High Dimensional Expansion Implies Amplified Local Testability

In this work, we define a notion of local testability of codes that is strictly stronger than the basic one (studied e.g., by recent works on high rate LTCs), and we term it amplified local testability. Amplified local testability is a notion close to the result of optimal testing for Reed-Muller codes achieved by Bhattacharyya et al. We present a scheme to get amplified locally testable codes from high dimensional expanders. We show that single orbit Affine invariant codes, and in particular Reed-Muller codes, can be described via our scheme, and hence are amplified locally testable. This gives the strongest currently known testability result of single orbit affine invariant codes, strengthening the celebrated result of Kaufman and Sudan

High Dimensional Expansion Implies Amplified Local Testability

In this work, we define a notion of local testability of codes that is strictly stronger than the basic one (studied e.g., by recent works on high rate LTCs), and we term it amplified local testability. Amplified local testability is a notion close to the result of optimal testing for Reed-Muller codes achieved by Bhattacharyya et al. We present a scheme to get amplified locally testable codes from high dimensional expanders. We show that single orbit Affine invariant codes, and in particular Reed-Muller codes, can be described via our scheme, and hence are amplified locally testable. This gives the strongest currently known testability result of single orbit affine invariant codes, strengthening the celebrated result of Kaufman and Sudan

The UK National Health Service’s 'innovation agenda': lessons on commercialization and trust

The UK National Health Service (the 'NHS'), encouraged by the 2011 report Innovation Health and Wealth, Accelerating Adoption and Diffusion in the NHS, and empowered by the Health and Social Care Act 2012, is in the process of adopting a new agenda for stimulating innovation in healthcare. For this, the bodies, body materials, and confidential health information of NHS patients may be co-opted. We explain why this brings the NHS into a moral conflict with its basic goal of providing a universal healthcare service. Putting NHS databases at the disposal of industry, without addressing ethical concerns regarding the privacy, autonomy, and moral integrity of patients and without requiring a 'kick-back' to enhance the service that the NHS provides, is inappropriate. As this article shows, with reference to the commercial arena of direct-to-consumer genetic testing, it is crucial that patient and public trust in the NHS is not eroded

Modified Gravity Away from a Λ\LambdaCDM Background

Within the effective field theory approach to cosmic acceleration, the background expansion can be specified separately from the gravitational modifications. We explore the impact of modified gravity in a background different from a cosmological constant plus cold dark matter ($\Lambda$CDM) on the stability and cosmological observables, including covariance between gravity and expansion parameters. In No Slip Gravity the more general background allows more gravitational freedom, including both positive and negative Planck mass running. We examine the effects on cosmic structure growth, as well as showing that a viable positive integrated Sachs-Wolfe effect crosscorrelation easily arises from this modified gravity theory. Using current data we constrain parameters with a Monte Carlo analysis, finding a maximum running $|\alpha_M|\lesssim 0.03$. We provide the modified {\tt hi\_class} code publicly on GitHub, now enabling computation and inclusion of the redshift space distortion observable $f\sigma_8$ as well as the No Slip Gravity modifications.Comment: 14 pages, 13 figures. Matches published version in JCAP, LCDM discussion adde

Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries

A local tester for an error correcting code $C\subseteq \Sigma^{n}$ is a tester that makes $Q$ oracle queries to a given word $w\in \Sigma^n$ and decides to accept or reject the word $w$. An optimal local tester is a local tester that has the additional properties of completeness and optimal soundness. By completeness, we mean that the tester must accept with probability $1$ if $w\in C$. By optimal soundness, we mean that if the tester accepts with probability at least $1-\epsilon$ (where $\epsilon$ is small), then it must be the case that $w$ is $O(\epsilon/Q)$-close to some codeword $c\in C$ in Hamming distance. We show that Generalized Reed-Muller codes admit optimal testers with $Q = (3q)^{\lceil{ \frac{d+1}{q-1}\rceil}+O(1)}$ queries. Here, for a prime power $q = p^{k}$, the Generalized Reed-Muller code, RM[n,q,d], consists of the evaluations of all $n$-variate degree $d$ polynomials over $\mathbb{F}_q$. Previously, no tester achieving this query complexity was known, and the best known testers due to Haramaty, Shpilka and Sudan(which is optimal) and due to Ron-Zewi and Sudan(which was not known to be optimal) both required $q^{\lceil{\frac{d+1}{q-q/p} \rceil}}$ queries. Our tester achieves query complexity which is polynomially better than by a power of $p/(p-1)$, which is nearly the best query complexity possible for generalized Reed-Muller codes. The tester we analyze is due to Ron-Zewi and Sudan, and we show that their basic tester is in fact optimal. Our methods are more general and also allow us to prove that a wide class of testers, which follow the form of the Ron-Zewi and Sudan tester, are optimal. This result applies to testers for all affine-invariant codes (which are not necessarily generalized Reed-Muller codes).Comment: 42 pages, 8 page appendi

On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks

Most of our knowledge on the nonlinear development of the magneto-rotational instability (MRI) relies on the results of numerical simulations employing the shearing box (SB) approximation. A number of difficulties arising from this approach have recently been pointed out in the literature. We thoroughly examine the effects of the assumptions made and numerical techniques employed in SB simulations. This is done in order to clarify and gain better understanding of those difficulties as well as of a number of additional serious problems, raised here for the first time, and of their impact on the results. Analytical derivations and estimates as well as comparative analysis to methods used in the numerical study of turbulence are used. Numerical experiments are performed to support some of our claims and conjectures. The following problems, arising from the (virtually exclusive) use of the SB simulations as a tool for the understanding and quantification of the nonlinear MRI development in disks, are analyzed and discussed: (i) inconsistencies in the application of the SB approximation itself; (ii) the limited spatial scale of the SB; (iii) the lack of convergence of most ideal MHD simulations; (iv) side-effects of the SB symmetry and the non-trivial nature of the linear MRI; (v) physical artifacts arising on the too small box scale due to periodic boundary conditions. The computational and theoretical challenge posed by the MHD turbulence problem in accretion disks cannot be met by the SB approximation, as it has been used to date. A new strategy to confront this challenge is proposed, based on techniques widely used in numerical studies of turbulent flows - developing (e.g., with the help of local numerical studies) a sub-grid turbulence model and implementing it in global calculations.Comment: Accepted for publication in Astronomy and Astrophysic