scholarly journals A dual process for the coupled Wright–Fisher diffusion

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Martina Favero ◽  
Henrik Hult ◽  
Timo Koski
Keyword(s):  
Counting Process ◽  
Pairwise Interaction ◽  
Dual Process ◽  
Transition Rates ◽  
Typical Structure ◽  
Locus Selection ◽  
Selection Parameters ◽  
The One ◽  
Special Case ◽  
Independent Mutation

AbstractThe coupled Wright–Fisher diffusion is a multi-dimensional Wright–Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, an ancestral process, which is dual to the coupled Wright–Fisher diffusion, is derived. The dual process corresponds to the block counting process of coupled ancestral selection graphs, one for each locus. Jumps of the dual process arise from coalescence, mutation, single-branching, which occur at one locus at the time, and double-branching, which occur simultaneously at two loci. The coalescence and mutation rates have the typical structure of the transition rates of the Kingman coalescent process. The single-branching rate not only contains the one-locus selection parameters in a form that generalises the rates of an ancestral selection graph, but it also contains the two-locus selection parameters to include the effect of the pairwise interaction on the single loci. The double-branching rate reflects the particular structure of pairwise selection interactions of the coupled Wright–Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright–Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.

scholarly journals Congruence pairs of principal MS-algebras and perfect extensions

2020 ◽  
Vol 70 (6) ◽  
pp. 1275-1288
Author(s):  
Abd El-Mohsen Badawy ◽  
Miroslav Haviar ◽  
Miroslav Ploščica
Keyword(s):  
Boolean Algebra ◽  
Congruence Lattices ◽  
Descriptive Solution ◽  
The One ◽  
Special Case ◽  
Congruence Pair

AbstractThe notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [6], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [4].An analogy of a well-known Grätzer’s problem [11: Problem 57] formulated for distributive p-algebras, which asks for a characterization of the congruence lattices in terms of the congruence pairs, is presented here for the principal MS-algebras (Problem 1). Unlike a recent solution to such a problem for the principal p-algebras in [2], it is demonstrated here on the class of principal MS-algebras, that a possible solution to the problem, though not very descriptive, can be simple and elegant.As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. It is shown that this is exactly when de Morgan subalgebra L°° of L is a perfect extension of the Boolean algebra B(L). Two examples illustrating when this special case happens and when it does not are presented.

Shelah's work on non-semi-proper iterations, II

2001 ◽  
Vol 66 (4) ◽  
pp. 1865-1883 ◽  
Author(s):  
Chaz Schlindwein
Keyword(s):  
Closed Subset ◽  
Stationary Subset ◽  
Finite Support ◽  
Countable Support ◽  
Final Model ◽  
Axiom A ◽  
Mahlo Cardinal ◽  
The One ◽  
Image Position ◽  
Special Case

One of the main goals in the theory of forcing iteration is to formulate preservation theorems for not collapsing ω1 which are as general as possible. This line leads from c.c.c. forcings using finite support iterations to Axiom A forcings and proper forcings using countable support iterations to semi-proper forcings using revised countable support iterations, and more recently, in work of Shelah, to yet more general classes of posets. In this paper we concentrate on a special case of the very general iteration theorem of Shelah from [5, chapter XV]. The class of posets handled by this theorem includes all semi-proper posets and also includes, among others, Namba forcing.In [5, chapter XV] Shelah shows that, roughly, revised countable support forcing iterations in which the constituent posets are either semi-proper or Namba forcing or P[W] (the forcing for collapsing a stationary co-stationary subset ofwith countable conditions) do not collapse ℵ1. The iteration must contain sufficiently many cardinal collapses, for example, Levy collapses. The most easily quotable combinatorial application is the consistency (relative to a Mahlo cardinal) of ZFC + CH fails + whenever A ∪ B = ω2 then one of A or B contains an uncountable sequentially closed subset. The iteration Shelah uses to construct this model is built using P[W] to “attack” potential counterexamples, Levy collapses to ensure that the cardinals collapsed by the various P[W]'s are sufficiently well separated, and Cohen forcings to ensure the failure of CH in the final model.In this paper we give details of the iteration theorem, but we do not address the combinatorial applications such as the one quoted above.These theorems from [5, chapter XV] are closely related to earlier work of Shelah [5, chapter XI], which dealt with iterated Namba and P[W] without allowing arbitrary semi-proper forcings to be included in the iteration. By allowing the inclusion of semi-proper forcings, [5, chapter XV] generalizes the conjunction of [5, Theorem XI.3.6] with [5, Conclusion XI.6.7].

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

Revisiting Generation and Meshing Properties of Beveloid Gears

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Tooth Surface ◽  
Generation Process ◽  
Spur Gears ◽  
Helical Gears ◽  
Additional Degree ◽  
Beveloid Gears ◽  
Fixed Space ◽  
Fixed Axis ◽  
The One ◽  
Special Case

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known. Beveloid gears are often regarded as a generalization of involute cylindrical gears involving one additional degree-of-freedom, in that the midplane of their (virtual) generating rack is inclined with respect to the axis of the gear being generated. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis); the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to revisit this type of generation-by-envelope process and to profitably use it to explore peculiar design layouts, in particular for the case of motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the possibility of involute helicoid profiles (beveloids) transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to the derivation of designs featuring insensitivity of the transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

scholarly journals ORGANIZATIONAL AND FUNCTIONAL FEATURES OF REGIONAL ELECTION CAMPAIGNS IN RUSSIA

2021 ◽  
Vol 5 (2) ◽  
pp. 179-185
Author(s):  
E.V. x E.V. Efanova
Keyword(s):  
Political Process ◽  
Election Campaigns ◽  
Electoral Process ◽  
Structural Element ◽  
Typical Structure ◽  
Political Actors ◽  
Electoral Campaigns ◽  
Election Process ◽  
Functional Features ◽  
The One

The article presents a structural and functional analysis of election campaigns in Russia. It is obvious that electoral campaigns of candidates are unfolding during the election period, which, through interaction with citizens, enlist their support and sympathy, which contributes to their achievement of the main goal - victory in the elections and, therefore, the seizure and retention of power. The election campaign, being a structural element of the electoral process, is a set of events carried out by various subjects of this process in order to win the election by attracting the votes of the electorate. In general, the electoral company, on the one hand, is a set of measures for organizing elections, regulated by law and carried out by election commissions, and, on the other, a set of actions of political actors involved in the electoral process. It was established that election campaigns have a typical structure, organizational features, political, administrative and socio-cultural characteristics at the federal and regional levels of the electoral process. Among the regional organizational and functional features of domestic election campaigns are: a high degree of intensity of the election process, the dependence of the success of regional election campaigns on the electoral activity of citizens, the orientation of candidates to the needs of the residents of the region, and a prompt response to criticism from the electoral community. The study of the features of the implementation of regional election campaigns is important for Russian reality, especially in the conditions of the ongoing formation and intensive development of the democratic political process in the Russian Federation at the present stage.

scholarly journals Selective trust in young children and distracted adults: halo-effects outweigh rational choices

2020 ◽  
Author(s):  
Jonas Hermes ◽  
Franziska Brugger ◽  
hannes rakoczy ◽  
Tanya Behne
Keyword(s):  
Young Children ◽  
Cognitive Strategies ◽  
Dual Process ◽  
Cognitive Resources ◽  
Older Children ◽  
Selective Trust ◽  
Rational Choices ◽  
Cognitive Foundations ◽  
The One ◽  
The Individual

Research has shown that young children are selective in whom they trust, for example, learning selectively from the previously more reliable sources. To explain what cognitive foundations this capacity may build upon, is has recently been proposed that children recruit different kinds of cognitive strategies. These may include, on the one hand, simple heuristics such as favoring the overall better protagonist or those who score high on a salient, accessible characteristic, and, on the other hand, more systematic and cognitively effortful strategies, e.g., taking into account the individual properties of a protagonist. Based on such dual-process account, the present studies investigated the prediction that the more systematic processes require cognitive resources and develop with age. Children and adults were familiarized with two protagonists: The strong-and-shy protagonist scored high on a highly accessible trait (strength), whereas the weak-and-extraverted protagonist scored high on a less accessible trait (extraversion). In test trials, participants chose between these two protagonists for strength- and extraversion-related tasks. The results were consistent with the prediction of the dual-process account: Older children, and adults under normal conditions, showed a pattern of systematic reasoning, selecting the protagonists with the relevant trait for a given task. Yet, younger children, and adults whose cognitive capacities were burdened with a secondary task, showed a pattern of heuristic reasoning, selecting the strong-and-shy protagonist not only in the strength tasks but often also in the extraversion tasks. This is the first piece of direct evidence for the applicability of a dual-process account on selective trust.

Henry James's Capricciosa: Christina Light in Roderick Hudson and The Princess Casamassima

PMLA ◽  
1960 ◽  
Vol 75 (3) ◽  
pp. 309-319 ◽  
Author(s):  
M. E. Grenander
Keyword(s):  
Twentieth Century ◽  
Revolutionary Movement ◽  
Critical Attention ◽  
The One ◽  
The Right ◽  
Short Essay ◽  
Train Of Thought ◽  
Special Case

In recent years, critical attention has focussed increasingly on The Princess Casamassima, Henry James's novel of the international revolutionary movement seething beneath the surface of society. The sad wisdom of the mid-twentieth century no longer finds incredible the plot earlier critics dismissed as footling melodrama; and with a recognition of its probability, students of James have undertaken a re-examination of the whole novel. Oddly enough, however, little attention has been paid to its reliance on Roderick Hudson, where the Princess Casamassima first appears. The one significant exception has been a short essay by Louise Bogan, though Christina's complexity and interest have attracted other writers. Yet Roderick Hudson deserves study for its own merits; and, as Miss Bogan has pointed out, the character of the Princess is difficult to interpret unless one also remembers her as Christina Light. It is not true, as Miss Bogan asserts (p. 472), that Christina is “the only figure [James] ever ‘revived’ and carried from one book to another,” for not only do Madame Grandoni and the Prince Casamassima share her transposition; the sculptor Gloriani, who makes his debut in Roderick Hudson, reappears in The Ambassadors. But it is true, as Cargill more accurately points out (p. 108), that “Christina is the only major [italics mine] character that James ever revived from an earlier work,” for he questioned the wisdom of indulging wholesale the writer's “revivalist impulse” to “go on with a character.” Hence Christina Light must have struck him as a very special case. He tells us that he felt, “toward the end of ‘Roderick,‘ that the Princess Casamassima had been launched, that, wound-up with the right silver key, she would go on a certain time by the motion communicated” (AN, p. 18). In the Preface to The Princess Casamassima he continues this train of thought: Christina Light, “extremely disponible” and knowing herself “striking, in the earlier connexion,… couldn't resign herself not to strike again” (AN, pp. 73, 74).

On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant

2009 ◽  
Vol 16 (4) ◽  
pp. 693-704
Author(s):  
Harun Karsli ◽  
Paulina Pych-Taberska
Keyword(s):  
Recent Result ◽  
Pointwise Convergence ◽  
Rates Of Convergence ◽  
Durrmeyer Operators ◽  
The One ◽  
Special Case ◽  
Appl Math ◽  
Bézier Variant

Abstract We consider the Bézier variant of Chlodovsky–Durrmeyer operators 𝐷𝑛,α for functions 𝑓 measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (𝐷𝑛,α 𝑓) (𝑥) at those 𝑥 > 0 at which the one-sided limits 𝑓(𝑥+), 𝑓(𝑥–) exist. In the special case α = 1 the recent result of [Ibikli, Karsli, J. Inequal. Pure Appl. Math. 6: 12, 2005] concerning the Chlodovsky–Durrmeyer operators 𝐷𝑛 is essentially improved and extended to more general classes of functions.

Form created by performance: Bartók's recording of his Improvisations op. 20

2007 ◽  
Vol 48 (1-2) ◽  
pp. 103-111
Author(s):  
Ron Atar
Keyword(s):  
Simple Structure ◽  
Folk Song ◽  
Personal Style ◽  
Performance Style ◽  
Current Article ◽  
The One ◽  
Folk Song Arrangements ◽  
Special Case

Abstract Bartók's “Continental” 1942 recording of Improvisations op. 20 provides us with invaluable insights into his aesthetics and nature. This is a special case study in which Bartók redesign the composition through his performance. In this rendition the simple structure of most of the eight pieces that construct the composition (alternations between arrangements of the Hungarian peasant songs and transitions section in between them), turn into temperamental micro-drama of associations, flowing without any hesitations from Bartók's mind to his fingers. The folk song arrangements are played in various performing styles, related directly to the written texture, while the transition sections played in more personal style. Here, in these transitional sections, Bartók the romantic, emotional pianist is revealed. These transitions are used by him as improvisatory pauses, used mainly for musical reflections dealing with his performance style of the preceded folk song arrangement or the one that follows. The current article introduces and examines some of the insights evoked by Bartók's recording of this composition.

Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

1999 ◽  
Vol 51 (5) ◽  
pp. 915-935 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Christoph Leuenberger
Keyword(s):  
Unit Circle ◽  
Complex Flow ◽  
One Dimensional ◽  
Holomorphic Motions ◽  
Strictly Convex ◽  
Fixed Domain ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
The One ◽  
Special Case

AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.

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