Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Effects of Acute Autonomic Modulation on Atrial Conduction Delay and Local Electrograms Duration in Paroxysmal Atrial Fibrillation

Slowed atrial conduction may contribute to reentry circuits and vulnerability for atrial fibrillation (AF). The autonomic nervous system (ANS) has modulating effects on electrophysiological properties. However, complex interactions of the ANS with the arrhythmogenic substrate make it difficult to understand the mechanisms underlying induction and maintenance of AF. AIM: To determine the effect of acute ANS modulation in atrial activation times in patients (P) with paroxysmal AF (PAF). METHODS AND RESULTS: 16P (9 men; 59±14years) with PAF, who underwent electrophysiological study before AF ablation, and 15P (7 men; 58±11years) with atrioventricular nodal reentry tachycardia, without documentation or induction of AF (control group). Each group included 7P with arterial hypertension but without underlying structural heart disease. The study was performed while off drugs. Multipolar catheters were placed at the high right atrium (HRA), right atrial appendage (RAA), coronary sinus (CS) and His bundle area (His). At baseline and with HRA pacing (600ms, shortest propagated S2) we measured: i) intra-atrial conduction time (IACT, between RAA and atrial deflection in the distal His), ii) inter-atrial conduction time (interACT, between RAA and distal CS), iii) left atrial activation time (LAAT, between atrial deflection in the distal His and distal CS), iv) bipolar electrogram duration at four atrial sites (RAA, His, proximal and distal CS). In the PAF group, measurements were also determined during handgrip and carotid sinus massage (CSM), and after pharmacological blockade of the ANS (ANSB). AF was induced by HRA programmed stimulation in 56% (self-limited - 6; sustained - 3), 68.8% (self-limited - 6; sustained - 5), and 50% (self-limited - 5; sustained - 3) of the P, in basal, during ANS maneuvers, and after ANSB, respectively (p=NS). IACT, interACT and LAAT significantly lengthened during HRA pacing in both groups (600ms, S2). P with PAF have longer IACT (p<0.05), a higher increase in both IACT, interACT (p<0.01) and electrograms duration (p<0.05) with S2, and more fragmented activity, compared with the control group. Atrial conduction times and electrograms duration were not significantly changed during ANS stimulation. Nevertheless, ANS maneuvers increased heterogeneity of the local electrograms duration. Also, P with sustained AF showed longer interACT and LAAT during CSM. CONCLUSION: Atrial conduction times, electrograms duration and fractionated activity are increased in PAF, suggesting a role for conduction delays in the arrhythmogenic substrate. Acute vagal stimulation is associated with prolonged interACT and LAAT in P with inducible sustained AF and ANS modulation may influence the heterogeneity of atrial electrograms duration.

Collateral, default penalties and infinite horizon equilibrium

Pascoa and Seghir (2009) noticed that when collateralized promises become subject to utility penalties on default, Ponzi schemes may occur. However, equilibrium exists in some interesting cases. Under low penalties, equilibrium exists if the collateral does not yield utility (for example, when it is a productive asset or a security). Equilibrium exists also under more severe penalties and collateral utility gains, when the promise or the collateral are nominal assets and the margin requirements are endogenous: relative inflation rates and margin coefficients can make the income effects dominate the penalty effects. An equilibrium refinement avoids no-trade equilibria with unduly repayment beliefs. Our refinement differs from the one used by Dubey, Geanakoplos and Shubik (2005) as it does not eliminate no trade equilibria whose low delivery rates are consistent with the propensity to default of agents that are on the verge of selling.

Measuring end-to-end delay in real-time auralisation systems

One of the major challenges in the development of an immersive system is handling the delay between the tracking of the user’s head position and the updated projection of a 3D image or auralised sound, also called end-to-end delay. Excessive end-to-end delay can result in the general decrement of the “feeling of presence”, the occurrence of motion sickness and poor performance in perception-action tasks. These latencies must be known in order to provide insights on the technological (hardware/software optimization) or psychophysical (recalibration sessions) strategies to deal with them. Our goal was to develop a new measurement method of end-to-end delay that is both precise and easily replicated. We used a Head and Torso simulator (HATS) as an auditory signal sensor, a fast response photo-sensor to detect a visual stimulus response from a Motion Capture System, and a voltage input trigger as real-time event. The HATS was mounted in a turntable which allowed us to precisely change the 3D sound relative to the head position. When the virtual sound source was at 90º azimuth, the correspondent HRTF would set all the intensity values to zero, at the same time a trigger would register the real-time event of turning the HATS 90º azimuth. Furthermore, with the HATS turned 90º to the left, the motion capture marker visualization would fell exactly in the photo-sensor receptor. This method allowed us to precisely measure the delay from tracking to displaying. Moreover, our results show that the method of tracking, its tracking frequency, and the rendering of the sound reflections are the main predictors of end-to-end delay.

Clinical Epidemiology of Buruli ulcer from Benin (2005-2013): effect of time-delay to diagnosis on clinical forms and severe phenotypes

Buruli Ulcer (BU) is a neglected infectious disease caused by Mycobacterium ulcerans that is responsible for severe necrotizing cutaneous lesions that may be associated with bone involvement. Clinical presentations of BU lesions are classically classified as papules, nodules, plaques and edematous infiltration, ulcer or osteomyelitis. Within these different clinical forms, lesions can be further classified as severe forms based on focality (multiple lesions), lesions' size (>15 cm diameter) or WHO Category (WHO Category 3 lesions). There are studies reporting an association between delay in seeking medical care and the development of ulcerative forms of BU or osteomyelitis, but the effect of time-delay on the emergence of lesions classified as severe has not been addressed. To address both issues, and in a cohort of laboratory-confirmed BU cases, 476 patients from a medical center in Allada, Benin, were studied. In this laboratory-confirmed cohort, we validated previous observations, demonstrating that time-delay is statistically related to the clinical form of BU. Indeed, for non-ulcerated forms (nodule, edema, and plaque) the median time-delay was 32.5 days (IQR 30.0-67.5), while for ulcerated forms it was 60 days (IQR 20.0-120.0) (p = 0.009), and for bone lesions, 365 days (IQR 228.0-548.0). On the other hand, we show here that time-delay is not associated with the more severe phenotypes of BU, such as multi-focal lesions (median 90 days; IQR 56-217.5; p = 0.09), larger lesions (diameter >15 cm) (median 60 days; IQR 30-120; p = 0.92) or category 3 WHO classification (median 60 days; IQR 30-150; p = 0.20), when compared with unifocal (median 60 days; IQR 30-90), small lesions (diameter =15 cm) (median 60 days; IQR 30-90), or WHO category 1+2 lesions (median 60 days; IQR 30-90), respectively. Our results demonstrate that after an initial period of progression towards ulceration or bone involvement, BU lesions become stable regarding size and focal/multi-focal progression. Therefore, in future studies on BU epidemiology, severe clinical forms should be systematically considered as distinct phenotypes of the same disease and thus subjected to specific risk factor investigation.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

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.

Delay and Haircuts in Sovereign Debt: Recovery and Sustainability

One of the striking aspects of recent sovereign debt restructurings is, conditional on default, delay length is positively correlated with the size of haircut. In this paper, we develop an incomplete information model of debt restructuring where the prospect of uncertain economic recovery and the signalling about sustainability concerns together generate multi-period delay. The results from our analysis show that there is a correlation between delay length and size of haircut. Such results are supported by evidence. We show that Pareto ranking of equilibria, conditional on default, can be altered once we take into account the ex ante incentive of sovereign debtor. We use our results to evaluate proposals advocated to ensure orderly resolution of sovereign debt crises.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Delay and Haircuts in Sovereign Debt: Recovery and Sustainability

One of the striking aspects of recent sovereign debt restructurings is, conditional on default, delay length is positively correlated with the size of "haircut", which is size of creditor losses. In this paper, we develop an incomplete information model of debt restructuring where the prospect of uncertain economic recovery and the signalling about sustainability concerns together generate multi-period delay. The results from our analysis show that there is a correlation between delay length and size of haircut. Such results are supported by evidence. We show that Pareto ranking of equilibria, conditional on default, can be altered once we take into account the ex ante incentive of sovereign debtor. We use our results to evaluate proposals advocated to ensure orderly resolution of sovereign debt crises.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

An algorithm for semi-infinite polynomial optimization

"Vegeu el resum a l'inici del document del fitxer adjunt."

Systematic evaluation of risk factors for diagnostic delay in inflammatory bowel disease.

The diagnosis of inflammatory bowel disease (IBD), comprising Crohn's disease (CD) and ulcerative colitis (UC), continues to present difficulties due to unspecific symptoms and limited test accuracies. We aimed to determine the diagnostic delay (time from first symptoms to IBD diagnosis) and to identify associated risk factors. A total of 1591 IBD patients (932 CD, 625 UC, 34 indeterminate colitis) from the Swiss IBD cohort study (SIBDCS) were evaluated. The SIBDCS collects data on a large sample of IBD patients from hospitals and private practice across Switzerland through physician and patient questionnaires. The primary outcome measure was diagnostic delay. Diagnostic delay in CD patients was significantly longer compared to UC patients (median 9 versus 4 months, P < 0.001). Seventy-five percent of CD patients were diagnosed within 24 months compared to 12 months for UC and 6 months for IC patients. Multivariate logistic regression identified age <40 years at diagnosis (odds ratio [OR] 2.15, P = 0.010) and ileal disease (OR 1.69, P = 0.025) as independent risk factors for long diagnostic delay in CD (>24 months). In UC patients, nonsteroidal antiinflammatory drug (NSAID intake (OR 1.75, P = 0.093) and male gender (OR 0.59, P = 0.079) were associated with long diagnostic delay (>12 months). Whereas the median delay for diagnosing CD, UC, and IC seems to be acceptable, there exists a long delay in a considerable proportion of CD patients. More public awareness work needs to be done in order to reduce patient and doctor delays in this target population.

Children Order Advisory Committee: Delay in Children Order Cases

Children Order Advisory Committee: Delay in Children Order Cases