A multiplicative comparison of MacLane homology and topological Hochschild homology

Let $Q$ denote MacLane's $Q$-construction, and $\otimes$ denote the smash product of spectra. In this paper we construct an equivalence $Q(R)\simeq \mathbb Z\otimes R$ in the category of $A_\infty$ ring spectra for any ring $R$, thus proving a conjecture made by Fiedorowicz, Schw\"anzl, Vogt and Waldhausen in "MacLane homology and topological Hochschild homology". More precisely, we construct is a symmetric monoidal structure on $Q$ (in the $\infty$-categorical sense) extending the usual monoidal structure, for which we prove an equivalence $Q(-)\simeq \mathbb Z\otimes -$ as symmetric monoidal functors, from which the conjecture follows immediately. From this result, we obtain a new proof of the equivalence $\mathrm{HML}(R,M)\simeq \mathrm{THH}(R,M)$ originally proved by Pirashvili and Waldaushen in "MacLane homology and topological Hochschild homology" (a different paper from the one cited above). This equivalence is in fact made symmetric monoidal, and so it also provides a proof of the equivalence $\mathrm{HML}(R)\simeq \mathrm{THH}(R)$ as $E_\infty$ ring spectra, when $R$ is a commutative ring.Comment: 26 page

Statics and dynamics of magnetocapillary bonds

When ferromagnetic particles are suspended at an interface under magnetic fields, dipole-dipole interactions compete with capillary attraction. This combination of forces has recently given promising results towards controllable self-assemblies, as well as low Reynolds swimming systems. The elementary unit of these assemblies is a pair of particles. Although equilibrium properties of this interaction are well described, dynamics remain unclear. In this letter, the properties of magnetocapillary bonds are determined by probing them with magnetic perturbations. Two deformation modes are evidenced and discussed. These modes exhibit resonances whose frequencies can be detuned to generate non-reciprocal motion. A model is proposed which can become the basis for elaborate collective behaviours

Remote control of self-assembled microswimmers

Physics governing the locomotion of microorganisms and other microsystems is dominated by viscous damping. An effective swimming strategy involves the non-reciprocal and periodic deformations of the considered body. Here, we show that a magnetocapillary-driven self-assembly, composed of three soft ferromagnetic beads, is able to swim along a liquid-air interface when powered by an external magnetic field. More importantly, we demonstrate that trajectories can be fully controlled, opening ways to explore low Reynolds number swimming. This magnetocapillary system spontaneously forms by self-assembly, allowing miniaturization and other possible applications such as cargo transport or solvent flows.Comment: 5 pages, 5 figures articl

Comportement des aggrégations de morues arctiques (Boreogadus saida) dans le golfe d'Amundsen (mer de Beaufort)

Au cours de l'Étude sur le chenal de séparation circumpolaire («Circumpolar Flaw Lead System Study», CFL) en 2007-2008, d'importantes agrégations hivernales de morues arctiques ont été détectées par l'échosondeur EK-60 du brise-glace de recherche NGCC Amundsen dans le Golfe d'Amundsen. La biomasse de ces agrégations a été calculée sur une période de dix mois et a atteint un maximum de 0.732 kg m" en février. Les agrégations ont uniquement été observées pendant la saison d'englacement, de décembre à avril. La distribution verticale de la morue arctique était alors reliée à la température et à la distribution de ses proies. Les morues préféraient généralement les eaux relativement chaudes (>0°C) de la couche Atlantique en hiver, mais une fraction des individus formant les agrégations les plus denses suivait occasionnellement le zooplancton jusque dans l'halocline Pacifique plus froide (-1.6 à 0°C). De plus, des migrations verticales journalières précisément synchronisées avec l'augmentation de la photopériode ont été observées parmi les agrégations. Au cours de l'hiver, les morues arctiques migrèrent progressivement vers des zones plus profondes (de 220 à 550 m de profondeur) en réponse à l'augmentation de l'intensité lumineuse, possiblement afin d'éviter les prédateurs visuels tels que le phoque annelé. La comparaison du Golfe d'Amundsen avec la Baie de Franklin démontre l'importance écologique de la séquestration de la morue arctique dans des baies relativement peu profondes en hiver. Ce mécanisme permet aux mammifères marins d'avoir accès à des concentrations élevées de proies, et ce à des profondeurs facilement accessibles

Turning Optical Complex Media into Universal Reconfigurable Linear Operators by Wavefront Shaping

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies and reconfigurability. Current designs of custom-tailored photonic devices or coherent photonic circuits only partially satisfy these needs. Here, we propose a way to perform linear operations by using complex optical media such as multimode fibers or thin scattering layers as a computational platform driven by wavefront shaping. Given a large random transmission matrix (TM) representing light propagation in such a medium, we can extract a desired smaller linear operator by finding suitable input and output projectors. We discuss fundamental upper bounds on the size of the linear transformations our approach can achieve and provide an experimental demonstration. For the latter, first we retrieve the complex medium's TM with a non-interferometric phase retrieval method. Then, we take advantage of the large number of degrees of freedom to find input wavefronts using a Spatial Light Modulator (SLM) that cause the system, composed of the SLM and the complex medium, to act as a desired complex-valued linear operator on the optical field. We experimentally build several $16\times16$ complex-valued operators, and are able to switch from one to another at will. Our technique offers the prospect of reconfigurable, robust and easy-to-fabricate linear optical analogue computation units

Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computations, yielding silent secure two-party computation protocols (protocols where the preprocessing phase requires almost no communication). An additional property called programmability allows to extend this to build N-party protocols. However, known constructions for programmable PCG's can only produce OLE's over large fields, and use rather new splittable Ring-LPN assumption. In this work, we overcome both limitations. To this end, we introduce the quasi-abelian syndrome decoding problem (QA-SD), a family of assumptions which generalises the well-established quasi-cyclic syndrome decoding assumption. Building upon QA-SD, we construct new programmable PCG's for OLE's over any field $\mathbb{F}_q$ with $q>2$. Our analysis also sheds light on the security of the ring-LPN assumption used in Boyle $\textit{et al.}$ (Crypto 2020). Using our new PCG's, we obtain the first efficient N-party silent secure computation protocols for computing general arithmetic circuit over $\mathbb{F}_q$ for any $q>2$.Comment: This is a long version of a paper accepted at CRYPTO'2

Evidence of temperature control on mesopelagic fish and zooplankton communities at high latitudes

Across temperate and equatorial oceans, a diverse community of fish and zooplankton occupies the mesopelagic zone, where they are detectable as sound-scattering layers. At high latitudes, extreme day-night light cycles may limit the range of some species, while at lower latitudes communities are structured by dynamic ocean processes, such as temperature. Using acoustic and oceanographic measurements, we demonstrate that latitudinal changes in mesopelagic communities align with polar boundaries defined by deep ocean temperature gradients. At the transition to cold polar water masses we observe abrupt weakening and vertical dispersion of acoustic backscatter of mesopelagic organisms, thereby altering the structure of the mesopelagic zone. In the Canadian Arctic, we used biological sampling to show that this boundary is associated with a significant change in the pelagic fish community structure. Rapid ocean warming projected at mesopelagic depths could shift these boundaries with far-reaching effects on ecosystem function and biogeochemical cycles

Magnetocapillary self-assemblies: Swimming and micromanipulation

Floating magnetic particles can self-assemble into structures, by a combination of a magnetic dipole-dipole interaction and an attraction due to the interfacial deformation. These structures are periodically deformed in a non reciprocal way using magnetic fields, which leads to controllable low Reynolds number locomotion. Such microswimmers provide a basis for micromanipulation applications such as transport of micro-objects, local mixing of fluids or surface cleaning