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Full-Text Articles in Physical Sciences and Mathematics
Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos
Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos
Mathematics and Statistics Faculty Publications
Imbalanced class distribution is an inherent problem in many real-world classification tasks where the minority class is the class of interest. Many conventional statistical and machine learning classification algorithms are subject to frequency bias, and learning discriminating boundaries between the minority and majority classes could be challenging. To address the class distribution imbalance in deep learning, we propose a class rebalancing strategy based on a class-balanced dynamically weighted loss function where weights are assigned based on the class frequency and predicted probability of ground-truth class. The ability of dynamic weighting scheme to self-adapt its weights depending on the prediction scores …
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Mathematics and Statistics Faculty Publications
We introduce random walks in a sparse random environment on ℤ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent regimes. The new model combines features of several existing models of random motion in random media and admits a transparent physical interpretation. More specifically, a random walk in a sparse random environment can be characterized as a “locally strong” perturbation of a simple random walk by a random potential induced by “rare impurities,” which are randomly distributed over the integer lattice. Interestingly, in the critical (recurrent) regime, …
Quandle Coloring And Cocycle Invariants Of Composite Knots And Abelian Extensions, W Edwin Clark, Masahico Saito, Leandro Vendramin
Quandle Coloring And Cocycle Invariants Of Composite Knots And Abelian Extensions, W Edwin Clark, Masahico Saito, Leandro Vendramin
Mathematics and Statistics Faculty Publications
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of …
An Efficient Scheme For Numerical Solution Of Burgers’ Equation Using Quintic Hermite Interpolating Polynomials, Shelly Arora, Inderpreet Kaur
An Efficient Scheme For Numerical Solution Of Burgers’ Equation Using Quintic Hermite Interpolating Polynomials, Shelly Arora, Inderpreet Kaur
Mathematics and Statistics Faculty Publications
A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the well-known non-linear Burgers’ equation. The quintic Hermite collocation method (QHCM) solves the non-linear Burgers’ equation directly without converting it into linear form using Hopf–Cole transformation. Stability of the QHCM has been checked using Eucledian and Supremum norms. Numerical values obtained from QHCM are compared with the values obtained from other techniques such as orthogonal collocation method, orthogonal collocation on finite elements and pdepe solver. Numerical values have been plotted using plane and surface plots to demonstrate the results graphically. …
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Mathematics and Statistics Faculty Publications
One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCLd,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCLd. An intersection of d languages in DCL1 defines DCLd. We prove that there is …