For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

Knowledge graph embedding aims to represent entities and relations in a large-scale knowledge graph as elements in a continuous vector space. Existing methods, e.g., TransE and TransH, learn embedding representation by defining a global margin-based loss function over the data. However, the optimal loss function is determined during experiments whose parameters are examined among a closed set o...

The performance of a reject option classifiers is quantified using 0 − d − 1 loss where d ∈ (0, .5) is the loss for rejection. In this paper, we propose double ramp loss function which gives a continuous upper bound for (0 − d − 1) loss. Our approach is based on minimizing regularized risk under the double ramp loss using difference of convex programming. We show the effectiveness of our approa...

The present paper deals with optimizing the maximum premium values using Hamiltonian-Jacobi-Bellamann equation. Here it is considering that quadratic and fractional power utility functions for different loss distributions of discrete analogues continuous distributions. It has seen function more beneficial to insured insurer. Numerical illustrations these two are given.

Abstract We discuss the numerical solution to a class of continuous time finite state mean field games. apply deep neural network (DNN) approach solving fully coupled forward and backward ordinary differential equation system that characterizes equilibrium value function probability measure game. prove error between true approximate is linear square root DNN loss function. give an example apply...

Artificial Development is a promising approach to evolutionary design optimization inspired by biological development. However, there is still no consensus as to which problem classes this approach has a clear advantage over classical direct encodings. We attack this problem by introducing the concept of fitness function modifiers based on complexity. Our results indicate that using these modif...

 A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

Background: Polycystic ovary syndrome (PCOS) is the most common cause of anovulatory infertility in women of reproductive age, affecting 7% of this population. Although not entirely understood, the etiology of PCOS is closely linked to obesity and abdominal adiposity that are considered to worsen the clinical presentation, particularly menstrual irregularities and hyperandrogenism. Lifestyle mo...

A general closed expression is given for the isothermal minimum free energy of a linear viscoelastic material with continuous spectrum response. Two quite distinct approaches are adopted, which give the same final result. The first involves expressing a positive quantity, closely related to the loss modulus of the material, defined on the frequency domain, as a product of two factors with speci...