A large covariance matrix estimator under intermediate spikiness regimes

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such un-shrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when $n$ is at least $O(p^{\frac{3}{2}\delta})$, provided that the maximum number of non-zeros per row in the sparse component is $O(p^{\delta})$ with $\delta \leq \frac{1}{2}$. Consistent recovery is ensured if the latent eigenvalues scale to $p^{\alpha}$, $\alpha \in[0,1]$, while rank consistency is ensured if $\delta \leq \alpha$. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data

Dynamic Programming on Nominal Graphs

Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted) vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical) terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.Comment: In Proceedings GaM 2015, arXiv:1504.0244

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin

Network-Conscious π-calculus – A Model of Pastry

AbstractA peer-to-peer (p2p) system provides the networking substrate for the execution of distributed applications. It is made of peers that interact over an overlay network. Overlay networks are highly dynamic, as peers can join and leave at any time. Traditional process calculi, such as π-calculus, CCS and others, seem inadequate to capture these kinds of networks, their routing mechanisms, and to verify their properties. In order to model network architecture in a more explicit way, in [Ugo Montanari and Matteo Sammartino. Network conscious π-calculus: A concurrent semantics. ENTCS, 286:291–306, 2012; Matteo Sammartino. A Network-Aware Process Calculus for Global Computing and its Categorical Framework. PhD thesis, University of Pisa, 2013. available at http://www.di.unipi.it/~sammarti/publications/thesis.pdf; Ugo Montanari and Matteo Sammartino. A network-conscious π-calculus and its coalgebraic semantics. Theor. Comput. Sci., 546:188–224, 2014] we have introduced the Network Conscious π-calculus (NCPi), an extension of the π-calculus with names representing network nodes and links. In [Ugo Montanari and Matteo Sammartino. A network–conscious π-calculus and its coalgebraic semantics. Theor. Comput. Sci., 546:188–224, 2014] (a simpler version of) NCPi has been equipped with a coalgebraic operational models, along the lines of Fiore-Turi presheaf-based approach [Marcelo P. Fiore and Daniele Turi. Semantics of name and value passing. In LICS 2001, pages 93–104. IEEE Computer Society, 2001], and with an equivalent History Dependent Automaton [Ugo Montanari and Marco Pistore. Structured coalgebras and minimal hd-automata for the π-calculus. Theor. Comput. Sci., 340(3):539–576, 2005], i.e., an (often) finite-state automaton suitable for verification. In this paper we first give a brief account of these results. Then, our contribution is the sketch of a NCPi representation of the p2p architecture Pastry. In particular, we give models of its overlay network and of a Distributed Hash Table built on top of it, and we give evidence of their correctness by proving convergence of routing mechanisms

A bootstrap test to detect prominent Granger-causalities across frequencies

Granger-causality in the frequency domain is an emerging tool to analyze the causal relationship between two time series. We propose a bootstrap test on unconditional and conditional Granger-causality spectra, as well as on their difference, to catch particularly prominent causality cycles in relative terms. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. Our null hypothesis is that each causality or causality difference is equal to the median across frequencies computed on that process. In this way, we are able to disambiguate causalities which depart significantly from the median one obtained ignoring the causality structure. Our test shows power one as the process tends to non-stationarity, thus being more conservative than parametric alternatives. As an example, we infer about the relationship between money stock and GDP in the Euro Area via our approach, considering inflation, unemployment and interest rates as conditioning variables. We point out that during the period 1999-2017 the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at high frequencies

High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization

We propose a new estimator of the regression coefficients for a high-dimensional linear regression model, which is de rived by replacing the sample predictor covariance matrix in the OLS estimator with a different predictor covariance matrix estimate obtained by a nuclear norm plus l1 norm penalization. We call the estimator ALCE-reg. We make a direct theoretical comparison of the expected mean square error of ALCE-reg with OLS and RIDGE. We show in a sim ulation study that ALCE-reg is particularly effective when both the dimension and the sample size are large, due to its ability to find a good compromise between the large bias of shrinkage estimators (like RIDGE and LASSO) and the large variance of estimators conditioned by the sample predictor covariance matrix (like OLS and POET)

A network-conscious π-calculus and its coalgebraic semantics

Traditional process calculi usually abstract away from network details, modeling only communication over shared channels. They, however, seem inadequate to describe new network architectures, such as Software Defined Networks, where programs are allowed to manipulate the infrastructure. In this paper we present the Network Conscious @p-calculus ( NCPi), a proper extension of the @p-calculus with an explicit notion of network: network links and nodes are represented as names, in full analogy with ordinary @p-calculus names, and observations are routing paths through which data is transported. However, restricted links do not appear in the observations, which thus can possibly be as abstract as in the @p-calculus. Then we construct a presheaf-based coalgebraic semantics for NCPi along the lines of Turi-Plotkin's approach, by indexing processes with the network resources they use: we give a model for observational equivalence in this context, and we prove that it admits an equivalent nominal automaton (HD-automaton), suitable for verification. Finally, we give a concurrent semantics for NCPi where observations are multisets of routing paths. We show that bisimilarity for this semantics is a congruence, and this property holds also for the concurrent version of the @p-calculus

Two sides of the same coin: educational and professional pathway for surgical residents

Aim: To provide a review of medical malpractice cases ruled by the Italian Supreme Court with the aims at identifying lawsuits targeting involved with surgical residents. Material and methods: Legal cases ruled by the Italian Supreme Court, from September 2020 to October 2020, pertaining to medical claims involving surgical residents were examined, using the main online databases. Results: Of a total of eleven (n=11; 100%) cases identified, four (n= 4; 36,4%) cases addressed the standard of care pertaining to the surgical residents' medical activity. The legal reasoning of the Italian Supreme Court does not focus on the manual skill in the resident's medical performance, but rather on the choice to accept to treat the patient, regardless of the participation of the tutor. Conclusions: The performance of the surgical residents is made more difficult due to their peculiar nature, characterized by the complex interactions between the directives given by the tutor and the need to guarantee patients' needs

Palliative care and covid-19 pandemic between hospital-centric based approach and decentralisation of health services: a valuable opportunity to turn the corner?

Italy was the first Western EU country to have dealt with the severe effects of the widespread Covid-19 virus since the pandemic began. Many healthcare services were negatively affected, and the delivery of palliative care has been no exception. The Italian healthcare system has suffered more than others due to public spending cuts. The hospital-based approach has not allowed all patients to receive appropriate care. This situation was brought about not only by the pandemic emergency but mainly by pre-existing shortages due to the cut in financial resources before the Covid-19 pandemic. For countries similar to Italy, it is necessary to develop territorialised health care, decongestion hospitals, and strengthen the Third Sector, particularly the voluntary sector