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Wireless networks-on-chip (WNoCs) are an enticing complementary interconnect technology for multi-core chips but face severe resource constraints. Being limited to simple on-off-keying modulation, the reverberant nature of the chip enclosure imposes limits on allowed modulation speeds in sight of inter-symbol interference, casting doubts on the competitiveness of WNoCs as interconnect technology. Fortunately, this vexing problem was recently overcome by parametrizing the on-chip radio environment with a reconfigurable intelligent surface (RIS). By suitably configuring the RIS, selected channel impulse responses (CIRs) can be tuned to be (almost) pulse-like despite rich scattering thanks to judiciously tailored multi-bounce path interferences. However, the exploration of this "over-the-air" (OTA) equalization is thwarted by (i) the overwhelming complexity of the propagation environment, and (ii) the non-linear dependence of the CIR on the RIS configuration, requiring a costly and lengthy full-wave simulation for every optimization step. Here, we show that a reduced-basis physics-compliant model for RIS-parametrized WNoCs can be calibrated with a single full-wave simulation. Thereby, we unlock the possibility of predicting the CIR for any RIS configuration almost instantaneously without any additional full-wave simulation. We leverage this new tool to systematically explore OTA equalization in RIS-parametrized WNoCs regarding the optimal choice of delay time for the RIS-shaped CIR's peak. We also study the simultaneous optimization of multiple on-chip wireless links for broadcasting. Looking forward, the introduced tools will enable the efficient exploration of various types of OTA analog computing in RIS-parametrized WNoCs., Comment: 10 pages, 7 figures, submitted to an IEEE Journal

We construct random walks on free products of the form Z 3 * Z d , with d = 5 or 6 which are divergent and not spectrally positive recurrent. We then derive a local limit theorem for these random walks, proving that $\mu$ * n (e) $\sim$ CR --n n --5/3 if d = 5 and $\mu$ * n (e) $\sim$ CR --n n --3/2 log(n) --1/2 if d = 6, where $\mu$ * n is the nth convolution power of $\mu$ and R is the inverse of the spectral radius of $\mu$. This disproves a result of Candellero and Gilch [7] and a result of the authors of this paper that was stated in a rst version of [11]. This also shows that the classication of local limit theorems on free products of the form Z d 1 * Z d 2 or more generally on relatively hyperbolic groups with respect to virtually abelian subgroups is incomplete.

We present a simple method to produce giant lipid pseudo-vesicles (vesicles with an oily cap on the top), trapped in an agarose gel. The method can be implemented using only a regular micropipette and relies on the formation of a water/oil/water double droplet in liquid agarose. We characterize the produced vesicle with fluorescence imaging and establish the presence and integrity of the lipid bilayer by the successful insertion of {\alpha}-Hemolysin transmembrane proteins. Finally, we show that the vesicle can be easily mechanically deformed, non-intrusively, by indenting the surface of the gel.

We study random walks on relatively hyperbolic groups whose law is convergent, in the sense that the derivative of its Green function is finite at the spectral radius.When parabolic subgroups are virtually abelian, we prove that for such a random walk satisfies a local limit theorem of the form $p_n(e, e)\sim CR^{-n}n^{-d/2}$, where $p_n(e, e)$ is the probability of returning to the origin at time $n$, $R$ is the inverse of the spectral radius of the random walk and $d$ is the minimal rank of a parabolic subgroup along which the random walk is spectrally degenerate.This concludes the classification all possible behaviour for $p_n(e, e)$ on such groups.

In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincar\'e series, and entropy (pressure) of invariant measures. We show that these notions coincide. Thanks to these entropy and pressure at infinity, we investigate thoroughly the notion of strong positive recurrence in this geometric context. A potential is said strongly positively recurrent when its pressure at infinity is strictly smaller than the full topological pressure. We show in particular that if a potential is strongly positively recurrent, then it admits a finite Gibbs measure. We also provide easy criteria allowing to build such strong positively recurrent potentials and many examples.

The Faint Intergalactic Medium Redshifted Emission Balloon (FIREBall) is a mission designed to observe faint emission from the circumgalactic medium of moderate redshift (z~0.7) galaxies for the first time. FIREBall observes a component of galaxies that plays a key role in how galaxies form and evolve, likely contains a significant amount of baryons, and has only recently been observed at higher redshifts in the visible. Here we report on the 2018 flight of the FIREBall-2 Balloon telescope, which occurred on September 22nd, 2018 from Fort Sumner, New Mexico. The flight was the culmination of a complete redesign of the spectrograph from the original FIREBall fiber-fed IFU to a wide-field multi-object spectrograph. The flight was terminated early due to a hole in the balloon, and our original science objectives were not achieved. The overall sensitivity of the instrument and telescope was 90,000 LU, due primarily to increased noise from stray light. We discuss the design of the FIREBall-2 spectrograph, modifications from the original FIREBall payload, and provide an overview of the performance of all systems. We were able to successfully flight test a new pointing control system, a UV-optimized, delta-doped and coated EMCCD, and an aspheric grating. The FIREBall-2 team is rebuilding the payload for another flight attempt in the Fall of 2021, delayed from 2020 due to COVID-19., Comment: 23 Pages, 14 Figures, Accepted for Publication in ApJ

We study the critical exponents of discrete subgroups of a higher rank semi-simple real linear Lie group $G$. Let us fix a Cartan subspace $\mathfrak a\subset \mathfrak g$ of the Lie algebra of $G$. We show that if $\Gamma< G$ is a discrete group, and $\Gamma' \triangleleft \Gamma$ is a Zariski dense normal subgroup, then the limit cones of $\Gamma$ and $\Gamma'$ in $\mathfrak a$ coincide. Moreover, for all linear form $\phi : \mathfrak a\to \mathbb R$ positive on this limit cone, the critical exponents in the direction of $\phi$ satisfy $\displaystyle \delta_\phi(\Gamma') \geq \frac 1 2 \delta_\phi(\Gamma)$. Eventually, we show that if $\Gamma'\backslash \Gamma$ is amenable, these critical exponents coincide.

We prove the equidistribution of (weighted) periodic orbits of the geodesic ow on noncompact negatively curved manifolds toward equilibrium states in the narrow topology, i.e. in the dual of bounded continuous functions. We deduce an exact asymptotic counting for periodic orbits (weighted or not), which was previously known only for geometrically nite manifolds.

Here we discuss advances in UV technology over the last decade, with an emphasis on photon counting, low noise, high efficiency detectors in sub-orbital programs. We focus on the use of innovative UV detectors in a NASA astrophysics balloon telescope, FIREBall-2, which successfully flew in the Fall of 2018. The FIREBall-2 telescope is designed to make observations of distant galaxies to understand more about how they evolve by looking for diffuse hydrogen in the galactic halo. The payload utilizes a 1.0-meter class telescope with an ultraviolet multi-object spectrograph and is a joint collaboration between Caltech, JPL, LAM, CNES, Columbia, the University of Arizona, and NASA. The improved detector technology that was tested on FIREBall-2 can be applied to any UV mission. We discuss the results of the flight and detector performance. We will also discuss the utility of sub-orbital platforms (both balloon payloads and rockets) for testing new technologies and proof-of-concept scientific ideas, Comment: Submitted to the Proceedings of SPIE, Defense + Commercial Sensing (SI19)

We study sequences of conformal deformations of a smooth closed Riemannian manifold of dimension $n$, assuming uniform volume bounds and $L^{n/2}$ bounds on their scalar curvatures. Singularities may appear in the limit. Nevertheless, we show that under such bounds the underlying metric spaces are pre-compact in the Gromov-Hausdorff topology. Our study is based on the use of $A_\infty$-weights from harmonic analysis, and provides geometric controls on the limit spaces thus obtained. Our techniques also show that any conformal deformation of the Euclidean metric on $R^n$ with infinite volume and finite $L^{n/2}$ norm of the scalar curvature satisfies the Euclidean isoperimetric inequality.

Let $\Gamma'<\Gamma$ be two discrete groups acting properly by isometries on a Gromov-hyperbolic space $X$. We prove that their critical exponents coincide if and only if $\Gamma'$ is co-amenable in $\Gamma$, under the assumption that the action of $\Gamma$ on $X$ is strongly positively recurrent, i.e. has a growth gap at infinity. This generalizes all previously known results on this question, which required either $X$ to be the real hyperbolic space and $\Gamma$ geometrically finite, or $X$ Gromov hyperbolic and $\Gamma$ cocompact. This result is optimal: we provide several counterexamples when the action is not strongly positively recurrent.

We consider smooth isotropic immersions from the 2-dimensional torus into $R^{2n}$, for $n \geq 2$. When $n = 2$ the image of such map is an immersed Lagrangian torus of $R^4$. We prove that such isotropic immersions can be approximated by arbitrarily $C^0$-close piecewise linear isotropic maps. If $n \geq 3$ the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well. The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, we introduce a numerical flow in finite dimension, whose limit provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in $R^4$. The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie., Comment: Revised version, minor updates, 9 figures. For related software download, see http://www.math.sciences.univ-nantes.fr/~rollin/index.php?page=flow

In this work, we introduce the notion of entropy at infinity, and define a wide class of noncompact manifolds with negative curvature, those which admit a critical gap between entropy at infinity and topological entropy. We call them strongly positively recurrent manifolds (SPR), and provide many examples. We show that dynamically, they behave as compact manifolds. In particular, they admit a finite measure of maximal entropy. Using the point of view of currents at infinity, we show that on these SPR manifolds the topological entropy of the geodesic flow varies in a C 1 -way along (uniformly) C 1 -perturbations of the metric. This result generalizes former work of Katok (1982) and Katok-Knieper-Weiss (1991) in the compact case., Comment: 65 pages, 7 figures

We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\'e series converges at the critical exponent $\delta_\Gamma$. We obtain an explicit asymptotic for their orbital growth function. Namely, for any $\alpha \in ]1, 2[ $ and any slowly varying function $L : \mathbb R\to (0, +\infty)$, we construct $N$-dimensional Hadamard manifolds $(X, g)$ of negative and pinched curvature, whose group of oriented isometries admits convergent geometrically finite subgroups $\Gamma$ such that, as $R\to +\infty$, $$ N_\Gamma(R):= \#\left\{\gamma\in \Gamma \; ; \; d(o, \gamma \cdot o)\leq R\right\} \sim C_\Gamma \frac{L(R)}{R^\alpha} \ e^{\delta_\Gamma R}, $$ for some constant $C_\Gamma >0$., Comment: 20 pages

Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane strategy induced many feed rate reductions, especially when boundaries of the feature have a lot of curvatures and are not parallel. Several machining experiments on hardened material lead to the conclusion that a tool path implying stable cutting conditions might guarantee a better part surface integrity. To ensure this stability, the shape machined must be decomposed when conventional strategies are not suitable. In this paper, an experimental approach based on high-speed performance simulation is conducted on a master bottom machining feature in order to highlight the influence of the curvatures towards a suitable decomposition of machining area. The decomposition is achieved through the construction of intermediate curves between the closed boundaries of the feature. These intermediate curves are used as guidance curve for the tool paths generation with an alternative machining strategy called "guidance curve strategy". For the construction of intermediate curves, key parameters reflecting the influence of their proximity with each closed boundary and the influence of the curvatures of this latter are introduced. Based on the results, a method for defining guidance curves in four steps is proposed.

Complex shapes are widely used to design products in several industries such as aeronautics, automotive and domestic appliances. Several variations of their curvatures and orientations generate difficulties during their manufacturing or the machining of dies used in moulding, injection and forging. Analysis of several parts highlights two levels of difficulties between three types of shapes: prismatic parts with simple geometrical shapes, aeronautic structure parts composed of several shallow pockets and forging dies composed of several deep cavities which often contain protrusions. This paper mainly concerns High Speed Machining (HSM) of these dies which represent the highest complexity level because of the shapes' geometry and their topology. Five axes HSM is generally required for such complex shaped parts but 3 axes machining can be sufficient for dies. Evolutions in HSM CAM software and machine tools lead to an important increase in time for machining preparation. Analysis stages of the CAD model particularly induce this time increase which is required for a wise choice of cutting tools and machining strategies. Assistance modules for prismatic parts machining features identification in CAD models are widely implemented in CAM software. In spite of the last CAM evolutions, these kinds of CAM modules are undeveloped for aeronautical structure parts and forging dies. Development of new CAM modules for the extraction of relevant machining areas as well as the definition of the topological relations between these areas must make it possible for the machining assistant to reduce the machining preparation time. In this paper, a model developed for the description of complex shape parts topology is presented. It is based on machining areas extracted for the construction of geometrical features starting from CAD models of the parts. As topology is described in order to assist machining assistant during machining process generation, the difficulties associated with tasks he carried out are analyzed at first. The topological model presented after is based on the basic geometrical features extracted. Topological relations which represent the framework of the model are defined between the basic geometrical features which are gathered afterwards in macro-features. Approach used for the identification of these macro-features is also presented in this paper. Detailed application on the construction of the topological model of forging dies is presented in the last part of the paper.

In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces, we obtain optimal meromorphic extensions of weighted dynamical zeta functions and asymptotic counting estimates for the number of weighted closed geodesics. A meromorphic extension of the standard dynamical zeta function and the prime orbit theorem follow as corollaries. Finally, we investigate interactions between the dynamics and spectral theory of these spaces.

Recent evolutions on forging process induce more complex shape on forging die. These evolutions, combined with High Speed Machining (HSM) process of forging die lead to important increase in time for machining preparation. In this context, an original approach for generating machining process based on machining knowledge is proposed in this paper. The core of this approach is to decompose a CAD model of complex forging die in geometric features. Technological data and topological relations are aggregated to a geometric feature in order to create machining features. Technological data, such as material, surface roughness and form tolerance are defined during forging process and dies design. These data are used to choose cutting tools and machining strategies. Topological relations define relative positions between the surfaces of the die CAD model. After machining features identification cutting tools and machining strategies currently used in HSM of forging die, are associated to them in order to generate machining sequences. A machining process model is proposed to formalize the links between information imbedded in the machining features and the parameters of cutting tools and machining strategies. At last machining sequences are grouped and ordered to generate the complete die machining process. In this paper the identification of geometrical features is detailed. Geometrical features identification is based on machining knowledge formalization which is translated in the generation of maps from STL models. A map based on the contact area between cutting tools and die shape gives basic geometrical features which are connected or not according to the continuity maps. The proposed approach is illustrated by an application on an industrial study case which was accomplished as part of collaboration.

Let $(M,g)$ be a non-compact riemannian $n$-manifold with bounded geometry at order $k\geq\frac{n}{2}$. We show that if the spectrum of the Laplacian starts with $q+1$ discrete eigenvalues isolated from the essential spectrum, and if the metric is generic for the $\Cl C^{k+2}$-strong topology, then the eigenvalues are distinct and their associated eigenfunctions are Morse. This generalizes to non-compact manifolds some arguments developped by K. Uhlenbeck. We deduce from this result that if $M^n$ has bounded geometry at order $k\geq\frac{n}{2}$ and has an isolated first eigenvalue for its Laplacian, then for any riemannian covering $p : M'\ra M$, we have $\lambda_0(M) = \sup_D \lambda_0(D)$, where $D\subset M'$ runs over all connected fundamental domains for $p$, and $\lambda_0(D)$ is the bottom of the spectrum of $D$ with Neumann boundary conditions., Comment: 33 pages, 1 figure

From a graph $G$ with constant valency $v$ and a (non-compact) manifold $C$ with $v$ boundary components, we build a $G$-periodic manifold $M$. This process gives a class of topologically infinite manifolds which generalizes periodic manifolds and includes all riemannian coverings with finitely generated deck-group. Our main result is that, when the first eigenfunction of $C$ extends to $M$, the bottom of the spectrum of $M$ is equal to $C$'s if and only if the graph $G$ is amenable. When $G$ is not amenable, we control explicitly the gap between these bottom of the spectrum. In particular, we show that if $p : M\ra N$ is a riemannian covering and the metric of $N$ is generic, then $\lambda_0(M)\geq \lambda_0(N)$ with equality if and only if the deck-group is amenable. This generalizes a result of R. Brooks., Comment: 37 pages, 4 figures, language = French, submitted

This paper will provide a method to decompose forging dies for machining planning in the case of high speed machining finishing operations. This method lies on a machining feature approach model presented in the following paper. The two main decomposition phases, called Basic Machining Features Extraction and Process Planning Generation, are presented. These two decomposition phases integrates machining resources models and expert machining knowledge to provide an outstanding process planning.

Nowadays high speed machining (HSM) machine tool combines productivity and part quality. So mould and die maker invested in HSM. Die and mould features are more and more complex shaped. Thus, it is difficult to choose the best machining strategy according to part shape. Geometrical analysis of machining features is not sufficient to make an optimal choice. Some research show that security, technical, functional and economical constrains must be taken into account to elaborate a machining strategy. During complex shape machining, production system limits induce feed rate decreases, thus loss of productivity, in some part areas. In this paper we propose to analyse these areas by estimating tool path quality. First we perform experiments on HSM machine tool to determine trajectory impact on machine tool behaviour. Then, we extract critical criteria and establish models of performance loss. Our work is focused on machine tool kinematical performance and numerical controller unit calculation capacity. We implement these models on Esprit CAM Software. During machining trajectory creation, critical part areas can be visualised and analysed. Parameters, such as, segment or arc lengths, nature of discontinuities encountered are used to analyse critical part areas. According to this visualisation, process development engineer should validate or modify the trajectory.

Today's forging die manufacturing process must be adapted to several evolutions in machining process generation: CAD/CAM models, CAM software solutions and High Speed Machining (HSM). In this context, the adequacy between die shape and HSM process is in the core of machining preparation and process planning approaches. This paper deals with an original approach of machining preparation integrating this adequacy in the main tasks carried out. In this approach, the design of the machining process is based on two levels of decomposition of the geometrical model of a given die with respect to HSM cutting conditions (cutting speed and feed rate) and technological constrains (tool selection, features accessibility). This decomposition assists machining assistant to generate an HSM process. The result of this decomposition is the identification of machining features.

Today's High-Speed Machining (HSM) machine tool combines productivity and part quality. The difficulty inherent in HSM operations lies in understanding the impact of machine tool behaviour on machining time and part quality. Analysis of some of the relevant ISO standards (230-1998, 10791-1998) and a complementary protocol for better understanding HSM technology are presented in the first part of this paper. These ISO standards are devoted to the procedures implemented in order to study the behavior of machine tool. As these procedures do not integrate HSM technology, the need for HSM machine tool tests becomes critical to improving the trade-off between machining time and part quality. A new protocol for analysing the HSM technology impact during circular interpolation is presented in the second part of the paper. This protocol which allows evaluating kinematic machine tool behaviour during circular interpolation was designed from tests without machining. These tests are discussed and their results analysed in the paper. During the circular interpolation, axis capacities (such as acceleration or Jerk) related to certain setting parameters of the numerical control unit have a significant impact on the value of the feed rate. Consequently, a kinematic model for a circular-interpolated trajectory was developed on the basis of these parameters. Moreover, the link between part accuracy and kinematic machine tool behaviour was established. The kinematic model was ultimately validated on a bore machining simulation.

In several fields like aeronautics, die and automotive, the machining of the parts is done more and more on high speed machines tools. Today, the offer for purchasing these machine tools is very wide. This situation poses the problem of the judicious and objective choice meeting industrial needs that must be necessary well expressed. The choice remains difficult insofar as the technical data provided to the customers by the manufacturers of machine tools are insufficient as well quantitatively as qualitatively. In this paper we present a protocol for the characterization of machines tools in order to direct the choice. The protocol is based on the one hand on no-load complementary tests to those recommended by the standards ISO 230 and ISO 10791 and on the other hand on the tests in load on a part test. In the first part, we present the industrial needs as well as an analysis of the technical data of machine tools. The second part is devoted to the study of the standards, the description of the protocol and the presentation of the results.

This article presents some methods to control the bottom of the spectrum of the Laplacian $\lambda_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $\lambda_0$ of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built by gluing copies of a geometrically finite surface with boundary according to the plan of an infinite graph. We control the $\lambda_0$ of the so-obtained infinite surfaces by constants coming from spectral properties of the building brick and combinatorial datae of the graph. We then use these methods to control the $\lambda_0$ of two other kind of infinite type hyperbolic surfaces : those admitting a splitting into bounded pieces, and some riemannian coverings.