On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

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

Convergence of multi-dimensional quantized SDESDE's

We quantize a multidimensional $SDE$ (in the Stratonovich sense) by solving the related system of $ODE$'s in which the $d$-dimensional Brownian motion has been replaced by the components of functional stationary quantizers. We make a connection with rough path theory to show that the solutions of the quantized solutions of the $ODE$ converge toward the solution of the $SDE$. On our way to this result we provide convergence rates of optimal quantizations toward the Brownian motion for $\frac 1q$-H\" older distance, $q>2$, in $L^p(\P)$.Comment: 43 page

Quantitative electroencephalography reveals different physiological profiles between benign and remitting-relapsing multiple sclerosis patients

<p>Abstract</p> <p>Background</p> <p>A possible method of finding physiological markers of multiple sclerosis (MS) is the application of EEG quantification (QEEG) of brain activity when the subject is stressed by the demands of a cognitive task. In particular, modulations of the spectral content that take place in the EEG of patients with multiple sclerosis remitting-relapsing (RRMS) and benign multiple sclerosis (BMS) during a visuo-spatial task need to be observed.</p> <p>Methods</p> <p>The sample consisted of 19 patients with RRMS, 10 with BMS, and 21 control subjects. All patients were free of medication and had not relapsed within the last month. The power spectral density (PSD) of different EEG bands was calculated by Fast-Fourier-Transformation (FFT), those analysed being delta, theta, alpha, beta and gamma. Z-transformation was performed to observe individual profiles in each experimental group for spectral modulations. Lastly, correlation analyses was performed between QEEG values and other variables from participants in the study (age, EDSS, years of evolution and cognitive performance).</p> <p>Results</p> <p>Nearly half (42%) the RRMS patients showed a statistically significant increase of two or more standard deviations (SD) compared to the control mean value for the beta-2 and gamma bands (F = 2.074, p = 0.004). These alterations were localized to the anterior regions of the right hemisphere, and bilaterally to the posterior areas of the scalp. None of the BMS patients or control subjects had values outside the range of ± 2 SD. There were no significant correlations between these values and the other variables analysed (age, EDSS, years of evolution or behavioural performance).</p> <p>Conclusion</p> <p>During the attentional processing, changes in the high EEG spectrum (beta-2 and gamma) in MS patients exhibit physiological alterations that are not normally detected by spontaneous EEG analysis. The different spectral pattern between pathological and controls groups could represent specific changes for the RRMS patients, indicative of compensatory mechanisms or cortical excitatory states representative of some phases during the RRMS course that are not present in the BMS group.</p

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

Quantitative EEG findings in patients with acute, brief depression combined with other fluctuating psychiatric symptoms: a controlled study from an acute psychiatric department

<p>Abstract</p> <p>Background</p> <p>Patients with brief depressive episodes and concurrent rapidly fluctuating psychiatric symptoms do not fit current diagnostic criteria and they can be difficult to diagnose and treat in an acute psychiatric setting. We wanted to study whether these patients had signs of more epileptic or organic brain dysfunction than patients with depression without additional symptomatology.</p> <p>Methods</p> <p>Sixteen acutely admitted patients diagnosed with a brief depressive episode as well as another concurrent psychiatric diagnosis were included. Sixteen patients with major depression served as controls. Three electroencephalographic studies (EEG) were visually interpreted and the background activity was also analysed with quantitative electroencephalography (QEEG).</p> <p>Results</p> <p>The group with brief depression and concurrent symptoms had multiple abnormal features in their standard EEG compared to patients with major depression, but they did not show significantly more epileptiform activity. They also had significantly higher temporal QEEG delta amplitude and interhemispheric temporal delta asymmetry.</p> <p>Conclusion</p> <p>Organic brain dysfunction may be involved in the pathogenesis of patients with brief depressive episodes mixed with rapidly fluctuating psychiatric symptoms. This subgroup of depressed patients should be investigated further in order to clarify the pathophysiology and to establish the optimal evaluation scheme and treatment in an acute psychiatric setting.</p

Increased Resting-State Functional Connectivity in Obese Adolescents; A Magnetoencephalographic Pilot Study

BACKGROUND: Obesity is not only associated with metabolic abnormalities, but also with cognitive dysfunction and changes in the central nervous system. The present pilot study was carried out to investigate functional connectivity in obese and non-obese adolescents using magnetoencephalography (MEG). METHODOLOGY/PRINCIPAL FINDINGS: Magnetoencephalographic recordings were performed in 11 obese (mean BMI 38.8+/-4.6 kg/m(2)) and 8 lean (mean BMI 21.0+/-1.5 kg/m(2)) female adolescents (age 12-19 years) during an eyes-closed resting-state condition. From these recordings, the synchronization likelihood (SL), a common method that estimates both linear and non-linear interdependencies between MEG signals, was calculated within and between brain regions, and within standard frequency bands (delta, theta, alpha1, alpha2, beta and gamma). The obese adolescents had increased synchronization in delta (0.5-4 Hz) and beta (13-30 Hz) frequency bands compared to lean controls (P(delta total) = 0.001; P(beta total) = 0.002). CONCLUSIONS/SIGNIFICANCE: This study identified increased resting-state functional connectivity in severe obese adolescents. Considering the importance of functional coupling between brain areas for cognitive functioning, the present findings strengthen the hypothesis that obesity may have a major impact on human brain function. The cause of the observed excessive synchronization is unknown, but might be related to disturbed motivational pathways, the recently demonstrated increase in white matter volume in obese subjects or altered metabolic processes like hyperinsulinemia. The question arises whether the changes in brain structure and communication are a dynamic process due to weight gain and whether these effects are reversible or not

The government of migrant mobs: Temporary divisible multiplicities in border zones

This article engages with the production and government of migrant multiplicities in border zones of Europe, arguing that the specificity of migrant multiplicities consists in their temporary and divisible character. It is argued that there are three different forms of migrant multiplicities: (1) the multiplicity produced due to migrants’ spatial proximity; (2) the virtual multiplicity generated through data; and (3) the visualized and narrated multiplicity that emerges from media portraits of the ‘spectacle’ of the arrivals of migrants. It is claimed that multiplicities are made to divide and partition the migrants and thus prevent the formation of a collective political subject. In the concluding section, the article deals with the ambivalent character of the term ‘the mob’, addressing the twofold dimension of migrant multiplicities: these are in fact generated by techniques of power, at the same time exceeding them and representing potential emerging political subjects