Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Points to consider for prioritizing clinical genetic testing services: a European consensus process oriented at accountability for reasonableness.

Given the cost constraints of the European health-care systems, criteria are needed to decide which genetic services to fund from the public budgets, if not all can be covered. To ensure that high-priority services are available equitably within and across the European countries, a shared set of prioritization criteria would be desirable. A decision process following the accountability for reasonableness framework was undertaken, including a multidisciplinary EuroGentest/PPPC-ESHG workshop to develop shared prioritization criteria. Resources are currently too limited to fund all the beneficial genetic testing services available in the next decade. Ethically and economically reflected prioritization criteria are needed. Prioritization should be based on considerations of medical benefit, health need and costs. Medical benefit includes evidence of benefit in terms of clinical benefit, benefit of information for important life decisions, benefit for other people apart from the person tested and the patient-specific likelihood of being affected by the condition tested for. It may be subject to a finite time window. Health need includes the severity of the condition tested for and its progression at the time of testing. Further discussion and better evidence is needed before clearly defined recommendations can be made or a prioritization algorithm proposed. To our knowledge, this is the first time a clinical society has initiated a decision process about health-care prioritization on a European level, following the principles of accountability for reasonableness. We provide points to consider to stimulate this debate across the EU and to serve as a reference for improving patient management.

Testausmenetelmien ja testauksen lähestymistapojen valintaperusteet kirjallisuudessa

Testaustapausten valitseminen on testauksessa tärkeää, koska kaikkia testaustapauksia ei voida testata aika- ja raharajoitteiden takia. Testaustapausten valintaan on paljon eri menetelmiä joista eniten esillä olevat ovat malleihin perustuva valinta, kombinaatiovalinta ja riskeihin perustuva valinta. Kaikkiin edellä mainittuihin menetelmiin testaustapaukset luodaan ohjelman spesifikaation perusteella. Malleihin perustuvassa menetelmässä käytetään hyväksi ohjelman toiminnasta olevia malleja, joista valitaan tärkeimmät testattavaksi. Kombinaatiotestauksessa testitapaukset on muodostettu ominaisuuspareina jolloin yhden parin testaamisesta päätellään kahden ominaisuuden toiminta. Kombinaatiotestaus on tehokas löytämään virheitä, jotka johtuvat yhdestä tai kahdesta tekijästä. Riskeihin perustuva testaus pyrkii arvioimaan ohjelman riskejä ja valitsemaan testitapaukset niiden perusteella. Kaikissa menetelmissä priorisointi on tärkeässä roolissa, jotta testauksesta saadaan riittävä luotettavuus ilman kustannusten nousua.

Social competence and loneliness during the school years - Issues in assessment, interrelations and intergenerational transmission

Väitöskirjassa tarkastellaan kouluikäisten lasten ja nuorten sosiaalisen kompetenssin ja yksinäisyyden mittaamista, yhteyksiä ja periytyvyyttä vanhemmilta heidän lapsilleen. Alakouluikäisten lasten tutkimusaineisto (n=985) koostuu lapsilta itseltään, heidän luokkatovereiltaan, opettajiltaan ja vanhemmiltaan vuosina 2000 - 2004 osana Merkitystä etsimässä – tutkimusprojektia (M. Vauras) kerätystä aineistosta. Mukana on itse-, toveri-, opettaja- ja vanhempien arviot lasten sosiaalisesta kompetenssista, seuranta-aineisto lasten yksinäisyydestä, opettajien arviot lasten motivationaalisesta orientaatiosta, standardoiduin testisarjoin arvioidut akateemiset taidot sekä lasten äitien ja isien arviot omasta yksinäisyydestään ja koetusta kyvykkyydestään toimia vanhempana. Yläkouluikäisten nuorten (n=386) aineisto koostuu vuosina 2006 – 2007 osana Sosioemotionaalinen oppiminen ja hyvinvointi yläkouluyhteisössä (P. M. Niemi) kerätystä nuorten yksinäisyyden, sosiaalisen ahdistuneisuuden ja sosiaalisen fobian seuranta-aineistosta. Mitattavuutta (päätavoite 1) tutkittiin erityisesti monitahoarviointien rakenteiden yhtenäisyyksiä, subjektiivisten arvioiden ajallista pysyvyyttä sekä mittareiden validiteettia ja reliabiliteettia testaamalla. Sosiaalisen kompetenssin ja yksinäisyyden keskinäisten yhteyksien lisäksi tarkasteltiin näiden yhteyttä alakoululaisten oppimiseen sekä yläkou¬lulaisten psykososiaaliseen hyvinvointiin (päätavoite 2). Kolmantena päätavoitteena oli selvittää yksinäisyyden mahdollista periytymistä vanhemmilta lapsille. Osana ensimmäistä päätavoitetta kehitettiin Monitahoarviointi sosiaalisesta kompetenssista (MASK) -arviointimenetelmä (artikkeli 1). Konfirmatorisen faktorianalyysin tulosten perusteella nelifaktorinen rakenne (prososiaalisuus sisältäen yhteistyötaidot ja empatiakyvyn sekä antisosiaalisuus sisältäen impulsiivisuuden ja häiritsevyyden) sopi sekä lasten itsensä, heidän luokkatovereidensa, opettajiensa että vanhempiensa tekemiin arviointeihin. Eri tahojen arviointien väliset korrelaatiot olivat tilastollisesti merkitseviä, joskin suhteellisen matalia, ts. eri tahojen näkökulmat lapsen sosiaalisesta kompetenssista ovat toisistaan eriäviä. Täten eri arvioitsijatahojen käyttäminen on kokonaisuuden tutkimisen kannalta tärkeää. Toisena mittaamiseen liittyvänä tavoitteena oli validoida Hozan, Bukowskin ja Beeryn (2000) sosiaalisen ja emotionaalisen yksinäisyyden mittari suomalaisille lapsille (artikkeli 3) ja nuorille (artikkeli 4) soveltuvaksi sekä tutkia, ovatko lasten ja nuorten arviot omasta yksinäisyydestään ajallisesti pysyviä. Alakoululaisten lasten osalta yksinäisyys, erityisesti sosiaalinen yksinäisyys osoittautui suhteellisen pysyväksi, mutta vahvistui entisestään yläkouluikäisten nuorten aineistoa tarkasteltaessa. Huomionarvoista sekä ala- että yläkoululaisten aineistoissa oli poikien kokema vahva emotionaalinen yksinäisyys. Molempien mittareiden osalta sekä validiteetti että reliabiliteetti todettiin hyväksyttäväksi ja niitä voidaan suositella lasten ja nuorten sosiaalisen kompetenssin ja yksinäisyyden arviointimenetelmiksi. Toisena päätavoitteena oli rakenneyhtälömallinnuksen keinoin tarkastella sosiaalisen kompetenssin ja yksinäisyyden yhteyksiä sekä keskenään (artikkelit 2 ja 3) että suhteessa lasten oppimiseen (artikkeli 2) ja nuorten psykososiaaliseen hyvinvointiin (artikkeli 4). Alakouluikäisten lasten osalta sosiaalinen kompetenssi oli yhteydessä pait¬si yksinäisyyteen myös opettajien oppilaistaan tekemiin motivationaalisen orientaation arvioihin sekä standardoiduin testien arvioituihin akateemisiin taitoihin. Yläkouluikäisten nuorten osalta yksinäisyys oli yhteydessä sosiaaliseen ahdistuneisuuteen ja sosiaaliseen fobiaan. Täten sosiaalisen kompetenssin voidaan katsoa olevan koululaisten hyvinvointia ja oppimista vahvistava, ja toisaalta yksinäisyyden nuorten psykososiaalista hyvinvointia heikentävä tekijä. Viimeisenä päätavoitteena mallinnettiin yksinäisyyden mahdollista periytyvyyttä. Ensimmäisessä vaiheessa periytyvyyttä tarkasteltiin koko perheen sisällä, vanhempien tai lasten sukupuolta erottelematta (artikkeli 2). Tässä rakenneyhtälömallissa vanhempien kokema yksinäisyys ennusti heikompaa kyvykkyydentunnetta vanhemmuudesta, joka edelleen ennusti lapsen heikompaa toveriarvioitua sosiaalista kompetenssia koulussa ja tätä kautta vahvempaa yksinäisyyden kokemusta. Toisessa mallissa eroteltiin äitien ja isien sekä tyttöjen ja poikien aineistot, jotta periytyvyyttä voitiin tarkastella äiti-tytär, äiti-poika, isä-tytär ja isä-poika dyadisuhteissa. Rakenneyhtälömallinnuksen tulosten perusteella sekä äitien että isien kokema yksinäisyys ennusti

Non-Commitment and Savings in Dynamic Risk-Sharing Contracts

We characterize the solution to a model of consumption smoothing using financing under non-commitment and savings. We show that, under certain conditions, these two different instruments complement each other perfectly. If the rate of time preference is equal to the interest rate on savings, perfect smoothing can be achieved in finite time. We also show that, when random revenues are generated by periodic investments in capital through a concave production function, the level of smoothing achieved through financial contracts can influence the productive investment efficiency. As long as financial contracts cannot achieve perfect smoothing, productive investment will be used as a complementary smoothing device.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

A unifying framework for metrics for aggregating the climate effect of different emissions

Multi-gas approaches to climate change policies require a metric establishing ‘equivalences’ among emissions of various species. Climate scientists and economists have proposed four kinds of such metrics and debated their relative merits. We present a unifying framework that clarifies the relationships among them. We show, as have previous authors, that the global warming potential (GWP), used in international law to compare emissions of greenhouse gases, is a special case of the global damage potential (GDP), assuming (1) a finite time horizon, (2) a zero discount rate, (3) constant atmospheric concentrations, and (4) impacts that are proportional to radiative forcing. Both the GWP and GDP follow naturally from a cost–benefit framing of the climate change issue. We show that the global temperature change potential (GTP) is a special case of the global cost potential (GCP), assuming a (slight) fall in the global temperature after the target is reached. We show how the four metrics should be generalized if there are intertemporal spillovers in abatement costs, distinguishing between private (e.g., capital stock turnover) and public (e.g., induced technological change) spillovers. Both the GTP and GCP follow naturally from a cost-effectiveness framing of the climate change issue. We also argue that if (1) damages are zero below a threshold and (2) infinitely large above a threshold, then cost-effectiveness analysis and cost–benefit analysis lead to identical results. Therefore, the GCP is a special case of the GDP. The UN Framework Convention on Climate Change uses the GWP, a simplified cost–benefit concept. The UNFCCC is framed around the ultimate goal of stabilizing greenhouse gas concentrations. Once a stabilization target has been agreed under the convention, implementation is clearly a cost-effectiveness problem. It would therefore be more consistent to use the GCP or its simplification, the GTP.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature I""(0) are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or ""by a finite number of operations""), it admits as corollary, under a continuity assumption, that all points of I""(0) are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

A new perspective on the PPP hypothesis

This paper the stastistical properties of the real exchange rates of G-5 countries for the Bretton-Woods peiod, and draw implications on the purchasing power parity (PPP) hypothesis. In contrast to most previous studies that consider only unit root and stationary process to describe the real exchange tae, this paper also considers two in-between processes, the locally persistent process ans the fractionally integrated process, to complement past studies. Seeking to be consistent with tha ample evidence of near unit in the real exchange rate movements very well. This finding implies that: 1) the real exchange movement is more persistent than the stationary case but less persistent than the unit root case; 2) the real exchange rate is non-stationary but the PPP reversion occurs and the PPP holds in the long run; 3) the real exchange rate does not exhibit the secular dependence of the fractional integration; 4) the real exchange rate evolves over time in a way that there is persistence over a range of time, but the effect of shocks will eventually disappear over time horizon longer than order O (nd), that is, at finite time horizon; 5) shocks dissipation is fasters than predicted by the fractional integracion, and the total sum of the effects of a unit innovation is finite, implying that a full PPP reversion occurs at finite horizons. These results may explain why pasrt empirical estudies could not provide a clear- conclusion on the real exchange rate processes and the PPP hypothesis.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.