Fractional conservation laws in optimal control theory

Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum, and the fractional derivative of the state variable.Comment: The original publication is available at http://www.springerlink.com Nonlinear Dynamic

Fecundity compensation and tolerance to a sterilizing pathogen in <em>Daphnia</em>

Hosts are armed with several lines of defence in the battle against parasites: they may prevent the establishment of infection, reduce parasite growth once infected or persevere through mechanisms that reduce the damage caused by infection, called tolerance. Studies on tolerance in animals have focused on mortality, and sterility tolerance has not been investigated experimentally. Here, we tested for genetic variation in the multiple steps of defence when the invertebrate Daphnia magna is infected with the sterilizing bacterial pathogen Pasteuria ramosa: anti-infection resistance, anti-growth resistance and the ability to tolerate sterilization once infected. When exposed to nine doses of a genetically diverse pathogen inoculum, six host genotypes varied in their average susceptibility to infection and in their parasite loads once infected. How host fecundity changed with increasing parasite loads did not vary between genotypes, indicating that there was no genetic variation for this measure of fecundity tolerance. However, genotypes differed in their level of fecundity compensation under infection, and we discuss how, by increasing host fitness without targeting parasite densities, fecundity compensation is consistent with the functional definition of tolerance. Such infection-induced life-history shifts are not traditionally considered to be part of the immune response, but may crucially reduce harm (in terms of fitness loss) caused by disease, and are a distinct source of selection on pathogens

Random Oracles in a Quantum World

The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore post-quantum secure. We conclude with a rich set of open problems in this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a related paper by Boneh and Zhandr

Low noise amplication of an optically carried microwave signal: application to atom interferometry

In this paper, we report a new scheme to amplify a microwave signal carried on a laser light at $\lambda$=852nm. The amplification is done via a semiconductor tapered amplifier and this scheme is used to drive stimulated Raman transitions in an atom interferometer. Sideband generation in the amplifier, due to self-phase and amplitude modulation, is investigated and characterized. We also demonstrate that the amplifier does not induce any significant phase-noise on the beating signal. Finally, the degradation of the performances of the interferometer due to the amplification process is shown to be negligible

Immunohistochemical detection of macrophage migration inhibitory factor in fetal and adult bovine epididymis: Release by the apocrine secretion mode?

Originally defined as a lymphokine inhibiting the random migration of macrophages, the macrophage migration inhibitory factor (MIF) is an important mediator of the host response to infection. Beyond its function as a classical cytokine, MIF is currently portrayed as a multifunctional protein with growth-regulating properties present in organ systems beyond immune cells. In previous studies, we detected substantial amounts of MIF in the rat epididymis and epididymal spermatozoa, where it appears to play a role during post-testicular sperm maturation and the acquisition of fertilization ability. To explore its presence in other species not yet examined in this respect, we extended the range of studies to the bull. Using a polyclonal antibody raised against MIF purified from bovine eye lenses, we detected MIF in the epithelium of the adult bovine epididymis with the basal cells representing a prominently stained cell type. A distinct accumulation of MIF at the apical cell pole of the epithelial cells and in membranous vesicles localized in the lumen of the epididynnal duct was obvious. In the fetal bovine epididymis, we also detected MIF in the epithelium, whereas MIF accumulation was evident at the apical cell surface and in apical protrusions. By immuno-electron microscopy of the adult bovine epididymis, we localized MIF in apical protrusions of the epithelial cells and in luminal membrane-bound vesicles that were found in close proximity to sperm cells. Although the precise origin of the MIF-containing vesicles remains to be delineated, our morphological observations support the hypothesis that they become detached from the apical surface of the epididymal epithelial cells. Additionally, an association of MIF with the outer dense fibers of luminal spermatozoa was demonstrated. Data obtained in this study suggest MIF release by an apocrine secretion mode in the bovine epididymis. Furthermore, MIF localized in the basal cells of the epithelium and in the connective tissue could be responsible for regulating the migration of macrophages in order to avoid contact of immune cells with spermatozoa that carry a wide range of potent antigens. Copyright (c) 2006 S. Karger AG, Basel

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

First-dose ChAdOx1 and BNT162b2 COVID-19 vaccines and thrombocytopenic, thromboembolic and hemorrhagic events in Scotland

Reports of ChAdOx1 vaccine–associated thrombocytopenia and vascular adverse events have led to some countries restricting its use. Using a national prospective cohort, we estimated associations between exposure to first-dose ChAdOx1 or BNT162b2 vaccination and hematological and vascular adverse events using a nested incident-matched case-control study and a confirmatory self-controlled case series (SCCS) analysis. An association was found between ChAdOx1 vaccination and idiopathic thrombocytopenic purpura (ITP) (0–27 d after vaccination; adjusted rate ratio (aRR) = 5.77, 95% confidence interval (CI), 2.41–13.83), with an estimated incidence of 1.13 (0.62–1.63) cases per 100,000 doses. An SCCS analysis confirmed that this was unlikely due to bias (RR = 1.98 (1.29–3.02)). There was also an increased risk for arterial thromboembolic events (aRR = 1.22, 1.12–1.34) 0–27 d after vaccination, with an SCCS RR of 0.97 (0.93–1.02). For hemorrhagic events 0–27 d after vaccination, the aRR was 1.48 (1.12–1.96), with an SCCS RR of 0.95 (0.82–1.11). A first dose of ChAdOx1 was found to be associated with small increased risks of ITP, with suggestive evidence of an increased risk of arterial thromboembolic and hemorrhagic events. The attenuation of effect found in the SCCS analysis means that there is the potential for overestimation of the reported results, which might indicate the presence of some residual confounding or confounding by indication. Public health authorities should inform their jurisdictions of these relatively small increased risks associated with ChAdOx1. No positive associations were seen between BNT162b2 and thrombocytopenic, thromboembolic and hemorrhagic events

On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio