0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 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 - THES AB - In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management. We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades. AU - Goharshady, Amir Kafshdar ID - 8934 SN - 2663-337X TI - Parameterized and algebro-geometric advances in static program analysis 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 - Pȩkalski, 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 - Schön, 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 -