Coalescence Point Research Articles

An Alternative Approach to the Institutional Economics of the Eurozone Crisis

I argue that the Eurozone crisis is neither a crisis of European sovereigns in the sense of governmental over-borrowing, nor a crisis of sovereign debt market over-lending. Rather, it is a function of the “sovereign debt market” institution itself. Crisis, I argue, is not an occurrence, but an element fulfilling a precise technical function within this institution. It ensures the possibility of designating — in the market’s day-to-day mechanisms rather than analytical hindsight — normal (tranquil, undisturbed) market functioning. To show this, I propose an alternative view on the institutional economics of sovereign debt markets. First, I engage literature on the emergent qualities of the institutions “market” and “firm” in product markets, concluding that the point of coalescence for markets is the approximation of an optimal observation of consumer tastes. I then examine the specific institution “financial markets,” where the optimal observation of economic fundamentals is decisive. For the specific sub-institution “sovereign debt market,” I conclude that the fundamentals in question — country fundamentals — oscillate between a status of observable fundamentals outside of markets and operationalized fundamentals influenced by market movements. This, in turn, allows me to argue that the specific case of the Eurozone crisis is due to neither of the two causes mentioned above. Rather, the notion of “crisis” takes on a technical sense within the market structure, guaranteeing the separation of herd behavior and isomorphic behavior on European sovereign debt markets. By the same token, the so-called Eurozone crisis ceases to be a crisis in the conventional sense.

Heritage and Community Regeneration in Northern Ireland: Finding Points of Coalescence in the Development Planning Process

ABSTRACTBringing heritage resources to the forefront in communities can serve to help heal long-standing divides with impacts not only in economic dimensions, but also social and cultural. It is an ironic turn—some of the heritage resources in Northern Ireland have been the site of intense and violent conflict over long periods of time—and now serve as focal points for bringing together divergent groups, helping heal divisions in communities. Seventeen communities throughout Northern Ireland are examined, gauging impacts and perceptions of community regeneration and redevelopment processes. Results provide insights for addressing lingering conflict and finding points of coalescence, with heritage playing a role in transformation.

Moments of the frequency spectrum of a splitting tree with neutral Poissonian mutations

We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the population counting process is a homogeneous, binary Crump-Mode-Jagers process. We suppose that mutations affect individuals independently at a constant rate θ during their lifetimes, under the infinite-alleles assumption: each new mutation gives a new type, called allele, to his carrier. We study the allele frequency spectrum which is the numbers A(k, t) of types represented by k alive individuals in the population at time t. Thanks to a new construction of the coalescent point process describing the genealogy of individuals in the splitting tree, we are able to compute recursively all joint factorial moments of (A(k, t)) k≥1. These moments allow us to give an elementary proof of the almost sure convergence of the frequency spectrum in a supercritical splitting tree.

Changes in Pore Structure of Metallurgical Cokes under Blast Furnace Conditions

Metallurgical cokes were subjected to gasification by CO–CO2–N2 gas with blast-furnace-like composition–temperature profile to 1673 K (1400 °C) and annealing under N2 at temperature up to 2273 K (2000 °C). Pore structure of cokes was examined using image analysis. Porosity and pore size were both enlarged under gasification and annealing conditions. The pore structure change during gasification was mainly a result of the Boudouard reaction; the pore structure development upon annealing was attributed to the reactions of mineral matters with carbon and further devolatilization. Annealing and gasification caused a decrease in average pore roundness, an increase in the fraction of low roundness pores and the increase of coalescence points in the pore area. The degradation of coke strength following reaction and annealing was characterized using tensile testing. Both gasification and annealing decreased the mechanical strength of coke. Degradation of more reactive cokes (cokes C and D) by gasification at 1673...

Communication: Three-electron coalescence points in two and three dimensions.

The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature of the wave function is characterized by the appearance of logarithmic terms, reminiscent of those that appear as both electrons approach the nucleus of the helium atom. The explicit form of these singularities is given in terms of the interelectronic distances for a doublet and two quartet states of three electrons in a harmonic well.

Radon emission evolution and rock failure

Previous experimental studies showed that the variation of Radon (Rn) emission is closely related to the development of rock deformation: Rn emission has a rapid increase with the growth of cracks and their surface areas (i.e. onset of fracture coalescence point), and reaches the maximum at rock failure. In this study, the stress level at the onset of fracture coalescence λ c is predicted with the renormalization group theory. It is assumed that rock is a strain-softening medium whose strength can be described by Weibull’s distribution. Result shows that λ c depends mainly on the homogeneity index or shape parameter m in the Weibull’s distribution for the rock. Both experimental and analytical results show that this point of rapid increase in Rn emission on the Rn-strain curve corresponds to the critical point on the stress–strain curve; for rock compression, the stress at this point is approximately 70–80 % of the peak strength. Hence a generalized crack damage threshold is proposed in the present study based on the characteristics of Rn emission during the loading process, for recognizing the critical point of rock fracture.

Permeability Evolution and Rock Brittle Failure

This paper reports an experimental study of the evolution of permeability during rock brittle failure and a theoretical analysis of rock critical stress level. It is assumed that the rock is a strain-softening medium whose strength can be described by Weibull’s distribution. Based on the two-dimensional renormalization group theory, it is found that the stress level λc (the ratio of the stress at the critical point to the peak stress) depends mainly on the homogeneity index or shape parameter m in the Weibull’s distribution for the rock. Experimental results show that the evolution of permeability is closely related to rock deformation stages: the permeability has a rapid increase with the growth of cracks and their surface areas (i.e., onset of fracture coalescence point), and reaches the maximum at rock failure. Both the experimental and analytical results show that this point of rapid increase in permeability on the permeability-pressure curve corresponds to the critical point on the stress-strain curve; for rock compression, the stress at this point is approximately 80% of the peak strength. Thus, monitoring the evolution of permeability may provide a new means of identifying the critical point of rock brittle fracture.

Singular analysis and coupled cluster theory.

The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.

The coalescent point process of multi-type branching trees

We define a multi-type coalescent point process of a general branching process with countably many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population providing types along ancestral lineages of all individuals in the standing population. We show that the coalescent process is a functional of a certain Markov chain defined by the planar embedding of the multi-type branching process.We use the multi-type coalescent process to determine statistical properties of the ancestral tree, such as the time to the most recent common ancestor (MRCA) of two consecutive individuals in the standing population, as well as of two individuals of the same type. These quantities are particularly simple to calculate for branching processes with a multi-type linear-fractional (LF) offspring distribution. We illustrate how an (a)symmetrical offspring distribution affects features of the ancestral tree in an example of a two-type LF branching processes.

General coalescence conditions for the exact wave functions. II. Higher-order relations for many-particle systems.

We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation.

The reconstructed tree in the lineage-based model of protracted speciation

A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree produced by a given model of diversification. Etienne and Rosindell in Syst Biol 61(2):204-213, (2012) proposed a lineage-based model of diversification, called protracted speciation, where species remain incipient during a random duration before turning good species, and showed that this can explain the slowdown in lineage accumulation observed in real phylogenies. However, they were unable to provide a general likelihood formula. Here, we present a likelihood formula for protracted speciation models, where rates at which species turn good or become extinct can depend both on their age and on time. Our only restrictive assumption is that speciation rate does not depend on species status. Our likelihood formula utilizes a new technique, based on the contour of the phylogenetic tree and first developed by Lambert in Ann Probab 38(1):348-395, (2010). We consider the reconstructed trees spanned by all extant species, by all good extant species, or by all representative species, which are either good extant species or incipient species representative of some good extinct species. Specifically, we prove that each of these trees is a coalescent point process, that is, a planar, ultrametric tree where the coalescence times between two consecutive tips are independent, identically distributed random variables. We characterize the common distribution of these coalescence times in some, biologically meaningful, special cases for which the likelihood reduces to an elegant analytical formula or becomes numerically tractable.

Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics

The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission, i.e. age of infection.Here we introduce an epidemiological model where infectives leave the epidemic, by either recovery or sampling, after some random time which may follow an arbitrary distribution.We derive an expression for the likelihood of the phylogenetic tree of sampled infectives under our general epidemiological model. The analytic concept developed in this paper will facilitate inference of past epidemiological dynamics and provide an analytical framework for performing very efficient simulations of phylogenetic trees under our model. The main idea of our analytic study is that the non-Markovian epidemiological model giving rise to phylogenetic trees growing vertically as time goes by can be represented by a Markovian “coalescent point process” growing horizontally by the sequential addition of pairs of coalescence and sampling times.As examples, we discuss two special cases of our general model, described in terms of influenza and HIV epidemics. Though phrased in epidemiological terms, our framework can also be used for instance to fit macroevolutionary models to phylogenies of extant and extinct species, accounting for general species lifetime distributions.

Study of planar defect filtering in InP grown on Si by epitaxial lateral overgrowth

InP thin films have been grown on InP/Si substrate by epitaxial lateral overgrowth (ELOG). The nature, origin and filtering of extended defects in ELOG layers grown from single and double openings in SiO2 mask have been investigated. Whereas ELOG layers grown from double openings occasionally exhibit threading dislocations (TDs) at certain points of coalescence, TDs are completely absent in ELOG from single openings. Furthermore, stacking faults (SFs) observed in ELOG layers grown from both opening types originate not from coalescence, but possibly from formation during early stages of ELOG or simply propagate from the seed layer through the mask openings. A model describing their propagation is devised and applied to the existent conditions, showing that SFs can effectively be filtered under certain conditions. ELOG layers grown from identical patterns on InP substrate contained no defects, indicating that the defect-forming mechanism is in any case not inherent to ELOG itself.

Birth–death models and coalescent point processes: The shape and probability of reconstructed phylogenies

Forward-in-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow “vertically” as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees (i.e., phylogenies of extant species). Alternatively, reconstructed trees can be modelled by coalescent point processes (CPPs), where trees grow “horizontally” by the sequential addition of vertical edges. Each new edge starts at some random speciation time and ends at the present time; speciation times are drawn from the same distribution independently. CPPs lead to extremely fast computation of tree likelihoods and simulation of reconstructed trees. Their topology always follows the uniform distribution on ranked tree shapes (URT).We characterize which forward-in-time models lead to URT reconstructed trees and among these, which lead to CPP reconstructed trees. We show that for any “asymmetric” diversification model in which speciation rates only depend on time and extinction rates only depend on time and on a non-heritable trait (e.g., age), the reconstructed tree is CPP, even if extant species are incompletely sampled. If rates additionally depend on the number of species, the reconstructed tree is (only) URT (but not CPP). We characterize the common distribution of speciation times in the CPP description, and discuss incomplete species sampling as well as three special model cases in detail: (1) the extinction rate does not depend on a trait; (2) rates do not depend on time; (3) mass extinctions may happen additionally at certain points in the past.

Effect of Dot Size on Exciton Binding Energy and Electron-Hole Recombination Probability in CdSe Quantum Dots.

Exciton binding energy and electron–hole recombination probability are presented as two important metrics for investigating effect of dot size on electron–hole interaction in CdSe quantum dots. Direct computation of electron–hole recombination probability is challenging because it requires an accurate mathematical description of the electron–hole wave function in the neighborhood of the electron–hole coalescence point. In this work, we address this challenge by solving the electron–hole Schrodinger equation using the electron–hole explicitly correlated Hartree–Fock (eh-XCHF) method. The calculations were performed for a series of CdSe clusters ranging from Cd20Se19 to Cd74608Se74837 that correspond to dot diameter range 1–20 nm. The calculated exciton binding energies and electron–hole recombination probabilities were found to decrease with increasing dot size. Both of these quantities were found to scale as Ddot–n with respect to the dot diameter D. One of the key insights from this study is that the electron–hole recombination probability decreases at a much faster rate than the exciton binding energy as a function of dot size. It was found that an increase in the dot size by a factor of 16.1, resulted in a decrease in the exciton binding energy and electron–hole recombination probability by a factor of 12.9 and 4.55 × 105, respectively.

General coalescence conditions for the exact wave functions: Higher-order relations for two-particle systems

We derived the necessary conditions that the non-relativistic time-independent exact wave functions for two-particle systems must satisfy at a coalescence (or cusp) point. Some of such necessary conditions are already known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In the present study, we extended and generalized those conditions, calling them generalized coalescence conditions (GCCs). Kato's CC and Rassolov and Chipman's CC were shown to be specific cases included in the GCCs. The GCCs can be applied not only to Coulombic systems but also to any systems where the interaction between two particles is represented in a power series of the inter-particle distance. We confirmed the correctness of our derivation of these GCCs by applying the free complement wave functions of a hydrogen atom in ground and excited states, a harmonic oscillator, and a system with an interacting potential of V = r.

‘Flip-flop’ and mergers-in-progress

During a merger-in-progress, occasionally one or two speakers will exhibit an unusual phonological pattern reminiscent offlip-flop(Labovet al. 1972). In such cases, the merging vowels appear to move past the point of coalescence in at least one phonetic dimension; difference is maintained but the vowel quality is opposite to the historical pattern on one or both dimensions. Flip-flop between thecotandcaughtvowels occurs for two speakers in a recent sample from San Francisco, California. The community shows robust change in progress toward a lower and frontercaughtvowel nucleus, and no change in apparent time forcot. Further analysis shows that this is leading to a change in apparent time toward merger, and that the rate of vowel convergence is stronger among Chinese Americans than European Americans. The two speakers who produce flip-flop are seen to represent a key transitional generation with respect to the ethnic identity of the neighborhood, where flip-flop may be but one linguistic consequence of a lifetime of active negotiation between conflicting local meanings. The analysis suggests that ethnographic detail and attention to individual outliers allows for more comprehensive models of the range of phenomena associated with vowel mergers.

Coalescence and growth of two coplanar short cracks in AA7050-T7451 aluminium alloys

Quantitative fractography was used to study fatigue test specimens (AA7050-T7451) with short surface cracks to determine their interaction and coalescence. Methods for predicting the coalescence of cracks described by ASME, BSI PD6493 and Iida were compared with the present experimental results. An improved method was developed to predict the coalescence of two coplanar short cracks and subsequent growth as a single larger crack by including a period of crack growth deceleration at the point of coalescence as observed in the present experiments, which appeared to be associated with the development of a single, larger semi-elliptical shaped crack (i.e. a coalesced crack).

The coalescent point process of branching trees

We define a doubly infinite, monotone labeling of Bienaymé–Galton–Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process $(A_{i};i\ge1)$, where $A_{i}$ is the coalescence time between individuals $i$ and $i+1$. There is a Markov process of point measures $(B_{i};i\ge1)$ keeping track of more ancestral relationships, such that $A_{i}$ is also the first point mass of $B_{i}$. This process of point measures is also closely related to an inhomogeneous spine decomposition of the lineage of the first surviving particle in generation $h$ in a planar BGW tree conditioned to survive $h$ generations. The decomposition involves a point measure $\rho$ storing the number of subtrees on the right-hand side of the spine. Under appropriate conditions, we prove convergence of this point measure to a point measure on $\mathbb{R}_{+}$ associated with the limiting continuous-state branching (CSB) process. We prove the associated invariance principle for the coalescent point process, after we discretize the limiting CSB population by considering only points with coalescence times greater than $\varepsilon $. The limiting coalescent point process $(B^{\varepsilon}_{i};i\ge1)$ is the sequence of depths greater than $\varepsilon$ of the excursions of the height process below some fixed level. In the diffusion case, there are no multiple ancestries and (it is known that) the coalescent point process is a Poisson point process with an explicit intensity measure. We prove that in the general case the coalescent process with multiplicities $(B^{\varepsilon}_{i};i\ge1)$ is a Markov chain of point masses and we give an explicit formula for its transition function. The paper ends with two applications in the discrete case. Our results show that the sequence of $A_{i}$’s are i.i.d. when the offspring distribution is linear fractional. Also, the law of Yaglom’s quasi-stationary population size for subcritical BGW processes is disintegrated with respect to the time to most recent common ancestor of the whole population.

Application of parametric equations of motion to study the resonance coalescence in $\text{H}_{2}^{+}$H2+

Recently, occurrence of coalescence point was reported in H(2)(+) undergoing multiphoton dissociation in strong laser field. We have applied parametric equations of motion and smooth exterior scaling method to study the coalescence phenomenon of H(2)(+). The advantage of this method is that one can easily trace the different states that are changing as the field parameters change. It was reported earlier that in the parameter space, only two bound states coalesce [R. Lefebvre, O. Atabek, M. Sindelka, and N. Moiseyev, Phys. Rev. Lett. 103, 123003 (2009)]. However, it is found that increasing the accuracy of the calculation leads to the coalescence between resonance states originating from the bound and the continuum states. We have also reported many other coalescence points.