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A systematic construction for supersymmetric negative (non-local) flows for mKdV and KdV based on $sl(2,1)$ with a principal gradation is proposed in this paper. We show that smKdV and sKdV can be mapped onto each other through a gauge super Miura transformation, together with an additional condition for the negative flows, which ensure the supersymmetry of the negative sKdV flow. In addition, we classify both smKdV and sKdV flows with respect to the vacuum (boundary) solutions accepted for each flow, whether zero or non-zero. Each vacuum is used to derive both soliton solutions and the Heisenberg subalgebra for the smKdV hierarchy, where we present novel vertex operators and solutions for non-zero bosonic and fermionic vacuum. Finally, the gauge Miura transformation is used to obtain the sKdV solutions, which exhibit a rich degeneracy due to both multiple gauge super Miura transformations and multiple vacuum possibilities., Comment: 49 pages, 2 figures

We aim to identify QSO2 candidates in the redshift desert using optical and infrared photometry. At this intermediate redshift range, most of the prominent optical emission lines in QSO2 sources (e.g. CIV1549; [OIII]4959,5008) fall either outside the wavelength range of the SDSS optical spectra or in particularly noisy wavelength ranges, making QSO2 identification challenging. Therefore, we adopted a semi-supervised machine learning approach to select candidates in the SDSS galaxy sample. Recent applications of machine learning in astronomy focus on problems involving large data sets, with small data sets often being overlooked. We developed a few-shot learning approach for the identification and classification of rare-object classes using limited training data (200 sources). The new AMELIA pipeline uses a transfer-learning based approach with decision trees, distance-based, and deep learning methods to build a classifier capable of identifying rare objects on the basis of an observational training data set. We validated the performance of AMELIA by addressing the problem of identifying QSO2s at 1 $\leq$ z $\leq$ 2 using SDSS and WISE photometry, obtaining an F1-score above 0.8 in a supervised approach. We then used AMELIA to select new QSO2 candidates in the redshift desert and examined the nature of the candidates using SDSS spectra, when available. In particular, we identified a sub-population of [NeV]3426 emitters at z $\sim$ 1.1, which are highly likely to contain obscured AGNs. We used X-ray and radio cross-matching to validate our classification and investigated the performance of photometric criteria from the literature showing that our candidates have an inherent dusty nature. Finally, we derived physical properties for our QSO2 sample using photoionisation models and verified the AGN classification using an SED fitting., Comment: 20 pages, 9 figures, Accepted for publication in A&A

The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integrable hierarchies are then classified in terms of a decomposition of the underlying affine Lie algebra $\hat {\cal{G}} $ into graded subspaces defined by a grading operator $Q$. In this paper we shall discuss explicitly the simplest case of the affine $\hat {sl}(2)$ Kac-Moody algebra within the principal gradation given rise to the KdV and mKdV hierarchies and extend to supersymmetric models. It is known that the positive mKdV sub-hierachy is associated to some positive odd graded abelian subalgebra with elements denoted by $E^{(2n+1)}$. Each of these elements in turn, defines a time evolution equation according to time $t=t_{2n+1}$. An interesting observation is that for negative grades, the zero curvature representation allows both, even or odd sub-hierarchies. In both cases, the flows are non-local leading to integro-differential equations. Whilst positive and negative odd sub-hierarchies admit zero vacuum solutions, the negative even admits strictly non-zero vacuum solutions. Soliton solutions can be constructed by gauge transforming the zero curvature from the vacuum into a non trivial configuration (dressing method). Inspired by the dressing transformation method, we have constructed a gauge-Miura transformation mapping mKdV into KdV flows. Interesting new results concerns the negative grade sector of the mKdV hierarchy in which a double degeneracy of flows (odd and its consecutive even) of mKdV are mapped into a single odd KdV flow. These results are extended to supersymmetric hierarchies based upon the affine $\hat {sl}(2,1)$ super-algebra., Comment: 22 pages Latex

We present a construction of a class of rational solutions of the Painlev\'e V equation that exhibit a two-fold degeneracy, meaning that there exist two distinct solutions that share identical parameters. The fundamental object of our study is the orbit of translation operators of $A^{(1)}_{3}$ affine Weyl group acting on the underlying seed solution that only allows action of some symmetry operations. By linking points on this orbit to rational solutions, we establish conditions for such degeneracy to occur after involving in the construction additional B\"acklund transformations that are inexpressible as translation operators. This approach enables us to derive explicit expressions for these degenerate solutions. An advantage of this formalism is that it easily allows generalization to higher Painlev\'e systems associated with dressing chains of even period $N>4$., Comment: 15 pages

Under special conditions the Painlev\'e V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbits of the fundamental shift operators of $A^{(1)}_{3}$ affine Weyl group with rational solutions we derive conditions for such non-uniqueness to occur. We identify the seed solutions from which the non-unique solutions are generated and put forward a method to systematically obtain their closed expressions from the underlying seed solutions., Comment: 20 pages

We show how the zero-curvature equations based on a loop algebra of $D_4$ with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled Painlev\'e III models with four canonical variables and $D_4^{(1)}$ affine Weyl group symmetry., Comment: 14 pages

In the era of huge astronomical surveys, machine learning offers promising solutions for the efficient estimation of galaxy properties. The traditional, `supervised' paradigm for the application of machine learning involves training a model on labelled data, and using this model to predict the labels of previously unlabelled data. The semi-supervised `pseudo-labelling' technique offers an alternative paradigm, allowing the model training algorithm to learn from both labelled data and as-yet unlabelled data. We test the pseudo-labelling method on the problems of estimating redshift, stellar mass, and star formation rate, using COSMOS2015 broad band photometry and one of several publicly available machine learning algorithms, and we obtain significant improvements compared to purely supervised learning. We find that the gradient-boosting tree methods CatBoost, XGBoost, and LightGBM benefit the most, with reductions of up to ~15% in metrics of absolute error. We also find similar improvements in the photometric redshift catastrophic outlier fraction. We argue that the pseudo-labellng technique will be useful for the estimation of redshift and physical properties of galaxies in upcoming large imaging surveys such as Euclid and LSST, which will provide photometric data for billions of sources., Comment: 10 pages, 6 figures, accepted for publication in MNRAS

We present a summary of our project that studies galaxies hosting type Ia supernova (SN Ia) at different redshifts. We present Gran Telescopio de Canarias (GTC) optical spectroscopy of six SN Ia host galaxies at redshift $z\sim 0.4-0.5$. They are joined to a set of SN Ia host galaxies at intermediate-high redshift, which include galaxies from surveys SDSS and COSMOS. The final sample, after a selection of galaxy spectra in terms of signal-to-noise and other characteristics, consists of 680 galaxies with redshift in the range $0.04 < z < 1$. We perform an inverse stellar population synthesis with the code {\sc fado} to estimate the star formation and enrichment histories of this set of galaxies, simultaneously obtaining their mean stellar age and metallicity and stellar mass. After analysing the correlations among these characteristics, we look for possible dependencies of the Hubble diagram residuals and supernova features (luminosity, color and strength parameter) on these stellar parameters. We find that the Hubble residuals show a clear dependence on the stellar metallicity weighted by mass with a slope of -0.061\,mag\,dex$^{-1}$, when represented in logarithmic scale, $\log{ \langle Z_{M}/Z_{\odot}\rangle }$. This result supports our previous findings obtained from gas oxygen abundances for local and SDSS-survey galaxies. Comparing with other works from the literature that also use the stellar metallicity, we find a similar value, but with more precision and a better significance (2.08 vs $\sim$ 1.1), due to the higher number of objects and wider range of redshift of our sample., Comment: 21 pages, 19 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalently $A^{(1)}_{N-1}$ invariant Painlev\'e equations. This construction identifies rational solutions with points on orbits of fundamental shift operators acting on first-order polynomial solutions derived for dressing chains of even periodicity. We also obtain conditions for the existence of special function solutions that occur for a special class of first-order polynomial solutions. For the special case of the N=4 dressing chain equations the method yields all the known rational solutions of Painlev\'e V equation. They are obtained through action of shift operators on the two independent first-order polynomial solutions. The formalism naturally extends to N=6 and beyond as shown in the paper., Comment: 29 pages

A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine $A_{2r}^{(2)}$ Lie algebra. The zero curvature representation of the time evolution equations are shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non zero) vacuum solutions. Another, consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting zero vacuum and another of constant, non zero vacuum solutions. The two dimensional gauge potentials in the vacuum plays a crucial ingredient and are shown to be expanded in powers of the vacuum parameter $v_0$. Soliton solutions are constructed from vertex operators, which for the non zero vacuum solutions, correspond to deformations characterized by $v_0$., Comment: Latex 24 pages

We propose a Hamiltonian formalism for $N$ periodic dressing chain with the even number $N$. The formalism is based on Dirac reduction applied to the $N+1$ periodic dressing chain with the odd number $N+1$ for which the Hamiltonian formalism is well known. The Hamilton dressing chain equations in the $N$ even case depend explicitly on a pair of conjugated Dirac constraints and are equivalent to $A^{(1)}_{N-1}$ invariant symmetric Painlev\'e equations., Comment: 13 pages, comment added in subsection 3.1

The construction of Miura and B\"acklund transformations for $A_n$ mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known $sl(2)$ case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miura-gauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of $A_n$ The construction of generalized gauge-B\"acklund transformation for the $A_n$-KdV hierarchy is obtained as a composition of Miura and B\"acklund-gauge transformations for $A_n$-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically B\"acklund transformations for the entirely hierarchy., Comment: Latex 18 pages, corrections and improvements in the text

High harmonic generation (HHG) in crystals has revealed a wealth of perspectives such as all-optical mapping of the electronic band structure, ultrafast quantum information and the creation of novel all-solid-state attosecond sources. Significant efforts have been made to understand the microscopic aspects of HHG in crystals, whereas the macroscopic effects, such as non-linear propagation effects of the driving pulse inside the dense solid media and its impact on the HHG process is often overlooked. In this work, we study macroscopic effects by comparing two materials with distinct optical properties, silicon (Si) and zinc oxide (ZnO). By scanning the focal position of 85 fs, 2.123 $\mu$m wavelength pulses inside the crystals (Z-scan) we reveal spectral shifts in the generated harmonics. We interpret the overall blueshift of the emitted harmonic spectrum as an imprint of the driving field spectral modulation occurring during the propagation inside the crystal. This is supported with numerical simulations. This study demonstrates that through manipulation of the fundamental driving field through non-linear propagation effects, precise control of the emitted HHG spectrum in solids can be realised. This method could offer a robust way to tailor HHG spectra for a range of spectroscopic applications., Comment: 6 pages,6 figures

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as non-resistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.

We identify the self-similarity limit of the second flow of $sl(N)$ mKdV hierarchy with the periodic dressing chain thus establishing % a connection to $A^{(1)}_{N-1}$ invariant Painlev\'e equations. The $A^{(1)}_{N-1}$ B\"acklund symmetries of dressing equations and Painlev\'e equations are obtained in the self-similarity limit of gauge transformations of the mKdV hierarchy realized as zero-curvature equations on the loop algebra $\widehat{sl}(N)$ endowed with a principal gradation.

Kernel pruning methods have been proposed to speed up, simplify, and improve explanation of convolutional neural network (CNN) models. However, the effectiveness of a simplified model is often below the original one. In this letter, we present new methods based on objective and subjective relevance criteria for kernel elimination in a layer-by-layer fashion. During the process, a CNN model is retrained only when the current layer is entirely simplified, by adjusting the weights from the next layer to the first one and preserving weights of subsequent layers not involved in the process. We call this strategy \emph{progressive retraining}, differently from kernel pruning methods that usually retrain the entire model after each simplification action -- e.g., the elimination of one or a few kernels. Our subjective relevance criterion exploits the ability of humans in recognizing visual patterns and improves the designer's understanding of the simplification process. The combination of suitable relevance criteria and progressive retraining shows that our methods can increase effectiveness with considerable model simplification. We also demonstrate that our methods can provide better results than two popular ones and another one from the state-of-the-art using four challenging image datasets., Comment: 7 pages, 4 figures. This paper was submitted to Pattern Recognition Letters

Intestinal parasites are responsible for several diseases in human beings. In order to eliminate the error-prone visual analysis of optical microscopy slides, we have investigated automated, fast, and low-cost systems for the diagnosis of human intestinal parasites. In this work, we present a hybrid approach that combines the opinion of two decision-making systems with complementary properties: ($DS_1$) a simpler system based on very fast handcrafted image feature extraction and support vector machine classification and ($DS_2$) a more complex system based on a deep neural network, Vgg-16, for image feature extraction and classification. $DS_1$ is much faster than $DS_2$, but it is less accurate than $DS_2$. Fortunately, the errors of $DS_1$ are not the same of $DS_2$. During training, we use a validation set to learn the probabilities of misclassification by $DS_1$ on each class based on its confidence values. When $DS_1$ quickly classifies all images from a microscopy slide, the method selects a number of images with higher chances of misclassification for characterization and reclassification by $DS_2$. Our hybrid system can improve the overall effectiveness without compromising efficiency, being suitable for the clinical routine -- a strategy that might be suitable for other real applications. As demonstrated on large datasets, the proposed system can achieve, on average, 94.9%, 87.8%, and 92.5% of Cohen's Kappa on helminth eggs, helminth larvae, and protozoa cysts, respectively., Comment: 18 pages, 11 figures

We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N = 1) is coupled with one wave (M = 1), is completely integrable, and the nonlinear effects reduce to the wave potential pulsating while the particle either remains trapped or circulates forever. On increasing the number of particles (N = 2, M = 1), integrability is lost and chaos develops. Our analyses identify the two standard ways for chaos to appear and grow (the homoclinic tangle born from a separatrix, and the resonance overlap near an elliptic fixed point). Moreover, a strong form of chaos occurs when the energy is high enough for the wave amplitude to vanish occasionally.

The construction of generalized Backlund transformation for the $A_n$ Affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of the underlying affine algebra which induces a classification of generalized Backlund transformations. Moreover, explicit examples for $su(3)$ and $su(4)$ lead to uncover interesting composition properties of various types of Backlund transformations. The universality character of the gauge-Backlund transformation method is extended to all equations of the hierarchy. Such interesting property provides a systematic framework to construct Backlund transformations to higher flow equations. Explicit example for the simplest higher flow of the $sl(3)$ hierarchy is presented., Comment: 23 pages, Latex

We extend Painlev\'e IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlev\'e IV and II equations for special limits of the underlying parameters. We derive the underlying B\"acklund transformations, symmetry structure and requirements to satisfy Painlev\'e property., Comment: 21 pages, to appear in J. Phys. A: Math. Theor. (2020)

In this work we perform investigations of the competition between domain-wall pinning and attraction by anti-notches and finite device borders. The conditions for optimal geometries, which can attain a stable domain-wall pinning, are presented. This allow us the proposition of a three-terminals device based on domain-wall pinning. We obtain, with very small pulses of current applied parallel to the nanotrack, a fast motion of the domain-wall between anti-notches. In addition to this, a swift stabilization of the pinned domain-wall is observed with a high percentage of orthogonal magnetization, enabling high magnetoresistive signal measurement. Thus, our proposed device is a promising magnetoresistive random access memories with good scalability, duration, and high speed information storage.

We discuss symmetries of Hamiltonians of I$_{38}$ and I$_{49}$ equations that appear on Ince's list of fifty second-order differential equations with Painlev\'e property. This study is informed by structure of Weyl symmetries of Painlev\'e P$_{III}$ and mixed Painlev\'e P$_{III-V}$ equations and provides insights into differences between the symmetries of Painlev\'e equations and symmetries of solvable equations on Ince's list., Comment: 9 pages, Proc. of the 32nd International Colloquium on Group Theoretical Methods in Physics (Group32), 2018, Prague, Czech Republic

The paper discusses P$_{III-V}$ equation for special values of its parameters for which this equation reduces to P$_{III}$, I$_{12}$, as well as, to some special cases of I$_{38}$ and I$_{49}$ equations from the Ince's list of $50$ second order differential equations possessing Painlev\'e property. These reductions also yield symmetries governing the reduced models obtained from the P$_{III-V}$ equation. We point out that the solvable equations on Ince's list emerge in this reduction scheme when the underlying reflections of the Weyl symmetry group no longer include an affine reflection through the hyperplane orthogonal to the highest root and therefore do not give rise to an affine Weyl group. We hypothesize that on the level of the underlying algebra and geometry this might be a fundamental feature that distinguishes the six Painlev\'e equations from the remaining $44$ solvable equations on the Ince's list., Comment: 10 pages, Proc. of the 32nd International Colloquium on Group Theoretical Methods in Physics (Group32), 2018, Prague, Czech Republic

We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change of sign in the group velocity. Second, a surface plasmon-magnon polariton formed as a linear superposition of graphene surface plasmon and the antiferromagnetic bare magnon. This polariton has a dispersion with two branches, formed by the anticrossing between the dispersive surface plasmon and the magnon. We discuss the potential these new modes have for combining photons, magnons, and plasmons to reach new functionalities., Comment: 12 pages, 4 figures