New Geothermal Prospect in North-Eastern Morocco

Geothermal data has been indicating promising potentialities in the north-eastern Morocco. This paperpresents new temperature data, recently recorded in water borehole located in the Berkane and Oujda areas. Generally, the observed temperature gradients are rather high. One hole near Berkane, revealed an average geothermal gradient of more than 110 ºC/km at depths greater than 300 m. This result confirms the geothermal gradient estimated in a mining borehole located about 30 km west of the Berkane borehole, in which water temperatures of 96 ºC are reached at a depth of about 700 m. Such a high geothermal gradient, exceeding by far the ones already determined for northeastern Morocco, could act as a stimulus to programs aimed at the geothermal exploitation of high temperature aquifers

On Linearity of Nonclassical Differentiation

We introduce a real vector space composed of set-valued maps on an open set X and note it by S. It is a complete metric space and a complete lattice. The set of continuous functions on X is dense in S as in a metric space and as in a lattice. Thus the constructed space plays the same role for the space of continuous functions with uniform convergence as the field of reals plays for the field of rationals. The classical gradient may be extended in the space S as a close operator. If a function f belongs to its domain then f is locally lipschitzian and the values of our gradient coincide with the values of Clarke's gradient. However, unlike Clarke's gradient, our gradient is a linear operator.Comment: Sorry, this article is being rewritten. Please email the author to be informed about its availabilit

Modified conjugated gradient method for diagonalising large matrices

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trail vectors, play a similar role of the conjugated gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitably for first principle calculations.Comment: 6 Pages, 2EPS figures. (To appear in Phys. Rev. E

Generalized Off-Policy Actor-Critic

We propose a new objective, the counterfactual objective, unifying existing objectives for off-policy policy gradient algorithms in the continuing reinforcement learning (RL) setting. Compared to the commonly used excursion objective, which can be misleading about the performance of the target policy when deployed, our new objective better predicts such performance. We prove the Generalized Off-Policy Policy Gradient Theorem to compute the policy gradient of the counterfactual objective and use an emphatic approach to get an unbiased sample from this policy gradient, yielding the Generalized Off-Policy Actor-Critic (Geoff-PAC) algorithm. We demonstrate the merits of Geoff-PAC over existing algorithms in Mujoco robot simulation tasks, the first empirical success of emphatic algorithms in prevailing deep RL benchmarks.Comment: NeurIPS 201

Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 \mu m above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schr\"odinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.Comment: 20 pages, 13 figure

Solving ill-posed inverse problems using iterative deep neural networks

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against FBP and TV reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the TV reconstruction while being significantly faster, giving reconstructions of 512 x 512 volumes in about 0.4 seconds using a single GPU