Mathematical Background Research Articles

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

Regular graph-based free route flight planning approach

PurposeThe purpose of this study is to provide an alternative graph-based airspace model for more effective free-route flight planning.Design/methodology/approachBased on graph theory and available data sets describing airspace, as well as weather phenomena, a new FRA model is proposed. The model is applied for near to optimal flight route finding. The software tool developed during the study and complexity analysis proved the applicability and timed effectivity of the flight planning approach.FindingsThe sparse bidirectional graph with edges connecting only (geographically) closest neighbours can naturally model local airspace and weather phenomena. It can be naturally applied to effective near to optimal flight route planning.Research limitations/implicationsPractical results were acquired for one country airspace model.Practical implicationsMore efficient and applicable flight planning methodology was introduced.Social implicationsAircraft following the new routes will fly shorter trajectories, which positively influence on the natural environment, flight time and fuel consumption.Originality/valueThe airspace model proposed is based on standard mathematical backgrounds. However, it includes the original airspace and weather mapping idea, as well as it enables to shorten flight planning computations.

Model-Free Control of UCG Based on Continual Optimization of Operating Variables: An Experimental Study

The underground coal gasification (UCG) represents an effective coal mining technology, where coal is transformed into syngas underground. Extracted syngas is cleaned and processed for energy production. Various gasification agents can be injected into an underground georeactor, e.g., air, technical oxygen, or water steam, to ensure necessary temperature and produce syngas with the highest possible calorific value. This paper presents an experimental study where dynamic optimization of operating variables maximizes syngas calorific value during gasification. Several experiments performed on an ex situ reactor show that the optimization algorithm increased syngas calorific value. Three operation variables, i.e., airflow, oxygen flow, and syngas exhaust, were continually optimized by an algorithm of gradient method. By optimizing the manipulation variables, the calorific value of the syngas was increased by 5 MJ/m3, both in gasification with air and additional oxygen. Furthermore, a higher average calorific value of 4.8–5.1 MJ/m3 was achieved using supplementary oxygen. The paper describes the proposed ex situ reactor, the mathematical background of the optimization task, and results obtained during optimal control of coal gasification.

Teaching CAPM for a Pre-Finance Graduate Program at the STEM Undergraduate Level: Linear Algebra Perspective

Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mathematics and science, but they may not have studied financial theory. To facilitate the classroom teaching of the Capital Asset Pricing Model (CAPM) for STEM students, this paper seeks to expound on the essence of the theory starting at a two-asset framework. Adopting the concepts proposed by Merton (1972), this paper accomplishes the derivation by virtue of basic mathematical tools such as linear algebra, geometry, and statistics except for calculus. We show that the major aspects of Merton’s derivation of the CAPM for a universe of N assets may also be obtained in a two-asset world. Through the methods of this article, students will learn the in-depth theory of CAPM and its hands-on empirical tool. For example, students will realize that even if investors specify different threshold rewards, their different CAPMs will yield identical pricing for assets and portfolios.

Design Optimization and Dynamic Simulation of Steam Cycle Power Plants: A Review

After more than one century from its first use for electric power production, steam cycles are still the object of continuous research and development efforts worldwide. Indeed, owing to its favorable thermodynamic properties, steam cycles are not only used in coal-fired power plants but in a large variety of applications such as combined cycles, concentrated solar power plants and polygeneration plants. On the other hand, to cope with the efficiency and flexibility requirements set by today’s energy markets, the design and the operation of steam cycles must be carefully optimized. A key rule is played by the simulation and optimization codes developed in the last 30 years. This paper provides an introduction to the main types of simulation and optimization problems (design, off-design operation and dynamic), an overview of the mathematical background (possible solution approaches, numerical methods and available software), and a review of the main scientific contributions.

Accuracy comparison of interior orientation parameters from different photogrammetric software and direct linear transformation method

The integration of computer vision algorithms and photogrammetric methods leads to procedures that increasingly automate the image-based 3D modeling process. The main objective of photogrammetry is to obtain a three-dimensional model using terrestrial or aerial images. Calibration of the camera and detection of the orientation parameters are important for obtaining accurate and reliable 3D models. For this purpose, many methods have been developed in the literature. However, since each method has different mathematical background, calibration results may be different. In this study, the effect of camera interior orientation parameters obtained from different methods on the accuracy of three-dimensional model will be examined. In this context, a test area consisting of 21 points was used. The test network was coordinated in a local coordinate system using geodetic methods. Some points of the test area were selected as the check point and accuracy analysis was performed. Direct Linear Transformation (DLT) method, MATLAB, Agisoft Lens, Photomodeler, 3D Flow Zephyr software were analysed. The lowest error value of 7.7 cm was achieved by modelling with Agisoft Lens.

Improved extrapolation methods of data-driven background estimations in high energy physics

Data-driven methods of background estimations are often used to obtain more reliable descriptions of backgrounds. In hadron collider experiments, data-driven techniques are used to estimate backgrounds due to multi-jet events, which are difficult to model accurately. In this article, we propose an improvement on one of the most widely used data-driven methods in the hadron collision environment, the “ABCD” method of extrapolation. We describe the mathematical background behind the data-driven methods and extend the idea to propose improved general methods.

Development of the Czech Childhood Cancer Information System: Data Analysis and Interactive Visualization.

BackgroundThe knowledge of cancer burden in the population, its time trends, and the possibility of international comparison is an important starting point for cancer programs. A reliable interactive tool describing cancer epidemiology in children and adolescents has been nonexistent in the Czech Republic until recently.ObjectiveThe goal of this study is to develop a new web portal entitled the Czech Childhood Cancer Information System (CCCIS), which would provide information on childhood cancer epidemiology in the Czech Republic.MethodsData on childhood cancers have been obtained from the Czech National Cancer Registry. These data were validated using the clinical database of childhood cancer patients and subsequently combined with data from the National Register of Hospitalised Patients and with data from death certificates. These validated data were then used to determine the incidence and survival rates of childhood cancer patients aged 0 to 19 years who were diagnosed in the period 1994 to 2016 (N=9435). Data from death certificates were used to monitor long-term mortality trends. The technical solution is based on the robust PHP development Symfony framework, with the PostgreSQL system used to accommodate the data basis.ResultsThe web portal has been available for anyone since November 2019, providing basic information for experts (ie, analyses and publications) on individual diagnostic groups of childhood cancers. It involves an interactive tool for analytical reporting, which provides information on the following basic topics in the form of graphs or tables: incidence, mortality, and overall survival. Feedback was obtained and the accuracy of outputs published on the CCCIS portal was verified using the following methods: the validation of the theoretical background and the user testing.ConclusionsWe developed software capable of processing data from multiple sources, which is freely available to all users and makes it possible to carry out automated analyses even for users without mathematical background; a simple selection of a topic to be analyzed is required from the user.

Microscopic structure and mathematical background of the multiconfigurational dynamical symmetry

Background: The multiconfigurational dynamical symmetry (MUSY) is the common intersection of the shell, collective, and cluster models for the multi-major-shell problem. It is able to describe the spectra of different configurations in different energy windows in a unified way. It is based on some heuristic arguments, related to the connection of the wave functions, and energy eigenvalues. The detailed mathematical background has been worked out so far only for the simplest case of the two binary cluster configurations.Purpose: I intend to construct the exact algebraic framework for the general case of the MUSY, i.e., for any number of configurations and any number of clusters or nucleons. As an illustrative example, the spectrum of different configurations of the $^{44}\mathrm{Ti}$ nucleus is described by a simple Hamiltonian.Methods: Classification schemes defined by different algebra chains need to be combined; in particular, those of the major shell scheme and of the particle index scheme.Results: A class of Hamiltonians, which is invariant under the transformations from one configuration to the other, is determined. In case of the $^{44}\mathrm{Ti}$ low-lying shell-model spectrum, as well as $^{40}\mathrm{Ca}+^{4}\mathrm{He}$ and $^{28}\mathrm{Si}+^{16}\mathrm{O}$ cluster states are obtained in a unified way.Conclusions: The MUSY is based on two pillars: (i) a unified multiplet structure for shell, collective, and cluster model states and (ii) a Hamiltonian which is invariant with respect to the transformations from one configuration to the other.

ASSESSMENT OF PSYCHOLOGICAL TEST RESULTS OF FRESHMEN EDUCATION STUDENTS

Psychological testing in schools is a beneficial activity that helps a student achieve their goals and helps diagnosed social, cognitive, or behavioral problems. This study aimed to assess the psychological test results of education students in a Philippine state university. The study utilized secondary data from 443 education students at the university. Descriptive measures and multiple regression models were employed in evaluating the data and determining the influencing factor of psychological test results, respectively. Results revealed that the selected demographic variables as gender, degree program, type of high school, and over-all grade point average have no significant association with the psychological test results of education students. Furthermore, this study has documented the robust and positive evidence that Mathematics and English grade point average contributed to the psychological test scores of the students. The results go to infer that students with a good background in Mathematics and English subjects in high school have a good foundation in analytical and logical thinking during college.

Another form of undermatching? A mixed‐methods examination of first‐year engineering students' calculus placement

AbstractBackgroundA strong calculus foundation is essential to undergraduate engineering success. However, some students may be self‐selecting to begin their mathematics sequence in a lower‐level calculus course than their prior achievement and aptitude would suggest is appropriate (i.e., undermatch).PurposeThis study examined (a) the relationship between engineering students' academic outcomes and first‐year calculus course taken, (b) the extent to which first‐year engineering students select calculus courses appropriate for their prior mathematics achievement and background, and (c) students' rationales for calculus course selection.Design/MethodThe study used a mixed‐methods approach consisting of quantitative t‐test, multiple regression, and classification decision tree model analyses of student records of (a) first‐year engineering students from 2009 to 2016 (n = 2689) at a highly selective public research university and (b) qualitative focus groups of 95 undergraduate engineering students in 2017–2018.ResultsStudents who begin their math sequence in Calculus I had lower graduating grade point averages, longer time‐to‐degree, and were less likely to major in popular engineering fields than those who started in Calculus II. Of first‐year undergraduates, 18.4% undermatched their choice of calculus course. Students' rationales for choosing a particular calculus course included (a) prior achievement, (b) recommendations from others, and (c) self‐confidence.ConclusionsResults suggest that undermatching the choice of first calculus course may lead to negative consequences for students' STEM pathways even at a highly selective engineering school. These results hold implications for practice, especially in terms of advising at the high school and college levels.

Deriving structures of FFT based filter banks by signal flow graphs

The design of filter banks, which is a frequently used operator for many practical applications, has been widely reported in the literature. The requirements of using extensive mathematical manipulations for finding computationally efficient structures of filter banks have imposed severe difficulties for those who lack sufficient mathematical background. This paper is to report procedures of deriving computationally efficient filter bank structures by using a few graphic transformations of equivalent multi-rate operations. It is seen that these procedures used in the derivation process are elegantly simple and straight forwards in concept. In particular, these procedures can be flexibly used to find the computationally efficient structures of both maximally decimated (p=1) and non-maximally decimated (p>1) filter banks, where p is the oversampling factor. For the non-maximally decimated filter banks, the computational complexity needed by our derived structure is less than that needed by the structures reported in the literature.

Introduction to topiCS Volume 13, Issue 3.

With the current issue of Topics in Cognitive Science, we are proud to present award-winning research again, starting off with a scholar's lifetime achievements distinguished by the Rumelhart Prize, then introducing the Best Papers from the 18th International Conference on Cognitive Modeling. The first topic honors Michelene (“Micki”) T. H. Chi (Arizona State University), the 19th recipient of the David E. Rumelhart Prize. With a background in mathematics and a strong interest in the science of education, Chi has conducted pioneering, widely cited, and highly influential work on the active role of learners in the learning process, from self-explanations to the development of expertise. Having been active in the society for almost her entire academic life, and elected one of its inaugural fellows in 2003, she received the award also referred to as “the Nobel Prize in Cognitive Science” in 2019, for having “challenged basic assumptions about the mind” more than once and for having “defined new approaches that have shaped a generation of cognitive and learning scientists.” Following a pithy introduction by former topiCS editor Wayne Gray, we are happy to present the paper based on her Rumelhart Lecture, on “Translating a theory of active learning,” in which she attempts to close the gap between research and practice by outlining a multistep translation research framework. The second part of this issue comprises revised and expanded versions of the four best papers presented at the 18th International Conference on Cognitive Modeling, which took place last year fully virtually as was the case for so many other conferences. This batch has been curated by Topic Editors Terrence C. Stewart (National Research Council Canada) and Christopher Myers (Air Force Research Laboratory), who also introduce this selection of papers in more detail. Congratulations to all our authors for their awards––we hope you continue the outstanding work you are doing! topiCS encourages letters and commentaries on all topics, as well as proposals for new topics. Letters are not longer than two published pages (ca. 400–1000 words). Commentaries (between 1000 and 2000 words) are often solicited by Topic Editors prior to the publication of their topic, but they may also be considered after publication. Letters and commentaries typically come without abstract and with few references, if any. The Executive Editor and the Senior Editorial Board (SEB) are constantly searching for new and exciting topics for topiCS. Feel free to open communications with a short note to the Executive Editor ([email protected]) or a member of the SEB (for a list, see the publisher's homepage for topiCS: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1756-8765/homepage/EditorialBoard.html).

High throughput resource efficient reconfigurable interleaver for MIMO WLAN application.

Demand for high-speed wireless broadband internet service is ever increasing. Multiple-input-multiple-output (MIMO) Wireless LAN (WLAN) is becoming a promising solution for such high-speed internet service requirements. This paper proposes a novel algorithm to efficiently model the address generation circuitry of the MIMO WLAN interleaver. The interleaver used in the MIMO WLAN transceiver has three permutation steps involving floor function whose hardware implementation is the most challenging task due to the absence of corresponding digital hardware. In this work, we propose an algorithm with a mathematical background for the address generator, eliminating the need for floor function. The algorithm is converted into digital hardware for implementation on the reconfigurable FPGA platform. Hardware structure for the complete interleaver, including the read address generator and memory module, is designed and modeled in VHDL using Xilinx Integrated Software Environment (ISE) utilizing embedded memory and DSP blocks of Spartan 6 FPGA. The functionality of the proposed algorithm is verified through exhaustive software simulation using ModelSim software. Hardware testing is carried out on Zynq 7000 FPGA using Virtual Input Output (VIO) and Integrated Logic Analyzer (ILA) core. Comparisons with few recent similar works, including the conventional Look-Up Table (LUT) based technique, show the superiority of our proposed design in terms of maximum improvement in operating frequency by 196.83%, maximum reduction in power consumption by 74.27%, and reduction of memory occupancy by 88.9%. In the case of throughput, our design can deliver 8.35 times higher compared to IEEE 802.11n requirement.

The social brain of social media \u2013 a physiological boundary to the number of online relations

Based on the research done by Dunbar and the resulting Social Brain Hypothesis, the present study introduced a mathematical model for the development of follower numbers and the number of followed accounts regarding users/influencers of Social Media platforms. Under very simple assumptions the mathematical model suggests that an universal upper bound to follower and followed numbers exists. The theoretical upper bound is then empirically validated by using a representative data set of 255 influencers on Instagram from the field of women’s fashion. The follower numbers show convergence to a common boundary for the years 2018 to 2019 and stagnation for 2019 to 2020, while the number of followed accounts show stagnation for 2018 to 2019 and convergence for 2019 and 2020. The model in conjunction with its empirical validation therefore provides the mathematical background to establish the socio-biological Social Brain Hypothesis in the field of influencer marketing in regards to Social Media platforms.

A hierarchical component model of students’ difficulties of learning mathematics in a distance higher education

The main purpose of the research was to explore the students’ difficulties in learning mathematics at a distance higher education. The method used was a survey of 304 students of the study program of S-1 PGSD in the Pontianak Regional office center of Universitas Terbuka (UPBJJ-UT Pontianak). The data analysis used a partial least squares structural equation model (PLS-SEM) to reveal the hierarchical component model of the students’ difficulties in learning mathematics at Universitas Terbuka. The research confirmed that the difficulties in learning mathematics were reflected by five latent variables as indicated by path coefficients and level of significance: (1) the nature of mathematics, (2) the characteristics of distance learning, (3) learning material, (4) learning support services, and (5) motivation. The recommendation was that to facilitate the students’ learning mathematics, an institution of distance higher education should be focused on resolving the difficulties perceived by the students, such as students’ mathematical background, self-directed learning skills, and skill for learning through media.

Sliding mode control of a servo system in LabVIEW: Comparing different control methods

AbstractThe main contribution of this paper is to present the efficiency of LabVIEW in simulating and controlling a servo system with conventional methods (PI and PID control), as well as sliding mode control (SMC). The control of an actual system with LabVIEW and NI hardware provides an efficient implementation platform, using both LabVIEW’s graphical programming and the text-based m-file language MathScript RT. Both programming environments and the connection to NI hardware are relatively easy to use, therefore, ideal for education. The graphical “coding” can help novice users to see through their algorithms. However, the mathematical background of sliding mode control is difficult compared to conventional PID control; the SMC implementation for practical uses can be quite simple, as the presented example demonstrates. The first didactic step is a simulation with the Control Design and Simulation, as well as MathScript RT Modules. Then a myRIO Student Embedded Device is used to control a real servo system. LabVIEW code can be compiled to run on computers, (soft) real-time targets, and FPGAs (hard real-time targets), so students can easily and quickly step up to real industrial measurement and control problems without the need to learn new programming environments.

On a Quantitative Approach to Clinical Neuroscience in Psychiatry: Lessons from the Kuramoto Model.

The human brain is a complex system comprising subregions that dynamically exchange information between its various parts through synchronization. These dynamic, complex interactions ultimately play a role in perception, emotion, cognition, and behavior, as well as in various maladaptive neurologic and psychiatric processes. It is therefore important to understand how brain dynamics might be implicated in these processes. Over the past few years, network neuroscience and computational neuroscience have highlighted the importance of measures such as metastability (a property whereby members of an oscillating system tend to linger at the edge of synchronicity without permanently becoming synchronized) in quantifying brain dynamics. Altered metastability has been implicated in various psychiatric illnesses, such as traumatic brain injury and Alzheimer's disease. Computational models, which range in complexity, have been used to assess how various parameters affect metastability, synchronization, and functional connectivity. These models, though limited, can act as heuristics in understanding brain dynamics. This article (aimed at the clinical psychiatrist who might not possess an extensive mathematical background) is intended to provide a brief and qualitative summary of studies that have used a specific, highly simplified computational model of coupled oscillators (Kuramoto model) for understanding brain dynamics-which might bear some relevance to clinical psychiatry.

Exploring SERS from complex patterns fabricated by multi-exposure laser interference lithography

Designing uniform plasmonic surfaces in a large area is highly recommended for surface-enhanced Raman scattering (SERS). As periodic morphologies exhibit uniform SERS and optical tunability, diverse fabrication methods of periodic nanostructures have been reported for SERS applications. Laser interference lithography (LIL) is one of the most versatile tools since it can rapidly fabricate periodic patterns without the usage of photomasks. Here, we explore complex interference patterns for spatially uniform SERS sensors and its cost-effective fabrication method termed multi-exposure laser interference lithography (MELIL). MELIL can produce nearly periodic profiles along every direction confirmed by mathematical background, and in virtue of periodicity, we show that highly uniform Raman scattering (relative standard deviation <6%) can also be achievable in complex geometries as the conventional hole patterns. We quantitatively characterize the Raman enhancement of the MELIL complex patterns after two different metal deposition processes, Au e-beam evaporation and Ag electroplating, which results in 0.387 × 105 and 1.451 × 105 in enhancement factor respectively. This alternative, vacuum-free electroplating method realizes an even more cost-effective process with enhanced performance. We further conduct the optical simulation for MELIL complex patterns which exhibits the broadened and shifted absorption peaks. This result supports the potential of the expanded optical tunability of the suggested process.

Engineering Origami: A Comprehensive Review of Recent Applications, Design Methods, and Tools

AbstractOrigami‐based designs refer to the application of the ancient art of origami to solve engineering problems of different nature. Despite being implemented at dimensions that range from the nano to the meter scale, origami‐based designs are always defined by the laws that govern their geometrical properties at any scale. It is thus not surprising to notice that the study of their applications has become of cross‐disciplinary interest. This article aims to review recent origami‐based applications in engineering, design methods and tools, with a focus on research outcomes from 2015 to 2020. First, an introduction to origami history, mathematical background and terminology is given. Origami‐based applications in engineering are reviewed largely in the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Second, design methods, design tools, and related manufacturing constraints are discussed. Finally, the article concludes with open questions and future challenges.