New Promising Therapeutic Avenues of Curcumin in Brain Diseases

Curcumin, the dietary polyphenol isolated from Curcuma longa (turmeric), is commonly used as an herb and spice worldwide. Because of its bio-pharmacological effects curcumin is also called “spice of life”, in fact it is recognized that curcumin possesses important proprieties such as anti-oxidant, anti-inflammatory, anti-microbial, antiproliferative, anti-tumoral, and anti-aging. Neurodegenerative diseases such as Alzheimer’s Diseases, Parkinson’s Diseases, and Multiple Sclerosis are a group of diseases characterized by a progressive loss of brain structure and function due to neuronal death; at present there is no effective treatment to cure these diseases. The protective effect of curcumin against some neurodegenerative diseases has been proven by in vivo and in vitro studies. The current review highlights the latest findings on the neuroprotective effects of curcumin, its bioavailability, its mechanism of action and its possible application for the prevention or treatment of neurodegenerative disorders.     

Human mobility and COVID-19 initial dynamics

Nonlinear Dynamics - Countries in Europe took different mobility containment measures to curb the spread of COVID-19. The European Commission asked mobile network operators to share on a...     

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.     

Effects of Regioisomerism on the Antiproliferative Activity of Hydroxystearic Acids on Human Cancer Cell Lines

A series of regioisomers of the hydroxystearic acid (HSA) was prepared, and the effect of the position of the hydroxyl group along the chain on a panel of human cancer cell lines was investigated. Among the various regioisomers, those carrying the hydroxyl at positions 5, 7, and 9 had growth inhibitor activity against various human tumor cell lines, including CaCo-2, HT29, HeLa, MCF7, PC3, and NLF cells. 10-HSA and 11-HSA showed a very weak effect. 8-HSA did not show inhibitory activity in all cell lines. The biological role of 7-HSA and 9-HSA is widely recognized, while little is known about the effects of 5-HSA. Therefore, the biological effects of 5-HSA in HeLa, HT29, MCF7, and NLF cell lines were investigated using the Livecyte’s ptychography technology, which allows correlating changes in proliferation, motility, and morphology as a function of treatment at the same time. 5-HSA not only reduces cell proliferation but also induces changes in cell displacement, directionality, and speed. It is important to characterize the biological effects of 5-HSA, this molecule being an important component of fatty acyl esters of hydroxy fatty acids (FAHFA), a class of endogenous mammalian lipids with noticeable anti-diabetic and anti-inflammatory effects.     

Nonlinear dynamos: A complex generalization of the Lorenz equations

Plane nonlinear dynamo waves can be described by a sixth order system of nonlinear ordinary differential equations which is a complex generalization of the Lorenz system. In the regime of interest for modelling magnetic activity in stars there is a sequence of bifurcations, ending in chaos, as a stability parameter D (the dynamo number) is increased. We show that solutions undergo three successive Hopf bifurcations, followed by a transition to chaos. The system possesses a symmetry and can therefore be reduced to a fifth order system, with trajectories that lie on a 2-torus after the third bifurcation. As D is then increased, frequency locking occurs, followed by a sequence of period-doubling bifurcations that leads to chaos. This behaviour is probably caused by the Shil'nikov mechanism, with a (conjectured) homoclinic orbit when D is infinite.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs

A theoretical model of disorder for the etched holes or pillars in a generic two-dimensional photonic crystal slab is presented. This model is employed to calculate the effects of size disorder on propagation losses in linear photonic crystal waveguides as well as on quality (Q)-factors in photonic crystal nano-cavities. The main results obtained by the present theory and shown in this work are: (a) large single-mode bandwidth and low-loss (<0.1 dB/mm) propagation of light is predicted for increased-width membrane-type photonic crystal waveguides, (b) pillar-based lattices show reduced sensitivity to size fluctuations than hole-based ones, (c) the effects of disorder on cavity Q-factors are quantitatively evaluated. An extension of the model is also introduced in order to take into account the side-wall micro-roughness of the perfectly vertical holes, and preliminary results of this more general approach are discussed.     

Axiomatic foundations of quantum physics: Critiques and misunderstandings. Piron's question-proposition system

Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the aim of clarifying their true significance, taking Piron's approach as conceptual framework. In particular, we deal with the following topics: the wrong identification of Piron's questions and Mackey's questions, and some curious alleged empirical consequences; the role of propositions as suitable equivalence classes of questions, their partial order structure, and the paradoxical consequences of the erroneous assignment to questions of some lattice properties involving propositions; the logical and the empirical purport of some negative theorems; the standard Hilbert space model of the theory and the consequent metaphysical disasters related to some identifications, which are peculiar of this model. A controversy between Foulis-Piron-Randall and Hadjisavvas-Thieffine-Mugur-Schächter is analyzed on the basis of the proposed Hilbert space model (in which Piron's questions are realized by Hilbertian effects, i.e., linear bounded operatorsF such that which clarify the different point of views. As an example, we treat the unsharp localization operators inL ₂().     

Brouwer-Zadeh (Fuzzy-intuitionistic) posets for unsharp quantum mechanics

The partial ordered structure which plays for unsharp quantum mechanics the same role of orthomodular lattices for ordinary quantum mechanics is introduced. Differently from the unsharp case, in which one can identify quantum propositions (i.e., Hilbert space subspaces) with yes-no devices (i.e., orthogonal projections) they are tested by, in the unsharp case this identification is broken down: every quantum generalized proposition (i.e., pair of mutually orthogonal subspaces) is tested by many different yes-no devices (i.e., Hilbert space effects). The set of all quantum effects has a structure of Brouwer-Zadeh poset, canonically embeddable in a (minimal) Brouwer-Zadeh lattice, whereas the set of all quantum generalized propositions has a structure of Brouwer-Zadeh complete lattice.A Brouwer-Zadeh poset is defined as a partially ordered structure equipped with two nonusual orthocomplementations: a regular degenerate (Zadeh or fuzzy-like) one and a weak (Brouwer or intuitionistic-like) one linked by an interconnection rule. Using these two orthocomplementations it is possible to introduce the two modal-like operators of necessity and possibility.     

Waves and stability

The connection between stability of equilibrium and propagation of small disturbances through a general elastic medium has been stated, since 1903, by J. Hadamard. However a doubtful element in the original proof of the theorem was pointed out by P. Duhem. A more elaborated proof, which seems to be satisfactory even in a more general hypothesis, has been later proposed by the author of this report. That proof is reconsidered in this article which deals, in a general context, with the relations between wave propagation and linear stability. A new elegant proof of Hadamard's theorem, recently proposed by G. Fichera, is briefly reported at the end of the article.

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Résumé Les liens entre la stabilité de l'équilibre et la propagation des ondes dans un milieu élastique ont été codifiés dès 1903, par J. Hadamard. La démonstration originaire du théorème présente toutefois un point douteux, mis en évidence par P. Duhem. Une démonstration plus élaborée, qui parait mathématiquement corrècte même en des conditions physiques plus générales, a été proposée plus tard par l'auteur de cet exposé. Cette démonstration est reprise dans l'article suivant, qui envisage dans un contexte général les relations entre la propagation des ondes et la stabilité linéaire. Une nouvelle et élégante démonstration du théorème de Hadamard, proposée récemment par G. Fichera, est résumée à la fin de l'article.

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Lecture delivered at the Italy-USA Seminar on Existence and Stability in Elasticity, Udine, June 26–30, 1971.