Bounding regions to plane steepest descent curves of quasi convex families

Two dimensional steepest descent curves (SDC) for a quasi convex family are considered; the problem of their extensions (with constraints) outside of a convex body $K$ is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on $K$. These regions are bounded by arcs of involutes of the boundary of $K$ and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self contracting sets (with opposite orientation) are considered, necessary and/or sufficients conditions for them to be subsets of a SDC are proved.Comment: 34 pages, 4 figure

Linked open graph: Browsing multiple SPARQL entry points to build your own LOD views

AbstractA number of accessible RDF stores are populating the linked open data world. The navigation on data reticular relationships is becoming every day more relevant. Several knowledge base present relevant links to common vocabularies while many others are going to be discovered increasing the reasoning capabilities of our knowledge base applications. In this paper, the Linked Open Graph, LOG, is presented. It is a web tool for collaborative browsing and navigation on multiple SPARQL entry points. The paper presented an overview of major problems to be addressed, a comparison with the state of the arts tools, and some details about the LOG graph computation to cope with high complexity of large Linked Open Dada graphs. The LOG.disit.org tool is also presented by means of a set of examples involving multiple RDF stores and putting in evidence the new provided features and advantages using dbPedia, Getty, Europeana, Geonames, etc. The LOG tool is free to be used, and it has been adopted, developed and/or improved in multiple projects: such as ECLAP for social media cultural heritage, Sii-Mobility for smart city, and ICARO for cloud ontology analysis, OSIM for competence/knowledge mining and analysis

Progettazione e Sviluppo di un Transpiler da Scratch/Snap! a Wiring/Arduino: il Progetto Smart T-Shirt come Caso di Studio

In questa tesi di laurea è affrontato il progetto e lo sviluppo di un transpiler (Snap2ino) in grado di convertire progetti (micromondi) realizzati attraverso il linguaggio e l'ambiente Snap!, in progetti basati sul framework Wiring, con riferimento al caricamento e all'esecuzione di questi sulla nota piattaforma a microcontrollore Arduino. Nato a partire dalle necessità sorte nel contesto del progetto Smart T-Shirt, per il quale sono trattati nella prima parte della tesi il contesto applicativo (Educational e progetto COGITO) e quello tecnologico (sistemi embedded programmabili), Snap2ino è sviluppato seguendo un'approccio incrementale e attraverso la realizzazione di due prototipi successivi. La versione attuale del transpiler, unitamente all'ambiente Snap!, fornisce un vero e proprio framework per lo sviluppo di qualsiasi progetto in ambito di sistemi embedded/IoT basati su Wiring, nel quale si voglia sfruttare la programmazione visuale a blocchi, con particolare riferimento al mondo making e degli atelier digitali e creativi. Tra le caratteristiche peculiari rispetto a soluzioni già esistenti (p.e. Snap4Arduino), che rendono il framework realizzato potenzialmente significativo per l'intera comunità internazionale, troviamo: la possibilità di definire i propri blocchi su Snap! e come questi debbano essere mappati con le effettive implementazioni per il dispositivo di destinazione, consentendo la definizione del proprio "linguaggio" e del proprio "livello di astrazione", nonché di estendere e personalizzare i blocchi predefiniti supportati dal framework; la possibilità di utilizzare librerie e codice Wiring esistenti, e i relativi sensori e attuatori, rendendo il framework quanto più possibile aperto; la possibilità di utilizzare il dispositivo programmato (Arduino) senza la necessità che questo sia collegato a un pc nel quale è in esecuzione Snap!; il supporto ad aspetti avanzati come la gestione degli eventi e l'esecuzione di task (script/Sprite) concorrenti

Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed

Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed