Global Gevrey hypoellipticity for the twisted Laplacian on forms

We study in this paper the global hypoellipticity property in the Gevrey category for the generalized twisted Laplacian on forms. Different from the 0-form case, where the twisted Laplacian is a scalar operator, this is a system of differential operators when acting on forms, each component operator being elliptic locally and degenerate globally. We obtain here the global hypoellipticity in anisotropic Gevrey space

On the local solvability of a class of degenerate second order operators with complex coefficients

We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one previously studied in Federico and Parmeggiani (CPDEs 2016, Vol. 41), in that in this paper we consider some cases of operators with complex coefficients that were not present in Federico and Parmeggiani. The class of operators considered here ideally encompasses classes of degenerate parabolic and Schrodinger type operators. We will give local solvability theorems. In general, one has L-2 local solvability, but also cases of local solvability with better Sobolev regularity will be presented

Experimentalismo versus Hermenéutica: G. Deleuze

It is difficult to place Deleuze’s philosophy within the hermeneutic paradigm that characterizes the philosophy of the second half of the XXth century, since he contrasted always the experimentation principle to the concepts of understanding and interpretation. Deleuze intended to forge his philosophy as experimental thought, as an alternative to the intents to establish everywhere ‘interpretation machines’. This paper thus seeks to sketch, the singularities of Deleuze’s experimentalism, from his practice as a historian of phi- losophy, to his project of a philosophical constructivism

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Motor proteins traffic regulation by supply-demand balance of resources

In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.Comment: 31 pages, 10 figure

Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport

We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We find three regimes for steady state transport, corresponding to the scale of the network, of individual segments or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram.Comment: 5 pages, 7 figure

Structured Optical Materials Controlled by Light

Materials of which the optical response is determined by their structure are of much interest both for their fundamental properties and applications. Examples range from simple gratings to photonic crystals. Obtaining control over the optical properties is of crucial importance in this context, and it is often attempted by electro-optical effect or by using magnetic fields. In this paper, we introduce the use of light to switch and tune the optical response of a structured material, exploiting a physical deformation induced by light itself. In this new strategy, light drives an elastic reshaping, which leads to different spectral properties and hence to a change in the optical response. This is made possible by the use of liquid crystalline networks structured by Direct Laser Writing. As a proof of concept, a grating structure with sub-millisecond time-response is demonstrated for optical beam steering exploiting an optically induced reversible shape-change. Experimental observations are combined with finite-element modeling to understand the actuation process dynamics and to obtain information on how to tune the time and the power response of this technology. This optical beam steerer serves as an example for achieving full optical control of light in broad range of structured optical materials

Between the point of view and the point of being: the space of the stereoscopic tours

One of the most interesting features of the travel stereoviews series is not the three-dimensional effect but rather the intertwined outcome of realism and \u201cbeing-thereness\u201d for the early-20th-century armchair traveler\u2019s experience. On the set of Italy through the Stereoscope, the viewer\u2019s \u201cpath of the gaze\u201d was a novelty compared to with 2D photographs and stereoviews. The Underwood & Underwood publishing company created a stereoscopic multimodal tour to improve the impression of realism with a proprioceptive perception of the scene. The procedure of textual d\ue9brayage, the description of the experience as it is happening here and now, the direction of the viewer\u2019s gaze with a narrative itinerary, the changing of the visual convergence along with the variation of the points of attention: All of these elements fostered a synesthesia for the spectator. The result is immersion in an explorable space between the \u201cpoint of view\u201d (2D images) and the \u201cpoint of being\u201d (virtual reality)

Guardare Venezia: la citt\ue0 come dispositivo visuale

This essay develops a previous paper (Parmeggiani, 2010) with the issues of Venice as a visual apparatus (Foucault, 1980), of the tourists as fl\ue2neurs (Benjamin, 1991), of their sightseeing and dynamic gazing at the urban landscape, and of their searching for the backstage (Goffman, 1959) and looking for icons to achieve cultural capital (Bourdieu, 2011). It analyzes how tourists relate to icons of a globalized visual culture where Venice has produced many other simulacra (Baudrillard, 1994), and it focuses on how social activists have tried to remediate (Bolter & Grusin, 1999) some icons of Venice to protest against the mass tourism and the loss of local identity . The identity of the city, as represented by tourist images, is the result of a long cultural process that has taken place since the Renaissance and continues to exert its effects even today. The author uses visual sociology to analyze both a corpus of mass media images (photographs on websites, postcards, brochures, stock photography) and a visual documentation of the practices of tourists visiting Venice. Following this methodology, the article describes how pictures of the city have become one of the key drivers of mass tourism there, which is considered unsustainable by a portion of the resident community. The first part of this approach (analysis of the images) concerns the urban icons, those that become standard generative models for other visual representations. Some pictures are used to describe the genesis of the icons as well as their reproduction, distribution, and remediation throughout time. The second part of the methodology (analysis with the images) concerns some documentation (photographs and videos) observing the performances of tourists in Venice. Mass tourism is described by its social practices of looking, gazing, photographing, and acquiring images. The focus is on the cycle of the production and consumption of cultural capital and icons through visual practices. The article uses a selection of photographs as an integral part of research. Photographs, postcards, and artwork that have influenced the process of creating Venetian icons help in the investigation of the tourists\u2019 relationships with the urban space and its residents, and they also help to explain the visual identity of the Serenissima in our collective imagination