Multidimensional integration through Markovian sampling under steered function morphing: a physical guise from statistical mechanics

We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial appropriate profile. Thanks to an abstract reformulation of Jarzynski's equality applied in stochastic thermodynamics to evaluate the free-energy profiles along selected reaction coordinates via non-equilibrium transformations, it is possible to cast the original integral into the exponential average of the distribution of the pseudo-work (that we may term "computational work") involved in doing the function morphing, which is straightforwardly solved. Several tests illustrate the basic implementation of the idea, and show its performance in terms of computational time, accuracy and precision. The formulation for integrand functions with zeros and possible sign changes is also presented. It will be stressed that our usage of Jarzynski's equality shares similarities with a practice already known in statistics as Annealed Importance Sampling (AIS), when applied to computation of the normalizing constants of distributions. In a sense, here we dress the AIS with its "physical" counterpart borrowed from statistical mechanics.Comment: 3 figures Supplementary Material (pdf file named "JEMDI_SI.pdf"

Network geography: relations, interactions, scaling and spatial processes in GIS

This chapter argues that the representational basis of GIS largely avoidseven the most rudimentary distortions of Euclidean space as reflected, forexample, in the notion of the network. Processes acting on networks whichinvolve both short and longer term dynamics are often absent from GIscience. However a sea change is taking place in the way we view thegeography of natural and man-made systems. This is emphasising theirdynamics and the way they evolve from the bottom up, with networks anessential constituent of this decentralized paradigm. Here we will sketchthese developments, showing how ideas about graphs in terms of the waythey evolve as connected, self-organised structures reflected in theirscaling, are generating new and important views of geographical space.We argue that GI science must respond to such developments and needs tofind new forms of representation which enable both theory andapplications through software to be extended to embrace this new scienceof networks

Programming temporal morphing of self-actuated shells

Advances in shape-morphing materials, such as hydrogels, shape-memory polymers and light-responsive polymers have enabled prescribing self-directed deformations of initially flat geometries. However, most proposed solutions evolve towards a target geometry without considering time-dependent actuation paths. To achieve more complex geometries and avoid self-collisions, it is critical to encode a spatial and temporal shape evolution within the initially flat shell. Recent realizations of time-dependent morphing are limited to the actuation of few, discrete hinges and cannot form doubly curved surfaces. Here, we demonstrate a method for encoding temporal shape evolution in architected shells that assume complex shapes and doubly curved geometries. The shells are non-periodic tessellations of pre-stressed contractile unit cells that soften in water at rates prescribed locally by mesostructure geometry. The ensuing midplane contraction is coupled to the formation of encoded curvatures. We propose an inverse design tool based on a data-driven model for unit cells’ temporal responses

Programming temporal morphing of self-actuated shells

Advances in shape-morphing materials, such as hydrogels, shape-memory polymers and light-responsive polymers have enabled prescribing self-directed deformations of initially flat geometries. However, most proposed solutions evolve towards a target geometry without considering time-dependent actuation paths. To achieve more complex geometries and avoid self-collisions, it is critical to encode a spatial and temporal shape evolution within the initially flat shell. Recent realizations of time-dependent morphing are limited to the actuation of few, discrete hinges and cannot form doubly curved surfaces. Here, we demonstrate a method for encoding temporal shape evolution in architected shells that assume complex shapes and doubly curved geometries. The shells are non-periodic tessellations of pre-stressed contractile unit cells that soften in water at rates prescribed locally by mesostructure geometry. The ensuing midplane contraction is coupled to the formation of encoded curvatures. We propose an inverse design tool based on a data-driven model for unit cells’ temporal responses

The Perceived Attractiveness of Adult Facial Prototypes

This study investigated attractiveness ratings of individual faces and facial prototypes while controlling for symmetry. Symmetry was controlled by comparing symmetric individual faces to prototypes composed of 2, 4, 8, and 16 symmetric faces, morphed together by blending facial features such as eyes, nose, eyebrows, mouth, and outer contour. Adult male and female participants (N = 139, M age = 19.12 years) viewed stimuli presented on a computer monitor and rated the attractiveness of each facial stimuli on a 10 point scale, with higher values representing increased attractiveness. Results indicated that attractiveness ratings increased as the number of faces in the prototype increased, F(4,104) = 145.24,p\u3c.0005. Since symmetry was controlled in this study, other factors must contribute to a prototype\u27s attractiveness

Evolutive 3D modeling: A proposal for a new generative design methodology

At present, traditional 3D modeling programs consist of a set of tools that reflect conventional means of mechanical manufacturing and have limitations in relation with the current manufacturing capacities. On the other hand, organic and morphing 3D modeling programs are designed to transform a model from one known shape to another also known shape. Generative design helps the designers to detach themselves during the design process and can provide them with completely unexpected geometrical solutions. In this paper, starting from 3D morphing techniques and genetic algorithms, a new methodology of product shape definition is developed, capable of imitating processes that occur in nature and aimed at creating new and different product designs. This methodology enables to overcome the limitations imposed by design fixation and allows better exploitation of the great possibilities granted by the new manufacturing techniques, most notably additive manufacturing. The initial process of research and information gathering gives this work a solid basis to develop the new methodology. The results of this initial process are briefly resumed in this paper in order to explain the main motivation for developing this work. The workflow of this methodology is presented as a theoretical process, since its implementation has not been, at least for the moment, put into practice. Before presenting the conclusion for this proposal, several examples have been formulated in order to help the reader to catch the point of the entire process