scholarly journals Gamma distributions for stationary Poisson flat processes

2009 ◽  
Vol 41 (4) ◽  
pp. 911-939 ◽  
Author(s):  
Volker Baumstark ◽  
Günter Last
Keyword(s):  
Poisson Process ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Voronoi Tessellation ◽  
Isotropic Case ◽  
Intensity Measure ◽  
First Case ◽  
Gamma Distributions ◽  
The Face ◽  
The Mean

We consider a stationary Poisson process X of k-flats in ℝd with intensity measure Θ and a measurable set S of k-flats depending on F1,…,Fn∈ X, x∈ℝd, and X in a specific equivariant way. If (F1,…,Fn,x) is properly sampled (in a ‘typical way’) then Θ(S) has a gamma distribution. This result generalizes and unifies earlier work by Miles (1971), Møller and Zuyev (1996), and Zuyev (1999). As a new example, we will show that the volume of the fundamental region of a typical j-face of a stationary Poisson–Voronoi tessellation is conditionally gamma distributed. This is true in the area-biased and the area-debiased cases. In the first case the shape parameter is not integer valued. As another new example, we will show that the generalized integral-geometric contents of the (area-biased and area-debiased) typical j-face of a Poisson hyperplane tessellation are conditionally gamma distributed. In the isotropic case the contents boil down to the mean breadth of the face.

scholarly journals Gamma distributions for stationary Poisson flat processes

2009 ◽  
Vol 41 (04) ◽  
pp. 911-939 ◽  
Author(s):  
Volker Baumstark ◽  
Günter Last
Keyword(s):  
Poisson Process ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Voronoi Tessellation ◽  
Isotropic Case ◽  
Intensity Measure ◽  
First Case ◽  
Gamma Distributions ◽  
The Face ◽  
The Mean

We consider a stationary Poisson process X of k-flats in ℝd with intensity measure Θ and a measurable set S of k-flats depending on F 1,…,F n ∈ X, x∈ℝd, and X in a specific equivariant way. If (F 1,…,F n ,x) is properly sampled (in a ‘typical way’) then Θ(S) has a gamma distribution. This result generalizes and unifies earlier work by Miles (1971), Møller and Zuyev (1996), and Zuyev (1999). As a new example, we will show that the volume of the fundamental region of a typical j-face of a stationary Poisson–Voronoi tessellation is conditionally gamma distributed. This is true in the area-biased and the area-debiased cases. In the first case the shape parameter is not integer valued. As another new example, we will show that the generalized integral-geometric contents of the (area-biased and area-debiased) typical j-face of a Poisson hyperplane tessellation are conditionally gamma distributed. In the isotropic case the contents boil down to the mean breadth of the face.

scholarly journals Evolution of the Shape of the Raindrop Size Distribution in Simulated Shallow Cumulus

2016 ◽  
Vol 73 (6) ◽  
pp. 2279-2297 ◽  
Author(s):  
Ann Kristin Naumann ◽  
Axel Seifert
Keyword(s):  
Size Distribution ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Cumulus Clouds ◽  
Microphysics Scheme ◽  
Space And Time ◽  
Shallow Cumulus ◽  
Raindrop Size Distribution ◽  
The Mean ◽  
Raindrop Size

Abstract In this paper, the evolution of the raindrop size distribution (RSD) is investigated for two isolated shallow cumulus clouds that are modeled with large-eddy simulations. For a two-moment bulk rain microphysics scheme that assumes the RSD to follow a gamma distribution, it is shown that the evolution of the rainwater content of an individual shallow cumulus cloud—in particular, its subcloud-layer rainwater amount and its surface precipitation rate—is highly sensitive to the choice of the shape parameter of the gamma distribution. To further investigate the shape of the RSD, a Lagrangian drop model is used to represent warm rain microphysics without a priori assumptions on the RSD. It is found that the shape parameter is highly variable in space and time and that existing closure equations, which are established from idealized studies of more heavily precipitating cases, are not appropriate for shallow cumulus. Although a relation of the shape parameter to the mean raindrop diameter is also found for individual shallow cumulus clouds, this relation differs already for the two clouds considered. It is therefore doubtful whether a two-moment scheme with a diagnostic parameterization of the shape parameter (i.e., a local closure in space and time) can be sufficient, especially when being applied across different cloud regimes. A three-moment bulk rain microphysics scheme is able to capture the general development of the relation of the shape parameter to the mean raindrop diameter for the two simulated clouds but misses some relevant features.

Anisotropic Growth of Voronoi Cells

1994 ◽  
Vol 26 (1) ◽  
pp. 43-53 ◽  
Author(s):  
Thomas H. Scheike
Keyword(s):  
Poisson Process ◽  
Euclidean Distance ◽  
Voronoi Tessellation ◽  
Simple Extension ◽  
Anisotropic Growth ◽  
Homogeneous Poisson Process ◽  
Translation Invariant ◽  
Voronoi Cells ◽  
Invariant Distance ◽  
The Mean

This paper discusses a simple extension of the classical Voronoi tessellation. Instead of using the Euclidean distance to decide the domains corresponding to the cell centers, another translation-invariant distance is used. The resulting tessellation is a scaled version of the usual Voronoi tessellation. Formulas for the mean characteristics (e.g. mean perimeter, surface and volume) of the cells are provided in the case of cell centers from a homogeneous Poisson process. The resulting tessellation is stationary and ergodic but not isotropic.

scholarly journals Distribution among Sample Test Results when Testing Shelled Corn Lots for Fumonisin

2001 ◽  
Vol 84 (3) ◽  
pp. 770-776 ◽  
Author(s):  
Thomas B Whitaker ◽  
Winston M Hagler ◽  
Anders S Johansson ◽  
Francis G Giesbrecht ◽  
Mary W Trucksess
Keyword(s):  
Gamma Distribution ◽  
Gamma Function ◽  
Characteristic Curve ◽  
Test Procedure ◽  
Test Results ◽  
Significance Level ◽  
Gamma Distributions ◽  
Sample Test ◽  
The Mean ◽  
Power Divergence

Abstract The statistical distribution known as the compound gamma function was studied for suitability in describing the distribution of sample test results associated with testing lots of shelled corn for fumonisin. Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s2, among the 32 sample fumonisin test results along with the parameters for the compound gamma function were determined for each of the 16 observed distributions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test. The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied. Parameters of the compound gamma distribution were calculated from the 32-fumonisin sample test results using the method of moments. Using regression analysis, equations were developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin test procedure. An operating characteristic curve was developed for a fumonisin sampling plan to demonstrate the use of the compound gamma function.

Anisotropic Growth of Voronoi Cells

1994 ◽  
Vol 26 (01) ◽  
pp. 43-53 ◽  
Author(s):  
Thomas H. Scheike
Keyword(s):  
Poisson Process ◽  
Euclidean Distance ◽  
Voronoi Tessellation ◽  
Simple Extension ◽  
Anisotropic Growth ◽  
Homogeneous Poisson Process ◽  
Translation Invariant ◽  
Voronoi Cells ◽  
Invariant Distance ◽  
The Mean

This paper discusses a simple extension of the classical Voronoi tessellation. Instead of using the Euclidean distance to decide the domains corresponding to the cell centers, another translation-invariant distance is used. The resulting tessellation is a scaled version of the usual Voronoi tessellation. Formulas for the mean characteristics (e.g. mean perimeter, surface and volume) of the cells are provided in the case of cell centers from a homogeneous Poisson process. The resulting tessellation is stationary and ergodic but not isotropic.

Who Was the ‘Heroine’ of Freud's First Case History? Problems and Issues in the Identification of Freud's patients

2017 ◽  
Vol 19 (1) ◽  
pp. 7-54 ◽  
Author(s):  
Richard Skues
Keyword(s):  
Case History ◽  
The Real ◽  
Hypnotic Suggestion ◽  
Social Circle ◽  
First Case ◽  
The Face ◽  
Historical Investigation

In 1892–3 Freud published his first substantial case history, which concerned a patient treated by means of hypnotic suggestion. For some years this has been one of the few remaining of Freud's dedicated cases histories where the patient has not been identified. More recently, however, two publications independently arrived at the conclusion that the patient was none other than Freud's wife, Martha. This paper sets out the reasons why this identification should always have been treated with suspicion, even if the real identity was not known. Nevertheless, the paper goes on to offer a more plausible identification from among Freud's known social circle. The second part of the paper questions the circumstances under which the original misidentification could plausibly have been sustained in the face of such glaring evidence to the contrary. It concludes that, among other reasons, recent tendencies in controversies about Freud's trustworthiness have the hazard of leading to unreliable assumptions about Freud's honesty being taken as a basis for sound historical investigation.

The Difference in Facial Movement Between the Medial and the Lateral Midface: A 3D Skin Surface Vector Analysis

2021 ◽  
Author(s):  
David L Freytag ◽  
Michael G Alfertshofer ◽  
Konstantin Frank ◽  
Dmitry V Melnikov ◽  
Nicholas Moellhoff ◽  
...  
Keyword(s):  
3D Imaging ◽  
Functional Anatomy ◽  
Skin Surface ◽  
Facial Movements ◽  
Anatomic Location ◽  
Objective Evidence ◽  
The Face ◽  
Functional Boundary ◽  
The Mean ◽  
The Difference

Abstract Background Our understanding of the functional anatomy of the face is constantly improving. To date, it is unclear whether the anatomic location of the line of ligaments has any functional importance during normal facial movements such as smiling. Objectives It is the objective of the present study to identify differences in facial movements between the medial and lateral midface by means of skin vector displacement analyses derived from 3D imaging and to further ascertain whether the line of ligaments has both a structural and functional significance in these movements. Methods The study sample consisted of 21 healthy volunteers (9 females & 12 males) of Caucasian ethnic background with a mean age of 30.6 (8.3) years and a mean BMI of 22.57 (2.5) kg/m 2. 3D images of the volunteers’ faces in repose and during smiling (Duchenne type) were taken. 3D imaging-based skin vector displacement analyses were conducted. Results The mean horizontal skin displacement was 0.08 (2.0) mm in the medial midface (lateral movement) and was -0.08 (1.96) mm in the lateral midface (medial movement) (p = 0.711). The mean vertical skin displacement (cranial movement of skin toward the forehead/temple) was 6.68 (2.4) mm in the medial midface whereas it was 5.20 (2.07) mm in the lateral midface (p = 0.003). Conclusions The results of this study provide objective evidence for an antagonistic skin movement between the medial and the lateral midface. The functional boundary identified by 3D imaging corresponds to the anatomic location of the line of ligaments.

scholarly journals Clinical, Laboratory and Histological Features of Dipeptidyl Peptidase-4 Inhibitor Related Noninflammatory Bullous Pemphigoid

2021 ◽  
Vol 10 (9) ◽  
pp. 1916
Author(s):  
Ágnes Kinyó ◽  
Anita Hanyecz ◽  
Zsuzsanna Lengyel ◽  
Dalma Várszegi ◽  
Péter Oláh ◽  
...  
Keyword(s):  
Bullous Pemphigoid ◽  
Clinical Laboratory ◽  
Case Series ◽  
Dipeptidyl Peptidase ◽  
Area Index ◽  
Histological Features ◽  
Dipeptidyl Peptidase 4 ◽  
First Case ◽  
Dipeptidyl Peptidase 4 Inhibitor ◽  
The Mean

Bullous pemphigoid (BP) is an autoimmune blistering disease of elderly patients that has shown increasing incidence in the last decades. Higher prevalence of BP may be due to more frequent use of provoking agents, such as antidiabetic dipeptidyl peptidase-4 inhibitor (DPP4i) drugs. Our aim was to assess DPP4i-induced bullous pemphigoid among our BP patients and characterize the clinical, laboratory and histological features of this drug-induced disease form. In our patient cohort, out of 127 BP patients (79 females (62.2%), 48 males (37.7%)), 14 (9 females and 5 males) were treated with DPP4i at the time of BP diagnosis. The Bullous Pemphigoid Disease Area Index (BPDAI) urticaria/erythema score was significantly lower, and the BPDAI damage score was significantly higher in DPP4i-BP patients compared to the nonDPP4i group. Both the mean absolute eosinophil number and the mean periblister eosinophil number was significantly lower in DPP4i-BP patients than in nonDPP4i cases (317.7 ± 0.204 vs. 894.0 ± 1.171 cells/μL, p < 0.0001; 6.75 ± 1.72 vs. 19.09 ± 3.1, p = 0.0012, respectively). Our results provide further evidence that DPP4i-associated BP differs significantly from classical BP, and presents with less distributed skin symptoms, mild erythema, normal or slightly elevated peripheral eosinophil count, and lower titers of BP180 autoantibodies. To our knowledge, this is the first case series of DPP4i-related BP with a non-inflammatory phenotype in European patients.

Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks

2000 ◽  
Vol 32 (01) ◽  
pp. 1-18 ◽  
Author(s):  
F. Baccelli ◽  
K. Tchoumatchenko ◽  
S. Zuyev
Keyword(s):  
Communication Networks ◽  
Mobile Networks ◽  
Path Length ◽  
Euclidean Distance ◽  
Voronoi Tessellation ◽  
Voronoi Cells ◽  
Ergodic Properties ◽  
Potential Applications ◽  
The Mean ◽  
Mobile Communication Networks

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line defines a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and find its stationary distribution. As a corollary, we obtain the ratio of the mean path length to the Euclidean distance between the end points, and hence a bound for the mean asymptotic length of the shortest path. We apply these results to define a family of simple incremental algorithms for constructing short paths on the Delaunay graph and discuss potential applications to routeing in mobile communication networks.

Studies on the storage of potatoes. III. The composition of the atmosphere in a potato clamp

1950 ◽  
Vol 40 (3) ◽  
pp. 227-232 ◽  
Author(s):  
E. M. Crook ◽  
D. J. Watson
Keyword(s):  
Multiple Regression ◽  
Wind Velocity ◽  
Practical Importance ◽  
Oxygen Depletion ◽  
Unsaturated Compounds ◽  
The Face ◽  
Flow Through ◽  
The Mean ◽  
Oxygen Concentrations

The CO2 concentration in the atmosphere of a potato clamp varied between 0·06 and 0·86%. The sum of CO2 and oxygen concentrations remained approximately constant at 21%. The CO2 concentration increased with time from December to April. This was attributed to increase in the rate of respiration of the potatoes caused by rise of temperature. Wind blowing in the direction normal to the face of the clamp reduced the COa concentration, presumably by causing external air to flow through the clamp coverings. A multiple regression of CO2 concentration on temperature of the potatoes at the time of sampling, and on the mean component of wind velocity normal to the clamp face estimated over a period of 3 hr. before the time of sampling, accounted for 64% of the variance between sampling occasions.Unsaturated compounds were detected in the clamp atmosphere by absorption in bromine; the concentration of these, expressed as ethylene, varied between 0·004 and 0·025%.The magnitude of CO2 accumulation and oxygen depletion in the clamp atmosphere was too small to produce effects of practical importance on the storage behaviour of the potatoes. If the unsaturated compounds were ethylene, the concentration present was sufficient to cause appreciable retardation of sprouting.

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