A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations

Effects of Geometric Phases in Josephson Junction Arrays

We show that the en route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect in the classical limit. However, geometric phases due to the finite superfluid density at superconductor grains have a profound influence on the quantum dynamics of vortices. Subsequently we find rich and complex Hall behaviors analogous to the Thouless-Kohmoto-Nightingale-den Nijs effect in the quantum regime.Comment: Latex, 11 pages, appeared in Phys. Rev. Lett. v.77, 562 (1996) with minor change

Proteomics of Cytochrome c Oxidase-Negative versus -Positive Muscle Fiber Sections in Mitochondrial Myopathy

The mosaic distribution of cytochrome c oxidase(+) (COX+) and COX - muscle fibers in mitochondrial disorders allows the sampling of fibers with compensated and decompensated mitochondrial function from the same individual. We apply laser capture microdissection to excise individual COX+ and COX- fibers from the biopsies of mitochondrial myopathy patients. Using mass spectrometry-based proteomics, we quantify >4,000 proteins per patient. While COX+ fibers show a higher expression of respiratory chain components, COX- fibers display protean adaptive responses, including upregulation of mitochondrial ribosomes, translation proteins, and chaperones. Upregulated proteins include C1QBP, required for mitoribosome formation and protein synthesis, and STOML2, which organizes cardiolipin-enriched microdomains and the assembly of respiratory supercomplexes. Factoring in fast/slow fiber type, COX (-) slow fibers show a compensatory upregulation of beta-oxidation, the AAA(+) protease AFG3L1, and the OPA1-dependent cristae remodeling program. These findings reveal compensatory mechanisms in muscle fibers struggling with energy shortage and metabolic stress

Magnetoresistance and collective Coulomb blockade in super-lattices of ferromagnetic CoFe nanoparticles

We report on transport properties of millimetric super-lattices of CoFe nanoparticles surrounded by organic ligands. R(T)s follow R(T) = R_0.exp(T/T_0)^0.5 with T_0 ranging from 13 to 256 K. At low temperature I(V)s follow I=K[(V-V_T)/V_T]^ksi with ksi ranging 3.5 to 5.2. I(V) superpose on a universal curve when shifted by a voltage proportional to the temperature. Between 1.8 and 10 K a high-field magnetoresistance with large amplitude and a strong voltage-dependence is observed. Its amplitude only depends on the magnetic field/temperature ratio. Its origin is attributed to the presence of paramagnetic states present at the surface or between the nanoparticles. Below 1.8 K, this high-field magnetoresistance abruptly disappears and inverse tunnelling magnetoresistance is observed, the amplitude of which does not exceed 1%. At this low temperature, some samples display in their I(V) characteristics abrupt and hysteretic transitions between the Coulomb blockade regime and the conductive regime. The increase of the current during these transitions can be as high as a factor 30. The electrical noise increases when the sample is near the transition. The application of a magnetic field decreases the voltage at which these transitions occur so magnetic-field induced transitions are also observed. Depending on the applied voltage, the temperature and the amplitude of the magnetic field, the magnetic-field induced transitions are either reversible or irreversible. These abrupt and hysteretic transitions are also observed in resistance-temperature measurements. They could be the soliton avalanches predicted by Sverdlov et al. [Phys. Rev. B 64, 041302 (R), 2001] or could also be interpreted as a true phase transition between a Coulomb glass phase to a liquid phase of electrons

Calculation of the Hidden Symmetry Operator for a \cP\cT-Symmetric Square Well

It has been shown that a Hamiltonian with an unbroken \cP\cT symmetry also possesses a hidden symmetry that is represented by the linear operator \cC. This symmetry operator \cC guarantees that the Hamiltonian acts on a Hilbert space with an inner product that is both positive definite and conserved in time, thereby ensuring that the Hamiltonian can be used to define a unitary theory of quantum mechanics. In this paper it is shown how to construct the operator \cC for the \cP\cT-symmetric square well using perturbative techniques.Comment: 10 pages, 2 figure

Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations

Post-hoc explanations of machine learning models are crucial for people to understand and act on algorithmic predictions. An intriguing class of explanations is through counterfactuals, hypothetical examples that show people how to obtain a different prediction. We posit that effective counterfactual explanations should satisfy two properties: feasibility of the counterfactual actions given user context and constraints, and diversity among the counterfactuals presented. To this end, we propose a framework for generating and evaluating a diverse set of counterfactual explanations based on determinantal point processes. To evaluate the actionability of counterfactuals, we provide metrics that enable comparison of counterfactual-based methods to other local explanation methods. We further address necessary tradeoffs and point to causal implications in optimizing for counterfactuals. Our experiments on four real-world datasets show that our framework can generate a set of counterfactuals that are diverse and well approximate local decision boundaries, outperforming prior approaches to generating diverse counterfactuals. We provide an implementation of the framework at https://github.com/microsoft/DiCE.Comment: 13 page

Atomic and electronic structure of ultra-thin Al/AlOx/Al interfaces

Interfaces between metals based on AlO$_{x}$ represent the most popular basis for Josephson junctions or, more recently, also for junctions exhibiting substantial tunneling magneto-resistance. We have performed a computational study of possible local geometric structures of such interfaces at the ab-initio DFT/GGA level of approximation to complement recent experimental data on ultra-thin AlO$_{x}$-based interfaces. We present two competing structures that we characterise with their electronic properties: fragmentation and interface energies.Comment: Presented at the ECOSS24, submitted to the proceeding - special issue of Surf. Scienc