Related papers: On the Monotonicity of Work Function in k-Server C…
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
A Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$ is said to be $\eps$-far from monotone if $f$ needs to be modified in at least $\eps$-fraction of the points to make it monotone. We design a randomized tester that is given oracle access to…
This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the…
This article employs techniques from convex analysis to present characterizations of (maximal) $n-$monotonicity, similar to the well-established characterizations of (maximal) monotonicity found in the existing literature. These…
The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated system's Hamiltonian. A similar expression…
In this paper, we study the weighted $k$-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) $k$-server problem which has a polynomial-time…
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
This paper considers the scheduling of stochastic jobs on parallel identical machines to minimize the expected total weighted completion time. While this is a classical problem with a significant body of research on approximation algorithms…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
Historically, much of machine learning research has focused on the performance of the algorithm alone, but recently more attention has been focused on optimizing joint human-algorithm performance. Here, we analyze a specific type of…
We consider the graph dynamical systems known as k-reversible processes. In such processes, each vertex in the graph has one of two possible states at each discrete time step. Each vertex changes its state between the current time and the…
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is…
In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…
We give an alternative proof of skew information via operator algebra approach and show its strong monotonicity under particular quantum TPCP maps. We then formulate a family of new resource measure if the resource can be characterized by a…
We initiate a formal study of fairness for the $k$-server problem, where the objective is not only to minimize the total movement cost, but also to distribute the cost equitably among servers. We first define a general notion of…
Fej\'er monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fej\'er* monotonicity, which was initially proposed in [SIAM…
We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.