A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

The New Political History

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66569/2/10.1177_000276427702100204.pd

The SARAO MeerKAT 1.3 GHz Galactic Plane Survey

We present the SARAO MeerKAT Galactic Plane Survey (SMGPS), a 1.3 GHz continuum survey of almost half of the Galactic Plane (251○ ≤l ≤ 358○ and 2○ ≤l ≤ 61○ at |b| ≤ 1 5). SMGPS is the largest, most sensitive and highest angular resolution 1 GHz survey of the Plane yet carried out, with an angular resolution of 8″ and a broadband RMS sensitivity of ∼10–20 μJy beam−1. Here we describe the first publicly available data release from SMGPS which comprises data cubes of frequency-resolved images over 908–1656 MHz, power law fits to the images, and broadband zeroth moment integrated intensity images. A thorough assessment of the data quality and guidance for future usage of the data products are given. Finally, we discuss the tremendous potential of SMGPS by showcasing highlights of the Galactic and extragalactic science that it permits. These highlights include the discovery of a new population of non-thermal radio filaments; identification of new candidate supernova remnants, pulsar wind nebulae and planetary nebulae; improved radio/mid-IR classification of rare Luminous Blue Variables and discovery of associated extended radio nebulae; new radio stars identified by Bayesian cross-matching techniques; the realisation that many of the largest radio-quiet WISE H II region candidates are not true H II regions; and a large sample of previously undiscovered background H I galaxies in the Zone of Avoidance

The MeerKAT Galaxy Cluster Legacy Survey: I. Survey overview and highlights

Please abstract in the article.The South African Radio Astronomy Observatory (SARAO), the National Research Foundation (NRF), the National Radio Astronomy Observatory, US National Science Foundation, the South African Research Chairs Initiative of the DSI/NRF, the SARAO HCD programme, the South African Research Chairs Initiative of the Department of Science and Innovation.http://www.aanda.orghj2022Physic

Comparison of three methods of feeding sows in gestation and the subsequent effects on lactation performance

A total of 684 sows from breeding groups over six weeks were used to compare three methods of feeding during gestation and to assess the subsequent effects on lactation performance. Control gilts and sows were fed according to body condition based on a scale of 1 to 5, (1=thin, 5=fat). Sows were visually assessed for body condition at breeding and were assigned a daily feed allowance to achieve a body condition score of 3 at farrowing. Sow body condition was evaluated every two weeks throughout gestation, and feed allowance was adjusted as required. Treatment two used feeding levels based on backfat thickness (measured between d 0 and 5 after breeding) and weight at weaning for sows or weight at service for gilts. Feed allowance was calculated to achieve a target backfat of 19 mm at farrowing. Sow feeding level remained constant from d 0 to 101 of gestation. Feed allowances were based on modeled calculations of energy and nutrient requirements to achieve target sow maternal weight and backfat gain. Treatment three was identical to treatment two except that feeding pattern was altered for thin sows and gilts (21 mm) but no difference in the percentage of thin sows (<17 mm) compared to the standard method of feeding based on body condition. Gestation feeding method had no effect on performance during lactation. Feed intake in lactation was lower for high backfat sows (>21 mm) at farrowing compared to sows with <21 mm. The high proportion of sows in the optimum backfat category demonstrates that feeding based on backfat and body weight has potential for facilitating more precise gestation feeding

Finding Maximal Pairs with Bounded Gap

Brodal GS, Lyngsø RB, Pedersen CNS, Stoye J. Finding Maximal Pairs with Bounded Gap. In: Proc. of CPM 1999. LNCS. Vol 1645. 1999: 134-149

Basic Observables for Processes

We propose a general approach to define behavioural preorders over process terms by considering the pre-congruences induced by three basic observables. These observables provide information about the initial communication capabilities of processes and about their possibility of engaging in an infinite internal chattering. We show that some of the observables-based pre-congruences do correspond to behavioral preorders long studied in the literature. The coincidence proofs shed light on the differences between the must preorder of De Nicola and Hennessy and the fair/should preorder of Cleaveland and Natarajan and of Brinksma, Rensink and Vogler, and on the rôle played in their definition by tests for internal chattering