Effective Coupling for Open Billiards

We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation. Deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account. The influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide are also discussed. Finally we show that the mean value of the dimensionless coupling constants tends to the critical value when the eigenstates of the billiard follow random-matrix theory

Quantum master equation for a system influencing its environment

A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in a finite total system. This master quantum describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in isolated nanoscopic total system.Comment: 39 pages, 10 figure

Orbital effect of in-plane magnetic field on quantum transport in chaotic lateral dots

We show how the in-plane magnetic field, which breaks time-reversal and rotational symmetries of the orbital motion of electrons in a heterostructure due to the momentum-dependent inter-subband mixing, affects weak localisation correction to conductance of a large-area chaotic lateral quantum dot and parameteric dependences of universal conductance fluctuations in it.Comment: 4 pages with a figur

Calcium dependent plasticity applied to repetitive transcranial magnetic stimulation with a neural field model

The calcium dependent plasticity (CaDP) approach to the modeling of synaptic weight change is applied using a neural field approach to realistic repetitive transcranial magnetic stimulation (rTMS) protocols. A spatially-symmetric nonlinear neural field model consisting of populations of excitatory and inhibitory neurons is used. The plasticity between excitatory cell populations is then evaluated using a CaDP approach that incorporates metaplasticity. The direction and size of the plasticity (potentiation or depression) depends on both the amplitude of stimulation and duration of the protocol. The breaks in the inhibitory theta-burst stimulation protocol are crucial to ensuring that the stimulation bursts are potentiating in nature. Tuning the parameters of a spike-timing dependent plasticity (STDP) window with a Monte Carlo approach to maximize agreement between STDP predictions and the CaDP results reproduces a realistically-shaped window with two regions of depression in agreement with the existing literature. Developing understanding of how TMS interacts with cells at a network level may be important for future investigation

Effects of Fermi energy, dot size and leads width on weak localization in chaotic quantum dots

Magnetotransport in chaotic quantum dots at low magnetic fields is investigated by means of a tight binding Hamiltonian on L x L clusters of the square lattice. Chaoticity is induced by introducing L bulk vacancies. The dependence of weak localization on the Fermi energy, dot size and leads width is investigated in detail and the results compared with those of previous analyses, in particular with random matrix theory predictions. Our results indicate that the dependence of the critical flux Phi_c on the square root of the number of open modes, as predicted by random matrix theory, is obscured by the strong energy dependence of the proportionality constant. Instead, the size dependence of the critical flux predicted by Efetov and random matrix theory, namely, Phi_c ~ sqrt{1/L}, is clearly illustrated by the present results. Our numerical results do also show that the weak localization term significantly decreases as the leads width W approaches L. However, calculations for W=L indicate that the weak localization effect does not disappear as L increases.Comment: RevTeX, 8 postscript figures include

Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure

Biophysical modeling of neural plasticity induced by transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a widely used noninvasive brain stimulation method capable of inducing plastic reorganisation of cortical circuits in humans. Changes in neural activity following TMS are often attributed to synaptic plasticity via process of long-term potentiation and depression (LTP/LTD). However, the precise way in which synaptic processes such as LTP/LTD modulate the activity of large populations of neurons, as stimulated en masse by TMS, are unclear. The recent development of biophysical models, which incorporate the physiological properties of TMS-induced plasticity mathematically, provide an excellent framework for reconciling synaptic and macroscopic plasticity. This article overviews the TMS paradigms used to induce plasticity, and their limitations. It then describes the development of biophysically-based numerical models of the mechanisms underlying LTP/LTD on population-level neuronal activity, and the application of these models to TMS plasticity paradigms, including theta burst and paired associative stimulation. Finally, it outlines how modeling can complement experimental work to improve mechanistic understandings and optimize outcomes of TMS-induced plasticity

Invariant Natural Killer T-cells and their subtypes may play a role in the pathogenesis of endometriosis

Objective: To evaluate the frequencies of iNKT cells and their subsets in patients with deep endometriosis. Methods: A case-control study was conducted between 2013 and 2015, with 73 patients distributed into two groups: 47 women with a histological diagnosis of endometriosis and 26 controls. Peripheral blood, endometriosis lesions, and healthy peritoneal samples were collected on the day of surgery to determine the frequencies of iNKT cells and subtypes via flow cytometry analysis. Results: The authors observed a lower number of iNKT (p = 0.01) and Double-Negative (DN) iNKT cells (p = 0.02) in the blood of patients with endometriosis than in the control group. The number of DN iNKT IL-17+ cells in the secretory phase was lower in the endometriosis group (p = 0.049). There was an increase in the secretion of IL-17 by CD4+ iNKT cells in the blood of patients with endometriosis and severe dysmenorrhea (p = 0.038), and severe acyclic pelvic pain (p = 0.048). Patients with severe dysmenorrhea also had a decreased number of CD4+ CCR7+ cells (p = 0.022). Conclusion: The decreased number of total iNKT and DN iNKT cells in patients with endometriosis suggests that iNKT cells play a role in the pathogenesis of endometriosis and can be used to develop new diagnostic and therapeutic agents

G-CORE a core for future graph query languages

We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity

G-CORE a core for future graph query languages

We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity