Ensemble Average Theory of Gravity

We put forward the idea that all the theoretically consistent models of gravity have contributions to the observed gravity interaction. In this formulation, each model comes with its own Euclidean path-integral weight where general relativity (GR) has automatically the maximum weight in high-curvature regions. We employ this idea in the framework of Lovelock models and show that in four dimensions the result is a specific form of the $f(R,G)$ model. This specific $f(R,G)$ satisfies the stability conditions and possesses self-accelerating solutions. Our model is consistent with the local tests of gravity since its behavior is the same as in GR for the high-curvature regime. In the low-curvature regime the gravitational force is weaker than in GR, which can be interpreted as the existence of a repulsive fifth force for very large scales. Interestingly, there is an intermediate-curvature regime where the gravitational force is stronger in our model compared to GR. The different behavior of our model in comparison with GR in both low- and intermediate-curvature regimes makes it observationally distinguishable from $\Lambda$CDM.Comment: 6 pages, typos corrected, comments are welcome, replaced with published versio

Learning-based Ensemble Average Propagator Estimation

By capturing the anisotropic water diffusion in tissue, diffusion magnetic resonance imaging (dMRI) provides a unique tool for noninvasively probing the tissue microstructure and orientation in the human brain. The diffusion profile can be described by the ensemble average propagator (EAP), which is inferred from observed diffusion signals. However, accurate EAP estimation using the number of diffusion gradients that is clinically practical can be challenging. In this work, we propose a deep learning algorithm for EAP estimation, which is named learning-based ensemble average propagator estimation (LEAPE). The EAP is commonly represented by a basis and its associated coefficients, and here we choose the SHORE basis and design a deep network to estimate the coefficients. The network comprises two cascaded components. The first component is a multiple layer perceptron (MLP) that simultaneously predicts the unknown coefficients. However, typical training loss functions, such as mean squared errors, may not properly represent the geometry of the possibly non-Euclidean space of the coefficients, which in particular causes problems for the extraction of directional information from the EAP. Therefore, to regularize the training, in the second component we compute an auxiliary output of approximated fiber orientation (FO) errors with the aid of a second MLP that is trained separately. We performed experiments using dMRI data that resemble clinically achievable $q$-space sampling, and observed promising results compared with the conventional EAP estimation method.Comment: Accepted by MICCAI 201

Entanglement of a microcanonical ensemble

We replace time-averaged entanglement by ensemble-averaged entanglement and derive a simple expression for the latter. We show how to calculate the ensemble average for a two-spin system and for the Jaynes-Cummings model. In both cases the time-dependent entanglement is known as well so that one can verify that the time average coincides with the ensemble average.Comment: 10 page

The spectral form factor is not self-averaging

The spectral form factor, k(t), is the Fourier transform of the two level correlation function C(x), which is the averaged probability for finding two energy levels spaced x mean level spacings apart. The average is over a piece of the spectrum of width W in the neighborhood of energy E0. An additional ensemble average is traditionally carried out, as in random matrix theory. Recently a theoretical calculation of k(t) for a single system, with an energy average only, found interesting nonuniversal semiclassical effects at times t approximately unity in units of {Planck's constant) /(mean level spacing). This is of great interest if k(t) is self-averaging, i.e, if the properties of a typical member of the ensemble are the same as the ensemble average properties. We here argue that this is not always the case, and that for many important systems an ensemble average is essential to see detailed properties of k(t). In other systems, notably the Riemann zeta function, it is likely possible to see the properties by an analysis of the spectrum.Comment: 4 pages, RevTex, no figures, submitted to Phys. Rev. Lett., permanent e-mail address, [email protected]

Sensor-AssistedWeighted Average Ensemble Model for Detecting Major Depressive Disorder

The present methods of diagnosing depression are entirely dependent on self-report ratings or clinical interviews. Those traditional methods are subjective, where the individual may or may not be answering genuinely to questions. In this paper, the data has been collected using self-report ratings and also using electronic smartwatches. This study aims to develop a weighted average ensemble machine learning model to predict major depressive disorder (MDD) with superior accuracy. The data has been pre-processed and the essential features have been selected using a correlation-based feature selection method. With the selected features, machine learning approaches such as Logistic Regression, Random Forest, and the proposedWeighted Average Ensemble Model are applied. Further, for assessing the performance of the proposed model, the Area under the Receiver Optimization Characteristic Curves has been used. The results demonstrate that the proposed Weighted Average Ensemble model performs with better accuracy than the Logistic Regression and the Random Forest approaches

Eulerian and Newtonian dynamics of quantum particles

We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by the Schrodinger equation, can be considered as an inviscid gas obeying the ideal gas law with quickly oscillating sign-alternating temperature. This statistical ensemble performs the complex movements consisting of smooth average movement and fast oscillations. It is shown that average movements of statistical ensemble are described by Schrodinger equation. A model of quantum motion within the limits of classical mechanics which corresponds to the considered hydrodynamic system is suggested.Comment: 25 page