From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

H\"older-continuous rough paths by Fourier normal ordering

We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). H\"older continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article \cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or \cite{Unt09ter} for a short survey in that case).Comment: 50 pages, 6 figure

Promised Land? Immigration, Religiosity, and Space in Southern California

This article looks at how immigrants and their supporters appropriate and use religious space and other public spaces for religious and socio-political purposes in Southern California. While the everyday living conditions of many immigrants, particularly the unauthorized Latino immigrants, force unto them an embodied disciplinarity that maintains spatialities of restricted citizenship, the public appropriations of space for and through religious practices allow for them -even if only momentarily -to express an embodied transgression. This practice in public space helps realize spaces of freedom and hope, however ephemerally. Potentially, these rehearsing exercises can help revert internalized disempowering subjectivities and create social empowerment. Negative stereotypes about immigrants held by the larger public can also be challenged through these spatial practices, as the public demonstrations make visible the invisible. We focus on “Posadas Without Borders” and “the New Sanctuary Movement,” considering both the role of progressive civic and religious institutions in supporting immigrants and the agency of the immigrants themselves. The theoretical analysis builds on concepts drawn from a conversation between geography and religious and theological studies. We use a triangulated methodological approach that includes observation and participant observation, content-analysis of multimedia, interviews, and intellectual advocacy for the immigrant movement. The cases discussed here show that progressive religious groups and coalitions can be important allies to progressive planners, geographers, and policy makers in advancing social and environmental justice for the disenfranchised. They also show that the theological underpinnings of such groups share a lot in common with planning epistemologies for the just city

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

EEG Biofeedback as a Treatment for Substance Use Disorders: Review, Rating of Efficacy, and Recommendations for Further Research

Electroencephalographic (EEG) biofeedback has been employed in substance use disorder (SUD) over the last three decades. The SUD is a complex series of disorders with frequent comorbidities and EEG abnormalities of several types. EEG biofeedback has been employed in conjunction with other therapies and may be useful in enhancing certain outcomes of therapy. Based on published clinical studies and employing efficacy criteria adapted by the Association for Applied Psychophysiology and Biofeedback and the International Society for Neurofeedback and Research, alpha theta training—either alone for alcoholism or in combination with beta training for stimulant and mixed substance abuse and combined with residential treatment programs, is probably efficacious. Considerations of further research design taking these factors into account are discussed and descriptions of contemporary research are given

The Study of Irregular Migration

AbstractThe study of irregular migration as a specific social phenomenon took off during the 70s in the US. Since then, the academic interest has continually grown and spread, first to Europe and, in the last years, to other regions worldwide. This interest can certainly be related to the increasing attention paid to the study of migrations more in general (Castles & Miller, 1993). The trend can be linked to those broad and complex social and economic changes, often subsumed under the concept of globalization. The specific focus on irregular migration, though gaining momentum throughout the 1980s, reached preeminent attention in the 1990s. On both sides of the Atlantic, the explosion of the so-called "migration crisis" (Zolberg & Benda, 2001) and the emergence of irregular migration as a widespread social fact raised the attention of public opinion and academics alike. Moreover, in recent years, what seemed at first to be an issue concerning only the high-income regions of the planet, now involves also medium and low-income ones, making irregular migration a truly global structural phenomenon (Cvajner & Sciortino, 2010a; Düvell, 2006)

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Irregular Migration Theories

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