Oriented manifold-based error tracking control for nonholonomic wheeled autonomous vehicles on Lie group for curvilinear approach

This paper considers the trajectory tracking control of wheeled autonomous vehicles (WAV) with slipping in the wheels, i.e., when the kinematic constraints are not satisfied. Usually, the coordinates system used to represent all control problems suggest invariant subspaces mutually orthogonal, but this approach can not be enough to treat curvatures significative large at different navigation speed. In order to get a slight im- provement on this topic, there are previous works showing that the kinematic problem (commonly associated with an outer loop) can be resynthesized by using other invariant subspaces, i.e., another representation of the configuration space. For this reason, the proposal reported here uses an oriented-manifold parametrized by a coordinate system on a curve viewpoint of the trajectory to describe the kinematic problem, however, the dynamic control law remains faithful to the singular perturbation approach with invariant subspaces mutually orthogonal, thus, it is possible to include the flexibility through a small factor in the dynamic model (well-known as ε), responsible to avoid the good-performance of the kinematic constraints. Only a common curvature-transformation between orthogonal and curve coordinates will be used to couple both approaches. Finally, it will be observed that when the controller is applied to the control scheme the behavior of the tracking is meaningfully improved.

CONSTRUCTION OF STABILITY AREAS FOR CONTROLLED SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTY

The subject of research in the article is sigularly perturbed controllable systems of differential equations containing terms with a small parameters on the right-hand side, which are not completely known, but only satisfy some constraints. The aim of the work is to expand the study of the behavior of solutions of singularly perturbed systems of differential equations to the case when the system is influenced not only by dynamic (small factor at the derivative) but also parametric (small factor at the right side of equations) uncertainties and to determine conditions under which such systems will be asymptotically resistant to any perturbations, estimate the upper limit of the small parameter, so that for all values of this parameter less than the obtained estimate, the undisturbed solution of the system was asymptotically stable. The following problems are solved in the article: singularly perturbed systems of differential equations with regular perturbations in the form of terms with a small parameter in the right-hand sides, which are not fully known, are investigated; an estimate is made of the areas of asymptotic stability of the unperturbed solution of such systems, that is, the class of systems that can be investigated for stability is expanded, the formulas obtained that allow one to analyze the asymptotic stability of solutions to systems even under conditions of incomplete information about the perturbations acting on them. The following methods are used: mathematical modeling of complex control systems; vector Lyapunov functions investigation of asymptotic stability of solutions of systems of differential equations. The following results were obtained: an estimate was made for the upper bound of a small parameter for sigularly perturbed systems of differential equations with fully known parametric (fully known) and dynamic uncertainties, such that for all values of this parameter less than the obtained estimate, such an unperturbed solution is asymptotically stable; a theorem is proved in which sufficient conditions for the uniform asymptotic stability of such a system are formulated. Conclusions: the method of vector Lyapunov functions extends to the class of singularly perturbed systems of differential equations with a small factor in the right-hand sides, which are not completely known, but only satisfy certain constraints.

Annihilating dark matter search with 12 yr of Fermi LAT data in nearby galaxy clusters

ABSTRACT Galaxy clusters are the largest virialized objects in the Universe and, as such, have high dark matter (DM) concentrations. This abundance of dark matter makes them promising targets for indirect DM searches. Here we report the details of a search, utilizing almost 12 yr of Fermi/LAT data, for gamma-ray signatures from the pair annihilation of WIMP dark matter in the GeV energy band. From this, we present the constraints on the annihilation cross-section for the $b\overline{b}$, W+W−, and γγ channels, derived from the non-detection of a characteristic signal from five nearby, high Galactic latitude, galaxy clusters (Centaurus, Coma, Virgo, Perseus, and Fornax). We discuss the potential of a boost to the signal due to the presence of substructures in the DM haloes of selected objects, as well as the impact of uncertainties in DM profiles on the presented results. We assert that the obtained limits are, within a small factor, comparable to the best available limits of those based on Fermi/LAT observations of dwarf spheroidal galaxies.

Solar Limb Darkening Color Imaging of the Sun with the Extreme Brightness Capability CAOS Camera

Experimentally demonstrated for the first time is Coded Access Optical Sensor (CAOS) camera-based imaging of the Sun. Only by using both the shortest 0.029 ms integration time of the scientific CMOS sensor and a very large factor of 10,000 optical attenuation at the entrance of the CMOS camera, one is able to produce the desired unsaturated image of the Sun. In sharp contrast, a small factor of 3.2 optical attenuation is required over a much smaller single photo-detector zone of the CAOS camera to capture the unsaturated Sun image, including color images obtained using red, green, and blue filters. Image data processing shows that both the CMOS camera and CAOS camera show similar Sun limb darkening measurements consistent with prior-art works. The CAOS camera empowers optically and operationally efficient full spectrum (e. g., 350 nm to 2700 nm) imaging of bright heavenly bodies in space, with the potential for creating impact for solar energy farms, space navigation, space exploration and astronomical science.

Do Student Mindsets Differ by Socioeconomic Status and Explain Disparities in Academic Achievement in the United States?

Students from higher–socioeconomic status (SES) backgrounds show a persistent advantage in academic outcomes over lower-SES students. It is possible that students’ beliefs about academic ability, or mindsets, play some role in contributing to these disparities. Data from a recent nationally representative sample of ninth-grade students in U.S. public schools provided evidence that higher SES was associated with fewer fixed beliefs about academic ability (a group difference of .22 standard deviations). Also, there was a negative association between a fixed mindset and grades that was similar regardless of a student’s SES. Finally, student mindsets were a significant but small factor in explaining the existing relationship between SES and achievement. Altogether, mindsets appear to be associated with socioeconomic circumstances and academic achievement; however, the vast majority of the existing socioeconomic achievement gap in the U.S. is likely driven by the root causes of inequality.

What the odor is not: Estimation by elimination

The olfactory system uses a small number of broadly sensitive receptors to combinatorially encode a vast number of odors. We propose that the brain decodes this distributed representation by exploiting a statistical fact: receptors that do not respond to an odor carry more information than receptors that do because they signal the absence of all odorants that bind to them. Thus, it is easier to identify what the odor is not, rather than what the odor is. For biologically realistic numbers of receptors, response functions, and odor complexity, this method of elimination turns an underconstrained decoding problem into a solvable one, allowing accurate determination of odorants in a mixture and their concentrations. A neural network realization of our algorithm resembles circuit architecture in the piriform cortex. We propose several experimental tests and show an excellent match to data from olfactory discrimination experiments. Our theory also suggests why animals from the fly to the elephant have a few hundred olfactory receptor types, give or take a small factor.

A study of differences by industry using factor models influencing software development estimates

Recently, IoT and AI/machine learning have attracted attention, and software development has been a critical activity for the companies that use IT. The investment in IT has been increasing, and it varies with the industry. In addition, software development has become complex with the growing sophistication in the target applications; therefore, it is a challenging task for the software vendors to prepare an accurate estimate. Consequently, the estimates grossly deviate from the true value. In this paper, we propose a method based on the previous research that uses the factors related to productivity of software development to find factors that affect the estimation of man-hours. We analyzed the parameters among populations using two factors and simultaneous analysis of multiple populations from nine industries. We used two-factor models extracted from “the study of software estimation factors extracted using covariance structure analysis” and verified the method by applying five constraints, including factor load amount and error variance, simultaneously for the nine industries. As a result, it was possible to separate industries with large factor variance and those with small factor variance. Moreover, it was possible to separate industries with large correlation coefficient between factors and industries with small factor correlation coefficient. For industries with small variance of factors, the factors are consistent within the industry, and in industries with large correlation between factors; the relationship between the two factors is more relevant. In other words, we could find out the relationship of factors influencing software estimation for each industry type. In addition, the variance of these two factors and the correlation coefficient between the factors were grouped, and a cluster analysis was performed. It was found that there was a difference in the estimate for each group of Business-to-Business and Business-to-Customer industry groups. Based on these results, while preparing software estimates, IT vendors would capture the characteristics of the factors for each type of industry and clarify the influential factors of fluctuation by being conscious of the productivity fluctuation factors related to the two factors.

Interface closure in the root region of steady deep-cellular growth in directional solidification

The present paper investigates the mechanism of interface closure in the root region of the solutions for steady deep-cellular growth. This phenomenon is determined by a transcendentally small factor beyond all orders. It is found that the root region comprises three inner-inner regions; the inner system in the root region has a simple turning point, whose presence generates the so-called trapped-waves mechanism, which is responsible for the interface closure at the bottom of root. The quantization condition derived from the trapped-waves mechanism yields the eigenvalue that determines the location of interface closure and its dependence on the interfacial energy and other physical parameters.