Composite lacunary polynomials and the proof of a conjecture of Schinzel

Let $g(x)$ be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if $g(h(x))$ has boundedly many terms, then h(x)\in \C[x] must also have boundedly many terms. Solving an older conjecture raised by R\'enyi and by Erd\"os, Schinzel had proved this in the special cases $g(x)=x^d$; however that method does not extend to the general case. Here we prove the full Schinzel's conjecture (actually in sharper form) by a completely different method. Simultaneously we establish an "algorithmic" parametric description of the general decomposition $f(x)=g(h(x))$, where $f$ is a polynomial with a given number of terms and $g,h$ are arbitrary polynomials. As a corollary, this implies for instance that a polynomial with $l$ terms and given coefficients is non-trivially decomposable if and only if the degree-vector lies in the union of certain finitely many subgroups of $\Z^l$.Comment: 9 page

Case Study of a Global Simulation in French as a Foreign Language with Beginner Level Learners at the University Of Namibia: A Search for an Authentic Language and Culture Exposure in an African Anglophone Country

In a communicative based approach, the French Foreign Language learning teaching activities offered in classrooms favour exposing learners to authentic communicative situations that are relevant in a French or Francophone “genuine” context. This quest for “reality” or “authenticity” might be challenging in some linguistic environments such as African Anglophone countries where learners do not benefit from many opportunities to practice the foreign language and/or to get accustomed to its culture beyond the classroom. From this perspective, roleplays proved to positively provide learners with efficient communication skills that closely resembled “real” communication contexts. This paper aims at defining the Global Simulation (GS) process and its technicalities. The paper also aims at describing the adaptation from Debyser’s Global Simulation guide, L’Immeuble, to the context of the study: second year level students at the University of Namibia. The impact of applying GS on learners’ needs and expectations will be analysed.Keywords: Global Simulation, French Foreign Language Didactic, Communicative Approach, African Anglophone Contex

On some notions of good reduction for endomorphisms of the projective line

Let $\Phi$ be an endomorphism of \SR(\bar{\Q}), the projective line over the algebraic closure of \Q, of degree $\geq2$ defined over a number field $K$. Let $v$ be a non-archimedean valuation of $K$. We say that $\Phi$ has critically good reduction at $v$ if any pair of distinct ramification points of $\Phi$ do not collide under reduction modulo $v$ and the same holds for any pair of branch points. We say that $\Phi$ has simple good reduction at $v$ if the map $\Phi_v$, the reduction of $\Phi$ modulo $v$, has the same degree of $\Phi$. We prove that if $\Phi$ has critically good reduction at $v$ and the reduction map $\Phi_v$ is separable, then $\Phi$ has simple good reduction at $v$.Comment: 15 page

Calibration-Free and High-Sensitivity Microwave Detectors Based on InAs/InP Nanowire Double Quantum Dots

At the cutting-edge of microwave detection technology, novel approaches which exploit the interaction between microwaves and quantum devices are rising. In this study, microwaves are efficiently detected exploiting the unique transport features of InAs/InP nanowire double quantum dot-based devices, suitably configured to allow the precise and calibration-free measurement of the local field. Prototypical nanoscale detectors are operated both at zero and finite source-drain bias, addressing and rationalizing the microwave impact on the charge stability diagram. The detector performance is addressed by measuring its responsivity, quantum efficiency and noise equivalent power that, upon impedance matching optimization, are estimated to reach values up to approximate to 2000 A W-1, 0.04 and root HZ, respectively. The interaction mechanism between the microwave field and the quantum confined energy levels of the double quantum dots is unveiled and it is shown that these semiconductor nanostructures allow the direct assessment of the local intensity of the microwave field without the need for any calibration tool. Thus, the reported nanoscale devices based on III-V nanowire heterostructures represent a novel class of calibration-free and highly sensitive probes of microwave radiation, with nanometer-scale spatial resolution, that may foster the development of novel high-performance microwave circuitries

Real-Time TDM-based optimization of continuous-infusion meropenem for improving treatment outcome of febrile neutropenia in oncohaematological patients: Results from a prospective, monocentric, interventional study

Objectives: To assess the role that real-Time therapeutic drug monitoring (TDM)-guided optimization of continuous-infusion (CI) meropenem may have in maximizing empirical treatment and in preventing breakthrough infection and/or colonization with carbapenem-resistant Enterobacteriaceae (CRE) among oncohaematological patients with febrile neutropenia (FN). Methods: A monocentric, interventional, prospective study was conducted. The pharmacodynamic (PD) target was a steady-state meropenem concentration-To-MIC ratio (Css/MIC) of 4-8. The primary endpoint was 14 day all-cause mortality. The secondary endpoint was the prevalence of CRE colonization in rectal swabs of patients rehospitalized within 3months. Results: Among the 75 patients enrolled, most (56%) had AML, almost half (37/75, 49.3%) underwent HSCT and one-Third (32%) received meropenem as monotherapy. Meropenem dosages were adjusted in 30.1% of TDM reassessments. Gram-negative infections were microbiologically documented in 20.0% of patients. All of the 12 patients having infections caused by in vitro meropenem-susceptible pathogens attained the desired PD target and were cured. Three patients had infections caused by in vitro meropenem-resistant pathogens. Two of these achieved a Css/MIC target of 1 and were cured; the other one achieved a suboptimal PD target (0.59) and died. The 14 day all-cause mortality (10.7%) was significantly associated, at multivariate regression, with HSCT (OR 0.086, 95% CI 0.008-0.936, P = 0.044) and with augmented renal clearance (OR 10.846, 95% CI 1.534-76.672, P = 0.017). None of the patients who had hospital readmissions in the 3month follow-up (63/75) had CRE colonization in rectal swabs. Conclusions: Real-Time TDM-guided CI meropenem may be a useful approach for attaining adequate exposure and preventing CRE emergence in FN oncohaematological patients

Microwave-Assisted Tunneling in Hard-Wall InAs/InP Nanowire Quantum Dots

With downscaling of electronic circuits, components based on semiconductor quantum dots are assuming increasing relevance for future technologies. Their response under external stimuli intrinsically depend on their quantum properties. Here we investigate single-electron tunneling in hard-wall InAs/InP nanowires in the presence of an off-resonant microwave drive. Our heterostructured nanowires include InAs quantum dots (QDs) and exhibit different tunnel-current regimes. In particular, for source-drain bias up to few mV Coulomb diamonds spread with increasing contrast as a function of microwave power and present multiple current polarity reversals. This behavior can be modelled in terms of voltage fluctuations induced by the microwave field and presents features that depend on the interplay of the discrete energy levels that contribute to the tunneling process

Predictive value of pretransplantation molecular minimal residual disease assessment by WT1 gene expression in FLT3-positive acute myeloid leukemia

The FMS-like tyrosine kinase 3 (FLT3) mutation in acute myeloid leukemia (AML) is a negative prognostic factor and, in these cases, allogeneic stem cell transplantation (allo-SCT) can represent an important therapeutic option, especially if performed in complete remission (CR). However, it is increasingly clear that not all cytological CRs (cCRs) are the same and that minimal residual disease (MRD) before allo-SCT could have an impact on AML outcome. Unfortunately, FLT3, due its instability of expression, is still not considered a good molecular MRD marker. We analyzed the outcome of allo-SCT in a population of FLT3-positive AML patients according to molecular MRD at the pretransplantation workup, assessed by the quantitative expression evaluation of the panleukemic marker Wilms\u2019 tumor (WT1) gene. Sixty-two consecutive AML FLT3-positive patients received allo-SCT between 2005 and 2016 in our center. The median age at transplantation was 55 years. The quantitative analysis of the WT1 gene expression (bone marrow samples) was available in 54 out of 62 (87%) cases, both at diagnosis (100% overexpressing WT1 with a mean of 9747 \ub1 8064 copies) and before allo-SCT (33 WT1-negative and 21 WT1-positive cases at the pretransplantation workup). Of these cases, 33/54 (61%) were both in cCR and molecular remission (WT1-negative) at the time of transplantation, 13/54 (24%) were in cCR but not in molecular remission (WT1-positive), and 8/54 (15%) showed a cytological evidence of disease (relapsed or refractory). Both post-allo-SCT overall survival (OS) and disease-free survival (DFS) were significantly better in patients who were WT1-negative (WT1 250 copies), with a median OS and DFS not reached in the WT1-negative group and 10.2 and 5.5 months, respectively, in the WT1-positive group (OS log\u2013rank p = 0.0005; hazard ratio [HR] = 3.7, 95% confidence interval [95% CI] = 1.5\u20139; DFS log\u2013rank p = 0.0001; HR = 4.38, 95% CI = 1.9\u201310). Patients with cCR who were WT1-positive had the same negative outcome as those with a cytological evidence of disease. The relapse rate after allo-SCT was 9% (3/33) in pre-allo-SCT WT1-negative cases and 54% (7/13) in WT1-positive cases (p = 0.002). At multivariate analysis, WT1 negativity before allo-SCT and grade <2 acute graft versus host disease were the only independent prognostic factors for improved OS and DFS. These data show that pre-allo-SCT molecular MRD evaluation through WT1 expression is a powerful predictor of posttransplantation outcomes (OS, DFS, relapse rate). Patients with both cCR and a WT1-negative marker before allo-SCT have a very good outcome with very low relapse rate; conversely, patients with positive molecular MRD and refractory/relapsed patients have a negative outcome. The WT1 MRD stratification in FLT3-positive AML is a valuable tool with which to identify patients who are at high risk of relapse and that could be considered from post-allo-SCT prophylaxis with FLT3 inhibitors or other strategies (donor lymphocyte infusion, tapering of immunosuppression, azacitidine). \ua9 2017 ISEH - International Society for Experimental Hematolog

Fludarabine, high-dose cytarabine and idarubicin-based induction may overcome the negative prognostic impact of flt3-itd in npm1 mutated aml, irrespectively of flt3-itd allelic Burden

The mutations of NPM1 and FLT3-ITD represent the most frequent genetic aberration in acute myeloid leukemia. Indeed, the presence of an NPM1 mutation reduces the negative prognostic impact of FLT3-ITD in patients treated with conventional “3+7” induction. However, little information is available on their prognostic role with intensified regimens. Here, we investigated the efficacy of a fludarabine, high-dose cytarabine and idarubicin induction (FLAI) in 149 consecutive fit AML patients (median age 52) carrying the NPM1 and/or FLT3-ITD mutation, treated from 2008 to 2018. One-hundred-and-twenty-nine patients achieved CR (86.6%). After a median follow up of 68 months, 3-year overall survival was 58.6%. Multivariate analysis disclosed that both NPM1mut (p &lt; 0.05) and ELN 2017 risk score (p &lt; 0.05) were significant predictors of survival. NPM1-mutated patients had a favorable outcome, with no significant differences between patients with or without concomitant FLT3-ITD (p = 0.372), irrespective of FLT3-ITD allelic burden. Moreover, in landmark analysis, performing allogeneic transplantation (HSCT) in first CR proved to be beneficial only in ELN 2017 high-risk patients. Our data indicate that FLAI exerts a strong anti-leukemic effect in younger AML patients with NPM1mut and question the role of HSCT in 1st CR in NPM1mut patients with concomitant FLT3-ITD