Aperiodic tilings and entropy

In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected

QSO hosts and environments at z=0.9 to 4.2: JHK images with adaptive optics

We have observed nine QSOs with redshifts 0.85 to 4.16 at near-IR wavelengths with the adaptive optics bonnette of the Canada-France-Hawaii telescope. Exposure times ranged from 1500 to 24000s (mostly near 7000s) in J, H, or K bands, with pixels 0.035 arcsec on the sky. The FWHM of the co-added images at the location of the quasars are typically 0.16 arcsec. Including another QSO published previously, we find associated QSO structure in at least eight of ten objects, including the QSO at z = 4.16. The structures seen in all cases include long faint features which appear to be tidal tails. In four cases we have also resolved the QSO host galaxy, but find them to be smooth and symmetrical: future PSF removal may expand this result. Including one object previously reported, of the nine objects with more extended structure, five are radio-loud, and all but one of these appear to be in a dense small group of compact galaxy companions. The radio-quiet objects do not occupy the same dense environments, as seen in the NIR. In this small sample we do not find any apparent trends of these properties with redshift, over the range 0.8 < z < 2.4. The colors of the host galaxies and companions are consistent with young stellar populations at the QSO redshift. Our observations suggest that adaptive optic observations in the visible region will exhibit luminous signatures of the substantial star-formation activity that must be occurring.Comment: 22 pages including 10 tables, plus 11 figures. To appear in A

Composite mirror facets for ground based gamma ray astronomy

Composite mirrors for gamma-ray astronomy have been developed to fulfill the specifications required for the next generation of Cherenkov telescopes represented by CTA (Cherenkov Telescope Array). In addition to the basic requirements on focus and reflection efficiency, the mirrors have to be stiff, lightweight, durable and cost efficient. In this paper, the technology developed to produce such mirrors is described, as well as some tests that have been performed to validate them. It is shown that these mirrors comply with the needs of CTA, making them good candidates for use on a significant part of the array.Comment: 16 pages, 13 figures, accepted to be published on NIM

Computing Aggregate Properties of Preimages for 2D Cellular Automata

Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm --- incremental aggregation --- that can compute aggregate properties of the set of precursors exponentially faster than na{\"i}ve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach

Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA

Update on the ICUD-SIU consultation on multi-parametric magnetic resonance imaging in localised prostate cancer

Introduction: Prostate cancer (PCa) imaging is a rapidly evolving field. Dramatic improvements in prostate MRI during the last decade will probably change the accuracy of diagnosis. This chapter reviews recent current evidence about MRI diagnostic performance and impact on PCa management. Materials and methods: The International Consultation on Urological Diseases nominated a committee to review the literature on prostate MRI. A search of the PubMed database was conducted to identify articles focussed on MP-MRI detection and staging protocols, reporting and scoring systems, the role of MP-MRI in diagnosing PCa prior to biopsy, in active surveillance, in focal therapy and in detecting local recurrence after treatment. Results: Differences in opinion were reported in the use of the strength of magnets [1.5 Tesla (T) vs. 3T] and coils. More agreement was found regarding the choice of pulse sequences; diffusion-weighted MRI (DW-MRI), dynamic contrast-enhanced MRI (DCE MRI), and/or MR spectroscopy imaging (MRSI) are recommended in addition to conventional T2-weighted anatomical sequences. In 2015, the Prostate Imaging Reporting and Data System (PI-RADS version 2) was described to standardize image acquisition and interpretation. MP-MRI improves detection of clinically significant PCa (csPCa) in the repeat biopsy setting or before the confirmatory biopsy in patients considering active surveillance. It is useful to guide focal treatment and to detect local recurrences after treatment. Its role in biopsy-naive patients or during the course of active surveillance remains debated. Conclusion: MP-MRI is increasingly used to improve detection of csPCa and for the selection of a suitable therapeutic approach

The Expanded Very Large Array

In almost 30 years of operation, the Very Large Array (VLA) has proved to be a remarkably flexible and productive radio telescope. However, the basic capabilities of the VLA have changed little since it was designed. A major expansion utilizing modern technology is currently underway to improve the capabilities of the VLA by at least an order of magnitude in both sensitivity and in frequency coverage. The primary elements of the Expanded Very Large Array (EVLA) project include new or upgraded receivers for continuous frequency coverage from 1 to 50 GHz, new local oscillator, intermediate frequency, and wide bandwidth data transmission systems to carry signals with 16 GHz total bandwidth from each antenna, and a new digital correlator with the capability to process this bandwidth with an unprecedented number of frequency channels for an imaging array. Also included are a new monitor and control system and new software that will provide telescope ease of use. Scheduled for completion in 2012, the EVLA will provide the world research community with a flexible, powerful, general-purpose telescope to address current and future astronomical issues.Comment: Added journal reference: published in Proceedings of the IEEE, Special Issue on Advances in Radio Astronomy, August 2009, vol. 97, No. 8, 1448-1462 Six figures, one tabl

Trace Complexity of Chaotic Reversible Cellular Automata

Delvenne, K\r{u}rka and Blondel have defined new notions of computational complexity for arbitrary symbolic systems, and shown examples of effective systems that are computationally universal in this sense. The notion is defined in terms of the trace function of the system, and aims to capture its dynamics. We present a Devaney-chaotic reversible cellular automaton that is universal in their sense, answering a question that they explicitly left open. We also discuss some implications and limitations of the construction.Comment: 12 pages + 1 page appendix, 4 figures. Accepted to Reversible Computation 2014 (proceedings published by Springer