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We study an open question at the interplay between the classical and the dynamical Mordell-Lang conjectures in positive characteristic. Let K be an algebraically closed field of positive characteristic, let G be a finitely generated subgroup of the multiplicative group of K, and let X be an (irreducible) quasiprojective variety defined over K. We consider K-valued sequences of the form an : = f(φn(x0)), where φ : X → X and f : X → P¹ are rational maps defined over K and x0 ∈ X is a point whose forward orbit avoids the indeterminacy loci of φ and f. We show that the set of n for which an ∈ G is a finite union of arithmetic progressions along with a set of Banach density zero. [ABSTRACT FROM AUTHOR]

Given a right-infinite word x over a finite alphabet A, the rank of x is the size of the smallest set S of words over A such that x can be realized as an infinite concatenation of words in S. We show that the property of having rank two is decidable for the class of k-automatic words for each integer k ≥ 2. [ABSTRACT FROM AUTHOR]

According to Winthrop Bell's analysis of the idea of Canada, a pioneering account of Canadian philosophy written during World War I, Canada's essence involves intercultural interpretation. In terms familiar to the phenomenology and pragmatism in which he was trained, Bell shows how Canada, by creating a new culture founded upon intercultural respect, could replace monocultural imperialism and materialism with something better: a culturally diverse nation, serving wisdom from a unique conversation among Canadian peoples, but that is for all people. In this article, we describe Bell's philosophy of Canada as interpretation and further apply it to the idea, practice, and end of reparations to Canada's Indigenous peoples as an expression of loyalty to Canadian philosophy today. [ABSTRACT FROM AUTHOR]

We prove a uniform version of the Dynamical Mordell–Lang Conjecture for étale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary endomorphism of a quasiprojective variety defined over a number field. More precisely, for our 1st result, we assume |$X$| is a quasi-projective variety defined over a field |$K$| of characteristic |$0$|⁠ , endowed with the action of an étale endomorphism |$\Phi $|⁠ , and |$f\colon X\longrightarrow Y$| is a morphism with |$Y$| a quasi-projective variety defined over |$K$|⁠. Then for any |$x\in X(K)$|⁠ , if for each |$y\in Y(K)$|⁠ , the set |$S_{x,y}:=\{n\in{\mathbb{N}}\colon f(\Phi ^n(x))=y\}$| is finite, then there exists a positive integer |$N_x$| such that |$\sharp S_{x,y}\le N_x$| for each |$y\in Y(K)$|⁠. For our 2nd result, we let |$K$| be a number field, |$f:X\dashrightarrow{\mathbb{P}}^1$| is a rational map, and |$\Phi $| is an arbitrary endomorphism of |$X$|⁠. If |${\mathcal{O}}_{\Phi }(x)$| denotes the forward orbit of |$x$| under the action of |$\Phi $|⁠ , then either |$f({\mathcal{O}}_{\Phi }(x))$| is finite, or |$\limsup _{n\to \infty } h(f(\Phi ^n(x)))/\log (n)>0$|⁠ , where |$h(\cdot)$| represents the usual logarithmic Weil height for algebraic points. [ABSTRACT FROM AUTHOR]

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras. [ABSTRACT FROM AUTHOR]

Background: Dilation and evacuation is a method of second trimester pregnancy termination introduced recently in Ethiopia. However, little is known about the safety and effectiveness of this method in an Ethiopian setting. Therefore, the study is intended to determine the safety and effectiveness of dilation and evacuation for surgical abortion as compared to medical abortion between 13–20 weeks' gestational age. Methods: This is a quasi-experimental study of women receiving second trimester termination of pregnancy between 13–20 weeks. Patients were allocated to either medical or surgical abortion based on their preference. A structured questionnaire was used to collect demographic information and clinical data upon admission. Procedure related information was collected after the procedure was completed and before the patient was discharged. Additionally, women were contacted 2 weeks after the procedure to evaluate for post-procedural complications. The primary outcome of the study was a composite complication rate. Data were collected using Open Data Kit and then analyzed using Stata version 14.2. Univariate analyses were performed using means (standard deviation), or medians (interquartile range) when the distribution was not normal. Multiple logistic regression was also performed to control for confounders. Results: Two hundred nineteen women chose medical abortion and 60 chose surgical abortion. The composite complication rate is not significantly different among medical and surgical abortion patients (15% versus 10%; p = 0.52). Nine patients (4.1%) in the medical arm required additional intervention to complete the abortion, while none of the surgical abortion patients required additional intervention. Median (IQR) hospital stay was significantly longer in the medical group at 24 (12–24) hours versus 6(4–6) hours in the surgical group p<0.001. Conclusion: From the current study findings, we concluded that there is no difference in safety between surgical and medical methods of abortion. This study demonstrates that surgical abortion can be used as a safe and effective alternative to medical abortion and should be offered equivalently with medical abortion, per the patient's preference. [ABSTRACT FROM AUTHOR]

In today's highly globalised, increasingly interlinked and extremely competitive auto industry, it is important to understand how some countries succeed in adopting the latest technologies while others are left behind. The creation of a competitive auto industry requires a deep supply chain. One that can compete in the global automotive space and develop and apply technologies as well as penetrate niche markets. Building on comparative research, this article seeks to understand the factors and power relations that led to the deepening of the Thai auto sector, specifically of its automotive component manufacturers, and how South Africa can learn from it. [ABSTRACT FROM AUTHOR]

Abstract Background Statistical methods to tentatively identify differentially expressed genes in microarray studies typically assume larger sample sizes than are practical or even possible in some settings. Results The performance of several probe-level and probeset models was assessed graphically and numerically using three spike-in datasets. Based on the Affymetrix GeneChip, a novel nested factorial model was developed and found to perform competitively on small-sample spike-in experiments. Conclusions Statistical methods with test statistics related to the estimated log fold change tend to be more consistent in their performance on small-sample gene expression data. For such small-sample experiments, the nested factorial model can be a useful statistical tool. This method is implemented in freely-available R code (affyNFM), available with a tutorial document at http://www.stat.usu.edu/~jrstevens.

Background: Mild traumatic brain injury (mTBI) results from an external force to the head or body causing neurophysiological changes within the brain. The number and severity of symptoms can vary, with some individuals experiencing rapid recovery, and others having persistent symptoms for months to years, impacting their quality of life. Current rehabilitation is limited in its ability to treat persistent symptoms and novel approaches are being sought to improve outcomes following mTBI. Neuromodulation is one technique used to encourage adaptive neuroplasticity within the brain. Objective: To systematically review the literature on the efficacy of neuromodulation in the mTBI population. Method: A systematic review was conducted using Medline, Embase, PsycINFO, PsycARTICLES and EBM Review. Preferred Reporting Items for Systematic Reviews and the Synthesis Without Meta-analysis reporting guidelines were used and a narrative review of the selected studies was completed. Fourteen articles fulfilled the inclusion criteria which were published in English, investigating an adult sample and using a pre- and post-intervention design. Studies were excluded if they included non-mild TBI severities, pediatric or older adult populations. Results: Thirteen of fourteen studies reported positive reductions in mTBI symptomatology following neuromodulation. Specifically, improvements were reported in post-concussion symptom ratings, headaches, dizziness, depression, anxiety, sleep disturbance, general disability, cognition, return to work and quality of life. Normalization of working memory activation patterns, vestibular field potentials, hemodynamics of the dorsolateral prefrontal cortex and excessive delta wave activity were also seen. The studies reviewed had several methodological limitations including small, heterogenous samples and varied intervention protocols, limiting generalisability. Further research is required to understand the context in which neuromodulation may be beneficial. Conclusions: While these positive effects are observed, limitations included unequal representation of neuromodulation modalities in the literature, and lack of literature describing the efficacy of neuromodulation on the development or duration of persistent mTBI symptoms. Better clarity regarding neuromodulation efficacy could have a significant impact on mTBI patients, researchers, clinicians, and policy makers, facilitating a more productive post-mTBI population. Despite the limitations, the literature indicates that neuromodulation warrants further investigation. PROSPERO registration number: CRD42020161279. [ABSTRACT FROM AUTHOR]

We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number > 2 5 is the sum of at most three natural numbers whose base- 2 representation has an equal number of 0 's and 1 's. [ABSTRACT FROM AUTHOR]