Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups

We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of uncontrolled evolutions and the engineering of controlled dynamics for quantum information processing. Our results include two Hilbert space decompositions that allow for deciding the stability of the subspace of interest and for estimating of the speed of convergence, as well as a formula to obtain the limit probability distribution for a set of orthogonal invariant subspaces.Comment: 14 pages, no figures, to appear in Journal of Physics A, 201

Renormalization Group results for lattice surface models

We study the phase diagram of statistical systems of closed and open interfaces built on a cubic lattice. Interacting closed interfaces can be written as Ising models, while open surfaces as Z(2) gauge systems. When the open surfaces reduce to closed interfaces with few defects, also the gauge model can be written as an Ising spin model. We apply the lower bound renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev. Lett. 34, 1005 (1975)) to study the Ising models describing closed and open surfaces with few defects. In particular, we have studied the Ising-like transition of self-avoiding surfaces between the random-isotropic phase and the phase with broken global symmetry at varying values of the mean curvature. Our results are compared with previous numerical work. The limits of the LBRG transformation in describing regions of the phase diagram where not ferromagnetic ground-states are relevant are also discussed.Comment: 24 pages, latex, 5 figures (available upon request to [email protected]

Nonlinear resonance and excitability in interconnected systems

Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. While in the context of equilibrium dynamics there is a well-developed theory that can account for robustness and optimality in this process, we still lack a corresponding methodology for nonequilibrium dynamics and in particular oscillatory behaviours. With the aim of fostering such a theory, this thesis studies two basic interconnections in the contexts of nonlinear resonance and excitability, two phenomena with the potential of encompassing a large number of applications. The first interconnection is considered in the context of vibration absorption. It corresponds to coupling two Duffing oscillators, the prototypical example of nonlinear resonator. Of primary interest is the frequency response of the system, which quantifies the behaviour in presence of harmonic forces. The analysis focuses on how isolated families of solutions appear and merge with a main one. Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods. The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. Following this, the analysis moves to the complete interconnection, and in particular on how it can generate different patterns of bursting activity

S100B inhibitor pentamidine attenuates reactive gliosis and reduces neuronal loss in a mouse model of Alzheimer's disease

Among the different signaling molecules released during reactive gliosis occurring in Alzheimer’s disease (AD), the astrocytederived S100B protein plays a key role in neuroinflammation, one of the hallmarks of the disease. The use of pharmacological tools targeting S100B may be crucial to embank its effects and some of the pathological features of AD. The antiprotozoal drug pentamidine is a good candidate since it directly blocks S100B activity by inhibiting its interaction with the tumor suppressor p53. We used a mouse model of amyloid beta- (A-) induced AD, which is characterized by reactive gliosis and neuroinflammation in the brain, and we evaluated the effect of pentamidine on the main S100B-mediated events. Pentamidine caused the reduction of glial fibrillary acidic protein, S100B, and RAGE protein expression, which are signs of reactive gliosis, and induced p53 expression in astrocytes. Pentamidine also reduced the expression of proinflammatory mediators and markers, thus reducing neuroinflammation in AD brain. In parallel, we observed a significant neuroprotection exerted by pentamidine on CA1 pyramidal neurons. We demonstrated that pentamidine inhibits A-induced gliosis and neuroinflammation in an animal model of AD, thus playing a role in slowing down the course of the disease

Machine Learning Approach for Lowest Transition State Research of High Number Degrees of Freedom Homogeneous Catalysts

Nowadays, interesting problems in computational chemistry are found in studying complex systems with a high number of degrees of freedom. It is thus fundamental to provide a new way to handle them with a suitable tool capable of giving us the best compromise between accuracy and reliability using the minimum amount of computational time. In particular, these systems exhibit a high number of conformational isomers interconnected by low energy barriers and an accurate representation of their potential energy surface would allow us to identify the most stable isomer, the global minimum, and the transition state with the lowest energy. The challenge of this project is to provide a tool that helps us in this research, starting from a conformational analysis of four different homogeneous organocatalysts. This work aims to combine the Density Functional Theory accuracy and Molecular Mechanic Force Fields computational properties to explore the potential energy landscape using a Machine Learning approach

Folding transitions in three-dimensional space with defects

A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed in terms of Ising-like variables with nearest-neighbor and plaquette interactions in the hexagonal lattice; its phase diagram is determined by the Cluster Variation Method. The results found by varying the curvature and defect energy show that the introduction of defects turns the first-order crumpling transitions of the model without defects into continuous transitions. New phases also appear by decreasing the energy cost of defects and the behavior of their densities has been analyzed

The geometry of rest–spike bistability

Funder: Qualcomm; doi: http://dx.doi.org/10.13039/100005144Abstract: Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. We show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature