0 there exists a large subset of a â FĂp such that for kl a,1,p : x â e((ax+x) / p) we have M(kla,1,p) â„ (1âÎ”/â2Ï + o(1)) log log p, as pââ. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}aâFĂp. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary).
AU - Bonolis, Dante
ID - 9364
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 03050041
TI - On the size of the maximum of incomplete Kloosterman sums
ER -
TY - JOUR
AB - When short-range attractions are combined with long-range repulsions in colloidal particle systems, complex microphases can emerge. Here, we study a system of isotropic particles, which can form lamellar structures or a disordered fluid phase when temperature is varied. We show that, at equilibrium, the lamellar structure crystallizes, while out of equilibrium, the system forms a variety of structures at different shear rates and temperatures above melting. The shear-induced ordering is analyzed by means of principal component analysis and artificial neural networks, which are applied to data of reduced dimensionality. Our results reveal the possibility of inducing ordering by shear, potentially providing a feasible route to the fabrication of ordered lamellar structures from isotropic particles.
AU - PÈ©kalski, J.
AU - Rzadkowski, Wojciech
AU - Panagiotopoulos, A. Z.
ID - 7956
IS - 20
JF - The Journal of chemical physics
TI - Shear-induced ordering in systems with competing interactions: A machine learning study
VL - 152
ER -
TY - JOUR
AB - Neurodevelopmental disorders (NDDs) are a class of disorders affecting brain development and function and are characterized by wide genetic and clinical variability. In this review, we discuss the multiple factors that influence the clinical presentation of NDDs, with particular attention to gene vulnerability, mutational load, and the two-hit model. Despite the complex architecture of
mutational events associated with NDDs, the various proteins involved appear to converge on common pathways, such as synaptic plasticity/function, chromatin remodelers and the mammalian target of rapamycin (mTOR) pathway. A thorough understanding of the mechanisms behind these pathways will hopefully lead to the identification of candidates that could be targeted for treatment approaches.
AU - Parenti, Ilaria
AU - Garcia Rabaneda, Luis E
AU - SchĂ¶n, Hanna
AU - Novarino, Gaia
ID - 7957
IS - 8
JF - Trends in Neurosciences
SN - 01662236
TI - Neurodevelopmental disorders: From genetics to functional pathways
VL - 43
ER -
TY - JOUR
AB - Let A={A1,âŠ,An} be a family of sets in the plane. For 0â€i