scholarly journals On Asymptotics of Exchangeable Coalescents with Multiple Collisions

2008 ◽  
Vol 45 (04) ◽  
pp. 1186-1195 ◽  
Author(s):  
Alexander Gnedin ◽  
Alex Iksanov ◽  
Martin Möhle
Keyword(s):  
Unit Interval ◽  
Finite Characteristic ◽  
Absorption Time ◽  
Coupling Technique ◽  
External Branch ◽  
Multiple Collisions ◽  
Characteristic Measure

We study the number of collisions,Xn, of an exchangeable coalescent with multiple collisions (Λ-coalescent) which starts withnparticles and is driven by rates determined by a finite characteristic measure η(dx) =x−2Λ(dx). Via a coupling technique, we derive limiting laws ofXn, using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws ofXninclude normal, stable with index 1 ≤ α < 2, and Mittag-Leffler distributions. The results apply, in particular, to the case when η is a beta(a− 2,b) distribution with parametersa> 2 andb> 0. The approach taken allows us to derive asymptotics of three other functionals of the coalescent: the absorption time, the length of an external branch chosen at random from thenexternal branches, and the number of collision events that occur before the randomly selected external branch coalesces with one of its neighbours.

scholarly journals On Asymptotics of Exchangeable Coalescents with Multiple Collisions

2008 ◽  
Vol 45 (4) ◽  
pp. 1186-1195 ◽  
Author(s):  
Alexander Gnedin ◽  
Alex Iksanov ◽  
Martin Möhle
Keyword(s):  
Unit Interval ◽  
Finite Characteristic ◽  
Absorption Time ◽  
Coupling Technique ◽  
External Branch ◽  
Multiple Collisions ◽  
Characteristic Measure

We study the number of collisions, Xn, of an exchangeable coalescent with multiple collisions (Λ-coalescent) which starts with n particles and is driven by rates determined by a finite characteristic measure η(dx) = x−2Λ(dx). Via a coupling technique, we derive limiting laws of Xn, using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws of Xn include normal, stable with index 1 ≤ α < 2, and Mittag-Leffler distributions. The results apply, in particular, to the case when η is a beta(a − 2, b) distribution with parameters a > 2 and b > 0. The approach taken allows us to derive asymptotics of three other functionals of the coalescent: the absorption time, the length of an external branch chosen at random from the n external branches, and the number of collision events that occur before the randomly selected external branch coalesces with one of its neighbours.

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

A temporal factorization at the maximum for certain positive self-similar Markov processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Absorption Time ◽  
The Laplace Transform ◽  
Self Similar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

A numerical study on combined baffles quick-separation device

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ehsan Dehdarinejad ◽  
Morteza Bayareh ◽  
Mahmud Ashrafizaadeh
Keyword(s):  
Turbulent Flows ◽  
Separation Efficiency ◽  
Numerical Study ◽  
Turbulence Models ◽  
Complete Separation ◽  
Solid Particles ◽  
Flow Rates ◽  
Separation Device ◽  
Coupling Technique ◽  
Laminar And Turbulent Flows

Abstract The transfer of particles in laminar and turbulent flows has many applications in combustion systems, biological, environmental, nanotechnology. In the present study, a Combined Baffles Quick-Separation Device (CBQSD) is simulated numerically using the Eulerian-Lagrangian method and different turbulence models of RNG k-ε, k-ω, and RSM for 1–140 μm particles. A two-way coupling technique is employed to solve the particles’ flow. The effect of inlet flow velocity, the diameter of the splitter plane, and solid particles’ flow rate on the separation efficiency of the device is examined. The results demonstrate that the RSM turbulence model provides more appropriate results compared to RNG k-ε and k-ω models. Four thousand two hundred particles with the size distribution of 1–140 µm enter the device and 3820 particles are trapped and 380 particles leave the device. The efficiency for particles with a diameter greater than 28 µm is 100%. The complete separation of 22–28 μm particles occurs for flow rates of 10–23.5 g/s, respectively. The results reveal that the separation efficiency increases by increasing the inlet velocity, the device diameter, and the diameter of the particles.

scholarly journals GENETICS OF ARGININE BIOSYNTHESIS IN NEUROSPORA CRASSA

Genetics ◽  
1979 ◽  
Vol 93 (3) ◽  
pp. 557-575
Author(s):  
Rowland H Davis
Keyword(s):  
Neurospora Crassa ◽  
Gene Product ◽  
Unit Interval ◽  
Starting Material ◽  
Limited Extent ◽  
Arginine Biosynthesis ◽  
Regulatory Mutants ◽  
Intragenic Complementation ◽  
Translocation Breakpoints ◽  
Bifunctional Gene

ABSTRACT A large number of arginine-requiring mutants of Neurospora was isolated, using a strain already partially impaired in an enzyme of the pathway. Among the mutants, all previously described loci, except one, were represented, and several new loci were defined and mapped. Four groups of mutants were of particular interest. First, thc large group of arg-6 mutants, when tested for intragenic complementation, suggested a bifunctional gene, possibly controlling two steps in ornithine synthesis. This is consistent with the limited enzymic information about this locus. Second, the arg-13 locus was represented by 14 new mutants. All five tested were quite leaky. suggesting that the function controlled by this gene can be rarried out to a limited extent spontaneously or by another gene product. Third, a new locus, arg-14, was defined. It controls a step in ornithine synthesis. It lies in a 1 to 2 map-unit interval between arg-2 and pyr-3 on LG IVR, as shown by mapping in relation tG translocation breakpoints. Fourth, a second new locus whose mutants render the partial mutation in starting material auxotrophic was defined and mapped near the centromere of LG VIL. These new mutants are unable to derepress enzymes of the pathway and may qualify as regulatory mutants.

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