Applied Mathematics Commons^™

Deep Learning Model Compression Techniques: Advances, Opportunities, And Perspective, Hubert Msuya

Tanzania Journal of Engineering and Technology (TJET)

Recently, deep learning (DL) models have excelled in a wide range of fields. All of these successes are built on intricate DL models. The hundreds of millions or even billions of parameters and high-performance computing graphical processing units or tensor processing units are largely responsible for their achievement. DL model integration into real-time devices with tight latency limitations, limited memory, and power-constrained requirements is the key driving force behind investigation of DL model compression techniques. Also, there is an increase in data availability that encourages multimodal fusion in DL models to boost the models' predictive accuracy. In order to create …

Continuous Time Dynamic Mode Decomposition In The Presence Of Partial Knowledge And Streaming Data, Efrain H. Gonzalez

USF Tampa Graduate Theses and Dissertations

Dynamic mode decomposition (DMD) is a physically interpretable data driven technique for modeling dynamical systems. The DMD method uses time series data where each data point is referred to as a snapshot and represents the value of the state at a particular moment in time. The important patterns found in the data are extracted and then used to create a model for the system. Once the important pieces have been obtained reduced order modeling can be used to reduce the complexity of the model.

But, DMD has evolved since its inception. After its association with the Koopman operator, DMD has …

Waste Treatment Facility Location For Hotel Chains, Dolores R. Santos-Peñate, Rafael R. Suárez-Vega, Carmen Florido De La Nuez

ITSA 2022 Gran Canaria - 9th Biennial Conference: Corporate Entrepreneurship and Global Tourism Strategies After Covid 19

Tourism generates huge amounts of waste. About half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. We consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. An optimization model is applied to locate the facilities and allocate the waste and products, and several scenarios are analysed. The study shows that, …

Said-Ball Polynomials For Solving Linear Systems Of Ordinary Differential Equations, Mubark Al-Subaai Dr., Ahmes Saleh Kherd

Emirates Journal for Engineering Research

Said-Ball polynomials with collocation method are used to numerically solve a system of linear ordinary differential equations. The matrix forms of Said-Ball polynomials of the solution, derivatives, and conditions are done. The linear system of ordinary differential equations with appropriate conditions is reduced to the linear algebraic equations system with unknown Said-Ball coefficients. Solving the resulting system determines the coefficients of Said-Ball polynomials. By Substituting these values in the polynomial, we get the problem's exact and approximate solutions. The obtaining numerical results show the proposed method's accuracy and reliability when compared with the other works and exact solutions

Temporality-Induced Chaos In The Kuramoto Model, Keanu Mason Rock, Hamza Dirie, Sean P. Cornelius

Northeast Journal of Complex Systems (NEJCS)

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in …

Extending The Spectral Difference Method With Divergence Cleaning (Sddc) To The Hall Mhd Equations, Russell J. Hankey, Kuangxu Chen, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is …

Periodic, Nonperiodic, And Chaotic Solutions For A Class Of Difference Equations With Negative Feedback, Benjamin B. Kennedy

Math Faculty Publications

We study the scalar difference equation x(k + 1) = x(k) + (f(x(k - N))) / N,

where f is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation x'(t) = f(x(t - 1)).

We examine explicit families of such equations for which we can find, for infinitely many values of N and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our …

Using Medicare Claims To Estimate Risk-Adjusted Performance Of Pennsylvania Trauma Centers, Alexis M Zebrowski, Phillipe Loher, David G Buckler, Isidore Rigoutsos, Brendan G Carr, Douglas J Wiebe

Computational Medicine Center Faculty Papers

Trauma centers use registry data to benchmark performance using a standardized risk adjustment model. Our objective was to utilize national claims to develop a risk adjustment model applicable across all hospitals, regardless of designation or registry participation. Patients from 2013-14 Pennsylvania Trauma Outcomes Study (PTOS) registry data were probabilistically matched to Medicare claims using demographic and injury characteristics. Pairwise comparisons established facility linkages and matching was then repeated within facilities to link records. Registry models were estimated using GLM and compared with five claims-based LASSO models: demographics, clinical characteristics, diagnosis codes, procedures codes, and combined demographics/clinical characteristics. Area under the …

(R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, Ashutosh Rajput, Tanvi ., Rajiv Aggarwal, Arpana Sharma, Shiv Kumar Sahdev, Manoj Kumar, Jaimala .

Applications and Applied Mathematics: An International Journal (AAM)

The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain …

(R1951) Numerical Solution For A Class Of Nonlinear Emden-Fowler Equations By Exponential Collocation Method, Mohammad Aslefallah, Saeid Abbasbandy, Şuayip Yüzbaşi

Applications and Applied Mathematics: An International Journal (AAM)

In this research, exponential approximation is used to solve a class of nonlinear Emden-Fowler equations. This method is based on the matrix forms of exponential functions and their derivatives using collocation points. To demonstrate the usefulness of the method, we apply it to some different problems. The numerical approximate solutions are compared with available (existing) exact (analytical) solutions to show the accuracy of the proposed method. The method has been checked with several examples to show its validity and reliability. The reported examples illustrate that the method is reasonably efficient and accurate.

(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya

Applications and Applied Mathematics: An International Journal (AAM)

This research aims to study atmospheric internal waves which occur within the fluid rather than on the surface. The mathematical model of the shallow fluid hypothesis leads to a coupled nonlinear system of partial differential equations. In the shallow flow model, the primary assumption is that vertical size is smaller than horizontal size. This model can precisely replicate atmospheric internal waves because waves are dispersed over a vast horizontal area. A semi-analytical approach, namely modified differential transform, is applied successfully in this research. The proposed method obtains an approximate analytical solution in the form of convergent series without any linearization, …

(R1997) Distance Measures Of Complex Fermatean Fuzzy Number And Their Application To Multi-Criteria Decision-Making Problem, V. Chinnadurai, S. Thayalan, A. Bobin

Applications and Applied Mathematics: An International Journal (AAM)

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a …

(R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Virendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have investigated resonant curve due to frequencies − angular rate of rotation of the Earth and the rate of change of Earth’s equatorial ellipticity parameter. Perturbation equations are used to convert the non-linear equations of motion of geo-synchronous satellite to the linear form. With the help of graphs, we have shown the effect of Earth’s equatorial ellipticity parameter on oscillatory amplitude and variation in orbital radius of satellite. By defining different perturbations, we have also drawn resonant curve due to frequencies steady-state orbital angular rate of satellite and the rate of change of Earth’s equatorial ellipticity …

(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …

(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …

(R1975) Map/Ph(1), Ph(2)/2 Queue With Multiple Vacation, Optional Service, Consultations And Interruptions, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s …

On Colorings And Orientations Of Signed Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.

Detecting Coherent Transport Structures In Ocean Surface Flows, Leah Hoogstra

Master's Theses

Ocean surface transport plays a critical role in marine ecosystems, influencing the complex spatiotemporal patterns of both marine species and pollutants. The theory of Lagrangian coherent structures (LCSs) aims to identify fundamental patterns within time-dependent, nonlinear fluid flows. LCSs are material surfaces that act as dividing lines which fluid does not cross for a relevant period of time. LCS theory is still under active development, and there are multiple proposed ways to mathematically determine an LCS. Each proposed mathematical definition aims to capture the same physical properties, and some capture those properties more successfully and consistently than others. Here we …

Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis, Jackie Driscoll

Master's Theses

Pluripotent stem cells have been observed to segregate into Turing-like patterns during the early stages of Dox-inducible hiPSC differentiation. In this thesis, we de- velop a tool to quantify the tortuosity in the patterns formed by colonies of pluripo- tent stem cells using methods from topological data analysis. We use clustering techniques and the mapper algorithm to create simplicial complexes representing samples of cells and detail a method of evaluating the tortuosity of these complexes. We use the resulting persistence landscapes and their associated norms to evaluate experimental data and simulated data from an agent based model. This thesis finds …

Gradient-Based Trade-Off Design For Engineering Applications, Lena A. Royster, Gene Hou

Mechanical & Aerospace Engineering Faculty Publications

The goal of the trade-off design method presented in this study is to achieve newly targeted performance requirements by modifying the current values of the design variables. The trade-off design problem is formulated in the framework of Sequential Quadratic Programming. The method is computationally efficient as it is gradient-based, which, however, requires the performance functions to be differentiable. A new equation to calculate the scale factor to control the size of the design variables is introduced in this study, which can ensure the new design achieves the targeted performance objective. Three formal approaches are developed in this study for trade-off …