A fractional spline collocation method for the fractional order logistic equation

We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method.We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method

A multiscale collocation method for fractional differential problems

We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown.We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.Comment: 15 page

Translating “Under the Sign of Invention”: Gilberto Gil’s Song Lyric Translation

The translation of song lyrics shares in the difficulties of constrained translation, as well as in the impossibilities of poetic translation. In Gilberto Gil’s adaptation of the song “I just called to say I love you” by Stevie Wonder, two translation procedures stand out: (1) to take broad semantic fields as translation units, and (2) to opt for cultural adaptation in terms of the translation’s poles of domesticating/foreignizing. The way Gil faces up to the challenges of the translation of the song is consistent with Haroldo de Campos ideas on transcreation.La traduction de chansons partage avec la traduction subordonnée les mêmes difficultés et, avec la traduction poétique, les mêmes impossibilités. Dans sa version de “I just called to say I love you” de Stevie Wonder, Gilberto Gil fait appel à deux procédés : d’une part, le découpage de larges champs sémantiques comme unités de traduction, et d’autre part, le choix délibéré d’une adaptation culturelle de la traduction. La manière dont Gilberto Gil traite les difficultés de la traduction de la chanson n’est pas sans évoquer les principes de la transcréation de Haroldo de Campos

Crystal structure of Hop2-Mnd1 and mechanistic insights into its role in meiotic recombination

In meiotic DNA recombination, the Hop2-Mnd1 complex promotes Dmc1-mediated single-stranded DNA (ssDNA) invasion into homologous chromosomes to form a synaptic complex by a yet-unclear mechanism. Here, the crystal structure of Hop2-Mnd1 reveals that it forms a curved rod-like structure consisting of three leucine zippers and two kinked junctions. One end of the rod is linked to two juxtaposed winged-helix domains, and the other end is capped by extra ?-helices to form a helical bundle-like structure. Deletion analysis shows that the helical bundle-like structure is sufficient for interacting with the Dmc1-ssDNA nucleofilament, and molecular modeling suggests that the curved rod could be accommodated into the helical groove of the nucleofilament. Remarkably, the winged-helix domains are juxtaposed at fixed relative orientation, and their binding to DNA is likely to perturb the base pairing according to molecular simulations. These findings allow us to propose a model explaining how Hop2-Mnd1 juxtaposes Dmc1-bound ssDNA with distorted recipient double-stranded DNA and thus facilitates strand invasion

Biological application of Compressed Sensing Tomography in the Scanning Electron Microscope

The three-dimensional tomographic reconstruction of a biological sample, namely collagen fibrils in human dermal tissue, was obtained from a set of projection-images acquired in the Scanning Electron Microscope. A tailored strategy for the transmission imaging mode was implemented in the microscope and proved effective in acquiring the projections needed for the tomographic reconstruction. Suitable projection alignment and Compressed Sensing formulation were used to overcome the limitations arising from the experimental acquisition strategy and to improve the reconstruction of the sample. The undetermined problem of structure reconstruction from a set of projections, limited in number and angular range, was indeed supported by exploiting the sparsity of the object projected in the electron microscopy images. In particular, the proposed system was able to preserve the reconstruction accuracy even in presence of a significant reduction of experimental projections

The European Green Deal: shaping environmentally friendly policies under Article 101 TFEU

In the light of the renewed general interest for environmental issues, resulting from the launch of the European Green Deal by President Von Der Leyen, the paper explores how the EU Commission could promote environmental considerations in the implementation of competition policies. More in detail, starting from the role currently played by environmental factors in the assessment of anticompetitive agreements, the paper will consider whether Article 101 TFEU, as it is formulated – read in the light of the Commission’s decisional practice and of the ECJ’s case law – would support a broader interpretation, according to which the importance of environment-related considerations would be increased, also in line with the expectations of President Von Der Leyen. For this purpose, the present analysis will be focused on the first and third paragraph of Article 101 TFEU, both already used in the past by the Commission – although on the basis of a different legal reasoning – in order to support the relevance of policy considerations (including those environment-related) within competition assessment. The results of such analysis will show that there is sufficient room for a change in the approach of the Commission, that could (and should) be followed also at national level. If such approach will effectively be adopted, the role played by environmental considerations in the implementation of competition policies could be immediately enhanced, without the need to wait for the adoption of a specific legislative act (or, even worse, for a Treaty amendment)