Generators and Bases for Monadic Closures

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To tackle this issue, a number of sub-classes of nondeterministic automata have been identified, all admitting canonical minimal representatives. In previous work, we have shown that such representatives can be recovered categorically in two steps. First, one constructs the minimal bialgebra accepting a given regular language, by closing the minimal coalgebra with additional algebraic structure over a monad. Second, one identifies canonical generators for the algebraic part of the bialgebra, to derive an equivalent coalgebra with side effects in a monad. In this paper, we further develop the general theory underlying these two steps. On the one hand, we show that deriving a minimal bialgebra from a minimal coalgebra can be realized by applying a monad on an appropriate category of subobjects. On the other hand, we explore the abstract theory of generators and bases for algebras over a monad

Nonlinear evolution PDEs in R^+ \times C^d: existence and uniqueness of solutions, asymptotic and Borel summability

We consider a system of $n$-th order nonlinear quasilinear partial differential equations of the form {\bf u}_t + \mathcal{P}(\partial_{\bf x}^{\bf j}){\bf u}+{\bf g} \left( {\bf x}, t, \{\partial_{\bf x}^{{\bf j}} {\bf u}\}) =0; {\bf {u}}({\bf x}, 0) = {\bf {u}}_I({\bf x}) with \mathbf{u}\in\CC^{r}, for $t\in (0,T)$ and large $|{\bf x}|$ in a poly-sector $S$ in $\mathbb{C}^d$ ($\partial_{\bf x}^{\bf j} \equiv \partial_{x_1}^{j_1} \partial_{x_2}^{j_2} ...\partial_{x_d}^{j_d}$ and $j_1+...+j_d\le n$). The principal part of the constant coefficient $n$-th order differential operator $\mathcal{P}$ is subject to a cone condition. The nonlinearity ${\bf g}$ and the functions \mb u_I and \mb u satisfy analyticity and decay assumptions in $S$.The paper shows existence and uniqueness of the solution of this problem and finds its asymptotic behavior for large $|\bf x|$. Under further regularity conditions on \mb g and \mb u_I which ensure the existence of a formal asymptotic series solution for large |\mb x| to the problem, we prove its Borel summability (and automatically its asymptoticity) to an actual solution \mb u.In special cases motivated by applications we show how the method can be adapted to obtain short-time existence, uniqueness and asymptotic behavior for small $t$,without size restriction on the space variable

Canonical Automata via Distributive Law Homomorphisms

The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the átomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor

Spatio-temporal variability of micro-, nano- and pico-phytoplankton in the Mediterranean Sea from satellite ocean colour data of SeaWiFS

Abstract. The seasonal and year-to-year variability of the phytoplankton size class (PSC) spatial distribution has been examined in the Mediterranean Sea by using the entire time series of Sea-viewing Wide Field-of-view Sensor (SeaWiFS) space observations (1998–2010). Daily maps of PSCs have been determined using an empirical model based on a synoptic relationship between surface chlorophyll a and diagnostic pigments referred to different taxonomic groups. The analysis of micro-, nano- and pico-phytoplankton satellite time series (1998–2010) describes, quantitatively, the algal assemblage structure over the basin and reveals that the main contribution to chlorophyll a in most of the Mediterranean Sea comes from the pico-phytoplankton component, especially in nutrient-poor environments. Regions with different and peculiar features are the Northwestern Mediterranean Sea, the Alborán Sea and several coastal areas, such as the North Adriatic Sea. In these areas, local interactions between physical and biological components modulate the composition of the three phytoplankton size classes. It results that, during the spring bloom season, micro-phytoplankton dominates in areas of intense vertical winter mixing and deep/intermediate water formation, while in coastal areas micro-phytoplankton dominates in all seasons because of the nutrient supply from the terrestrial inputs. In the Alborán Sea, where the Atlantic inflow modulates the nutrient availability, any predominance of one class over the other two has been observed. The nano-phytoplankton component instead remains widespread over the entire basin along the year, and its contribution to chlorophyll a is of the order of 30–40 %. The largest inter-annual signal occurs in the Northwestern Mediterranean Sea, driven by the year-to-year variation in intensity and extension of the spring bloom, followed by the Alborán Sea, in which the inter-annual variability is strongly modulated by the Atlantic inflow. In absence of sufficient in situ data of community composition, the satellite-based analysis demonstrated that pico-, nano- and micro-phytoplankton classes often coexist. The predominance of one group over the other ones is strongly dependent on the physical and biological processes occurring at the mesoscale. These processes directly influence the nutrient and light availability, which are the principal forcing for the algae growth

Platelet-rich plasma counteracts detrimental effect of high-glucose concentrations on mesenchymal stem cells from Bichat fat pad

Diabetic patients display increased risk of periodontitis and failure in bone augmentation procedures. Mesenchymal stem cells (MSCs) and platelet-rich plasma (PRP) represent a relevant advantage in tissue repair process and regenerative medicine. We isolated MSCs from Bichat's buccal fat pad (BFP) and measured the effects of glucose and PRP on cell number and osteogenic differentiation potential. Cells were cultured in the presence of 5.5-mM glucose (low glucose [LG]) or 25-mM glucose (high glucose [HG]). BFP–MSC number was significantly lower when cells were cultured in HG compared with those in LG. Following osteogenic differentiation procedures, calcium accumulation, alkaline phosphatase activity, and expression of osteogenic markers were significantly lower in HG compared with LG. Exposure of BFP–MSC to PRP significantly increased cell number and osteogenic differentiation potential, reaching comparable levels in LG and in HG. Thus, high-glucose concentrations impair BFP–MSC growth and osteogenic differentiation. However, these detrimental effects are largely counteracted by PRP

Middle to late Holocene environmental evolution of the Pisa coastal plain (Tuscany, Italy) and early human settlements

A cross-disciplinary (sedimentological, geochemical, micropalaeontological and archaeological) examination of 12 continuous cores, up to 20m long, integrated with stratigraphical, geomorphological and historical investigations, allows for reliable delineation of the middle-late Holocene environmental evolution in the Pisa old town area, with special emphasis on the Etruscan age transition. Depositional facies were identified through integration of sedimentological and micropalaeontological (benthic foraminifers, ostracods, phytoclasts and palynomorphs) data, while sediment dispersal patterns were reconstructed on the basis of geochemical analyses. Facies architecture was chronologically constrained by combined archaeological and radiocarbon dating. The turnaround from early Holocene, transgressive conditions to the ensuing (middle-late Holocene) phase of sea-level highstand is witnessed by a prominent shallowing-upward succession of lagoonal, paludal and then poorly drained floodplain deposits supplied by two river systems (Arno and Serchio). This 'regressive' trend, reflecting coastal progradation under nearly stable sea-level conditions, was interrupted by widespread swamp development close to the Iron-Etruscan age transition. The expansion of vast, low-lying paludal areas across the alluvial plain was mostly induced by the intricate, short-term evolution of the meandering Arno and Serchio river systems. These changes in the fluvial network, which occurred during a period of variable climate conditions, strongly influenced the early Etruscan culture (7th-5th century BC) in terms of human settlement and society behaviour. Conversely, a strong impact of human frequentation on depositional environments is observed at the transition to the Roman age (from the 1st century BC onwards), when the wetlands were drained and the modern alluvial plain started to form. The palaeoenvironmental reconstruction fits in with the original geographical descriptions mentioned in Strabo's Chronicles, and provides chronologically constrained data of fluvial evolution from the Pisa old town area. © 2013 Elsevier Ltd and INQUA

Ecoregions in the Mediterranean Sea Through the Reanalysis of Phytoplankton Functional Types and Carbon Fluxes

In this work we produced a long‐term reanalysis of the phytoplankton community structure in the Mediterranean Sea and used it to define ecoregions. These were based on the spatial variability of the phytoplankton type fractions and their influence on selected carbon fluxes. A regional ocean color product of four phytoplankton functional types (PFTs; diatoms, dinoflagellates, nanophytoplankton, and picophytoplankton) was assimilated into a coupled physical‐biogeochemical model of the Mediterranean Sea (Proudman Oceanographic Laboratory Coastal Ocean Modelling System‐European Regional Seas Ecosystem Model, POLCOMS–ERSEM) by using a 100‐member ensemble Kalman filter, in a reanalysis simulation for years 1998–2014. The reanalysis outperformed the reference simulation in representing the assimilated ocean color PFT fractions to total chlorophyll, although the skill for the ocean color PFT concentrations was not improved significantly. The reanalysis did not impact noticeably the reference simulation of not assimilated in situ observations, with the exception of a slight bias reduction for the situ PFT concentrations, and a deterioration of the phosphate simulation. We found that the Mediterranean Sea can be subdivided in three PFT‐based ecoregions, derived from the spatial variability of the PFT fraction dominance or relevance. Picophytoplankton dominates the largest part of open ocean waters; microphytoplankton dominates in a few, highly productive coastal spots near large‐river mouths; nanophytoplankton is relevant in intermediate‐productive coastal and Atlantic‐influenced waters. The trophic and carbon sedimentation efficiencies are highest in the microphytoplankton ecoregion and lowest in the picophytoplankton and nanophytoplankton ecoregions. The reanalysis and regionalization offer new perspectives on the variability of the structure and functioning of the phytoplankton community and related biogeochemical fluxes, with foreseeable applications in Blue Growth of the Mediterranean Sea

Fracture and migration in right atrium of a permanent venous central access system in a elderly patient: case report and literature review

Catheter dislocation and fracture with migration of central venous lines have been reported in the International literature. Catheter fracture with consequent migration has been observed in 0.5-3.0% and may either be consequent to catheter removal or it can occur spontane-ously. Our case report concerns the migration of a Hickman catheter connected to a venous port to the right atrium in a 61-year old patient. A literature up-to-date has been performed to assess the risk of port-a-cath positioning. The position of catheter tip is considered critical for the risk of migration, that is greater as higher the tip localization respect to the carina. The aim of our study is to underline the critical role of X-ray to visualize the exact location of the catheter tip, regard-less of the approach used for catheter positioning