Limitations to Fréchet’s metric embedding method

Fréchet’s classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Fréchet embedding is Bourgain's embedding [4]. The authors have recently shown [2] that for every ε>0, anyn-point metric space contains a subset of size at leastn ^1−ε which embeds into ℓ₂ with distortion . The embedding used in [2] is non-Fréchet, and the purpose of this note is to show that this is not coincidental. Specifically, for every ε>0, we construct arbitrarily largen-point metric spaces, such that the distortion of any Fréchet embedding into ℓ_p on subsets of size at leastn ^1/2+ε is Ω((logn)^1/p ). Supported in part by a grant from the Israeli National Science Foundation. Supported in part by a grant from the Israeli National Science Foundation. Supported in part by the Landau Center.     

La2-xCexCu1-yZnyO4 perovskites for high temperature water-gas shift reaction

The performance of La2-xCexCu1-yZnyO4 perovskites as catalysts for the high temperature water-gas shift reaction (HT-WGSR) was inves-tigated. The catalysts were characterized by EDS, XRD, BET surface area, TPR, and XANES. The results showed that all the perovskites exhibited the La2CuO4 orthorhombic structure, so the Pechini method is suitable for the preparation of pure perovskite. However, the La1.90Ce0.10CuO4 perovskite alone, when calcined at 350/700℃, also showed a (La0.935Ce0.065)2CuO4 perovskite with tetragonal struc-ture, which produced a surface area higher than the other perovskites. The perovskites that exhibited the best catalytic performance were those calcined at 350/700 ℃ and, among these, La1.90Ce0.10CuO4 was outstanding, probably because of the high surface area associated with the presence of the (La0.935Ce0.065) 2CuO4 perovskite with tetragonal structure and orthorhombic La2CuO4 phase.     

Realizing a variable isotropic depolarizer

We demonstrate an isotropic depolarizing channel with a controllable degree of depolarization. The depolarizer is composed of four birefringent crystals and half-wave plates. Quantum process tomography results of the depolarization effect on single photons agree well with the theoretical prediction. This depolarizer can be used to test quantum communication protocols with photons.     

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.     

Revisiting Sequential Information Bottleneck: New Implementation and Evaluation

We introduce a modern, optimized, and publicly available implementation of the sequential Information Bottleneck clustering algorithm, which strikes a highly competitive balance between clustering quality and speed. We describe a set of optimizations that make the algorithm computation more efficient, particularly for the common case of sparse data representation. The results are substantiated by an extensive evaluation that compares the algorithm to commonly used alternatives, focusing on the practically important use case of text clustering. The evaluation covers a range of publicly available benchmark datasets and a set of clustering setups employing modern word and sentence embeddings obtained by state-of-the-art neural models. The results show that in spite of using the more basic Term-Frequency representation, the proposed implementation provides a highly attractive trade-off between quality and speed that outperforms the alternatives considered. This new release facilitates the use of the algorithm in real-world applications of text clustering.     

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Ohne Zusammenfassung     

On the Interactive Capacity of Finite-State Protocols

The interactive capacity of a noisy channel is the highest possible rate at which arbitrary interactive protocols can be simulated reliably over the channel. Determining the interactive capacity is notoriously difficult, and the best known lower bounds are far below the associated Shannon capacity, which serves as a trivial (and also generally the best known) upper bound. This paper considers the more restricted setup of simulating finite-state protocols. It is shown that all two-state protocols, as well as rich families of arbitrary finite-state protocols, can be simulated at the Shannon capacity, establishing the interactive capacity for those families of protocols.