The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach

We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of $N$-representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of N$_2$

Test like you Train in Implicit Deep Learning

Implicit deep learning has recently gained popularity with applications ranging from meta-learning to Deep Equilibrium Networks (DEQs). In its general formulation, it relies on expressing some components of deep learning pipelines implicitly, typically via a root equation called the inner problem. In practice, the solution of the inner problem is approximated during training with an iterative procedure, usually with a fixed number of inner iterations. During inference, the inner problem needs to be solved with new data. A popular belief is that increasing the number of inner iterations compared to the one used during training yields better performance. In this paper, we question such an assumption and provide a detailed theoretical analysis in a simple setting. We demonstrate that overparametrization plays a key role: increasing the number of iterations at test time cannot improve performance for overparametrized networks. We validate our theory on an array of implicit deep-learning problems. DEQs, which are typically overparametrized, do not benefit from increasing the number of iterations at inference while meta-learning, which is typically not overparametrized, benefits from it

Resolution limits of quantum ghost imaging

Quantum ghost imaging uses photon pairs produced from parametric downconversion to enable an alternative method of image acquisition. Information from either one of the photons does not yield an image, but an image can be obtained by harnessing the correlations between them. Here we present an examination of the resolution limits of such ghost imaging systems. In both conventional imaging and quantum ghost imaging the resolution of the image is limited by the point-spread function of the optics associated with the spatially resolving detector. However, whereas in conventional imaging systems the resolution is limited only by this point spread function, in ghost imaging we show that the resolution can be further degraded by reducing the strength of the spatial correlations inherent in the downconversion process

Experimental limits of ghost diffraction: Popper’s thought experiment

Quantum ghost diffraction harnesses quantum correlations to record diffraction or interference features using photons that have never interacted with the diffractive element. By designing an optical system in which the diffraction pattern can be produced by double slits of variable width either through a conventional diffraction scheme or a ghost diffraction scheme, we can explore the transition between the case where ghost diffraction behaves as conventional diffraction and the case where it does not. For conventional diffraction the angular extent increases as the scale of the diffracting object is reduced. By contrast, we show that no matter how small the scale of the diffracting object, the angular extent of the ghost diffraction is limited (by the transverse extent of the spatial correlations between beams). Our study is an experimental realisation of Popper’s thought experiment on the validity of the Copenhagen interpretation of quantum mechanics. We discuss the implication of our results in this context and explain that it is compatible with, but not proof of, the Copenhagen interpretation

Mycophilic or Mycophobic? Legislation and Guidelines on Wild Mushroom Commerce Reveal Different Consumption Behaviour in European Countries

Mycophiles forage for and pick vast quantities of a wide variety of wild mushroom species. As a result, mushroom intoxications are comparatively frequent in such countries with mycophiles. Thus, national governments are forced to release guidelines or enact legislation in order to ensure the safe commerce of wild mushrooms due to food safety concerns. It is in these guidelines and laws that one can observe whether a country is indeed mycophobic or mycophilic. Furthermore, these laws and guidelines provide valuable information on mushroom preferences and on the consumption habits of each country. As such we were interested in the questions as to whether mushroom consumption behaviour was different within Europe, and if it was possible to discover the typical or distinctive culinary preferences of Slavic or Romanic speaking people, people from special geographical regions or from different zones. This work is based on the analysis of edible mushroom lists available in specific guidelines or legislation related to the consumption and commerce of mushrooms in 27 European countries. The overall diversity of edible mushrooms authorised to be commercialised in Europe is very high. However, only 60 out of a total 268 fungal species can be cultivated. This highlights the importance of guidelines or legislation for the safe commerce of wild mushrooms. The species richness and composition of the mushrooms listed for commerce is very heterogeneous within Europe. The consumption behaviour is not only languagefamily- related, but is strongly influenced by geographical location and neighbouring countries. Indicator species were detected for different European regions ; most of them are widespread fungi, and thus prove culture-specific preferences for these mushrooms. Our results highlight tradition and external input such as trade and cultural exchange as strong factors shaping mushroom consumption behaviour

Perception of Multisensory Wind Representation in Virtual Reality

International audienceThe set of physical and sensitive phenomena that interacts with the urban morphology acts on the resulting perception from the users of a place. Its study and representation provides elements beyond the aesthetics aspects that can allow a better understanding of the space and future urban projects. We aim to analyze the effects of three different wind representations in terms of perception and sense of presence in virtual reality (VR). We focus on the following conditions: (R) reference scene with the audiovisual representation of the mechanical effects of the wind on the elements of the context, (V) reference scene plus the visualization of the wind flow, present (among others) in the architecture field, (T) reference scene plus tactile restitution of wind and eventually (V+T) assembling all previous conditions. For the experiment, we present to the participants (R), then (V) followed by (T), and finish with (V+T). 37 participants evaluated 12 different stop points (divided into four routes in the same simulated street), where they had to determine the perceived wind force and direction concerning the four different conditions (each one corresponding to one route). At the end of each route, participants evaluated their sense of presence in the VR scene. Our analysis showed significant effects of tactile restitution over the visual effects used in the study, both for understanding wind properties and for increasing the sense of presence in the VR scene. In terms of wind direction, (T) reduced the estimation error by 27% compared to (V). Concerning wind force, the reduction was 9.8%. As far as presence was concerned, (T) increased the sense of presence by 12.2% compared to (V)

Turbulent separated shear flow control by surface plasma actuator: experimental optimization by genetic algorithm approach

The potential benefits of active flow control are no more debated. Among many others applications, flow control provides an effective mean for manipulating turbulent separated flows. Here, a nonthermal surface plasma discharge (dielectric barrier discharge) is installed at the step corner of a backward-facing step (U 0 = 15 m/s, Re h  = 30,000, Re θ  = 1650). Wall pressure sensors are used to estimate the reattaching location downstream of the step (objective function #1) and also to measure the wall pressure fluctuation coefficients (objective function #2). An autonomous multi-variable optimization by genetic algorithm is implemented in an experiment for optimizing simultaneously the voltage amplitude, the burst frequency and the duty cycle of the high-voltage signal producing the surface plasma discharge. The single-objective optimization problems concern alternatively the minimization of the objective function #1 and the maximization of the objective function #2. The present paper demonstrates that when coupled with the plasma actuator and the wall pressure sensors, the genetic algorithm can find the optimum forcing conditions in only a few generations. At the end of the iterative search process, the minimum reattaching position is achieved by forcing the flow at the shear layer mode where a large spreading rate is obtained by increasing the periodicity of the vortex street and by enhancing the vortex pairing process. The objective function #2 is maximized for an actuation at half the shear layer mode. In this specific forcing mode, time-resolved PIV shows that the vortex pairing is reduced and that the strong fluctuations of the wall pressure coefficients result from the periodic passages of flow structures whose size corresponds to the height of the step model

Multi-input genetic algorithm for experimental optimization of the reattachment downstream of a backward-facing step with surface plasma actuator

The practical interest of flow control approaches is no more debated as flow control provides an effective mean for considerably increasing the performances of ground or air transport systems, among many others applications. Here a fundamental configuration is investigated by using non-thermal surface plasma discharge. A dielectric barrier discharge is installed at the step corner of a backward-facing step (Reh=30000, Re¿=1650). Wall pressure sensors are used to estimate the reattaching location downstream of the step. The primary objective of this paper is the coupling of a numerical optimizer with an experiment. More specifically, optimization by genetic algorithm is implemented experimentally in order to minimize the reattachment point downstream of the step model. Validation through inverse problem is firstly demonstrated. When coupled with the plasma actuator and the wall pressure sensors, the genetic algorithm finds the optimum forcing conditions with a good convergence rate, the best control design variables being in agreement with the literature that uses other types of control devices than plasma. Indeed, the minimum reattaching position is achieved by forcing the flow at the shear layer mode where a large spreading rate is obtained by increasing the periodicity of the vortex street and by enhancing the vortex pairing phenomena. At the best forcing conditions, the mean flow reattachment is reduced by 20%. This article, with its experiment-based approach, demonstrates the robustness of a single-objective multi-design optimization method, and its feasibility for wind tunnel experiments.Postprint (published version