Articles you may be interested inSimple Harish-Chandra modules over super Schrödinger algebra in (1+1) dimensional spacetime J. Math. Phys. 55, 091701 (2014); 10.1063/1.4894506 Critical scaling dimension of D-module representations of N = 4 , 7 , 8 superconformal algebras and constraints on superconformal mechanics J. Math. Phys. 53, 103518 (2012); 10.1063/1.4758923 D-module representations of N = 2 , 4 , 8 superconformal algebras and their superconformal mechanics J. Math. Phys. 53, 043513 (2012); 10.1063/1.4705270 Classification of modules of the intermediate series over Ramond N = 2 superconformal algebras (Super)conformal mechanics in one dimension is induced by parabolic or hyperbolic/trigonometric transformations, either homogeneous (for a scaling dimension λ) or inhomogeneous (at λ = 0, with ρ an inhomogeneity parameter). Four types of (super)conformal actions are thus obtained. With the exclusion of the homogeneous parabolic case, dimensional constants are present. Both the inhomogeneity and the insertion of λ generalize the construction of Papadopoulos [Class. Quant. Grav. 30, 075018 (2013); e-print arXiv:1210.1719]. Inhomogeneous D-module reps are presented for the d = 1 superconformal algebras osp(1|2), sl(2|1), B(1, 1), and A(1, 1). For centerless superVirasoro algebras, D-module reps are presented (in the homogeneous case for N = 1, 2, 3, 4; in the inhomogeneous case for N = 1, 2, 3). The four types of d = 1 superconformal actions are derived for N = 1, 2, 4 systems. When N = 4, the homogeneously induced actions are D(2, 1; α)-invariant (α is critically linked to λ); the inhomogeneously induced actions are A(1, 1)-invariant. C 2014 AIP Publishing LLC. [http://dx.Hyperbolic versus trigonometric transformations are mutually recovered via an analytic continuation. The passage from parabolic to hyperbolic transformations, see, e.g., formula (12), requires a singular change of variable. Under this change of variable the properties of their respective Dmodule reps (the scaling λ or, in the inhomogeneous case, the parameter ρ) are easily recovered. The singularity of the change of variable is, on the other hand, responsible for the appearance in the Lagrangians of the extra potential terms that we mentioned before.On algebraic grounds the crucial difference between the hyperbolic and the parabolic sl(2) transformations is the following. In the parabolic case, the operator proportional to a time-derivative (the "Hamiltonian") is given by the (positive or negative) sl(2) root, while in the hyperbolic case this Hamiltonian operator is associated with the sl(2) Cartan generator. This is the reason why, when we consider superalgebra extensions, the parabolic systems are supersymmetric in the ordinary sense, while the hyperbolic systems, despite being superconformally invariant, are not ordinary supersymmetric theories (see the discussion in Appendix D).We end up, for one-dimensional conformal systems and their supersymmetric extensions, with four types of D-module reps and their associated (super)conformally inv...

We develop a supervised machine learning algorithm that is able to learn topological phases for finite condensed matter systems in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector-ensembling procedure. We combine our algorithm with decision trees to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from lattice data in real space and show how the Gini impurity of ensembles of lattice eigenvectors can be used to retrieve a topological signal detailing how topological information is distributed along the lattice. The discovery of local Gini topological signals from the analysis of data from several thousand SSH systems illustrates how machine learning can advance the research and discovery of new quantum materials with exotic properties that may power future technological applications such as quantum computing.

In this paper we quantize superconformal σ-models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a DFF term, are considered. Without a DFF term (Calogero potential only) the supersymmetry is unbroken. The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory.Besides the osp(1|2) examples, we explicitly quantize the superconformally-invariant worldine σ-models defined by the N = 4 (1, 4, 3) supermultiplet (with D(2, 1; α) invariance, for α = 0, −1) and by the N = 2 (2, 2, 0) supermultiplet (with two-dimensional target and sl(2|1) invariance). The parameter α is the scaling dimension of the (1, 4, 3) supermultiplet and, in the DFF case, has a direct interpretation as a vacuum energy. In the DFF case, for the sl(2|1) models, the scaling dimension λ is quantized (either λ = 1 2 + Z or λ = Z). The ordinary two-dimensional oscillator is recovered, after imposing a superselection restriction, from the λ = − 1 2 model. In particular a single bosonic vacuum is selected. The spectrum of the unrestricted two-dimensional theory is decomposed into an infinite set of lowest weight representations of sl(2|1). Extra fermionic raising operators, not belonging to the original sl(2|1) superalgebra, allow (for λ = 1 2 + Z) to construct the whole spectrum from the two degenerate (one bosonic and one fermionic) vacua.

Here we apply the concept of transfer learning to time series forecasting models for mosquito-borne diseases. Transfer learning, in this application, allows us to use knowledge obtained from modeling one disease to predict an emerging one for which extensive data is still not available. Here we discuss the performances of two families of models for predicting Chikungunya and Zika using models trained with dengue time series, in two Brazilian cities: Rio de Janeiro and Fortaleza.