Deterministic vs non-deterministic graph property testing

A graph property \(\mathcal{P}\) is said to be testable if one can check whether a graph is close or far from satisfying \(\mathcal{P}\) using few random local inspections. Property \(\mathcal{P}\) is said to be non-deterministically testable if one can supply a “certificate” to the fact that a graph satisfies \(\mathcal{P}\) so that once the certificate is given its correctness can be tested. The notion of non-deterministic testing of graph properties was recently introduced by Lovász and Vesztergombi [9], who proved that (somewhat surprisingly) a graph property is testable if and only if it is non-deterministically testable. Their proof used graph limits, and so it did not supply any explicit bounds. They thus asked if one can obtain a proof of their result which will supply such bounds. We answer their question positively by proving their result using Szemerédi’s regularity lemma. An interesting aspect of our proof is that it highlights the fact that the regularity lemma can be interpreted as saying that all graphs can be approximated by finitely many “template” graphs.     

Quantum state restoration and single-copy tomography for ground states of Hamiltonians

Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.     

On almost precipitous ideals

With less than 0^# two generic extensions ofL are identified: one in which ${\aleph_1}With less than 0^# two generic extensions ofL are identified: one in which à₁{\aleph_1}, and the other à₂{\aleph_2}, is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it is shown that if δ is a Woodin cardinal and there is an f:w₁ ? w₁{f:\omega_1 \to \omega_1} with ||f||=w₂{\|f\|=\omega_2}, then after Col(à₂,d){Col(\aleph_2,\delta)} there is a normal precipitous ideal over à₁{\aleph_1}. The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal.     

Optical properties of the locally anisotropic liquid L-phase in a chiral anticlinic liquid crystal series

Optical Rotatory Power (ORP) measurements and Raman scattering experiments have been performed in various compounds of the nCTBB9 chiral series, which displays a locally anisotropic liquid phase referred to as “L-phase”. The ORP results are very reminiscent of the behaviour theoretically predicted for the Blue Phase III-to-Isotropic transition, close to and above the critical point in the temperature-chirality phase diagram. It is suggested however, considering both the Raman scattering results and the high stability of smectic phases in this series, that the supercritical state should be characterized by both chiral and smectic order with short correlation lengths. Received 20 December 1999 and Received in final form 6 March 2000     

Generating random graphs in biased Maker‐Breaker games

We present a general approach connecting biased Maker‐Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker‐Breaker games. In particular, we show that for , Maker can build a pancyclic graph (that is, a graph that contains cycles of every possible length) while playing a game on . As another application, we show that for , playing a game on , Maker can build a graph which contains copies of all spanning trees having maximum degree with a bare path of linear length (a bare path in a tree T is a path with all interior vertices of degree exactly two in T). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 47, 615–634, 2015     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X‐ray diffraction reveal a complex lamellar structure of benzamide form II needle‐like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non‐classical morphologies.     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X-ray diffraction reveal a complex lamellar structure of benzamide form II needle-like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non-classical morphologies.     

Dilute 57Fe and 151Eu as Probes for Magnetism in Ruthenium Magneto-Superconductors

Hyperfine Interactions - Mössbauer studies of 151Eu and/or dilute 57Fe in ruthenium oxides; R2?x Ce x Sr2RuCu2O10 (R=Eu, Gd), SrRuO3, CaRuO3, EuSr2RuCu2O8, EuSr2RuO6, Eu2RuO5 and...