Cointegration in functional autoregressive processes

This paper defines the class of $\mathcal{H}$-valued autoregressive (AR) processes with a unit root of finite type, where $\mathcal{H}$ is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order $d=1,2,\dots$. An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer $d$ and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and $(i)$ the order of integration, $(ii)$ the structure of the attractor space and the cointegrating space, $(iii)$ the expression of the cointegrating relations, and $(iv)$ the Triangular representation of the process. Except for the fact that the number of cointegrating relations that are integrated of order 0 is infinite, the representation of $\mathcal{H}$-valued ARs with a unit root of finite type coincides with that of usual finite dimensional VARs, which corresponds to the special case $\mathcal{H}=\mathbb{R}^p$

Inverting a matrix function around a singularity via local rank factorization

This paper proposes a recursive procedure, called the extended local rank factorization (elrf), that characterizes the order of the pole and the coefficients of the Laurent series representation of the inverse of a regular analytic matrix function around a given point. The elrf consists in performing a finite sequence of rank factorizations of matrices of nonincreasing dimension, at most equal to the dimension of the original matrix function. Each step of the sequence is associated with a reduced rank condition, while the termination of the elrf corresponds to a full rank condition; this last step reveals the order of the pole. The Laurent coefficients B n are calculated recursively as B_n = C n + sum_{k=1}^n D_k B_{n−k} , where C_n , D_k have simple closed form expressions in terms of the quantities generated by the elrf. It is also shown that the elrf characterizes the structure of Jordan pairs, Jordan chains, and the local Smith form. The procedure is easily cast in an algorithmic form, and a MATLAB implementation script is provided. It is further found that the elrf coincides with the complete reduction process (crp) in Avrachenkov, Haviv, and Howlett [SIAM J. Matrix Anal. Appl., 22 (2001), pp. 1175–1189]. Using this connection, the results on the elrf provide both an explicit recursive formula for B n implied by the crp, and the link between the crp and the structure of the local Smith form

Minimality of state space solutions of DSGE models and existence conditions for their VAR representation

Standard solution methods of DSGE models do not necessarily deliver minimal state space forms. When the ABCD form is non-minimal, the conditions in the literature are not necessary for the existence of a VAR representation of the observables. In this paper we present necessary and sufficient conditions that are valid in general, and hence can be applied to minimal and non-minimal ABCD forms. If the state space form is minimal, our conditions coincide with those in the literature. These results also clarify that it is possible to have unstable eigenvalues together with a (possibly finite) VAR representation of the observables.JRC.DDG.01-Econometrics and applied statistic

Intrinsic Lipschitz Graphs Within Carnot Groups

A Carnot group is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study the notions of intrinsic graphs and of intrinsic Lipschitz graphs within Carnot groups. Intrinsic Lipschitz graphs are the natural local analogue inside Carnot groups of Lipschitz submanifolds in Euclidean spaces, where \u201cnatural\u201d emphasizes that the notion depends only on the structure of the algebra. Intrinsic Lipschitz graphs unify different alternative approaches through Lipschitz parameterizations or level sets. We provide both geometric and analytic characterizations and a clarifying relation between these graphs and Rumin\u2019s complex of differential forms

Stochastic approach to hydraulic barrier design: an example in northeastern Italy

Volatile organic compounds, groundwater contamination, multi-layered aquifer syste

Spotting local environments in self-assembled monolayer-protected gold nanoparticles

Organic-inorganic (O-I) nanomaterials are versatile platforms for an incredible high number of applications, ranging from heterogeneous catalysis, molecular sensing, cell targeting, imaging, cancer diagnosis and therapy, just to name a few. Much of their potential stems from the unique control of organic environments around inorganic sites within a single O-I nanomaterial, which allows for new properties inaccessible using purely organic or inorganic materials. Structural and mechanistic characterization plays a key role in understanding and rationally designing such hybrid nanoconstructs. Here, we introduce a general methodology to identify and classify local (supra)molecular environments in an archetypal class of O-I nanomaterials, i.e. self-assembled monolayer-protected gold nanoparticles (SAM-AuNPs). By using an atomistic machine-learning guided workflow based on the Smooth Overlap of Atomic Positions (SOAP) descriptor, we analyze a collection of chemically different SAM-AuNPs, and detect and compare local environments in a way that is agnostic and automated, i.e. with no need of a-priori information and minimal user intervention. In addition, the computational results coupled with experimental electron spin resonance measurements prove that is possible to have more than one local environment inside SAMs, being thickness of the organic shell and solvation primary factors in determining number and nature of multiple co-existing environments. These indications are extended to complex mixed hydrophilic-hydrophobic SAMs. This work demonstrates that it is possible to spot out and compare local molecular environments in SAM-AuNPs exploiting atomistic machine-learning approaches, establishes ground rules to control them, and holds the potential for rational design of O-I nanomaterials instructed from data

Novel mutation in the ligand‐binding domain of the androgen receptor gene (1790p) associated with complete androgen insensitivity syndrome

Mutations in the X-linked androgen receptor (AR) gene cause androgen insensitivity syndrome (AIS), resulting in an impaired embryonic sex differentiation in 46,XY genetic men. Complete androgen insensitivity (CAIS) produces a female external phenotype, whereas cases with partial androgen insensitivity (PAIS) have various ambiguities of the genitalia. Mild androgen insensitivity (MAIS) is characterized by undermasculinization and gynecomastia. Here we describe a 2-month-old 46,XY female patient, with all of the characteristics of CAIS. Defects in testosterone (T) and dihydrotestosterone (DHT) synthesis were excluded. Sequencing of the AR gene showed the presence in exon 6 of a T to C transition in the second base of codon 790, nucleotide position 2369, causing a novel missense Leu790Pro mutation in the ligand-binding domain of the AR protein. The identification of a novel AR mutation in a girl with CAIS provides significant information due to the importance of missense mutations in the ligand-binding domain of the AR, which are able to induce functional abnormalities in the androgen binding capability, stabilization of active conformation, or interaction with coactivators

Renal function and volume of infants born with a very low birth-weight: a preliminary cross-sectional study.

AIM: The aim of our study was to compare the function and volumes of kidneys of very low birth-weight (VLBW) and of extremely low birth-weight (ELBW) infants at pre-school ages.PATIENTS AND METHODS: We did a revision of the neonatal records of infants born in our hospital that weighed < or =1500 g at birth. The children were divided into two groups according to their weight at birth: ELBW (<1000 g) and VLBW (1000-1500 g). At the age of 5.7 +/- 1.4 years, the children underwent clinical, laboratory and ultrasound renal assessments.RESULTS: Sixty-nine children fulfilled the requirements for the study. The rate of neonatal treatment with aminoglycosides was higher in ELBW preterms. Renal function parameters, i.e. estimated glomerular filtration rate and albuminuria, did not differ between the two groups of children. Urinary alpha1-microglobulin excretion was significantly higher and kidneys were significantly smaller in the ELBW group than in the VLBW group.CONCLUSION: No impairment or differences in renal parameters were found in pre-school children born ELBW compared with those born with VLBW, except for differences in kidney volume, renal cortical thickness and urinary alpha1-microglobulin excretion. Thus, patients born with ELBW would require a longer follow-up period