Related papers: Augmenting Automatic Differentiation for a Single-…
This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…
This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished…
If a document is about travel, we may expect that short snippets of the document should also be about travel. We introduce a general framework for incorporating these types of invariances into a discriminative classifier. The framework…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson…
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
We consider the problem of service placement at the network edge, in which a decision maker has to choose between $N$ services to host at the edge to satisfy the demands of customers. Our goal is to design adaptive algorithms to minimize…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential…
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…
We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
We study the bias of classical quantile regression and instrumental variable quantile regression estimators. While being asymptotically first-order unbiased, these estimators can have non-negligible second-order biases. We derive a…