scholarly journals Simply generated trees, conditioned Galton―Watson trees, random allocations and condensation: Extended abstract

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Random Trees ◽  
The Other ◽  
Random Allocation ◽  
Allocation Model ◽  
Standard Case ◽  
Infinite Degree ◽  
International Audience ◽  
Watson Process ◽  
Simply Generated Trees ◽  
High Degree

International audience We give a unified treatment of the limit, as the size tends to infinity, of random simply generated trees, including both the well-known result in the standard case of critical Galton-Watson trees and similar but less well-known results in the other cases (i.e., when no equivalent critical Galton-Watson tree exists). There is a well-defined limit in the form of an infinite random tree in all cases; for critical Galton-Watson trees this tree is locally finite but for the other cases the random limit has exactly one node of infinite degree. The random infinite limit tree can in all cases be constructed by a modified Galton-Watson process. In the standard case of a critical Galton-Watson tree, the limit tree has an infinite "spine", where the offspring distribution is size-biased. In the other cases, the spine has finite length and ends with a vertex with infinite degree. A node of infinite degree in the limit corresponds to the existence of one node with very high degree in the finite random trees; in physics terminology, this is a type of condensation. In simple cases, there is one node with a degree that is roughly a constant times the number of nodes, while all other degrees are much smaller; however, more complicated behaviour is also possible. The proofs use a well-known connection to a random allocation model that we call balls-in-boxes, and we prove corresponding results for this model.

scholarly journals The profile of unlabeled trees

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Bernhard Gittenberger
Keyword(s):  
Local Time ◽  
Joint Distribution ◽  
Random Trees ◽  
Rooted Trees ◽  
Brownian Excursion ◽  
Level Number ◽  
International Audience ◽  
The Times ◽  
Simply Generated Trees

International audience We consider the number of nodes in the levels of unlabeled rooted random trees and show that the joint distribution of several level sizes (where the level number is scaled by $\sqrt{n}$) weakly converges to the distribution of the local time of a Brownian excursion evaluated at the times corresponding to the level numbers. This extends existing results for simply generated trees and forests to the case of unlabeled rooted trees.

scholarly journals Pattern distribution in various types of random trees

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Gerard Kok
Keyword(s):  
Normal Distribution ◽  
Limiting Distribution ◽  
Random Trees ◽  
Rooted Trees ◽  
Finite Tree ◽  
International Audience ◽  
Pattern Distribution ◽  
Simply Generated Trees

International audience Let $\mathcal{T}_n$ denote the set of unrooted unlabeled trees of size $n$ and let $\mathcal{M}$ be a particular (finite) tree. Assuming that every tree of $\mathcal{T}_n$ is equally likely, it is shown that the number of occurrences $X_n$ of $\mathcal{M}$ as an induced sub-tree satisfies $\mathbf{E} X_n \sim \mu n$ and $\mathbf{V}ar X_n \sim \sigma^2 n$ for some (computable) constants $\mu > 0$ and $\sigma \geq 0$. Furthermore, if $\sigma > 0$ then $(X_n - \mathbf{E} X_n) / \sqrt{\mathbf{V}ar X_n}$ converges to a limiting distribution with density $(A+Bt^2)e^{-Ct^2}$ for some constants $A,B,C$. However, in all cases in which we were able to calculate these constants, we obtained $B=0$ and thus a normal distribution. Further, if we consider planted or rooted trees instead of $T_n$ then the limiting distribution is always normal. Similar results can be proved for planar, labeled and simply generated trees.

scholarly journals On the number of transversals in random trees

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Bernhard Gittenberger ◽  
Veronika Kraus
Keyword(s):  
Generating Functions ◽  
Singularity Analysis ◽  
Random Trees ◽  
Alternative Proof ◽  
Fixed Size ◽  
Random Subset ◽  
Polya Trees ◽  
Vertex Set ◽  
International Audience ◽  
Simply Generated Trees

International audience We study transversals in random trees with n vertices asymptotically as n tends to infinity. Our investigation treats the average number of transversals of fixed size, the size of a random transversal as well as the probability that a random subset of the vertex set of a tree is a transversal for the class of simply generated trees and for Pólya trees. The last parameter was already studied by Devroye for simply generated trees. We offer an alternative proof based on generating functions and singularity analysis and extend the result to Pólya trees.

scholarly journals P2P4GS : une spécification de grille pair-à-pair de services auto-gérés

2014 ◽  
Vol Volume 17 - 2014 - Special... ◽  
Author(s):  
Bassirou Gueye ◽  
Olivier Flauzac ◽  
Ibrahima Niang ◽  
Cyril Rabat
Keyword(s):  
Peer To Peer ◽  
The Other ◽  
Grid Services ◽  
End User ◽  
Management Protocol ◽  
Management Of Resources ◽  
International Audience ◽  
Adaptive Solution ◽  
High Degree ◽  
Grid Based

International audience The grid-based peer-to-peer architectures were used either for storage and data sharing or computing. So far, the proposed solutions with respect to grid services are based on hierarchical topologies, which present a high degree of centralization. The main issue of this centralization is the unified management of resources and the difficult to react rapidly against failure and faults that can affect grid users. In this paper, we propose a original specification, called P2P4GS, that enables selfmanaged service of peer-to- peer grid. Therefore, we design a self-adaptive solution for services deployment and invocation which take account the paradigm of peer-to-peer services. Furthermore, the deployment, and invocation are completely delegated to the platform and are done a transparent manner with respect to the end user. We propose a generic specification that is not related to a particular peer-to-peer architecture or a management protocol services defined in advance. On the other hand, we propose a study of algorithmic complexities of deployment and service localization primitives in P2P4GS by immersing them on the classical topologies of P2P stack ie the ring and tree. The obtained performances are satisfactory for these different topologies.

C-Terminal amino acid sequence of chicken pepsinogen and its homology with sequences of other acid proteases

1980 ◽  
Vol 45 (4) ◽  
pp. 1144-1154 ◽  
Author(s):  
Miroslav Baudyš ◽  
Helena Keilová ◽  
Vladimír Kostka
Keyword(s):  
Amino Acid ◽  
Amino Acid Sequence ◽  
The Other ◽  
Terminal Sequence ◽  
Terminal Part ◽  
Terminal Amino Acid ◽  
Tryptic Peptides ◽  
Terminal Amino ◽  
High Degree ◽  
Terminal Amino Acid Sequence

To determine the primary structure of the C-terminal part of the molecule of chicken pepsinogen the tryptic, chymotryptic and thermolytic digest of the protein were investigated and peptides derived from this region were sought. These peptides permitted the following 21-residue C-terminal sequence to be determined: ...Ile-Arg-Glu-Tyr-Tyr-Val-Ile-Phe-Asp-Arg-Ala-Asn-Asn-Lys-Val-Gly-Leu-Ser-Pro-Leu-Ser.COOH. A comparison of this structure with the C-terminal sequential regions of the other acid proteases shows a high degree of homology between chicken pepsinogen and these proteases (e.g., the degree of homology with respect to hog pepsinogen and calf prochymosin is about 66%). Additional tryptic peptides, derived from the N-terminal part of the zymogen molecule whose amino acid sequence has been reported before, were also obtained in this study. This sequence was extended by two residues using an overlapping peptide. An ancillary result of this study was the isolation of tryptic peptides derived from other regions of the zymogen molecule.

scholarly journals Involvement of loop 5 lysine residues and the N-terminal β-hairpin of the ribotoxin hirsutellin A on its insecticidal activity

2016 ◽  
Vol 397 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Miriam Olombrada ◽  
Lucía García-Ortega ◽  
Javier Lacadena ◽  
Mercedes Oñaderra ◽  
José G. Gavilanes ◽  
...  
Keyword(s):  
Active Sites ◽  
Structural Changes ◽  
The Other ◽  
Spatial Proximity ◽  
Ribonucleolytic Activity ◽  
The Family ◽  
Lysine Residues ◽  
Hirsutella Thompsonii ◽  
Close Spatial Proximity ◽  
High Degree

Abstract Ribotoxins are cytotoxic members of the family of fungal extracellular ribonucleases best represented by RNase T1. They share a high degree of sequence identity and a common structural fold, including the geometric arrangement of their active sites. However, ribotoxins are larger, with a well-defined N-terminal β-hairpin, and display longer and positively charged unstructured loops. These structural differences account for their cytotoxic properties. Unexpectedly, the discovery of hirsutellin A (HtA), a ribotoxin produced by the invertebrate pathogen Hirsutella thompsonii, showed how it was possible to accommodate these features into a shorter amino acid sequence. Examination of HtA N-terminal β-hairpin reveals differences in terms of length, charge, and spatial distribution. Consequently, four different HtA mutants were prepared and characterized. One of them was the result of deleting this hairpin [Δ(8-15)] while the other three affected single Lys residues in its close spatial proximity (K115E, K118E, and K123E). The results obtained support the general conclusion that HtA active site would show a high degree of plasticity, being able to accommodate electrostatic and structural changes not suitable for the other previously known larger ribotoxins, as the variants described here only presented small differences in terms of ribonucleolytic activity and cytotoxicity against cultured insect cells.

Methylene. III. Gas phase reactions with 1-chloropropane

1969 ◽  
Vol 312 (1509) ◽  
pp. 141-161 ◽  
Keyword(s):  
Gas Phase ◽  
Rate Constants ◽  
Hydrogen Abstraction ◽  
The Other ◽  
Gas Phase Reactions ◽  
Other Hand ◽  
Chlorine Substituent ◽  
High Degree ◽  
Singlet Methylene

The work described in this and the following paper is a continuation of that in parts I and II, devoted to elucidation of the mechanism of the reactions of methylene with chloroalkanes, with particular reference to the reactivities of singlet and triplet methylene in abstraction and insertion processes. The products of the reaction between methylene, prepared by the photolysis of ketene, and 1-chloropropane have been identified and estimated and their dependence on reactant pressures, photolysing wavelength and presence of foreign gases (oxygen and carbon mon­oxide) has been investigated. Both insertion and abstraction mechanisms contribute significantly to the over-all reaction, insertion being relatively much more important than with chloroethane. This type of process appears to be confined to singlet methylene. If, as seems likely, there is no insertion into C—Cl bonds under our conditions (see part IV), insertion into C2—H and C3—H bonds occurs in statistical ratio, approximately. On the other hand, the chlorine substituent reduces the probability of insertion into C—H bonds in its vicinity. As in the chloroethane system, both species of methylene show a high degree of selectivity in their abstraction reactions. We find that k S Cl / k S H >7.7, k T Cl / k T H < 0.14, where the k ’s are rate constants for abstraction, and the super- and subscripts indicate the species of methylene and the type of atom abstracted, respectively. Triplet methylene is discriminating in hydrogen abstraction from 1-C 3 H 7 Cl, the overall rates for atoms attached to C1, C2, C3 being in the ratios 2.63:1:0.

The In Vitro Sensitivities of 70 Strains of Shigella

PEDIATRICS ◽  
1964 ◽  
Vol 34 (5) ◽  
pp. 705-707
Author(s):  
WILLIAM D. DONALD
Keyword(s):  
Clinical Trials ◽  
Gastrointestinal Tract ◽  
Tetracycline Resistance ◽  
The Other ◽  
Drug Of Choice ◽  
High Degree ◽  
As Toxicity ◽  
Selection Of

In vitro sensitivities of 70 shigella strains isolated over a recent 18-month period are reported. The high degree of sulfadiazine resistance casts some doubt on the selection of this agent as the drug of choice in the treatment of shigellosis, at least in this community. Some of the other agents, although inhibiting the growth of the organisms in vitro, have disadvantages such as toxicity or failure of absorption from the gastrointestinal tract. Tetracycline resistance was found in only 7% of the organisms tested, but from this and other reports we may anticipate the occurrence of more organisms resistant to this agent. The results of the sensitivities to ampicillin are encouraging and further studies including clinical trials of this agent are in order.

Photoreceptor coupling in turtle retina

1998 ◽  
Vol 15 (4) ◽  
pp. 755-764 ◽  
Author(s):  
M.L. FIRSOV ◽  
D.G. GREEN
Keyword(s):  
Receptive Field ◽  
Gap Junctions ◽  
Direct Evidence ◽  
Physiological Responses ◽  
The Other ◽  
Morphological Data ◽  
Chelydra Serpentina ◽  
Intracellular Injection ◽  
Coupled Cells ◽  
High Degree

Photoreceptors in the isolated turtle retina of two species of turtle, Chelydra serpentina and Pseudemus scripta elegans, were penetrated with double-barrel electrodes. Physiological responses were recorded through one barrel and Neurobiotin tracer was injected from the other. Intracellular injection of Neurobiotin revealed patterns of tracer-coupled photoreceptors. Both the patterns of tracer coupling and the electrophysiology suggest a high degree of specificity of connections. Rods seem to be coupled only to rods and green and red cones seem to be coupled to cones of the same spectral type. Receptive-field profiles, measured with a thin, sharply focused slit of light, often had well-defined peaks and troughs in sensitivity. We have taken advantage of this observation and used the position of a peak in sensitivity to locate the position on the retina of a coupled cell. In one rod, it was possible to correlate physiological and morphological data and to show that the peaks in the physiological receptive field occurred at positions on the retina where there were dye-coupled cells. This provides direct evidence that gap junctions produce the physiological coupling between rods.

scholarly journals Żywiołowe rozprzestrzenianie się Poznania: profil morfologiczny i mikroekonomiczny

2020 ◽  
pp. 81-99
Author(s):  
Piotr Lityński
Keyword(s):  
Spatial Structure ◽  
Urban Sprawl ◽  
The Other ◽  
Moderate Degree ◽  
Financial Situation ◽  
Housing Preferences ◽  
Household Budget ◽  
High Degree ◽  
Financial Losses ◽  
Morphological Assessment

The aim of the article is to assess Poznań’s urban sprawl from the perspective of the morphology of space and financial situation of suburban households. The morphological assessment uses a method based on two grids of squares with a side: 1 km, 500 m; and data on the location of buildings from CCGCD. On the other hand, the assessment of households was carried out on the basis of the CSO Household Budget database. The results of the research indicate that the analyzed communes in the Poznań area are characterized by a moderate degree of disorder in the spatial structure. There are no communes with a completely compact specificity, there are also no communes with an absolutely high degree of spatial disorder. Households causing urban sprawl in Poznań are entities that incur moderate financial losses in order to maximize their housing preferences.

Sign in / Sign up

Export Citation Format

Share Document