The Experts below are selected from a list of 4095 Experts worldwide ranked by ideXlab platform
Dietrich Stoyan - One of the best experts on this subject based on the ideXlab platform.
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stochastic geometry and its applications
2009Co-Authors: Sung Nok Chiu, Dietrich Stoyan, Wilfrid S Kendall, Joseph MeckeAbstract:Mathematical Foundation. Point Processes I--The Poisson Point Process. Random Closed Sets I--The Boolean Model. Point Processes II--General Theory. Point Processes III--Construction of Models. Random Closed Sets II--The General Case. Random Measures. Random Processes of Geometrical Objects. Fibre and Surface Processes. Random Tessellations. Stereology. References. Indexes.
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On Some Qualitative Properties of the Boolean Model of Stochastic Geometry
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2006Co-Authors: Dietrich StoyanAbstract:For the Boolean Model, one of the basic Models of stochastic geometry and stereology, monotonicity and continuity properties are proved. In particular, for Boolean Models on the line the relation between primary and number granulometry is discussed, and monotonicity properties of the covariance function are studied. Finally, the probability of hitting of an arbitrary primary grain by one of the other ones is considered. Fur das Boolesche Modell, eines der GrundModelle der stochastischen Geometrie und Stereologie, werden Monotonie- und Stetigkeitseigenschaften bewiesen. Insbesondere werden die Beziehung zwischen der primary und number granulometry fur Boolesche Modelle auf der Geraden diskutiert und Monotonieeigenschaften der Kovarianzfunktion studiert. Schlieslich wird die Wahrscheinlichkeit dafur betrachtet, das ein beliebiges primary grain von einem der anderen beruhrt wird.
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the Boolean Model from matheron till today
2005Co-Authors: Dietrich Stoyan, Klaus MeckeAbstract:Until the 1970s random sets were only a marginal or exotic part of probability theory. This situation has changed completely since the publication of the fundamental and seminal book by Matheron [43]. This book has laid the fundamentals of the theory of random closed sets, provided the suitable measure-theoretic machinery and offered the fundamental theorems. It also spresented an excellent introduction to the theory of the Boolean Model.
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Directional analysis of fibre processes related to Boolean Models
Metrika, 1994Co-Authors: Ilya Molchanov, Dietrich StoyanAbstract:Directional characteristics of the boundary of a planar Boolean Model are studied. They are expressed in terms of characteristics of linear sections of the Boolean Model. The suggested estimation technique is applied to the analysis of the orientation of the miscrostructure of paper.
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Asymptotic properties of estimators for parameters of the Boolean Model
Advances in Applied Probability, 1994Co-Authors: Ilya Molchanov, Dietrich StoyanAbstract:This paper considers estimators of parameters of the Boolean Model which are obtained by means of the method of intensities. For an estimator of the intensity of the point process of germ points the asymptotic normality is proved and the corresponding variance is given. The theory is based on a study of second-order characteristics of the point process of lower-positive tangent points of the Boolean Model. An estimator of the distribution of a typical grain is also discussed. ASYMPTOTIC NORMALITY; INTENSITY; POINT PROCESS; RANDOM SET; PARTICLE SYSI EM AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 62M30 SECONDARY 60D05, 60G55
Ilya Molchanov - One of the best experts on this subject based on the ideXlab platform.
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Set-Valued Estimators for Mean Bodies Related to Boolean Models
Statistics, 2007Co-Authors: Ilya MolchanovAbstract:The stationary Boolean Model in the Euclidean space with a convex typical grain is considered. Relations between the mean (or the Aumann expectation) of the difference body of the grain and other characteristics of the Boolean Model are discussed, and set-valued estimators for the mean difference body are suggested.
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statistics of the Boolean Model for practitioners and mathematicians
1997Co-Authors: Ilya MolchanovAbstract:The Boolean Model. Estimation of Aggregate Parameters. Estimation of Functional Aggregate Parameters. Estimation of Numerical Individual Parameters. Estimation of Set-Valued Individual Parameters. Individual Parameters: Distributions. Other Sampling Schemes. Testing the Boolean Model Assumption. An Example. Concluding Remarks. References. Index.
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A limit theorem for scaled vacancies of the Boolean Model
Stochastics and Stochastics Reports, 1996Co-Authors: Ilya MolchanovAbstract:The vacancy of the high-intensity Boolean Model (or mosaic process) is considered. The main result gives a limit distribution for the scaled elementary connected vacant component. It is shown that the limiting set is the volume law polyhedron generated by a (in general anisouopic) Poisson network of hyperplanes driven by the expected surface measure of the typical grain of the Boolean Model. The associated zonoid of the network is equal to the projection body of the so-called Blaschke expectation of the typical grain. In difference to earlier results of P. Hall, few geometrical and no isotropy assumptions are imposed on the grain and the proofs are based on the translative integral geometric formula instead of direct analytical computations
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statistics of the Boolean Model from the estimation of means to the estimation of distributions
Advances in Applied Probability, 1995Co-Authors: Ilya MolchanovAbstract:Non-parametric estimators of the distribution of the grain of the Boolean Model are considered. The technique is based on the study of point processes of tangent points in different directions related to the Boolean Model. Their second- and higher-order characteristics are used to estimate the mean body and the distribution of the typical grain. Central limit theorems for the improved estimator of the intensity and surface measures of the Boolean Model are also proved
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Directional analysis of fibre processes related to Boolean Models
Metrika, 1994Co-Authors: Ilya Molchanov, Dietrich StoyanAbstract:Directional characteristics of the boundary of a planar Boolean Model are studied. They are expressed in terms of characteristics of linear sections of the Boolean Model. The suggested estimation technique is applied to the analysis of the orientation of the miscrostructure of paper.
Laleh Kazemzadeh - One of the best experts on this subject based on the ideXlab platform.
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Boolean Model of yeast apoptosis as a tool to study yeast and human apoptotic regulations
Frontiers in Physiology, 2012Co-Authors: Laleh Kazemzadeh, Marija Cvijovic, Dina PetranovicAbstract:Programmed cell death (PCD) is an essential cellular mechanism that is evolutionary conserved, mediated through various pathways and acts by integrating different stimuli. Many diseases such as neurodegenerative diseases and cancers are found to be caused by, or associated with, regulations in the cell death pathways. Yeast Saccharomyces cerevisiae, is a unicellular eukaryotic organism that shares with human cells components and pathways of the PCD and is therefore used as a Model organism. Boolean Modeling is becoming promising approach to capture qualitative behavior and describe essential properties of such complex networks. Here we present large literature-based and to our knowledge first Boolean Model that combines pathways leading to apoptosis (a type of PCD) in yeast. Analysis of the yeast Model confirmed experimental findings of anti-apoptotic role of Bir1p and pro-apoptotic role of Stm1p and revealed activation of the stress protein kinase Hog proposing the maximal level of activation upon heat stress. In addition we extended the yeast Model and created an in silico humanized yeast in which human pro- and anti-apoptotic regulators Bcl-2 family and Valosin-contain protein (VCP) are included in the Model. We showed that accumulation of Bax in silico humanized yeast shows apoptotic markers and that VCP is essential target of Akt Signaling. The presented Boolean Model provides comprehensive description of yeast apoptosis network behavior. Extended Model of humanized yeast gives new insights of how complex human disease like neurodegeneration can initially be tested.
M. Petrou - One of the best experts on this subject based on the ideXlab platform.
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Classification of binary textures using the 1-D Boolean Model
IEEE Transactions on Image Processing, 1999Co-Authors: P. Garcia-sevilla, M. PetrouAbstract:The one-dimensional (1-D) Boolean Model is used to calculate features for the description of binary textures. Each two-dimensional (2-D) texture is converted into several 1-D strings by scanning it according to raster vertical, horizontal or Hilbert sequences. Several different probability distributions for the segment lengths created this way are used to Model their distribution. Therefore, each texture is described by a set of Boolean Models. Classification is performed by calculating the overlapping probability between corresponding Models. The method is evaluated with the help of 32 different binary textures, and the pros and cons of the approach are discussed.
Tatsuya Akutsu - One of the best experts on this subject based on the ideXlab platform.
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computing smallest intervention strategies for multiple metabolic networks in a Boolean Model
Journal of Computational Biology, 2015Co-Authors: Wei Lu, Takeyuki Tamura, Jiangning Song, Tatsuya AkutsuAbstract:This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished Model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean Models and an elementary mode (EM)-based Model. Integer linear programming (ILP)-based methods are developed for these Models, since MKMN is NP-complete for both the Boolean Model and the EM-based Model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online.
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integer programming based method for designing synthetic metabolic networks by minimum reaction insertion in a Boolean Model
PLOS ONE, 2014Co-Authors: Wei Lu, Takeyuki Tamura, Jiangning Song, Tatsuya AkutsuAbstract:In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean Model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based Model, the solution of the FBA-based Model tends to include more reactions than that of the Boolean Model. However, solving MRI using the Boolean Model is computationally more expensive than using the FBA-based Model since the Boolean Model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean Model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean Model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean Model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.”
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finding minimum reaction cuts of metabolic networks under a Boolean Model using integer programming and feedback vertex sets
International Journal of Knowledge Discovery in Bioinformatics, 2010Co-Authors: Takeyuki Tamura, Kazuhiro Takemoto, Tatsuya AkutsuAbstract:In this paper, the authors consider the problem of, given a metabolic network, a set of source compounds and a set of target compounds, finding a minimum size reaction cut, where a Boolean Model is used as a Model of metabolic networks. The problem has potential applications to measurement of structural robustness of metabolic networks and detection of drug targets. They develop an integer programming-based method for this optimization problem. In order to cope with cycles and reversible reactions, they further develop a novel integer programming (IP) formalization method using a feedback vertex set (FVS). When applied to an E. coli metabolic network consisting of Glycolysis/Glyconeogenesis, Citrate cycle and Pentose phosphate pathway obtained from KEGG database, the FVS-based method can find an optimal set of reactions to be inactivated much faster than a naive IP-based method and several times faster than a flux balance-based method. The authors also confirm that our proposed method works even for large networks and discuss the biological meaning of our results.
