Avoidability of long kk-abelian repetitions

We study the avoidability of long $k$-abelian-squares and $k$-abelian-cubes on binary and ternary alphabets. For $k=1$, these are M\"akel\"a's questions. We show that one cannot avoid abelian-cubes of abelian period at least $2$ in infinite binary words, and therefore answering negatively one question from M\"akel\"a. Then we show that one can avoid $3$-abelian-squares of period at least $3$ in infinite binary words and $2$-abelian-squares of period at least 2 in infinite ternary words. Finally we study the minimum number of distinct $k$-abelian-squares that must appear in an infinite binary word

A Note On Computing Set Overlap Classes

Let ${\cal V}$ be a finite set of $n$ elements and ${\cal F}=\{X_1,X_2, >..., X_m\}$ a family of $m$ subsets of ${\cal V}.$ Two sets $X_i$ and $X_j$ of ${\cal F}$ overlap if $X_i \cap X_j \neq \emptyset,$ $X_j \setminus X_i \neq \emptyset,$ and $X_i \setminus X_j \neq \emptyset.$ Two sets $X,Y\in {\cal F}$ are in the same overlap class if there is a series $X=X_1,X_2, ..., X_k=Y$ of sets of ${\cal F}$ in which each $X_iX_{i+1}$ overlaps. In this note, we focus on efficiently identifying all overlap classes in $O(n+\sum_{i=1}^m |X_i|)$ time. We thus revisit the clever algorithm of Dahlhaus of which we give a clear presentation and that we simplify to make it practical and implementable in its real worst case complexity. An useful variant of Dahlhaus's approach is also explained

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

A preliminary timing analysis of two intermediate polars: UU Col and Swift J0939.7-3224

We present the preliminary timing analysis of confirmed intermediate polar UU Col and possible intermediate polar Swift J0939.7-3224 in the optical band with the help of long-term, high-cadence continuous photometry from Transiting Exoplanet Survey Satellite (TESS). For UU Col, we revise previously reported orbital and spin periods as 3.464 $\pm$ 0.005 h and 863.74 $\pm$ 0.08 s, respectively. Using the second harmonic of the beat frequency, the beat period is estimated as $\sim$928 s. These findings indicate that UU Col is a disc-fed dominated disc-overflow accretor. For J0939, we establish the spin period as 2671.8 $\pm$ 0.8 s and refine the provisionally suggested orbital period as 8.49 $\pm$ 0.03 h. The absence of beat frequency in J0939 signifies that it might be a pure disc-fed accretor; however, an X-ray study of this source will help to understand its true nature.Comment: 9 pages, 3 figures, 2 tables. Proceeding paper of the 3$^{rd}$ Belgo-Indian Network for Astronomy and Astrophysics (BINA) workshop, Accepted for publication in the Bulletin of Li\`{e}ge Royal Society of Science

On cardinalities of k-abelian equivalence classes

Two words $u$ and $v$ are $k$-abelian equivalent if for each word $x$ of length at most $k$, $x$ occurs equallymany times as a factor in both $u$ and $v$. The notion of $k$-abelian equivalence is an intermediate notion between the abelian equivalence and the equality of words. In this paper, we study the equivalence classes induced by the $k$-abelian equivalence, mainly focusing on the cardinalities of the classes. In particular, we are interested in the number of singleton $k$-abelian classes, i.e., classes containing only one element. We find a connection between thesingleton classes and cycle decompositions of the de Bruijn graph. We show that the number of classes of words of length $n$ containing one single element is of order $mathcal O (n^{N_m(k-1)-1})$, where $N_m(l)= frac{1}{l}sum_{dmid l}arphi(d)m^{l/d}$ is the number of necklaces of length $l$ over an $m$-ary alphabet. We conjecture that the upper bound is sharp. We also remark that, for $k$ even and $m=2$, the lower bound $Omega (n^{N_m(k-1)-1})$follows from an old conjecture on the existence of Gray codes for necklaces of odd length. We verify this conjecture for necklaces of length up to 15

Analysis with respect to instrumental variables for the exploration of microarray data structures

BACKGROUND: Evaluating the importance of the different sources of variations is essential in microarray data experiments. Complex experimental designs generally include various factors structuring the data which should be taken into account. The objective of these experiments is the exploration of some given factors while controlling other factors. RESULTS: We present here a family of methods, the analyses with respect to instrumental variables, which can be easily applied to the particular case of microarray data. An illustrative example of analysis with instrumental variables is given in the case of microarray data investigating the effect of beverage intake on peripheral blood gene expression. This approach is compared to an ANOVA-based gene-by-gene statistical method. CONCLUSION: Instrumental variables analyses provide a simple way to control several sources of variation in a multivariate analysis of microarray data. Due to their flexibility, these methods can be associated with a large range of ordination techniques combined with one or several qualitative and/or quantitative descriptive variables

Anomaly in the dielectric response at the charge orbital ordering transition of crystalline Pr0.67Ca0.33MnO3

The complex impedance of a Pr0.67Ca0.33MnO3 crystal has been measured. The frequency dependence is studied for a wide range of temperatures (50K-403K) and is found to be characteristic of relaxation process with a single Debye time relaxation constant, which is interpreted as a dielectric constant of the material. A strong peak is observed in this dielectric constant (up to two millions) at the charge ordering transition suggesting an interpretation in terms of ordering of electric dipoles at TCO or in term of phase separation. Comparison with Pr0.63Ca0.37MnO3 - in which the phase separation is much smaller and the peak in the dielectric constant is absent - suggests an interpretation in term of phase separation between insulating and metallic states.Comment: pdf fil

Enobosarm (GTx-024) modulates adult skeletal muscle mass independently of the androgen receptor in the satellite cell lineage

Androgens increase skeletal muscle mass, but their clinical use is hampered by lack of tissue selectivity and subsequent side-effects. Selective androgen receptor modulators (SARMs) elicit muscle-anabolic effects while only sparingly affecting reproductive tissues. The SARM GTx-024 (enobosarm) is being investigated for cancer cachexia, sarcopenia, and muscle wasting diseases. Here, we investigate the role of muscle androgen receptor (AR) in the anabolic effect of GTx-024. In mice lacking AR in the satellite cell lineage (satARKO), the weight of the androgen-sensitive levator ani muscle was lower, but decreased further upon orchidectomy. GTx-024 was as effective as dihydrotestosterone (DHT) in restoring levator ani weights to sham levels. Expression of the muscle-specific androgen-responsive genes S-adenosylmethionine decarboxylase and myostatin was decreased by orchidectomy and restored by GTx-024 and DHT in control mice, while expression was low and unaffected by androgen status in satARKO. In contrast, insulin-like growth factor IEa expression was not different between satARKO and control muscle, decreased upon castration, and was restored by DHT and GTx-024 in both genotypes. These data indicate that GTx-024 does not selectively modulate AR in the satellite cell lineage and that cells outside this lineage remain androgen-responsive in satARKO muscle. Indeed, residual AR positive cells were present in satARKO muscle, coexpressing the fibroblast-lineage marker vimentin. AR positive, muscle-resident fibroblasts could therefore be involved in the indirect effects of androgens on muscle. In conclusion, both DHT and GTx-024 target AR pathways in the satellite cell lineage, but cells outside this lineage also contribute to the anabolic effects of androgens.status: publishe

The global burden of cancer attributable to risk factors, 2010-19 : a systematic analysis for the Global Burden of Disease Study 2019

Background Understanding the magnitude of cancer burden attributable to potentially modifiable risk factors is crucial for development of effective prevention and mitigation strategies. We analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 to inform cancer control planning efforts globally. Methods The GBD 2019 comparative risk assessment framework was used to estimate cancer burden attributable to behavioural, environmental and occupational, and metabolic risk factors. A total of 82 risk-outcome pairs were included on the basis of the World Cancer Research Fund criteria. Estimated cancer deaths and disability-adjusted life-years (DALYs) in 2019 and change in these measures between 2010 and 2019 are presented. Findings Globally, in 2019, the risk factors included in this analysis accounted for 4.45 million (95% uncertainty interval 4.01-4.94) deaths and 105 million (95.0-116) DALYs for both sexes combined, representing 44.4% (41.3-48.4) of all cancer deaths and 42.0% (39.1-45.6) of all DALYs. There were 2.88 million (2.60-3.18) risk-attributable cancer deaths in males (50.6% [47.8-54.1] of all male cancer deaths) and 1.58 million (1.36-1.84) risk-attributable cancer deaths in females (36.3% [32.5-41.3] of all female cancer deaths). The leading risk factors at the most detailed level globally for risk-attributable cancer deaths and DALYs in 2019 for both sexes combined were smoking, followed by alcohol use and high BMI. Risk-attributable cancer burden varied by world region and Socio-demographic Index (SDI), with smoking, unsafe sex, and alcohol use being the three leading risk factors for risk-attributable cancer DALYs in low SDI locations in 2019, whereas DALYs in high SDI locations mirrored the top three global risk factor rankings. From 2010 to 2019, global risk-attributable cancer deaths increased by 20.4% (12.6-28.4) and DALYs by 16.8% (8.8-25.0), with the greatest percentage increase in metabolic risks (34.7% [27.9-42.8] and 33.3% [25.8-42.0]). Interpretation The leading risk factors contributing to global cancer burden in 2019 were behavioural, whereas metabolic risk factors saw the largest increases between 2010 and 2019. Reducing exposure to these modifiable risk factors would decrease cancer mortality and DALY rates worldwide, and policies should be tailored appropriately to local cancer risk factor burden. Copyright (C) 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe