Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Les temporalités des médicaments : trajectoires en soins palliatifs à l'hôpital

A partir d'un terrain ethnographique réalisé au sein d'une équipe mobile de soins palliatifs d'un hôpital universitaire, cette thèse de doctorat porte sur les médicaments dans le contexte de la fin de vie. Au carrefour d'une socio-anthropologie de la maladie grave, du mourir et des médicaments, elle interroge les rapports à la morphine, ainsi qu'à certains psychotropes et sédatifs utilisés en soins palliatifs. Entre temporalité vécue et temporalité institutionnelle, les manières d'investir le temps lorsqu'il est compté, y sont centrales. Dans une dimension microsociale, les résultats montrent que l'introduction de certains médicaments comme la morphine et l'entrée en scène d'une équipe mobile de soins palliatifs sont des points de repère et peuvent sonner comme une annonce, sorte de sanction, dans la trajectoire incertaine de la personne malade. En outre, les médicaments permettent d'agir sur « le temps qui reste » en plus de soulager les symptômes lorsque la maladie grave bascule en maladie incurable. Ils font l'objet d'usages détournés du but initial de soulagement des symptômes pour repousser, altérer ou accélérer la mort dans une perspective de maîtrise de sa fin de vie. Dans une dimension mésosociale, ce travail considère les médicaments à la base d'échanges entre groupements professionnels sur fond d'institutionnalisation des soins palliatifs par rapport à d'autres segments de la médecine actifs dans la gestion de la fin de vie. Dans une médecine caractérisée par l'incertitude et les décisions -avec une teinte toute particulière en Suisse où le suicide assisté est toléré - les médicaments en soins palliatifs peuvent être considérés comme des instruments de mort, qu'ils soient redoutés ou recherchés. Interrogeant les risques de reproduire un certain nombre d'inégalités de traitements à l'approche de la mort, qui s'accentuent dans un contexte de plus en plus favorable aux pratiques euthanasiques, ce travail se propose, en définitive, de discuter le temps contraint de la mort dans les institutions hospitalo-universitaires, entre acharnement et abstention thérapeutique.¦-¦Based on ethnographie fieldwork conducted within a palliative care mobile team in an academic hospital, this doctoral thesis focuses on medicines used in end of life contexts. At the intersection of a socio-anthropology of illness, dying and pharmaceuticals, the relations to morphine, as well as to some psychotropic and sedative drugs used in palliative care are questioned. Between "lived" experiences of temporality and institutional temporality, the ways by which actors invest time when it is counted, appeared to be central. In a microsocial dimension, the results showed that introducing drugs such as morphine, as well as the arrival of a palliative care mobile team, are landmarks and sound like an announcement, a sort of sanction, during the uncertain trajectory of the ill person. In addition, medicines can act on "the remaining time" when severe illness shifts into incurable illness. Indeed, medicines are being diverted from the initial aim of symptom relief in order to defer, alter or hasten death in a perspective of control over one's death. In a mesosocial dimension, pharmaceuticals are seen as core to professional exchanges and to palliative care institutionalisation compared to other active medical segments in end of life care. In a medical context characterised by uncertainty and decision-taking-with a special shade in Switzerland where assisted suicide is tolerated - palliative medicines can be seen as instruments of death, whether sought or feared. Questioning the risks of reproducing treatment inequalities at the approach of death, which are accentuated in a context increasingly favorable to euthanasia practices, this study aims, ultimately, at discussing death's constrained time in academic hospitals, between therapeutic intervention and abstention.

An interpretation of the deep seismic lines from the Penninic Alps of Valais (Switzerland)

The upper part of three deep seismic lines running across the Penninic Swiss Alps of Valais have been studied. Numerous reflectors illustrate the nappe structure of this internal part of the orogen. These reflectors, even at great depths (20-25 km), can be correlated with outcropping geological features and are most likely produced by lithological boundaries rather than by mylonites zones, which are hardly reflective in such an environment. Our interpretations, largely constrained by projections of the outcropping geology, have improved our knowledge of the deep structure of this segment of the Alpine belt, enhancing the importance of the backfolding and the crustal scale deformation phase which produced the Rawil-Valpelline depression and the Aar-Toce culmination. Furthermore we have here the possibility of correlating seismic patterns produced by ductile folds with the outcropping structures.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

The Dynamics of UK and US Inflation Expectations

This paper investigates the relationship between short term and long term in ation expectations in the US and the UK with a focus on iflation pass through (i.e. how changes in short term expectations affect long term expectations). An econometric methodology is used which allows us to uncover the relationship between in ation pass through and various explanatory variables. We relate our empirical results to theoretical models of anchored, contained and unmoored inflation expectations. For neither country do we find anchored or unmoored inflation expectations. For the US, contained inflation expectations are found. For the UK, our ndings are not consistent with the specifi =c model of contained inflation expectations presented here, but are consistent with a more broad view of expectations being constrained by the existence of an inflation target.

Electoral Uncertainty and the Deficit Bias in a New Keynesian Economy

Recent attempts to incorporate optimal fiscal policy into New Keynesian models subject to nominal inertia, have tended to assume that policy makers are benevolent and have access to a commitment technology. A separate literature, on the New Political Economy, has focused on real economies where there is strategic use of policy instruments in a world of political conflict. In this paper we combine these literatures and assume that policy is set in a New Keynesian economy by one of two policy makers facing electoral uncertainty (in terms of infrequent elections and an endogenous voting mechanism). The policy makers generally share the social welfare function, but differ in their preferences over fiscal expenditure (in its size and/or composition). Given the environment, policy shall be realistically constrained to be time-consistent. In a sticky-price economy, such heterogeneity gives rise to the possibility of one policy maker utilising (nominal) debt strategically to tie the hands of the other party, and influence the outcome of any future elections. This can give rise to a deficit bias, implying a sub-optimally high level of steady-state debt, and can also imply a sub-optimal response to shocks. The steady-state distortions and inflation bias this generates, combined with the volatility induced by the electoral cycle in a sticky-price environment, can significantly

Revealed cardinal preference

I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference.

A New Model Of Trend Inflation

This paper introduces a new model of trend (or underlying) inflation. In contrast to many earlier approaches, which allow for trend inflation to evolve according to a random walk, ours is a bounded model which ensures that trend inflation is constrained to lie in an interval. The bounds of this interval can either be fixed or estimated from the data. Our model also allows for a time-varying degree of persistence in the transitory component of inflation. The bounds placed on trend inflation mean that standard econometric methods for estimating linear Gaussian state space models cannot be used and we develop a posterior simulation algorithm for estimating the bounded trend inflation model. In an empirical exercise with CPI inflation we find the model to work well, yielding more sensible measures of trend inflation and forecasting better than popular alternatives such as the unobserved components stochastic volatility model.

Social evolution in the sweat bee Halictus scabiosae

The evolution of eusociality is one of the major evolutionary transitions of life on earth. For investigating the conditions and processes that are central to the origin of such integrated social organization, it is best to study organisms in which individuals have retained some flexibility in their reproductive strategies. Halictid bees are especially well suited as model organisms, because they show huge variation in social systems, both within and between species. In this thesis, I investigated female reproductive strategies in the primitively eusocial bee Halictus scabiosae, with a focus on the role of helpers, in order to get insight into the mechanisms governing the evolution and maintenance of eusociality. This species produces two broods per year. The females from the first brood can stay in the natal nest to help raise a second brood of males and gynes that become the next-generation foundresses in spring. We first compared the morphology of females from the two broods, as well as the nutrition they receive as larvae. Then we conducted a helper- removal experiment in the field to quantify the effects of the presence of helpers on colony survival and productivity. Finally, we reconstructed pedigree relationships of individuals using microsatellite markers in order to detect who reproduces in the nest and how much individuals drift between nests. We found that first brood females had a uniformly small size and low fat reserves, which may be caused by the restricted pollen and nectar provisions on which they develop. Colony survival and productivity was increased by the presence of a single helper, but the effect was small and mostly limited to small colonies. By inferring parentage within and across colonies, we could determine that females from the first brood rarely reproduce in their natal nests. However, foundresses are frequently replaced, and foundresses and females from the first brood occasionally move to and reproduce in foreign colonies. As a result, colonies often contain offspring from unrelated individuals, and the relatedness of females to the brood they rear is low. Overall, this thesis shows that the reproductive system of H. scabiosae is highly flexible. The production of helpers in the first brood is important for colony success and productivity, but there is a high colony failure rate and part of the first brood females drift and reproduce in foreign nests. Both foundresses and helpers appear to be constrained by harsh environmental conditions or social factors limiting reproduction and independent colony founding. - L'origine des insectes sociaux est un domaine fascinant pour la recherche. Pour comprendre les mécanismes et les conditions qui sont nécessaires pour l'évolution et le maintien de la vie en société, il est judicieux d'étudier des sociétés primitives d'insectes, où toutes les femelles ont conservé la capacité de se reproduire, même si leur rôle comportemental dans la colonie est d'aider sans se reproduire. Une des familles d'abeilles, les halictes, est idéale pour cette sorte de recherche, en raison de la grande variabilité dans leur comportement social. Dans cette thèse, j'ai étudié les stratégies reproductives des femelles de Halictus scabiosae pour mieux comprendre les mécanismes qui influencent l'évolution de la vie en société. Cette espèce produit deux cohortes de couvain par année. Les femelles du premier couvain restent souvent dans leur nid natal pour aider à élever le deuxième couvain, tandis que les femelles du deuxième couvain s'accouplent et hibernent pour devenir les nouvelles fondatrices au printemps suivant. Nous avons d'abord comparé la morphologie des femelles issues des deux couvains ainsi que leur nutrition au stade de larve. Puis, dans une expérience sur le terrain, nous avons quantifié l'apport d'une ouvrière pour la survie et la productivité de la colonie. Finalement, nous avons reconstruit des pedigrees en utilisant des marqueurs génétiques, pour savoir qui se reproduit dans la colonie et combien d'individus migrent entre colonies. Les résultats montrent que les femelles du premier couvain sont uniformément plus petites et plus maigres, ce qui indique que les fondatrices réduisent les provisions de nourriture pour leur premier couvain afin de les inciter à aider dans le nid au lieu de se reproduire indépendamment. Dans l'expérience sur le terrain, la survie et la productivité de la colonie augmentaient avec la présence d'une ouvrière additionnelle, mais l'effet était petit et limité aux petites colonies. Par la reconstruction de pedigrees, nous pouvions constater que les femelles du premier couvain pondent rarement dans leurs nids natals. Les fondatrices cependant sont souvent remplacées en cours de saison, et migrent fréquemment entre nids, tandis que les femelles du premier couvain pondent parfois des oeufs dans des nids étrangers. De ce fait, les colonies contiennent souvent des descendants d'individus étrangers, et la parenté génétique entre les femelles et le deuxième couvain est basse. Cette thèse démontre que le système reproductif de H. scabiosae est très flexible. La production d'ouvrières est importante pour la survie de la colonie et sa productivité, mais le taux d'échec est élevé et une partie des femelles du premier couvain migrent et pondent dans une colonie étrangère. Autant les fondatrices que les ouvrières semblent être contraintes par des conditions environnementales ou sociales qui limitent la reproduction et les nouvelles fondations de colonie. - Die Entstehung von sozialen Lebensformen ist eines der wichtigsten Entwicklungen in der Geschichte des Lebens. Um die Bedingungen oder Prozesse zu verstehen, welche bei der Entstehung und dem Erhalt von sozialen Merkmalen wichtig sind, sollte man Lebewesen untersuchen, welche je nach Umwelteinflüßen ihr soziales Verhalten flexibel ändern können. Furchenbienen (Halictidae) gehören dazu. Diese weisen nämlich ein breites Spektrum verschiedener sozialer Organisationsformen auf, oftmals sogar innerhalb der einzelnen Arten. In meiner Doktorarbeit befasste ich mich mit den Fortpflanzungsstrategien der Weibchen der Skabiosen-Furchenbiene Halictus scabiosae. Diese Art produziert zwei Brüten pro Jahr. Die Weibchen der ersten Brut bleiben dabei meist als Arbeiterinnen in ihrem Geburtsnest, wohingegen die Weibchen der zweiten Brut nach der Paarung überwintern, um im nächsten Frühling neue Kolonien zu gründen. In einem ersten Schritt verglichen wir die beiden Brüten bezüglich der Grösse und der Fettreserven der Weibchen sowie der Pollen-Nektar-Vorräte für die Larven. Dann bestimmten wir in einem Feldexperiment, wieviel eine zusätzliche Arbeiterin zum Überleben und zur Produktiviät der Kolonie beiträgt. Schliesslich ermittelten wir durch genetische Tests die Verwandtschaftsbeziehungen zwischen den Bienen, um herauszufinden, wer in den Kolonien tatsächlich die Eier legt und ob und wieviel die Bienen zwischen verschiedenen Nestern wandern. Wir stellten fest, dass die Weibchen von der ersten Brut einheitlich kleiner sind und weniger Fettreserven besitzen. Das weist daraufhin, dass die Nestgründerin die erste Brut unterernährt, um die Wahrscheinlichkeit zu erhöhen, dass diese Weibchen als Arbeiterinnen im Nest bleiben anstatt sich unabhängig fortzupflanzen. Schon eine einzelne zusätzliche Arbeiterin verbesserte die Überlebenschancen und Produktivität der Kolonie, der Effekt war allerdings klein und auf kleine Kolonien beschränkt. Die Verwandtschaftsanalysen zeigten, dass die Arbeiterinnen nur sehr selten ein Ei in ihr Geburtsnest legen. Erstaunlicherweise wanderten die Nestgründerinnen oft zwischen verschiedenen Nestern. Einige Weibchen der ersten Brut wanderten auch in ein fremdes Nest und produzierten dort Nachkommen. Diese Doktorarbeit zeigt, dass die Fortpflanzungsstrategien der Skabiosen-Furchenbiene tatsächlich sehr flexibel sind. Die Anwesenheit von Arbeiterinnen ist wichtig für das Überleben und die Produktivität der Kolonie. Die Misserfolgsraten bleiben jedoch hoch, und ein Teil der Weibchen der ersten Brut pflanzt sich in fremden Nestern fort. Sowohl die Nestgründerinnen als auch die Weibchen der ersten Brut scheinen durch Umweltsbedingungen oder durch soziale Faktoren in der Wahl ihrer Fortpflanzungs¬strategie eingeschränkt zu sein.

Pecuniary Externality through Credit Constraints: Two Examples without Uncertainty

This paper is a contribution to the growing literature on constrained inefficiencies in economies with financial frictions. The purpose is to present two simple examples, inspired by the stochastic models in Gersbach-Rochet (2012) and Lorenzoni (2008), of deterministic environments in which such inefficiencies arise through credit constraints. Common to both examples is a pecuniary externality, which operates through an asset price. In the second example, a simple transfer between two groups of agents can bring about a Pareto improvement. In a first best economy, there are no pecuniary externalities because marginal productivities are equalised. But when agents face credit constraints, there is a wedge between their marginal productivities and those of the non-credit-constrained agents. The wedge is the source of the pecuniary externality: economies with these kinds of imperfections in credit markets are not second-best efficient. This is akin to the constrained inefficiency of an economy with incomplete markets, as in Geanakoplos and Polemarchakis (1986).

Efficient Competition through Cheap Talk: Competing Auctions and Competitive Search without Ex Ante Price

We consider a frictional two-sided matching market in which one side uses public cheap talk announcements so as to attract the other side. We show that if the first-price auction is adopted as the trading protocol, then cheap talk can be perfectly informative, and the resulting market outcome is efficient, constrained only by search frictions. We also show that the performance of an alternative trading protocol in the cheap-talk environment depends on the level of price dispersion generated by the protocol: If a trading protocol compresses (spreads) the distribution of prices relative to the first-price auction, then an efficient fully revealing equilibrium always (never) exists. Our results identify the settings in which cheap talk can serve as an efficient competitive instrument, in the sense that the central insights from the literature on competing auctions and competitive search continue to hold unaltered even without ex ante price commitment.

On the real effects of financial pressure: Evidence from euro area firm-level employment during the recent financial crisis.

Using a large panel of unquoted euro-area firms over the period 2003-11, this paper examines the impact of financial pressure on firms’ employment. The analysis finds evidence that financial pressure negatively affects firms’ employment decisions. This effect is stronger during the 2007-2009 financial crisis, especially for firms in the periphery area compared to their counterparts in the core European economies. We also find that impact of financial pressure on employment is more potent for firms classified as financially constrained and operating in periphery economies during the financial crisis.

Dynamic Relational Contracts under Complete Information

This paper considers a long-term relationship between two agents who both undertake a costly action or investment that together produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Two cases are considered: (i) where agents are risk neutral and are subject to limited liability constraints and (ii) where agents are risk averse, have quasi-linear preferences in consumption and actions but where limited liability constraints do not bind. The question asked is how to structure the investments and division of the surplus over time so as to avoid expropriation. In the risk-neutral case, there may be an initial phase in which one agent overinvests and the other underinvests. However, both actions and surplus converge monotonically to a stationary state in which there is no overinvestment and surplus is at its maximum subject to the constraints. In the risk-averse case, there is no overinvestment. For this case, we establish that dynamics may or may not be monotonic depending on whether or not it is possible to sustain a first-best allocation. If the first-best allocation is not sustainable, then there is a trade-off between risk sharing and surplus maximization. In general, surplus will not be at its constrained maximum even in the long run.

The response of the external finance premium in Asian corporate bond markets to financial characteristics, financial constraints and two financial crises

Empirical investigation of the external finance premium has been conducted on the margin between internal finance and bank borrowing or equities but little attention has been given to corporate bonds, especially for the emerging Asian market. In this paper, we hypothesize that balance sheet indicators of creditworthiness could affect the external finance premium for bonds as they do for premia in other markets. Using bond-specific and firm-specific data for China, Hong Kong, Indonesia, Korea, Philippines, Singapore and Thailand during 1995-2009 we find that firms with better financial health face lower external finance premia in all countries. When we introduce firm-level heterogeneity, we show that financial variables appear to be both statistically and quantitatively more important for financially constrained firms. Finally, when we examine the effects of the 1997-98 Asian crisis and the 2007-09 global financial crisis, we find that the sensitivity of the premium is greater for constrained firms during the Asian crisis compared to other times.

Policy initiatives and firms’ access to external finance: Evidence from a panel of emerging Asian economies

This paper analyses the impact of policy initiatives co-ordinated by Asian national governments on firms' access to external finance, using a unique firm-level database of eight Asian countries- Hong Kong SAR, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan and Thailand over the period of 1996-2012. Using a difference-indifferences approach and controlling for firm-level and macroeconomic factors, the results show a significant impact of policy on firms' access to external finance. After splitting firms into constrained and unconstrained, using several criteria, the results document that unconstrained firms benefited significantly in obtaining external finance, compared to their constrained counterparts. Finally, we show that the increase in access to external finance after the policy initiative helped firms to raise their investment spending, especially for unconstrained firms.