Related papers: Distances Between Partial Preference Orderings
In this study, we focus on a form of joint transportation called mixed transportation and enumerate the combinations with high cooperation effects from among a number of transport lanes registered in a database (logistics big data). As a…
The second order partial difference equation of two variables $ \CD u:= A_{1,1}(x) \Delta_1 \nabla_1 u + A_{1,2}(x) \Delta_1 \nabla_2 u + A_{2,1}(x) \Delta_2 \nabla_1 u + A_{2,2}(x) \Delta_2 \nabla_2 u & \qquad \qquad \qquad \qquad + B_1(x)…
Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…
Computing an array of all pairs of geodesic distances between the pixels of an image is time consuming. In the sequel, we introduce new methods exploiting the redundancy of geodesic propagations and compare them to an existing one. We show…
The extraction of natural gas from the earth has been shown to be governed by differential equations concerning flow through a porous material. Recently, models such as fractional differential equations have been developed to model this…
Many studies on microscopic systems deal with Brownian particles embedded in media whose densities are different from that of the particles, causing them either to sink or float. The proximity to a wall modifies the friction force the…
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations…
We give a simple polynomial-time approximation algorithm for the total variation distance between two product distributions.
We consider the problem of computing the distance between two piecewise-linear bivariate functions $f$ and $g$ defined over a common domain $M$. We focus on the distance induced by the $L_2$-norm, that is $\|f-g\|_2=\sqrt{\iint_M (f-g)^2}$.…
We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order integration by parts formulae introduce nontrivial boundary…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
We introduce and study the Marco Polo problem, which is a combinatorial approach to geometric localization. In this problem, we are told there are one or more points of interest (POIs) within distance $n$ of the origin that we wish to…
This paper describes a novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run time needed to find the maximum distance of two points in E2. It can be easily modified for the E3 case in…
In this article, we study "questionable representations" of (partial or total) orders, introduced in our previous article "A class of orders with linear? time sorting algorithm". (Later, we consider arbitrary binary functional/relational…
It is challenging to quantify numerical preferences for different objectives in a multi-objective decision-making problem. However, the demonstrations of a user are often accessible. We propose an algorithm to infer linear preference…
Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…
We investigate three proposals of distance on the moduli space of metrics: (1) a distance derived from the symplectic form of phase space, (2) a distance obtained by moving BPS objects at small velocity, (3a) a distance proposed by DeWitt…
Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a…
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…
Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…