Suffix conjugates for a class of morphic subshifts

Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and T: X --> X is the shift map. Let S be a finite alphabet that is in bijective correspondence via a mapping c with the set of nonempty suffixes of the images f(a) for a in A. Let calS be a subset S^N be the set of infinite words s = (s_n)_{n\geq 0} such that \pi(s):= c(s_0)f(c(s_1)) f^2(c(s_2))... is in X. We show that if f is primitive and f(A) is a suffix code, then there exists a mapping H: calS --> calS such that (calS, H) is a topological dynamical system and \pi: (calS, H) --> (X, T) is a conjugacy; we call (calS, H) the suffix conjugate of (X, T). In the special case when f is the Fibonacci or the Thue-Morse morphism, we show that the subshift (calS, T) is sofic, that is, the language of calS is regular

Slow and fast micro-field components in warm and dense hydrogen plasmas

The aim of this work is the investigation of the statistical properties of local electric fields in an ion-electron two component plasmas for coupled conditions. The stochastic fields at a charged or at a neutral point in plasmas involve both slow and fast fluctuation characteristics. The statistical study of these local fields based on a direct time average is done for the first time. For warm and dense plasma conditions, typically $N_{e}\approx 10^{18}cm^{-3}$, $$, well controlled molecular dynamics (MD) simulations of neutral hydrogen, protons and electrons have been carried out. Relying on these \textit{ab initio} MD calculations this work focuses on an analysis of the concepts of statistically independent slow and fast local field components, based on the consideration of a time averaged electric field. Large differences are found between the results of these MD simulations and corresponding standard results based on static screened fields. The effects discussed are of importance for physical phenomena connected with stochastic electric field fluctuations, e.g., for spectral line broadening in dense plasmas.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Computing the kk-binomial complexity of the Thue--Morse word

Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the set of factors of length $n$ occurring in $\mathbf{x}$. This complexity measure has not been investigated very much. In this paper, we characterize the $k$-binomial complexity of the Thue--Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue--Morse word is aperiodic, its $k$-binomial complexity eventually takes only two values. In this paper, we first obtain general results about the number of occurrences of subwords appearing in iterates of the form $\Psi^\ell(w)$ for an arbitrary morphism $\Psi$. We also thoroughly describe the factors of the Thue--Morse word by introducing a relevant new equivalence relation

Pion production in deeply virtual Compton scattering

Using a soft pion theorem based on chiral symmetry and a $\Delta(1232)$ resonance model we propose an estimate for the production cross section of low energy pions in the deeply virtual Compton scattering (DVCS) process. In particular, we express the $e p \to e \gamma \pi N$ processes in terms of generalized parton distributions. We provide estimates of the contamination of the $e p \to e \gamma p$ DVCS observables due to this associated pion production processes when the experimental data are not fully exclusive, for a set of kinematical conditions representative of present or planned experiments at JLab, HERMES and COMPASS.Comment: 50 pages, 22 figure

Periodic points in random substitution subshifts

We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible random substitutions—random substitutions for which a well-defined abelianisation exists. We find some simple necessary criteria for primitive, compatible random substitutions to admit periodic points in their subshifts. In the case that the random substitution further has disjoint images and is of constant length, we provide a stronger criterion. A method is outlined for enumerating periodic points of any specified length in a random substitution subshift

Lorlatinib with or without chemotherapy in ALK-driven refractory/relapsed neuroblastoma: phase 1 trial results.

Neuroblastomas harbor ALK aberrations clinically resistant to crizotinib yet sensitive pre-clinically to the third-generation ALK inhibitor lorlatinib. We conducted a first-in-child study evaluating lorlatinib with and without chemotherapy in children and adults with relapsed or refractory ALK-driven neuroblastoma. The trial is ongoing, and we report here on three cohorts that have met pre-specified primary endpoints: lorlatinib as a single agent in children (12 months to <18 years); lorlatinib as a single agent in adults (≥18 years); and lorlatinib in combination with topotecan/cyclophosphamide in children (<18 years). Primary endpoints were safety, pharmacokinetics and recommended phase 2 dose (RP2D). Secondary endpoints were response rate and 123I-metaiodobenzylguanidine (MIBG) response. Lorlatinib was evaluated at 45-115 mg/m2/dose in children and 100-150 mg in adults. Common adverse events (AEs) were hypertriglyceridemia (90%), hypercholesterolemia (79%) and weight gain (87%). Neurobehavioral AEs occurred mainly in adults and resolved with dose hold/reduction. The RP2D of lorlatinib with and without chemotherapy in children was 115 mg/m2. The single-agent adult RP2D was 150 mg. The single-agent response rate (complete/partial/minor) for <18 years was 30%; for ≥18 years, 67%; and for chemotherapy combination in <18 years, 63%; and 13 of 27 (48%) responders achieved MIBG complete responses, supporting lorlatinib's rapid translation into active phase 3 trials for patients with newly diagnosed high-risk, ALK-driven neuroblastoma. ClinicalTrials.gov registration: NCT03107988

Detection of ALK fusion transcripts in FFPE lung cancer samples by NanoString technology

Background: ALK-rearranged lung cancers exhibit specific pathologic and clinical features and are responsive to anti-ALK therapies. Therefore, the detection of ALK-rearrangement is fundamental for personalized lung cancer therapy. Recently, new molecular techniques, such as NanoString nCounter, have been developed to detect ALK fusions with more accuracy and sensitivity. Methods: In the present study, we intended to validate a NanoString nCounter ALK-fusion panel in routine biopsies of FFPE lung cancer patients. A total of 43 samples were analyzed, 13 ALK-positive and 30 ALK-negative, as previously detected by FISH and/or immunohistochemistry. Results: The NanoString panel detected the presence of the EML4-ALK, KIF5B-ALK and TFG-ALK fusion variants. We observed that all the 13 ALK-positive cases exhibited genetic aberrations by the NanoString methodology. Namely, six cases (46.15%) presented EML-ALK variant 1, two (15.38%) presented EML-ALK variant 2, two (15.38%) presented EML-ALK variant 3a, and three (23.07%) exhibited no variant but presented unbalanced expression between 5'/3' exons, similar to other positive samples. Importantly, for all these analyses, the initial input of RNA was 100 ng, and some cases displayed poor RNA quality measurements. Conclusions: In this study, we reported the great utility of NanoString technology in the assessment of ALK fusions in routine lung biopsies of FFPE specimens.This study was partially funded by FINEP (MCTI/FINEP/MS/SCTIE/DECIT), Brazil. BIOPLAT (1302/13).info:eu-repo/semantics/publishedVersio