A New Class of Random Fields and Their Extreme Values

1994 ◽  
pp. 389-402
Author(s):  
Simeon M. Berman
Keyword(s):  
Random Fields ◽  
Extreme Values ◽  
New Class

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

scholarly journals Proteins from extremophiles as stable tools for advanced biotechnological applications of high social interest

2006 ◽  
Vol 4 (13) ◽  
pp. 183-191 ◽  
Author(s):  
Marcella de Champdoré ◽  
Maria Staiano ◽  
Mosè Rossi ◽  
Sabato D'Auria
Keyword(s):  
High Pressure ◽  
Low Temperatures ◽  
Extreme Values ◽  
Social Interest ◽  
Industrial Processes ◽  
Ecological Niches ◽  
Biotechnological Applications ◽  
New Class ◽  
Adverse Environmental Conditions ◽  
Micro Organisms

Extremophiles are micro-organisms adapted to survive in ecological niches defined as ‘extreme’ for humans and characterized by the presence of adverse environmental conditions, such as high or low temperatures, extreme values of pH, high salt concentrations or high pressure. Biomolecules isolated from extremophiles possess extraordinary properties and, in particular, proteins isolated from extremophiles represent unique biomolecules that function under severe conditions, comparable to those prevailing in various industrial processes. In this article, we will review some examples of recent applications of thermophilic proteins for the development of a new class of fluorescence non-consuming substrate biosensors for monitoring the levels of two analytes of high social interest, such as glucose and sodium.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (03) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Markov connected component fields

1998 ◽  
Vol 30 (01) ◽  
pp. 1-35 ◽  
Author(s):  
Jesper Møller ◽  
Rasmus Plenge Waagepetersen
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes ◽  
Connected Components ◽  
Spatial Continuity ◽  
New Class ◽  
Inference Problems ◽  
Markov Random

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood of a pixel is not fixed as for Markov random fields, but is given by the components which are adjacent to the pixel. The relationship to Markov random fields and marked point processes is explored and spatial Markov properties are established. Extensions to infinite lattices are also studied, and statistical inference problems including geostatistical applications and statistical image analysis are discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns, including images exhibiting intermediate degrees of spatial continuity and images of objects against background.

scholarly journals Random Fields with Pólya Correlation Structure

2014 ◽  
Vol 51 (4) ◽  
pp. 1037-1050 ◽  
Author(s):  
Richard Finlay ◽  
Eugene Seneta
Keyword(s):  
Random Fields ◽  
Cross Correlation ◽  
Marginal Distribution ◽  
Gaussian Random Fields ◽  
Correlation Structure ◽  
Finite Variance ◽  
Infinitely Divisible ◽  
New Class ◽  
Joint Characteristic ◽  
Non Gaussian

We construct random fields with Pólya-type autocorrelation function and dampened Pólya cross-correlation function. The marginal distribution of the random fields may be taken as any infinitely divisible distribution with finite variance, and the random fields are fully characterized in terms of their joint characteristic function. This makes available a new class of non-Gaussian random fields with flexible correlation structure for use in modeling and estimation.

Markov connected component fields

1998 ◽  
Vol 30 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Jesper Møller ◽  
Rasmus Plenge Waagepetersen
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes ◽  
Connected Components ◽  
Spatial Continuity ◽  
New Class ◽  
Inference Problems ◽  
Markov Random

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood of a pixel is not fixed as for Markov random fields, but is given by the components which are adjacent to the pixel. The relationship to Markov random fields and marked point processes is explored and spatial Markov properties are established. Extensions to infinite lattices are also studied, and statistical inference problems including geostatistical applications and statistical image analysis are discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns, including images exhibiting intermediate degrees of spatial continuity and images of objects against background.

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