Measuring Interactions in Categorical Datasets Using Multivariate Symmetrical Uncertainty

Interaction between variables is often found in statistical models, and it is usually expressed in the model as an additional term when the variables are numeric. However, when the variables are categorical (also known as nominal or qualitative) or mixed numerical-categorical, defining, detecting, and measuring interactions is not a simple task. In this work, based on an entropy-based correlation measure for n nominal variables (named as Multivariate Symmetrical Uncertainty (MSU)), we propose a formal and broader definition for the interaction of the variables. Two series of experiments are presented. In the first series, we observe that datasets where some record types or combinations of categories are absent, forming patterns of records, which often display interactions among their attributes. In the second series, the interaction/non-interaction behavior of a regression model (entirely built on continuous variables) gets successfully replicated under a discretized version of the dataset. It is shown that there is an interaction-wise correspondence between the continuous and the discretized versions of the dataset. Hence, we demonstrate that the proposed definition of interaction enabled by the MSU is a valuable tool for detecting and measuring interactions within linear and non-linear models.

Numerical simulation of thermal processes occurring in materials under the action of femtosecond laser pulses

In this work, a numerical study of the solutions of the parabolic and hyperbolic equations of heat conduction with the same physical parameters is carried out and a comparative analysis of the results obtained is carried out. The mathematical formulation of the problem is discussed. The action of the laser is taken into account through the source function, which was chosen as a double femtosecond laser pulse. In the hyperbolic equation, in contrast to the parabolic one, there is an additional parameter that characterizes the relaxation time of the heat flux. In addition, the source of the hyperbolic equation contains an additional term - the derivative of the power density of the source of the parabolic equation. This means that the temperature of the sample is influenced not only by the power density of the source, but also by the rate of its change. The profiles of the sample temperature at different times and its dynamics at different target depths are shown. The calculations were carried out for different time delays between pulses and for different relaxation parameters.

The Mach's Principle and Large-scale Modification of Newtonian Gravitation as Alternative Approach to Cold Dark Matter and Dark Energy

We take a heterodox approach to the ΛFRW Cosmology starting from the modification of Newtonian gravity by explicitly incorporating Mach's Principle through an additional term a great scale in the gravitation. The results show that at the after of the matter-radiation decoupling, the distribution of matter at scales greater than 10Mpc contributes with an inverse Yukawa-like field, which verifies the observations: resulting null in the inner solar system, weakly attractive in ranges of interstellar comoving distances, very attractive in comoving distance ranges comparable to the clusters of galaxies, and repulsive in cosmic scales. This additional term explains dark energy, removes the incompatibility between the density of matter and the flatness of the universe; and also allows the theoretical deduction of the Hubble-Lemaitre Law. Additionally, Birkhoff Theorem, Virial Theorem, the missing mass of Zwicky, the BAO, gravitational redshift are discussed. It is concluded that the dark energy and the missing mass can be approached with the usual physics if a classical, large-scale modification of the Inverse Square Law.

Reinforcement Learning with Dynamic Movement Primitives for Obstacle Avoidance

Dynamic movement primitives (DMPs) are a robust framework for movement generation from demonstrations. This framework can be extended by adding a perturbing term to achieve obstacle avoidance without sacrificing stability. The additional term is usually constructed based on potential functions. Although different potentials are adopted to improve the performance of obstacle avoidance, the profiles of potentials are rarely incorporated into reinforcement learning (RL) framework. In this contribution, we present a RL based method to learn not only the profiles of potentials but also the shape parameters of a motion. The algorithm employed is PI2 (Policy Improvement with Path Integrals), a model-free, sampling-based learning method. By using the PI2, the profiles of potentials and the parameters of the DMPs are learned simultaneously; therefore, we can optimize obstacle avoidance while completing specified tasks. We validate the presented method in simulations and with a redundant robot arm in experiments.

Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation)

The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling is usually based on dynamic traffic models, whose main input is a dynamic origin–destination (OD) matrix that describes the time dependencies of travel patterns; this is one of the reasons that have fostered large amounts of research on the topic of estimating OD matrices from the available traffic information. The complexity of the problem, its underdetermination, and the many alternatives that it offers are other reasons that make it an appealing research topic. The availability of new traffic data measurements that were prompted by the pervasive penetration of information and communications technology (ICT) applications offers new research opportunities. This study focused on GPS tracking data and explored two alternative modeling approaches regarding how to account for this new information to solve the dynamic origin–destination matrix estimation (DODME) problem, either including it as an additional term in the formulation model or using it in a data-driven modeling method to propose new model formulations. Complementarily, independently of the approach used, a key aspect is the quality of the estimated OD, which, as recent research has made evident, is not well measured by the conventional indicators. This study also explored this problem for the proposed approaches by conducting synthetic computational experiments to control and understand the process.

Longitudinal Modulation of Marangoni Wave Patterns in Thin Film Heated From Below: Instabilities and Control

Non-linear Marangoni waves, which are generated by the long-wave oscillatory instability of the conductive state in a thin liquid film heated from below in the case of a deformable free surface and a substrate of very low conductivity, are considered. Previously, the investigation of traveling Marangoni waves was restricted to the analysis of the bifurcation and stability with respect to disturbances with strongly different wave vectors. In the present article, for the first time, the modulational instability of traveling waves is investigated. We derive the amplitude equation for the modulated traveling wave, which describes non-linear interaction of the main convective pattern with the perturbations with slightly different wavenumbers. The amplitude equation differs from the conventional complex Ginzburg–Landau equation as it contains an additional term of the local liquid level rise. Linear stability analysis reveals two modulational instability modes: the amplitude modulational and the phase modulational (Benjamin–Feir) ones. It is shown that traveling rolls are stable against the longitudinal modulation for the uncontrolled convection. We also investigate the influence of the non-linear feedback control, which was applied previously to eliminate subcritical excitation of traveling rolls. Computations reveal both the modulational modes under the non-linear feedback control. The obtained results show that the modulational instabilities significantly influence the region of parameters where the non-linear feedback control is efficient for stabilization of waves.

Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.

KdV Equation Model in Open Cylindrical Channel under Precession

A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope $$\tau$$ τ from the inertial vertical $$z$$ z , in uniform rate $${\Omega }_{1}=\tau \Omega$$ Ω 1 = τ Ω , and the whole tank is elevated over other table rotating at rate $$\Omega$$ Ω . Under these conditions, a set of Kelvin waves is formed on the free surface depending on the angle of tilt, characterized by the slope $$\tau$$ τ , volume of water, and rotation rate. The resonant mode in the system appears in the form of a single Kelvin solitary wave, whose amplitude satisfies the Korteweg-de Vries equation with forced term. The equation was derived following classical perturbation methods, the additional term made the equation a non-integrable one, that cannot be solved without the help of numerical methods. Invoking the simple finite difference scheme method, it was found that the numerical results are in a good agreement with the experiment.

Capture of Massless and Massive Particles by Parameterized Black Holes

We study an influence of the leading coefficient of the parameterized line element of the spherically symmetric, static black hole on the capture of massless and massive particles. We have shown that negative (positive) values of ϵ decreases (increases) the radius of characteristic circular orbits and consequently, increases (decreases) the energy and decreases (increases) the angular momentum of the particle moving along these orbits. Moreover, we have calculated and compared the capture cross section of the massive particle in the relativistic and non-relativistic limits. It has been shown that in the case of small deviation from general relativity the capture cross section for the relativistic and nonrelativistic particle has an additional term being linear in the small dimensionless deviation parameter ϵ.