In this paper, the well known stagewise additive modeling using a multiclass exponential (SAMME) boosting algorithm is extended to address problems where there exists a natural order in the targets ...using a cost-sensitive approach. The proposed ensemble model uses an extreme learning machine (ELM) model as a base classifier (with the Gaussian kernel and the additional regularization parameter). The closed form of the derived weighted least squares problem is provided, and it is employed to estimate analytically the parameters connecting the hidden layer to the output layer at each iteration of the boosting algorithm. Compared to the state-of-the-art boosting algorithms, in particular those using ELM as base classifier, the suggested technique does not require the generation of a new training dataset at each iteration. The adoption of the weighted least squares formulation of the problem has been presented as an unbiased and alternative approach to the already existing ELM boosting techniques. Moreover, the addition of a cost model for weighting the patterns, according to the order of the targets, enables the classifier to tackle ordinal regression problems further. The proposed method has been validated by an experimental study by comparing it with already existing ensemble methods and ELM techniques for ordinal regression, showing competitive results.
Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function f ( R , R ) , where R is the metric ...scalar curvature and R the Palatini scalar curvature of the spacetime. We formulate the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system. The fixed points are obtained for four different forms of the function f ( R , R ) , and the behavior of the cosmic scale factor a ( t ) is computed. We show that due to the structure of the system, no global attractors can be present and also that two different classes of solutions for the scale factor a ( t ) exist. Numerical integrations of the dynamical system equations are performed with initial conditions consistent with the observations of the cosmological parameters of the present state of the Universe. In addition, using a redefinition of the dynamic variables, we are able to compute interesting solutions for static universes.
The extreme conditions experienced in the early universe, close to a black hole or in the interior of a neutron star, provide the environment where the most violent natural phenomena take place. Our ...understanding of the physical processes occurring in these regimes is affected by the notorious difficulty in the development of a theory of quantum gravity, modelling the intertwining of the gravitational field and the quantum properties of the fields responsible for the other forces in nature. A different point of view is then achieved by defining a “mesoscopic” scale lying below the Planck energy scale but well away from the classical general relativity domain. At such a scale, the theoretical framework describing how quantized fields propagate in a curved background has accomplished outstanding results, like particle production in gravitational fields and black hole evaporation, establishing a highly non-trivial connection between thermodynamics, gravity, and quantum field theory.
Aside from suggesting novel intersections between quantum fields and gravity, an unexplored landscape of original ideas is taking shape and inspiring new exciting problems. Quantum field theory in curved spacetime has recently been proposed as a new tool to probe nuclear and condensed matter physics phenomenology, with the recent advances in research at the nanoscale offering an intriguing test to the semiclassical approach even from tabletop experiments.
Following this trend, the goal of
Avenues of Quantum Field Theory in Curved Spacetime
has been to bring together researchers working in different areas of quantum field theory with interest in its curved space applications in the area of gravity and beyond. The 3-days workshop - the third of a series initiated in 2018 in Japan, continued in Modena, and that had an unexpected stop due to the sadly well-known Covid19 facts - aimed to exchange ideas on what is (or is expected soon to become) topical and discuss potential interdisciplinary interactions in a stimulating and collaborative environment.
List of The Editorial Board and Organising Committee is available in this pdf.
A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the ...level of the action, the only change made will be through the volume element which is used in the integration. This is achieved by the introduction of a fourth-order tensor which connects the spacetime metric to the new volume form. Using dynamical systems techniques, this model is studied in the context of cosmology. The most interesting result is that there exist parameter ranges where this model starts undergoing an epoch of accelerated expansion, followed by a decelerating expansion which evolves to a final epoch of accelerated expansion.
We construct exact solutions representing a Friedmann-Lemaître-Robsertson-Walker (FLRW) universe in a generalized hybrid metric-Palatini theory. By writing the gravitational action in a scalar-tensor ...representation, the new solutions are obtained by either making an ansatz on the scale factor or on the effective potential. Among other relevant results, we show that it is possible to obtain exponentially expanding solutions for flat universes even when the cosmology is not purely vacuum. We then derive the classes of actions for the original theory which generate these solutions.
The so-called f(X) hybrid metric-Palatini gravity, where X = R + T, with T the stress-energy trace and R the Ricci scalar, presents a unique viable generalization of the f(R) theories within the ...metric-affine formalism. In this paper, the cosmology of the f(X) theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalized) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power law or de Sitter expansion. The formalism is applied to two classes of f(X) models, revealing both standard cosmological fixed points and new accelerating solutions that can be attractors in the phase space. In addition, the fixed point with vanishing expansion rate is considered with special care in order to characterize the stability of Einstein static spaces and bouncing solutions.
In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enable one to ...choose between the easier approach for a given problem, and furthermore, we analyze six specific models. In general, we extract fixed points corresponding either to dark-matter-dominated, scaling decelerated solutions, or to dark-energy-dominated accelerated solutions. Additionally, we find that there is a small parameter region in which the model can experience the transition from the matter epoch to the dark-energy era. These features are in agreement with the observed evolution of the Universe, and make the theory a successful candidate for the description of nature.
Cosmology of f ( R , ❑ R ) gravity Carloni, Sante; Rosa, João Luís; Lemos, José P. S.
Physical review. D,
05/2019, Letnik:
99, Številka:
10
Journal Article
Recenzirano
Odprti dostop
Using dynamical system analysis, we explore the cosmology of theories of order up to eighth order of the form f(R,❑R). The phase space of these cosmologies reveals that higher-order terms can have a ...dramatic influence on the evolution of the cosmology, avoiding the onset of finite time singularities. We also confirm and extend some of results which were obtained in the past for this class of theories.
We present a new approach of the reconstruction method based on the use of the cosmic parameters instead of a time law for the scale factor. This solution generating technique allows the derivation ...and analysis of a set of new non-trivial exact cosmological solutions for f(R)-gravity. Specifically, we find two new cyclic solutions and we re-obtain a characteristic solution found also in the classical Starobinsky's model of higher order inflation.
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