Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells

2017 ◽  
Vol 27 (5) ◽  
Author(s):  
Aleksandra I. Afonina ◽  
Il’giz R. Kayumov ◽  
Aleksey N. Chuprunov
Keyword(s):  
Random Number ◽  
Conditional Probabilities ◽  
Number Of Particles

Abstract.Let

ON ASYMPTOTIC RELATIONS FOR THE CRITICAL GALTON – WATSON PROCESS

2021 ◽  
pp. 5-16
Author(s):  
K.E. Kudratov ◽  
◽  
Y.M. Khusanbaev ◽  
Keyword(s):  
Single Particle ◽  
Branching Process ◽  
Critical Case ◽  
Random Number ◽  
Branching Processes ◽  
Factorial Moment ◽  
Subcritical Case ◽  
Watson Process ◽  
Third Moment ◽  
Number Of Particles

Determining the asymptotics of the continuation probability for a Galton–Watson branching process is one of the most important problems in the theory of branching processes. This problem was solved by A.N. Kolmogorov (1938) in the case when the process starts with a single particle, and the classical result is obtained. A similar result for continuous branching processes was proved by B.A. Sevastyanov (1951). The next term in the expansion for continuous branching processes was obtained by V.M. Zolotarev (1957). The next term in the expansion for continuous branching processes in the critical case was obtained by V.P. Chistyakov (1957); the asymptotic expansion in the subcritical case under the condition of finiteness of the k-factorial moment was obtained by R. Mukhamedkhanova (1966). Asymptotic expansions for discrete branching processes in the subcritical and supercritical cases, provided that any m-factorial moment is finite, were obtained by S.V. Nagaev and R. Mukhamedkhanova (1966). In the critical case, the weak convergence of the conditional distribution of the quantity P(Z(n) > 0)Z(n) under the condition Z(n) > 0 to the exponential distribution was proved by A.M. Yaglom (1947) for processes starting with a single particle in the case of finiteness of the third moment of the number of generations. Subsequently, Spitzer, Kesten, and Ney (1966) proved this result under the condition that the second moment is finite. A similar result for branching processes with continuous parameters was established by V.M. Zolotarev (1957). In this paper, we study the asymptotics of the probability of continuation of the critical Galton-Watson process, starting with η particles. In addition, we prove an analogue of Yaglom’s theorem for critical Galton – Watson processes starting with a random number of particles.

The distribution of a random number of particles in cells

1967 ◽  
Vol 1 (5) ◽  
pp. 363-366 ◽  
Author(s):  
G. I. Ivchenko ◽  
Yu. I. Medvedev ◽  
B. A. Sevast'yanov
Keyword(s):  
Random Number ◽  
Number Of Particles ◽  
In Cells

Stereo Electron Microscopy Applied to High Resolution Freeze-Etch Replicas

1970 ◽  
Vol 28 ◽  
pp. 306-307
Author(s):  
L. Andrew Staehelin
Keyword(s):  
Electron Microscopy ◽  
Plastic Deformation ◽  
High Resolution ◽  
Smooth Surfaces ◽  
Small Particles ◽  
Membrane Surfaces ◽  
Wide Acceptance ◽  
New Information ◽  
Number Of Particles ◽  
Small Holes

Freeze-etched membranes usually appear as relatively smooth surfaces covered with numerous small particles and a few small holes (Fig. 1). In 1966 Branton (1“) suggested that these surfaces represent split inner mem¬brane faces and not true external membrane surfaces. His theory has now gained wide acceptance partly due to new information obtained from double replicas of freeze-cleaved specimens (2,3) and from freeze-etch experi¬ments with surface labeled membranes (4). While theses studies have fur¬ther substantiated the basic idea of membrane splitting and have shown clearly which membrane faces are complementary to each other, they have left the question open, why the replicated membrane faces usually exhibit con¬siderably fewer holes than particles. According to Branton's theory the number of holes should on the average equal the number of particles. The absence of these holes can be explained in either of two ways: a) it is possible that no holes are formed during the cleaving process e.g. due to plastic deformation (5); b) holes may arise during the cleaving process but remain undetected because of inadequate replication and microscope techniques.

Angular Calibration of Ribosomal Subuntts in Factor Space

1990 ◽  
Vol 48 (1) ◽  
pp. 462-463
Author(s):  
Minakhi Pujari ◽  
Joachim Frank
Keyword(s):  
Three Dimensional ◽  
Carbon Layer ◽  
Uranyl Acetate ◽  
Particle Analysis ◽  
Factor Space ◽  
Multivariate Statistical ◽  
Ribosomal Subunits ◽  
Layer Method ◽  
Dimensional Reconstruction ◽  
Number Of Particles

In single-particle analysis of macromolecule images with the electron microscope, variations of projections are often observed that can be attributed to the changes of the particle’s orientation on the specimen grid (“rocking”). In the multivariate statistical analysis (MSA) of such projections, a single factor is often found that expresses a large portion of these variations. Successful angle calibration of this “rocking factor” would mean that correct angles can be assigned to a large number of particles, thus facilitating three-dimensional reconstruction.In a study to explore angle calibration in factor space, we used 40S ribosomal subunits, which are known to rock around an axis approximately coincident with their long axis. We analyzed micrographs of a field of these particles, taken with 20° tilt and without tilt, using the standard methods of alignment and MSA. The specimen was prepared with the double carbon-layer method, using uranyl acetate for negative staining. In the MSA analysis, the untilted-particle projections were used as active, the tilted-particle projections as inactive objects. Upon tilting, those particles whose rocking axes are parallel to the tilt axis will change their appearance in the same way as under the influence of rocking. Therefore, each vector, in factor space, joining a tilted and untilted projection of the same particle can be regarded as a local 20-degree calibration bar.

A Sensitive On-Grid Immunoelectron Microscopic Procedure for Diagnosis of Rotavirus Infection

1980 ◽  
Vol 38 ◽  
pp. 506-507
Author(s):  
M. F. Miller ◽  
A. R. Rubenstein
Keyword(s):  
Electron Microscopy ◽  
Specific Antibody ◽  
Immune Complexes ◽  
Acute Gastroenteritis ◽  
Plant Viruses ◽  
Aggregation Process ◽  
Microscopic Technique ◽  
Fecal Material ◽  
Present Communication ◽  
Number Of Particles

Studies of rotavirus particles in humans, monkeys and various non-primates with acute gastroenteritis have involved detection of virus in fecal material by electron microscopy. The EM techniques most commonly employed have been the conventional negative staining (Fig. 1) and immune aggregation (Fig. 2) procedures. Both methods are somewhat insensitive and can most reliably be applied to samples containing large quantities of virus either naturaLly or as a result of concentration by ultracentrifugation. The formation of immune complexes by specific antibody in the immune aggregation procedures confirms the rotavirus diagnosis, but the number of particles per given microscope field is effectively reduced by the aggregation process. In the present communication, we describe use of an on-grid immunoelectron microscopic technique in which rotavirus particles are mounted onto microscope grids that were pre-coated with specific antibody. The technique is a modification of a method originalLy introduced by Derrick (1) for studies of plant viruses.

Stimulated Glanzmann’s Thrombasthenia Platelets Produce Microvesicles

1995 ◽  
Vol 74 (06) ◽  
pp. 1533-1540 ◽  
Author(s):  
Pål André Holme ◽  
Nils Olav Solum ◽  
Frank Brosstad ◽  
Nils Egberg ◽  
Tomas L Lindahl
Keyword(s):  
Complement System ◽  
Shape Change ◽  
Annexin V ◽  
Platelet Surface ◽  
Glanzmann’S Thrombasthenia ◽  
Large Numbers ◽  
Glanzmann's Thrombasthenia ◽  
Series Of Experiments ◽  
The Complement System ◽  
Number Of Particles

SummaryThe mechanism of formation of platelet-derived microvesicles remains controversial.The aim of the present work was to study the formation of microvesicles in view of a possible involvement of the GPIIb-IIIa complex, and of exposure of negatively charged phospholipids as procoagulant material on the platelet surface. This was studied in blood from three Glanzmann’s thrombasthenia patients lacking GPIIb-IIIa and healthy blood donors. MAb FN52 against CD9 which activates the complement system and produces microvesicles due to a membrane permeabilization, ADP (9.37 μM), and the thrombin receptor agonist peptide SFLLRN (100 μM) that activates platelets via G-proteins were used as inducers. In a series of experiments platelets were also preincubated with PGE1 (20 μM). The number of liberated microvesicles, as per cent of the total number of particles (including platelets), was measured using flow cytometry with FITC conjugated antibodies against GPIIIa or GPIb. Activation of GPIIb-IIIa was detected as binding of PAC-1, and exposure of aminophospholipids as binding of annexin V. With normal donors, activation of the complement system induced a reversible PAC-1 binding during shape change. A massive binding of annexin V was seen during shape change as an irreversible process, as well as formation of large numbers of microvesicles (60.6 ±2.7%) which continued after reversal of the PAC-1 binding. Preincubation with PGE1 did not prevent binding of annexin V, nor formation of microvesicles (49.5 ± 2.7%), but abolished shape change and PAC-1 binding after complement activation. Thrombasthenic platelets behaved like normal platelets after activation of complement except for lack of PAC-1 binding (also with regard to the effect of PGE1 and microvesicle formation). Stimulation of normal platelets with 100 μM SFLLRN gave 16.3 ± 1.2% microvesicles, and strong PAC-1 and annexin V binding. After preincubation with PGE1 neither PAC-1 nor annexin V binding, nor any significant amount of microvesicles could be detected. SFLLRN activation of the thrombasthenic platelets produced a small but significant number of microvesicles (6.4 ± 0.8%). Incubation of thrombasthenic platelets with SFLLRN after preincubation with PGE1, gave results identical to those of normal platelets. ADP activation of normal platelets gave PAC-1 binding, but no significant annexin V labelling, nor production of microvesicles. Thus, different inducers of the shedding of microvesicles seem to act by different mechanisms. For all inducers there was a strong correlation between the exposure of procoagulant surface and formation of microvesicles, suggesting that the mechanism of microvesicle formation is linked to the exposure of aminophospholipids. The results also show that the GPIIb-IIIa complex is not required for formation of microvesicles after activation of the complement system, but seems to be of importance, but not absolutely required, after stimulation with SFLLRN.

Random Number Generation Based on the Rossler Attractor

2014 ◽  
Vol 1 ◽  
pp. 272-275 ◽  
Author(s):  
Vincent Canals ◽  
Antoni Morro ◽  
Josep L. Rosselló
Keyword(s):  
Random Number ◽  
Random Number Generation ◽  
Number Generation
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