Quantum walks with an anisotropic coin I: spectral theory

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.Comment: 26 page

Generalized definition of time delay in scattering theory

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.Comment: 18 page

Time delay and Calabi invariant in classical scattering theory

We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H_0,H) on a symplectic manifold. As a by-product, we establish a classical version of the Eisenbud-Wigner formula of quantum mechanics. Using recent results of V. Buslaev and A. Pushnitski on the scattering matrix in Hamiltonian mechanics, we also obtain an explicit expression for the derivative of the Calabi invariant of the Poincar\'e scattering map. Our results are applied to dispersive Hamiltonians, to a classical particle in a tube and to Hamiltonians on the Poincar\'e ball.Comment: 22 page

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

The Use of Decision–Analytic Models in Atopic Eczema: A Systematic Review and Critical Appraisal

Objective: The objective of this systematic review was to identify and assess the quality of published economic decision–analytic models within atopic eczema against best practice guidelines, with the intention of informing future decision–analytic models within this condition. Methods: A systematic search of the following online databases was performed: MEDLINE, EMBASE, Cumulative Index to Nursing and Allied Health Literature (CINAHL), Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, Cochrane Database of Systematic Reviews, NHS Economic Evaluation Database, EconLit, Scopus, Health Technology Assessment, Cost-Effectiveness Analysis Registry and Web of Science. Papers were eligible for inclusion if they described a decision–analytic model evaluating both the costs and benefits associated with an intervention or prevention for atopic eczema. Data were extracted using a standardised form by two independent reviewers, whilst quality was assessed using the model-specific Philips criteria. Results: Twenty-four models were identified, evaluating either preventions (n = 12) or interventions (n = 12): 14 reported using a Markov modelling approach, four utilised decision trees and one a discrete event simulation, whilst five did not specify the approach. The majority, 22 studies, reported that the intervention was dominant or cost effective, given the assumptions and analytical perspective taken. Notably, the models tended to be short-term (16 used a time horizon of ≤1 year), often providing little justification for the limited time horizon chosen. The methodological and reporting quality of the studies was generally weak, with only seven studies fulfilling more than 50% of their applicable Philips criteria. Conclusions: This is the first systematic review of decision models in eczema. Whilst the majority of models reported favourable outcomes in terms of the cost effectiveness of the new intervention, the usefulness of these findings for decision-making is questionable. In particular, there is considerable scope for increasing the range of interventions evaluated, for improving modelling structures and reporting quality

Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition)

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. For example, a key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process versus those that measure fl ux through the autophagy pathway (i.e., the complete process including the amount and rate of cargo sequestered and degraded). In particular, a block in macroautophagy that results in autophagosome accumulation must be differentiated from stimuli that increase autophagic activity, defi ned as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (inmost higher eukaryotes and some protists such as Dictyostelium ) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the fi eld understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. It is worth emphasizing here that lysosomal digestion is a stage of autophagy and evaluating its competence is a crucial part of the evaluation of autophagic flux, or complete autophagy. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. Along these lines, because of the potential for pleiotropic effects due to blocking autophagy through genetic manipulation it is imperative to delete or knock down more than one autophagy-related gene. In addition, some individual Atg proteins, or groups of proteins, are involved in other cellular pathways so not all Atg proteins can be used as a specific marker for an autophagic process. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field

Quantum walks with an anisotropic coin I : spectral theory

International audienceWe perform the spectral analysis of the evolution operator U of quantum walks withan anisotropic coin, which include one-defect models, two-phase quantum walks, andtopological phase quantum walks as special cases. In particular, we determine theessential spectrum of U, we show the existence of locally U-smooth operators, weprove the discreteness of the eigenvalues of U outside the thresholds, and we provethe absence of singular continuous spectrum for U. Our analysis is based on newcommutator methods for unitary operators in a two-Hilbert spaces setting, which are ofindependent interest

Quantum walks with an anisotropic coin II : scattering theory

International audienceWe perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest