Adapted complex tubes on the symplectization of pseudo-Hermitian manifolds

Let $(M,\omega)$ be a pseudo-Hermitian space of real dimension $2n+1$, that is \RManBase is a \CR-manifold of dimension $2n+1$ and $\omega$ is a contact form on $M$ giving the Levi distribution $HT(M)\subset TM$. Let $M^\omega\subset T^*M$ be the canonical symplectization of $(M,\omega)$ and $M$ be identified with the zero section of $M^\omega$. Then $M^\omega$ is a manifold of real dimension $2(n+1)$ which admit a canonical foliation by surfaces parametrized by $\mathbb{C}\ni t+i\sigma\mapsto \phi_p(t+i\sigma)=\sigma\omega_{g_t(p)}$, where p\inM is arbitrary and $g_t$ is the flow generated by the Reeb vector field associated to the contact form $\omega$. Let $J$ be an (integrable) complex structure defined in a neighbourhood $U$ of $M$ in $M^\omega$. We say that the pair $(U,J)$ is an {adapted complex tube} on $M^\omega$ if all the parametrizations $\phi_p(t+i\sigma)$ defined above are holomorphic on $\phi_p^{-1}(U)$. In this paper we prove that if $(U,J)$ is an adapted complex tube on $M^\omega$, then the real function $E$ on $M^\omega\subset T^*M$ defined by the condition $\alpha=E(\alpha)\omega_{\pi(\alpha)}$, for each $\alpha\in M^\omega$, is a canonical equation for $M$ which satisfies the homogeneous Monge-Amp\`ere equation $(dd^c E)^{n+1}=0$. We also prove that if $M$ and $\omega$ are real analytic then the symplectization $M^\omega$ admits an unique maximal adapted complex tube.Comment: 6 page

Cache-Oblivious Peeling of Random Hypergraphs

The computation of a peeling order in a randomly generated hypergraph is the most time-consuming step in a number of constructions, such as perfect hashing schemes, random $r$-SAT solvers, error-correcting codes, and approximate set encodings. While there exists a straightforward linear time algorithm, its poor I/O performance makes it impractical for hypergraphs whose size exceeds the available internal memory. We show how to reduce the computation of a peeling order to a small number of sequential scans and sorts, and analyze its I/O complexity in the cache-oblivious model. The resulting algorithm requires $O(\mathrm{sort}(n))$ I/Os and $O(n \log n)$ time to peel a random hypergraph with $n$ edges. We experimentally evaluate the performance of our implementation of this algorithm in a real-world scenario by using the construction of minimal perfect hash functions (MPHF) as our test case: our algorithm builds a MPHF of $7.6$ billion keys in less than $21$ hours on a single machine. The resulting data structure is both more space-efficient and faster than that obtained with the current state-of-the-art MPHF construction for large-scale key sets

Complex Gradient Systems

Let $M$ be a complex manifold of complex dimension $n+k$. We say that the functions $u_1,...s,u_k$ and the vector fields $\xi_1,...,\xi_k$ on $M$ form a \emph{complex gradient system} if $\xi_1,...,\xi_k,J\xi_1,...,J\xi_k$ are linearly independent at each point $p\in M$ and generate an integrable distribution of $TM$ of dimension $2k$ and $du_\alpha(\xi_\beta)=0$, \d^c\u_\alpha(\xi_\beta)=\delta_{\alpha\beta} for $\alpha,\beta=1,...,k$. We prove a Cauchy theorem for such complex gradient systems with initial data along a \CR-submanifold of type (\CRdim,\CRcodim). We also give a complete local characterization for the complex gradient systems which are \emph{holomorphic} and \emph{abelian}, which means that the vector fields $\xi_\alpha^c=\xi_\alpha-J\xi_\beta$, $\alpha=1,...,k$ are holomorphic and satisfy $[\xi_alpha^c,\bar{\xi_\beta^c}]=0$ for each $\alpha,\beta=1,...,k$.Comment: 17 page

Performance analysis of a common-rail Diesel engine fuelled with different blends of waste cooking oil and gasoil

An experimental campaign was performed to study the behavior of a common-rail Diesel engine in automotive configuration when it is fuelled with blends of Diesel fuel (DF) and waste cooking oil (WCO). In particular the tested fuels are: B20 blend, composed of 20% WCO and 80% DF; B50, composed of 50% WCO and 50% DF; WCO 100% and 100% DF. In order to fuel the engine with fuel having a similar viscosity, this quantity, together with density, has been meas-ured at temperature ranging from rom to about 80 °C. According to these measurements, before fuelling the engine B20 was heated up to 35 °C and B50 to 75 °C. An in-house software was developed to acquire the data elaborated by the electronic control unit. Results show the trend in torque and global efficiency at different gas pedal position (gpp) and different engine speed. The experiments show that larger discrepancies are measured at smaller gpp values, while at larger ones dif-ferences become smaller. A similar trend is noticed for engine global efficiency

Optimization of WAAM Deposition Patterns for T-crossing Features

AbstractAmong emerging additive manufacturing technologies for metallic components, WAAM (Wire and Arc Additive Manufacturing) is one of the most promising. It is an arc based technology characterized by high productivity, high energy efficiency and low raw material cost. Anyway, it has some drawbacks limiting its diffusion in the industry. One is the open issue about the layer deposition strategy that must be manually optimized in order to reduce as possible the residual stress and strains, efficiently matching the geometrical characteristics of the component to build and assure a constant height for each layer. This work deals with the definition of deposition paths for WAAM. The choice of a path must be carried out as a compromise between productivity and material usage efficiency. In the present paper, the process to select an optimized strategy for the manufacturing of T-crossing features will be shown

Compressed weighted de Bruijn graphs

We propose a new compressed representation for weighted de Bruijn graphs, which is based on the idea of delta-encoding the variations of k-mer abundances on a spanning branching of the graph. Our new data structure is likely to be of practical value: to give an idea, when combined with the compressed BOSS de Bruijn graph representation, it encodes the weighted de Bruijn graph of a 16x-covered DNA read-set (60M distinct k-mers, k = 28) within 4.15 bits per distinct k-mer and can answer abundance queries in about 60 microseconds on a standard machine. In contrast, state of the art tools declare a space usage of at least 30 bits per distinct k-mer for the same task, which is confirmed by our experiments. As a by-product of our new data structure, we exhibit efficient compressed data structures for answering partial sums on edge-weighted trees, which might be of independent interest