The isocohomological property, higher Dehn functions, and relatively hyperbolic groups

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is of type $HF^\infty$, i.e. that has a classifying space with the homotopy type of a cellular complex with finitely many cells in each dimension, we show that the isocohomological property is equivalent to the universal cover of the classifying space satisfying polynomially bounded higher Dehn functions. If a group is hyperbolic relative to a collection of subgroups, each of which is polynomially combable (respectively $HF^\infty$ and isocohomological), then we show that the group itself has these respective properties too. Combining with the results of Connes-Moscovici and Dru{\c{t}}u-Sapir we conclude that a group satisfies the Novikov conjecture if it is relatively hyperbolic to subgroups that are of property RD, of type $HF^\infty$ and isocohomological.Comment: 35 pages, no figure

Binary image classification using collective optical modes of an array of nanolasers

Recent advancements in nanolaser design and manufacturing open up unprecedented perspectives in terms of high integration densities and ultra-low power consumption, making these devices ideal for high-performance optical computing systems. In this work, we exploit the symmetry properties of the collective modes of a nanolaser array for a simple binary classification task of small digit images. The implementation is based on a 8 × 8 nanolaser array and relies on the activation of a collective optical mode of the array—the so-called “zero-mode”—under spatially modulated pump patterns.This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay, Reference No. ANR-10-LABX-0035) and by Grant No. ANR UNIQ DS078. G.T. and C.M. are supported, in part, by Ministerio de Ciencia, Innovación y Universidades (Grant No. PID2021-123994NA-C22); C.M. also acknowledges funding from Institució Catalana de Recerca i Estudis Avançats (Academia). K.J. acknowledges support from the China Scholarship Council (Grant No. 202006970015).Peer ReviewedPostprint (published version

On the 'centre of gravity' method for measuring the composition of magnetite/maghemite mixtures, or the stoichiometry of magnetite-maghemite solid solutions, via Fe-57 Mossbauer spectroscopy

We evaluate the application of 57Fe Mössbauer spectroscopy to the determination of the composition of magnetite (Fe3O4)/maghemite (γ-Fe2O3) mixtures and the stoichiometry of magnetite-maghemite solid solutions. In particular, we consider a recently proposed model-independent method which does not rely on a priori assumptions regarding the nature of the sample, other than that it is free of other Fe-containing phases. In it a single parameter, δRT—the ‘centre of gravity’, or area weighted mean isomer shift at room temperature, T = 295 ± 5 K—is extracted by curve-fitting a sample’s Mössbauer spectrum, and is correlated to the sample’s composition or stoichiometry. We present data on highpurity magnetite and maghemite powders, and mixtures thereof, as well as comparison literature data from nanoparticulate mixtures and solid solutions, to show that a linear correlation exists between δRT and the numerical proportion of Fe atoms in the magnetite environment: α = Femagnetite/Fetotal = − ( ) δ δ RT o /m, where δo = 0.3206 ± 0.0022mm s−1 and m = 0.2135 ± 0.0076mm s−1 . We also present equations to relate α to the weight percentage w of magnetite in mixed phases, and the magnetite stoichiometry x = Fe2+/Fe3+ in solid solutions. The analytical method is generally applicable, but is most accurate when the absorption profiles are sharp; in some samples this may require spectra to be recorded at reduced temperatures. We consider such cases and provide equations to relate δ ( ) T to the corresponding α value

The momentum analyticity of two-point correlators from perturbation theory and AdS/CFT

The momentum plane analyticity of two point function of a relativistic thermal field theory at zero chemical potential is explored. A general principle regarding the location of the singularities is extracted. In the case of the N=4 supersymmetric Yang-Mills theory at large $N_c$, a qualitative change in the nature of the singularity (branch points versus simple poles) from the weak coupling regime to the strong coupling regime is observed with the aid of the AdS/CFT correspondence.Comment: 18 pages, 3 figures, typos fixed, 1 figure update

Azide-Alkyne Huisgen [3+2] Cycloaddition Using CuO Nanoparticles

Recent developments in the synthesis of CuO nanoparticles (NPs) and their application to the [3+2] cycloaddition of azides with terminal alkynes are reviewed. With respect to the importance of click chemistry, CuO hollow NPs, CuO hollow NPs on acetylene black, water-soluble double-hydrophilic block copolymer (DHBC) nanoreactors and ZnO-CuO hybrid NPs were synthesized. Non-conventional energy sources such as microwaves and ultrasound were also applied to these click reactions, and good catalytic activity with high regioselectivity was observed. CuO hollow NPs on acetylene black can be recycled nine times without any loss of activity, and water-soluble DHBC nanoreactors have been developed for an environmentally friendly process.open6

Studies of the electric dipole transitions of deformed rare-earth nuclei

Spectrum and electric dipole transition rates and relative intensities in $^{152-154}$Sm, $^{156-160}$Gd, $^{160-162}$Dy are studied in the framework of the interacting boson model with s,p,d,f bosons. It is found that E1 transition data among the low-lying levels are in good agreement with the SU(3) dynamical symmetry of the spdf interacting boson model proposed by Engel and Iachello to describe collective rotation with octupole vibration. These results show that these nuclei have SU(3) dynamic symmetry to a good approximation. Also in this work many algebraic expressions for electric dipole transitions in the SU(3) limit of the spdf-IBM have been obtained. These formulae together with the formulae given previously exhaust nearly all the E1 transitions for low-lying negative parity states. They are useful in analyzing experimental data.Comment: 26 pages, 1 figur

Collective Animal Behavior from Bayesian Estimation and Probability Matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is based on empirical fits to observations and we lack first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching.
In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability given by the Bayesian estimation that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior