Many Applications In Different Disciplines Research Articles

Fifty Years of the Cox Model

The Cox model is now 50 years old. The seminal paper of Sir David Cox has had an immeasurable impact on the analysis of censored survival data, with applications in many different disciplines. This work has also stimulated much additional research in diverse areas and led to important theoretical and practical advances. These include semiparametric models, nonparametric efficiency, and partial likelihood. In addition to quickly becoming the go-to method for estimating covariate effects, Cox regression has been extended to a vast number of complex data structures, to all of which the central idea of sampling from the set of individuals at risk at time t can be applied. In this article, we review the Cox paper and the evolution of the ideas surrounding it. We then highlight its extensions to competing risks, with attention to models based on cause-specific hazards, and to hazards associated with the subdistribution or cumulative incidence function. We discuss their relative merits and domains of application. The analysis of recurrent events is another major topic of discussion, including an introduction to martingales and complete intensity models as well as the more practical marginal rate models. We include several worked examples to illustrate the main ideas.

Higher-order optical rabi oscillations

Rabi oscillations express a phenomenon of periodic conversion between two wave states in a coupled system. The finding of Rabi oscillation has led to important applications in many different disciplines. Despite great progress, it is still unknown whether the Rabi oscillating state can be excited in the framework of the higher-order vector vortex regime. Here, we demonstrate in theory that the higher-order vector vortex light beams can be Rabi oscillating during evolution in an optical coupling system. This new classical oscillating state of light is characterized by a topologically shaped wavefront and coupled with spatially varying polarization. The vector vortex state exhibits a harmonic oscillatory property in the resonant and nonresonant conditions but differs greatly in Rabi oscillating frequencies. During Rabi oscillation, the complex state maintains its topology and intensity profile, while its intrinsic polarization pattern varies adiabatically in a periodic manner. We present an interpretation of the Rabi oscillation of the higher-order wave states in terms of the coupled-mode theory. Furthermore, we reveal a symmetry-protected transition between two Rabi oscillating modes, driven by a slowly varying phase mismatch. This Rabi transition has not been reported in either quantum mechanics or any other physical setting. This work advances the research of Rabi oscillation into the higher-order regime, and it may lead to novel applications in classical and quantum optics.

Toward a model for students’ combinatorial thinking

Combinatorics has many applications in different disciplines, however, only a few studies have explored students’ combinatorial thinking at the upper secondary and tertiary levels concurrently. The present research is a grounded theory study of eight Year 12 and five undergraduate students, who have participated in semi-structured interviews and responded to eight combinatorial tasks. Three types of combinatorial tasks were designed: combinatorial reasoning, evaluating, and problem-posing tasks. In the open coding phase of data analysis, seventy-one codes were identified which categorized into seven main categories at the axial coding phase. At the selective coding phase, five relationships between categories were identified that led to designing a model of students’ combinatorial thinking. The model consists of three movements: Horizontal, vertical downward, and vertical upward movement. It is asserted that this model could be used to improve the quality of teaching combinatorics, and also as a lens to explore students’ combinatorial thinking.

Further Theory of Neutrosophic Triplet Topology and Applications

In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets. This article is important because it opens new ways of research resulting in many applications in different disciplines, such as Biology, Computer Science, Physics, Robotics, Games and Puzzles and Fiber Art etc. Herein we study the application of NTT in Biology. The Neutrosophic Triplet Set (NTS) has a natural symmetric form, since this is a set of symmetric triplets of the form <A>, <anti(A)>, where <A> and <anti(A)> are opposites of each other, while <neuti(A)>, being in the middle, is their axis of symmetry. Further on, we obtain in this paper several properties of NTT, like bases, closure and subspace. As an application, we give a multicriteria decision making for the combining effects of certain enzymes on chosen DNA using the developed theory of NTT.

Large-scale passive laser gyroscope for earth rotation sensing

Earth rotation sensing has many applications in different disciplines, such as for the monitoring of ground motions, the establishment of UT1 and the test of the relativistic Lense-Thirring effect on the ground. We report the development of a 1 m*1 m heterolithic passive resonant gyroscope (PRG). By locking a pair of laser beams to adjacent modes of the square ring cavity in the clockwise and counter-clockwise directions, we achieve a rotation resolution of about 2E-9 rad/s at an integration time of 1000 s. The sensitivity of the PRG for rotations reaches a level of 2E-9 rad/s/rtHz in the 5-100~Hz region, currently limited by the detection noise, residual amplitude modulation and the mechanical instability of the cavity. Our initial results improve the reported rotation sensitivity of the PRGs and indicate that PRGs have a great potential for high-resolution Earth rotation sensing.

Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points

Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.

Optimizing Dynamical Network Structure for Pinning Control.

Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.

The first example of MEEKC-ICP-MS coupling and its application for the analysis of anticancer platinum complexes.

MEEKC is a powerful electrodriven separation technique with many applications in different disciplines, including medicinal chemistry; however, up to now the coupling to highly sensitive and selective MS detectors was limited due to the ion suppressive effect of the commonly used surfactant SDS. Herein, the first example of the coupling of MEEKC to ICP-MS is presented and an MEEKC method for the separation of Pt(II) and Pt(IV) anticancer drugs and drug candidates was developed. Different compositions of microemulsions were evaluated and the data were compared with those collected with standard ultraviolet/visible (UV/vis) spectroscopy detection. The MEEKC-ICP-MS system was found to be more sensitive than MEEKC-UV/vis and the analysis of UV/vis silent compounds is now achievable. The migration behavior of the Pt(II) and Pt(IV) compounds under investigation is correlated to their different chemical structures.

Model Validation and Performance Prediction in the Design of Micro Systems

Micro Electro Mechanical Systems are among the new and emerging technologies of the future and have many applications in different disciplines. Predicting the performance of such systems early in the design process can significantly impact the design cost and also improve the quality of the design. This study presents the model validation techniques integrated with some design methodologies to predict the performance of the micro systems. A two-dimensional micro scanner mirror was chosen as the case study to demonstrate the developed methodologies. The model validation methodology includes the verification of the finite element model using an experimental modal analysis setup for measuring the out-of-plane vibrations of the micro devices. The setup includes a laser doppler vibrometer, a microscope, a camera, a laser positioning system, and a data acquisition system to acquire the data. An experimental procedure was developed to collect the vibration data and then modal analysis was performed to determine the modal frequencies, mode shapes, and modal damping coefficients. The finite element analysis and experimental results were compared to identify the inaccuracies in the modeling assumptions. A validated finite element model was used to obtain the state space representation of the micro scanner mirror to proceed further with additional design studies. The state space model was used for disturbance analysis that was performed using Lyapunov approach to obtain root mean square values of the mirror rotation angle under the effect of a disturbance torque. The disturbance analysis framework was combined with the sensitivity analysis to determine the critical design parameters for improving the system performance. In addition to the disturbance sensitivity analysis, modal sensitivities of the design parameters were also investigated. This analysis was performed by perturbing the design parameters and investigating the change in the modal frequencies.

Stability in the Self-Organized Evolution of Networks

The modeling and analysis of large networks of autonomous agents is an important topic with applications in many different disciplines. One way of modeling the development of such networks is by means of an evolutionary process. The autonomous and selfishly acting agents are randomly chosen to become active according to an underlying probability distribution. They may apply some kind of local mutation operator to the network and decide about accepting these changes via some fitness-based selection whereas the fitness models the agent’s preferences. This general framework for the self-organized evolution of networks can be instantiated in many different ways. For interesting instances, one would like to know whether stable topologies eventually evolve and how long this process may take. Here, known results for an instantiation based on random spanning trees and a fitness-based selection according to global graph centrality measures are improved. Moreover, a more natural and local fitness-based selection using only the information on nearest neighbors is presented and analyzed with respect to the expected time needed to reach a stable state.

Interdisciplinary applications of a versatile spectral solar irradiance model: A review

A detailed review of different applications that have already been investigated with SMARTS, a versatile spectral solar irradiance model, is proposed here. This review provides examples of applications in many different disciplines, for which recent developments are discussed. Three main types of applications are considered, depending on their spectral range. Purely spectral applications encompass the determination of atmospheric constituents, the performance testing of spectroradiometers, and the improvement and validation of reference spectra for the rating of photovoltaic or glazing systems, or for new standards development in the field of weathering and material degradation. Narrow-band applications include the determination of different UV fluxes and of the UV index, and the prediction of illuminance on any horizontal or tilted surface, of the luminous efficacy of direct, diffuse or global radiation, of the photosynthetically active radiation, and of the irradiance transmitted by different bandpass filters. Finally, some specific broadband applications are reviewed: mesoscale predictions of radiation fluxes, evaluation of circumsolar effects in pyrheliometers, performance assessment of broadband radiation models, and turbidity determination from broadband irradiance data.

Interdisciplinary applications of a versatile spectral solar irradiance model: A review

A detailed review of different applications that have already been investigated with SMARTS, a versatile spectral solar irradiance model, is proposed here. This review provides examples of applications in many different disciplines, for which recent developments are discussed. Three main types of applications are considered, depending on their spectral range. Purely spectral applications encompass the determination of atmospheric constituents, the performance testing of spectroradiometers, and the improvement and validation of reference spectra for the rating of photovoltaic or glazing systems, or for new standards development in the field of weathering and material degradation. Narrow-band applications include the determination of different UV fluxes and of the UV index, and the prediction of illuminance on any horizontal or tilted surface, of the luminous efficacy of direct, diffuse or global radiation, of the photosynthetically active radiation, and of the irradiance transmitted by different bandpass filters. Finally, some specific broadband applications are reviewed: mesoscale predictions of radiation fluxes, evaluation of circumsolar effects in pyrheliometers, performance assessment of broadband radiation models, and turbidity determination from broadband irradiance data.