop analytical methods for characterising ENMs in biological matrices. It was generally agreed that one metric is not sufficient to describe fully ENMs. 3) Characterisation of ENMs in biological matrices starts with sample preparation. It was concluded that there currently is no standard approach/protocol for sample preparation to control agglomeration/aggregation and (re)dispersion. It was recommended harmonization should be initiated and that exchange of protocols should take place. The precise methods used to disperse ENMs should be specifically, yet succinctly described within the experimental section of a publication. 4) ENMs need to be characterised in the matrix as it is presented to the test system (in vitro/ in vivo). 5) Alternative approaches (e.g. biological or in silico systems) for the characterisation of ENMS are simply not possible with the current knowledge. Contributors: Iseult Lynch, Hans Marvin, Kenneth Dawson, Markus Berges, Diane Braguer, Hugh J. Byrne, Alan Casey, Gordon Chambers, Martin Clift, Giuliano Elia1, Teresa F. Fernandes, Lise Fjellsbø, Peter Hatto, Lucienne Juillerat, Christoph Klein, Wolfgang Kreyling, Carmen Nickel1, and Vicki Stone.

Minimal analytical characterization of engineered nanomaterials needed for hazard assessment in biological matrices.

Abstract This paper presents the outcomes from a workshop of the European Network on the Health and Environmental Impact of Nanomaterials (NanoImpactNet). During the workshop, 45 experts in the field of safety assessment of engineered nanomaterials addressed the need to systematically study sets of engineered nanomaterials with specific metrics to generate a data set which would allow the establishment of dose-response relations. The group concluded that international cooperation and worldwide standardization of terminology, reference materials and protocols are needed to make progress in establishing lists of essential metrics. High quality data necessitates the development of harmonized study approaches and adequate reporting of data. Priority metrics can only be based on well-characterized dose-response relations derived from the systematic study of the bio-kinetics and bio-interactions of nanomaterials at both organism and (sub)-cellular levels. In addition, increased effort is needed to develop and validate analytical methods to determine these metrics in a complex matrix.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound-states for the one-dimensional inversely linear background

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)