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  • Non-equilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasi-stationary non-thermal plateaux are often observed at intermediate times. The typical example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state can not escape the constraints imposed by the approximate integrability. Here we unveil a new mechanism of prethermalization, based on the presence of a symmetry of the pre-quench Hamiltonian, which is spontaneously broken at zero temperature, and is explicitly broken by the post-quench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasi-stationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full time evolution is computed analytically, and the (non integrable) ANNNI model, which is investigated numerically. Read More
  • Let $D$ be a bounded domain in $\mathbb R^n,$ with smooth boundary. Denote $V_D(\omega,t), \ \omega \in S^{n-1}, t \in \mathbb R,$ the Radon transform of the characteristic function $\chi_{D}$ of the domain $D,$ i.e., the $(n-1)-$ dimensional volume of the intersection $D$ with the hyperplane $\{x \in \mathbb R^n: <\omega,x>=t \}.$ If the domain $D$ is an ellipsoid, then the function $V_D$ is algebraic and if, in addition, the dimension $n$ is odd, then $V(\omega,t)$ is a polynomial with respect to $t.$ Whether odd-dimensional ellipsoids are the only bounded smooth domains with such a property? The article is devoted to partial verification and discussion of this question. Read More
  • I argue that access to quantum memory allows information processing with arbitrarily weak control signals. So, there is a class of computational problems that can be solved without speed limit at finite energy input. Read More
  • Introduction to deep neural networks and their history. Read More
  • Localisation of gamma-ray interaction points in monolithic scintillator crystals can simplify the design and improve the performance of a future Compton telescope for gamma-ray astronomy. In this paper we compare the position resolution of three monolithic scintillators: a 28x28x20 mm3 (length x breadth x thickness) LaBr3:Ce crystal, a 25x25x20 mm3 CeBr3 crystal and a 25x25x10 mm3 CeBr3 crystal. Each crystal was encapsulated and coupled to an array of 4x4 silicon photomultipliers through an optical window. The measurements were conducted using 81 keV and 356 keV gamma-rays from a collimated 133Ba source. The 3D position reconstruction of interaction points was performed using artificial neural networks trained with experimental data. Although the position resolution was significantly better for the thinner crystal, the 20 mm thick CeBr3 crystal showed an acceptable resolution of about 5.4 mm FWHM for the x and y coordinates, and 7.8 mm FWHM for the z-coordinate (crystal depth) at 356 keV. These values were obtained from the full position scans of the crystal sides. The position resolution of the LaBr3:Ce crystal was found to be considerably worse, presumably due to the highly diffusive optical in- terface between the crystal and the optical window of the enclosure. The energy resolution (FWHM) measured for 662 keV gamma-rays was 4.0% for LaBr3:Ce and 5.5% for CeBr3. The same crystals equipped with a PMT (Hamamatsu R6322-100) gave an energy resolution of 3.0% and 4.7%, respectively. Read More
  • This paper presents a novel method for selecting main effects and a set of reparametrized predictors called conditional main effects (CMEs), which capture the conditional effect of a factor at a fixed level of another factor. CMEs represent highly interpretable phenomena for a wide range of applications in engineering, social sciences and genomics. The challenge in model selection lies in the grouped collinearity structure of CMEs, which can cause poor selection and prediction performance for existing methods. We propose a new method called cmenet, which employs coordinate descent and two principles called CME coupling and reduction to efficiently perform model selection. Simulation studies demonstrate the improved performance of cmenet over existing selection methods, such as the LASSO and SparseNet. Applied to a gene association study on fly wing shape, cmenet not only provides improved predictive performance over existing techniques, but also reveals important insight on gene activation behavior. Efficient implementations of our algorithms are available in the R package cmenet in CRAN. Read More