Quenched glueball spectrum from functional equations

We give an overview of results for the quenched glueball spectrum from two-body bound state equations based on the 3PI effective action. The setup, which uses self-consistently calculated two- and three-point functions as input, is completely self-contained and does not have any free parameters except for the coupling. The results for JPC = 0±+, 2±+, 3±+, 4±+ are in good agreement with recent lattice results where available. For the pseudoscalar glueball, we present first results from a two-loop complete calculation, rendering also the bound state calculation fully self-consistent.

Flavor symmetries in an SU(5) model of grand unification

We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric SU(5) grand unified theory, without introducing additional flavor-related fields. Such symmetries reduce the number of free parameters in the model and therefore lead to more predictive models. We consider the Yukawa sector of the Lagrangian, and search for all possible flavor symmetries. As a result, we find 25 distinct realistic flavor symmetry cases, with ℤ2, ℤ3, ℤ4, and U(1) symmetries, and no non-Abelian cases.

Improved scaling law for the prediction of deuterium retention in beryllium co-deposits

Hydrogen isotope co-deposition with Be eroded from the first wall is expected to be the main fusion fuel retention mechanism in ITER. Since good fuel accounting is crucial for economic and safety reasons, reliable predictions of hydrogen isotope retention are needed. This study builds upon the well-established empirical De Temmerman scaling law [1] that predicts D/Be ratios in co-deposited layers based on deposition temperature, deposition rate, and deuterium particle energy. Expanding the data used in the original development of the scaling law with an additional dataset obtained with more recent measurements using a different technique to the original De Temmerman approach, allows us to obtain new values for free parameters and improve the prediction capabilities of the new scaling law. In an effort to improve the model even further, scaling with D2 background pressure was included and a new two-term model derived, describing D retention in low- and high-energy traps separately.

Reinterpreting the ATLAS bounds on heavy neutral leptons in a realistic neutrino oscillation model

Heavy neutral leptons (HNLs) are hypothetical particles, motivated in the first place by their ability to explain neutrino oscillations. Experimental searches for HNLs are typically conducted under the assumption of a single HNL mixing with a single neutrino flavor. However, the resulting exclusion limits may not directly constrain the corresponding mixing angles in realistic HNL models — those which can explain neutrino oscillations. The reinterpretation of the results of these experimental searches turns out to be a non-trivial task, that requires significant knowledge of the details of the experiment. In this work, we perform a reinterpretation of the latest ATLAS search for HNLs decaying promptly to a tri-lepton final state. We show that in a realistic model with two HNLs, the actual limits can vary by several orders of magnitude depending on the free parameters of the model. Marginalizing over the unknown model parameters leads to an exclusion limit on the total mixing angle which can be up to 3 orders of magnitude weaker than the limits reported in ref. [1]. This demonstrates that the reinterpretation of results from experimental searches is a necessary step to obtain meaningful limits on realistic models. We detail a few steps that can be taken by experimental collaborations in order to simplify the reuse of their results.

Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits

The family of Numerov-type methods that effectively uses seven stages per step is considered. All the coefficients of the methods belonging to this family can be expressed analytically with respect to four free parameters. These coefficients are trained through a differential evolution technique in order to perform best in a wide range of Keplerian-type orbits. Then it is observed with extended numerical tests that a certain method behaves extremely well in a variety of orbits (e.g., Kepler, perturbed Kepler, Arenstorf, Pleiades) for various steplengths used by the methods and for various intervals of integration.

Learning to Disentangle the Complex Causes of Data

<p>The ability to extract and model the meaning in data has been key to the success of modern machine learning. Typically, data reflects a combination of multiple sources that are mixed together. For example, photographs of people’s faces reflect the subject of the photograph, lighting conditions, angle, and background scene. It is therefore natural to wish to extract these multiple, largely independent, sources, which is known as disentangling in the literature. Additional benefits of disentangling arise from the fact that the data is then simpler, meaning that there are fewer free parameters, which reduces the curse of dimensionality and aids learning. While there has been a lot of research into finding disentangled representations, it remains an open problem. This thesis considers a number of approaches to a particularly difficult version of this task: we wish to disentangle the complex causes of data in an entirely unsupervised setting. That is, given access only to unlabeled, entangled data, we search for algorithms that can identify the generative factors of that data, which we call causes. Further, we assume that causes can themselves be complex and require a high-dimensional representation. We consider three approaches to this challenge: as an inference problem, as an extension of independent components analysis, and as a learning problem. Each method is motivated, described, and tested on a set of datasets build from entangled combinations of images, most commonly MNIST digits. Where the results fall short of disentangling, the reasons for this are dissected and analysed. The last method that we describe, which is based on combinations of autoencoders that learn to predict each other’s output, shows some promise on this extremely challenging problem.</p>

Learning to Disentangle the Complex Causes of Data

<p>The ability to extract and model the meaning in data has been key to the success of modern machine learning. Typically, data reflects a combination of multiple sources that are mixed together. For example, photographs of people’s faces reflect the subject of the photograph, lighting conditions, angle, and background scene. It is therefore natural to wish to extract these multiple, largely independent, sources, which is known as disentangling in the literature. Additional benefits of disentangling arise from the fact that the data is then simpler, meaning that there are fewer free parameters, which reduces the curse of dimensionality and aids learning. While there has been a lot of research into finding disentangled representations, it remains an open problem. This thesis considers a number of approaches to a particularly difficult version of this task: we wish to disentangle the complex causes of data in an entirely unsupervised setting. That is, given access only to unlabeled, entangled data, we search for algorithms that can identify the generative factors of that data, which we call causes. Further, we assume that causes can themselves be complex and require a high-dimensional representation. We consider three approaches to this challenge: as an inference problem, as an extension of independent components analysis, and as a learning problem. Each method is motivated, described, and tested on a set of datasets build from entangled combinations of images, most commonly MNIST digits. Where the results fall short of disentangling, the reasons for this are dissected and analysed. The last method that we describe, which is based on combinations of autoencoders that learn to predict each other’s output, shows some promise on this extremely challenging problem.</p>

Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M- Fractional Derivative

The present study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of Beta Derivative and Truncated M- fractional derivative. We employ new direct algebraic technique for nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three dimensional graphs. Which shows that for lower fractional orders i.e $\beta=0.1$, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders i.e $\beta=0.7$ and $\beta=0.99$, magnitude remains same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.

Three-dimensional exact solutions of the diffusion equation

При помощи метода быстрых разложений решается задача диффузии в параллелепипеде с граничными условиями 1-го рода и внутренним источником вещества, зависящим от координат точек параллелепипеда. Получено в общем виде решение, содержащее свободные параметры, с помощью которых можно получить множество новых точных решений с различными свойствами. Показан пример построения точного решения для случая внутреннего источника переменного только по оси OZ . Приведен анализ особенностей диффузионных потоков в параллелепипеде с указанным внутреннем источником. Получено, что концентрация вещества в центре параллелепипеда равна сумме среднеарифметического значения концентраций вещества в его вершинах и амплитуды внутреннего источника умноженного на величину The authors solve the problem of diffusion in a parallelepiped-shaped body with boundary conditions of the 1st kind and an internal source of substance, depending on the parallelepiped points coordinates with the fast expansions method. The proposed exact solution in general form contains free parameters, which can be used to obtain many new exact solutions with different properties. An example of constructing an exact solution with a variable internal source depending on one coordinate z is shown in the work. An analysis of the features of diffusion flows in a parallelepiped with the indicated internal source is given. It was found that the concentration of a substance in the center of a parallelepiped is equal to the sum of the arithmetic mean of the concentration of a substance at its vertices and the amplitude of the internal source multiplied by the value

Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions

Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phase-lag error, extend the interval of periodicity or even nullify the amplification. All of these latter properties come from a test problem that poses as a solution to an ideal trigonometric orbit. Here, we propose the training of the coefficients of the selected family of methods in a wide set of relevant problems. After performing this training using the differential evolution technique, we arrive at a certain method that outperforms the other ones from this family in an even wider set of oscillatory problems.