Synthesis of 2,4,6-tri-substituted-1,3,5-triazines

Several specific synthetic protocols were developed for the preparation from cyanuric chloride of a range of symmetric and non-symmetric di- and tri-substituted 1,3,5-triazines containing alkyl, aromatic, hindered, chiral and achiral hydroxyalkyl, ester and imidazole groups via sequential nucleophilic substitution of the C-Cl bond by C-O, C-N and C-S bonds.     

NMR Study of Water Distribution inside Tomato Cells: Effects of Water Stress

Tomato pericarp tissue was studied by low-field nuclear magnetic resonance (NMR) relaxometry. Two kinds of experiments were performed to investigate the correlation between multi-exponential NMR relaxation and the subcellular compartments. The longitudinal (T ₁) versus transverse (T ₂) relaxation times were first measured on fresh samples and then the transverse relaxation time was measured on samples exposed to water stress. Four signal components were found in all experiments. The results showed that all signal components corresponded to the water in different cell compartments, and that no signal from non-exchangeable protons was present. Moreover, we demonstrated that NMR relaxation is suitable for the continuous monitoring of water rebalancing between subcellular compartments of plant tissues.     

Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained models, which are in turn relevant for the study of glass and jamming transitions. We show that for generic tilings there exists a BP transition at a nontrivial critical density, 0<ρ _c <1. Thus, despite the presence of loops on all length scales in hyperbolic lattices, the behavior is very different from that on Euclidean lattices where the critical density is either zero or one. Furthermore, we show that the transition has a mixed character since it is discontinuous but characterized by a diverging correlation length, similarly to what happens on Bethe lattices and random graphs of constant connectivity.     

Quantum Fourier Transform-Based Arithmetic Logic Unit on a Quantum Processor

This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two-input and four-input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform-based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft-core processor on a quantum processing unit.     

Unbalanced optimal transport: Dynamic and Kantorovich formulations

This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation.     

Graded polynomial identities for matrices with the transpose involution over an infinite field

Let F be an infinite field and let M_n(F) be the algebra of n×n matrices over F endowed with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of M_n(F) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature, which were obtained for the field of complex numbers and for a particular class of elementary G-gradings.     

Stein’s method for diffusive limits of queueing processes

Queueing Systems - Donsker’s theorem is perhaps the most famous invariance principle result for Markov processes. It states that, when properly normalized, a random walk behaves...