Nonlinear internal models for output regulation

In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which we have presented in the recent paper entitled "Limit Sets, Zero Dynamics, and Internal Models in the Problem of Nonlinear Output Regulation"

Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200

Cluster Dynamical Mean-Field Methods for d-wave Superconductors: the Role of Geometry

We compare the accuracy of two cluster extensions of Dynamical Mean-Field Theory in describing d-wave superconductors, using as a reference model a saddle-point t-J model which can be solved exactly in the thermodynamic limit and at the same time reasonably describes the properties of high-temperature superconductors. The two methods are Cellular Dynamical Mean-Field Theory, which is based on a real-space perspective, and Dynamical Cluster Approximation, which enforces a momentum-space picture by imposing periodic boundary conditions on the cluster, as opposed to the open boundary conditions of the first method. We consider the scaling of the methods for large cluster size, but we also focus on the behavior for small clusters, such as those accessible by means of present techniques, with particular emphasis on the geometrical structure, which is definitely a relevant issue in small clusters.Comment: 11 pages, 10 figure

Rotationally-invariant slave-bosons for Strongly Correlated Superconductors

We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B {\bf 76}, 155102 (2007)], allows to study superconductivity in strongly correlated systems. We apply the formalism to a specific case of strongly correlated superconductivity, as that found in a multi-orbital Hubbard model for alkali-doped fullerides, where the superconducting pairing has phonic origin, yet it has been shown to be favored by strong correlation owing to the symmetry of the interaction. The method allows to treat on the same footing the strong correlation effects and the interorbital interactions driving superconductivity, and to capture the physics of strongly correlated superconductivity, in which the proximity to a Mott transition favors the superconducting phenomenon.Comment: 18 pages, 7 figure

The rare decay B --> X_s l^+ l^- to NNLL precision for arbitrary dilepton invariant mass

We present a new phenomenological analysis of the inclusive rare decay $B \to X_s \ell^+\ell^-$. In particular, we present the first calculation of the NNLL contributions due to the leading two-loop matrix elements, evaluated for arbitrary dilepton invariant mass. This allows to obtain the first NNLL estimates of the dilepton mass spectrum and the lepton forward-backward asymmetry in the high $M^2_{\ell^+ \ell^-}$ region, and to provide an independent check of previously published results in the low $M^2_{\ell^+ \ell^-}$ region. The numerical impact of these NNLL corrections in the high-mass region ($M^2_{\ell^+ \ell^-} > 14.4 GeV^2$) amounts to -13% in the integrated rate, and leads to a reduction of the scale uncertainty to $\pm 3$. The impact of non-perturbative contributions in this region is also discussed in detail.Comment: 40 pages, 12 figures. v2: extended phenomenological discussion; results unchanged; published versio

Flavour symmetries in the SMEFT

We analyse how $U(3)^5$ and $U(2)^5$ flavour symmetries act on the Standard Model Effective Field Theory, providing an organising principle to classify the large number of dimension-six operators involving fermion fields. A detailed counting of such operators, at different order in the breaking terms of both these symmetries, is presented. A brief discussion about possible deviations from these two reference cases, and a simple example of the usefulness of this classification scheme for high-$p_T$ analyses at the LHC, are also presented.Comment: 31 pages, 13 Table

Electromagnetism in nonleptonic weak interactions

We construct a low-energy effective field theory that permits the complete treatment of isospin-breaking effects in nonleptonic weak interactions to next-to-leading order. To this end, we enlarge the chiral Lagrangian describing strong and Delta S=1 weak interactions by including electromagnetic terms with the photon as additional dynamical degree of freedom. The complete and minimal list of local terms at next-to-leading order is given. We perform the one-loop renormalization at the level of the generating functional and specialize to K -> pi pi decays.Comment: 17 pages, 1 figure; 2 references added, final version for publication in Nucl. Phys.

Glycometabolic Alterations in Secondary Adrenal Insufficiency: Does Replacement Therapy Play a Role?

Secondary adrenal insufficiency (SAI) is a potentially life-threatening endocrine disorder due to an impairment of corticotropin (ACTH) secretion from any process affecting the hypothalamus or pituitary gland. ACTH deficit can be isolated or associated with other pituitary failures (hypopituitarism). An increased mortality due to cardiovascular, metabolic, and infectious diseases has been described in both primary and secondary adrenal insufficiency. However, few studies have provided compelling evidences on the underlying mechanism in SAI, because of the heterogeneity of the condition. Recently, some studies suggested that inappropriate glucocorticoid (GCs) replacement therapy, as for dose and/or timing of administration, may play a role. Hypertension, insulin resistance, weight gain, visceral obesity, increased body mass index, metabolic syndrome, impaired glucose tolerance, diabetes mellitus, dyslipidemia have all been associated with GC excess. These conditions are particularly significant when SAI coexists with other pituitary alterations, such as growth hormone deficiency, hypogonadism, and residual tumor. Novel regimen schemes and GC preparations have been introduced to improve compliance and better mimick endogenous cortisol rhythm. The controlled trials on the improved replacement therapies, albeit in the short-term, show some beneficial effects on cardiovascular risk, glucose metabolism, and quality of life. This review examines the current evidence from the available clinical trials investigating the association between different glucocorticoid replacement therapies (type, dose, frequency, and timing of treatment) and glycometabolic alterations in SAI