Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic

Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution

A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.Comment: 16 pages, dedicated to J.S. Dowker, version to appear in International Journal of Modern Physics

CMV matrices in random matrix theory and integrable systems: a survey

We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.Comment: Based on a talk given at the Short Program on Random Matrices, Random Processes and Integrable Systems, CRM, Universite de Montreal, 200

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for Rational Mechanics and Analysis.} The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-017-1131-

The pestivirus N terminal protease N(pro) redistributes to mitochondria and peroxisomes suggesting new sites for regulation of IRF3 by N(pro.)

The N-terminal protease of pestiviruses, N(pro) is a unique viral protein, both because it is a distinct autoprotease that cleaves itself from the following polyprotein chain, and also because it binds and inactivates IRF3, a central regulator of interferon production. An important question remains the role of N(pro) in the inhibition of apoptosis. In this study, apoptotic signals induced by staurosporine, interferon, double stranded RNA, sodium arsenate and hydrogen peroxide were inhibited by expression of wild type N(pro), but not by mutant protein N(pro) C112R, which we show is less efficient at promoting degradation of IRF3, and led to the conclusion that N(pro) inhibits the stress-induced intrinsic mitochondrial pathway through inhibition of IRF3-dependent Bax activation. Both expression of N(pro) and infection with Bovine Viral Diarrhea Virus (BVDV) prevented Bax redistribution and mitochondrial fragmentation. Given the role played by signaling platforms during IRF3 activation, we have studied the subcellular distribution of N(pro) and we show that, in common with many other viral proteins, N(pro) targets mitochondria to inhibit apoptosis in response to cell stress. N(pro) itself not only relocated to mitochondria but in addition, both N(pro) and IRF3 associated with peroxisomes, with over 85% of N(pro) puncta co-distributing with PMP70, a marker for peroxisomes. In addition, peroxisomes containing N(pro) and IRF3 associated with ubiquitin. IRF3 was degraded, whereas N(pro) accumulated in response to cell stress. These results implicate mitochondria and peroxisomes as new sites for IRF3 regulation by N(pro), and highlight the role of these organelles in the anti-viral pathway

LGP2 plays a critical role in sensitizing mda-5 to activation by double-stranded RNA.

The DExD/H box RNA helicases retinoic acid-inducible gene-I (RIG-I) and melanoma differentiation associated gene-5 (mda-5) sense viral RNA in the cytoplasm of infected cells and activate signal transduction pathways that trigger the production of type I interferons (IFNs). Laboratory of genetics and physiology 2 (LGP2) is thought to influence IFN production by regulating the activity of RIG-I and mda-5, although its mechanism of action is not known and its function is controversial. Here we show that expression of LGP2 potentiates IFN induction by polyinosinic-polycytidylic acid [poly(I:C)], commonly used as a synthetic mimic of viral dsRNA, and that this is particularly significant at limited levels of the inducer. The observed enhancement is mediated through co-operation with mda-5, which depends upon LGP2 for maximal activation in response to poly(I:C). This co-operation is dependent upon dsRNA binding by LGP2, and the presence of helicase domain IV, both of which are required for LGP2 to interact with mda-5. In contrast, although RIG-I can also be activated by poly(I:C), LGP2 does not have the ability to enhance IFN induction by RIG-I, and instead acts as an inhibitor of RIG-I-dependent poly(I:C) signaling. Thus the level of LGP2 expression is a critical factor in determining the cellular sensitivity to induction by dsRNA, and this may be important for rapid activation of the IFN response at early times post-infection when the levels of inducer are low

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

A cluster randomised control trial to evaluate the effectiveness and cost-effectiveness of the Italian medicines use review (I-MUR) for asthma patients

Background The economic burden of asthma, which relates to the degree of control, is €5 billion annually in Italy. Pharmacists could help improve asthma control, reducing this burden. This study aimed to evaluate the effectiveness and cost-effectiveness of Medicines Use Reviews provided by community pharmacists in asthma. Methods This cluster randomised, multi-centre, controlled trial in adult patients with asthma was conducted in 15 of the 20 regions of Italy between September 2014 and July 2015. After stratification by region, community pharmacists were randomly allocated to group A (trained in and delivered the intervention at baseline) or B (training and delivery 3 months later), using computerised random number generation in blocks of 10. Each recruited up to five patients, with both groups followed for 9 months. The intervention consisted of a systematic, structured face-to-face consultation with a pharmacist, covering asthma symptoms, medicines used, attitude towards medicines and adherence, recording pharmacist-identified pharmaceutical care issues (PCIs). The primary outcome was asthma control, assessed using the Asthma-Control-Test (ACT) score (ACT ≥ 20 represents good control). Secondary outcomes were: number of active ingredients, adherence, cost-effectiveness compared with usual care. Although blinding was not possible for either pharmacists or patients, assessment of outcomes was conducted by researchers blind to group allocation. Results Numbers of pharmacists and patients enrolled were 283 (A = 136; B = 147) and 1263 (A = 600; B = 663), numbers completing were 201 (A = 97; B = 104) and 816 (A = 400; B = 416), respectively. Patients were similar in age and gender and 56.13% (458/816) had poor/partial asthma control. Pharmacists identified 1256 PCIs (mean 1.54/patient), mostly need for education, monitoring and potentially ineffective therapy. Median ACT score at baseline differed between groups (A = 19, B = 18; p < 0.01). Odds ratio for improved asthma control was 1.76 (95% CI 1.33–2.33) and number needed to treat 10 (95% CI 6–28). Number of active ingredients reduced by 7.9% post-intervention (p < 0.01). Adherence improved by 35.4% 3 months post-intervention and 40.0% at 6 months (p < 0.01). The probability of the intervention being more cost-effective than usual care was 100% at 9 months. Conclusions This community pharmacist-based intervention demonstrated both effectiveness and cost-effectiveness. It has since been implemented as the first community pharmacy cognitive service in Italy