Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

On the critical periods of perturbed isochronous centers

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The Ideas Debate in International and European Studies: Towards a Cartography and Critical Assessment

The appeal to ideas as causal variables and/or constitutive features of political processes increasingly characterises political analysis. Yet, perhaps because of the pace of this ideational intrusion, too often ideas have simply been grafted onto pre-existing explanatory theories at precisely the point at which they seem to get into difficulties, with little or no consideration either of the status of such ideational variables or of the character or consistency of the resulting theoretical hybrid. This is particularly problematic for ideas are far from innocent variables – and can rarely, if ever, be incorporated seamlessly within existing explanatory and/or constitutive theories without ontological and epistemological consequence. We contend that this tendency along with the limitations of the prevailing Humean conception of causality, and associated epistemological polemic between causal and constitutive logics, continue to plague almost all of the literature that strives to accord an explanatory role to ideas. In trying to move beyond the current vogue for epistemological polemic, we argue that the incommensurability thesis between causal and constitutive logics is only credible in the context of a narrow, Humean, conception of causation. If we reject this in favour of a more inclusive (and ontologically realist) understanding then it is perfectly possible to chart the causal significance of constitutive processes and reconstrue the explanatory role of ideas as causally constitutive.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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Environmental Kuznets Curves for Carbon Emissions: A Critical Survey

The empirical finding of an inverse U-shaped relationship between per capita income and pollution, the so-called Environmental Kuznets Curve (EKC), suggests that as countries experience economic growth, environmental deterioration decelerates and thus becomes less of an issue. Focusing on the prime example of carbon emissions, the present article provides a critical review of the new econometric techniques that have questioned the baseline polynomial specification in the EKC literature. We discuss issues related to the functional form, heterogeneity, “spurious” regressions and spatial dependence to address whether and to what extent the EKC can be observed. Despite these new approaches, there is still no clear-cut evidence supporting the existence of the EKC for carbon emissions. JEL classifications: C20; Q32; Q50; O13 Keywords: Environmental Kuznets Curve; Carbon emissions; Functional form; Heterogeneity; “Spurious” regressions; Spatial dependence.Residential satisfaction is often used as a barometer to assess the performance of public policy and programmes designed to raise individuals' well-being. However, the fact that responses elicited from residents might be biased by subjective, non-observable factors casts doubt on whether these responses can be taken as trustable indicators of the individuals' housing situation. Emotional factors such as aspirations or expectations might affect individuals' cognitions of their true residential situation. To disentangle this puzzle, we investigated whether identical residential attributes can be perceived differently depending on tenure status. Our results indicate that tenure status is crucial not only in determining the level of housing satisfaction, but also regarding how dwellers perceive their housing characteristics. Keywords: Housing satisfaction, subjective well-being, homeownership. JEL classification: D1, R2.

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

A critical application of securitization theory: overcoming the normative dilemma of writing security

This article addresses the normative dilemma located within the application of `securitization,’ as a method of understanding the social construction of threats and security policies. Securitization as a theoretical and practical undertaking is being increasingly used by scholars and practitioners. This scholarly endeavour wishes to provide those wishing to engage with securitization with an alternative application of this theory; one which is sensitive to and self-reflective of the possible normative consequences of its employment. This article argues that discussing and analyzing securitization processes have normative implications, which is understood here to be the negative securitization of a referent. The negative securitization of a referent is asserted to be carried out through the unchallenged analysis of securitization processes which have emerged through relations of exclusion and power. It then offers a critical understanding and application of securitization studies as a way of overcoming the identified normative dilemma. First, it examines how the Copenhagen School’s formation of securitization theory gives rise to a normative dilemma, which is situated in the performative and symbolic power of security as a political invocation and theoretical concept. Second, it evaluates previous attempts to overcome the normative dilemma of securitization studies, outlining the obstacles that each individual proposal faces. Third, this article argues that the normative dilemma of applying securitization can be avoided by firstly, deconstructing the institutional power of security actors and dominant security subjectivities and secondly, by addressing countering or alternative approaches to security and incorporating different security subjectivities. Examples of the securitization of international terrorism and immigration are prominent throughout.

Higher education as formation of the self and citizenship: an ethnography of the University Students from Amman, Jordan

My interest in higher education and citizenship in the Middle East at large and in Jordan in particular is fostered by some of the reflections Eickelman proposed (1992). Being a quite recent phenomenon, intimately linked with the more general topic of state formation it seemed to me more suitable to study it in a little country with a recent history (a field study left almost unexplored until now as far as Jordan is concerned, to the best of my knowledge, since Antoun 1994 focuses on the migration as a quest for higher education). The process of state formation in Jordan is quite studied. I thus intended to study the higher education policies as an attempt both to create a national citizenry and more recently as a way of controlling the more problematic part of the population (youth, which constitutes more than the double of the population. See UNDP and Ministry of Planning 2000). How do the young students enter the university system, and in which way does this system work? How is this system designed, in order to retain social control of the students (since they are usually perceived to be a factor of social and political instability, as in Iran or in Egypt)? Is there any significant difference between different faculties? And if so, why? My conclusions at this stage are that the university system is an integral part of the survival of the regime. The system works quite well, and Jordan has one of the best educational position in the region. Yet there are important distinctions to be made: the access to the better faculties is socially selective while the less valued faculties are left to the poorer and less wealthy youth. This results in a different treatment of the students and of the courses that I analysed. In the better faculties the teaching standards are quite high, and the relationship between professors and students is almost on a same-level base, while in the less privileged faculties the opposite is true. Thus we can observe a concrete politics of divide et impera intended to split the youth in two. For the more privileged there are some freedoms, both within and outside classes, designed I guess at forging them as autonomous individuals. On the opposite the less privileged are kept under tight control, even if also these students are a privileged category among youth at large.

The ethnography of study abroad: what is study abroad as a cultural event?

Recent research in the field of study abroad shows that study abroad participation among all U.S. students increased 20% since 2001 and nearly 200,000 U.S. students currently go abroad each year. Additionally, about 8% of all undergraduate degree recipients receive part of their education abroad. Although quantitative studies have dominated research on study abroad, my research project calls for a qualitative approach since the goal is to understand what study abroad is as a cultural event, what authentic cultural immersion is, how program stakeholders understand and perceive cultural immersion, and how cultural immersion in programs can be improved. Following the tradition of ethnographic and case study approaches in study abroad research, my study also pivots on ethnography. As an ethnographer I collected data mainly through participant observation, semi-structured interviews, and document analysis. The study abroad participants were a group of undergraduate native speakers of English studying Spanish for seven weeks in Cádiz, a small costal city in southern Spain, as well as program coordinators, host community members, and professors. I also examined the specific program design features, particularly the in-class and out-of-class activities that students participated in. The goal was to understand if these features were conducive to authentic immersion in the language and culture. Eventually, I elaborated an ethnographic evaluation of the study abroad program and its design features suggesting improvements in order to enhance the significance and value of study abroad as a cultural event. Among other things, I discussed the difficulties that students had at the beginning of their sojourn to understand local people, get used to their host families’ small apartments, get adjusted to new schedules and eating habits, and venture out from the main group to individually explore the new social and cultural fabric and interact with the host community. The program evaluation revealed the need for carefully-designed pre-departure preparation sessions, pre-departure credit-bearing courses in intercultural communication, and additional language practice abroad and opportunities to come in contact with the local community through internships, volunteer or field work. My study gives an important contribution in study abroad research and education. It benefits students, teachers, and study abroad directors and coordinators in suggesting ideas on how to improve the program and optimize the students’ cultural experiences abroad. This study is also important because it investigated how US undergraduate learners studying the Spanish language and culture approach and perceive the study abroad experience in Spain.

Tropical cyclones as a critical phenomenon

It has been proposed that the number of tropical cyclones as a function of the energy they release is a decreasing power-law function, up to a characteristic energy cutoff determined by the spatial size of the ocean basin in which the storm occurs. This means that no characteristic scale exists for the energy of tropical cyclones, except for the finite-size effects induced by the boundaries of the basins. This has important implications for the physics of tropical cyclones. We discuss up to what point tropical cyclones are related to critical phenomena (in the same way as earthquakes, rainfall, etc.), providing a consistent picture of the energy balance in the system. Moreover, this perspective allows one to visualize more clearly the effects of global warming on tropical-cyclone occurrence.

Compositional amalgamations and balances: a critical approach

The amalgamation operation is frequently used to reduce the number of parts of compositional data but it is a non-linear operation in the simplex with the usual geometry,the Aitchison geometry. The concept of balances between groups, a particular coordinate system designed over binary partitions of the parts, could be an alternative to theamalgamation in some cases. In this work we discuss the proper application of bothconcepts using a real data set corresponding to behavioral measures of pregnant sows