Related papers: Effective Localization Using Double Ideal Quotient…
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…
Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the…
Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may…
We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can…
In this paper we consider monomial localizations of monomial ideals and conjecture that a monomial ideal is polymatroidal if and only if all its monomial localizations have a linear resolution. The conjecture is proved for squarefree…
The paper is a sequel to the paper "Application of localization to the multivariate moment problem" by the same author. A new criterion is presented for a positive semidefinite linear functional on the real polynomial algebra to correspond…
This paper reviews local and global optimality conditions in polynomial optimization. We summarize the relationship between them.
We propose local prediction pools as a method for combining the predictive distributions of a set of experts conditional on a set of variables believed to be related to the predictive accuracy of the experts. This is done in a two step…
The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a…
A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter…
This paper proposes a semi-sequential probabilistic model (SSP) that applies an additional short term memory to enhance the performance of the probabilistic indoor localization. The conventional probabilistic methods normally treat the…
Grothendieck point residue is considered in the context of computational complex analysis. A new effective method is proposed for computing Grothendieck point residues mappings and residues. Basic ideas of our approach are the use of…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
Localization is the challenge of determining the robot's pose in a mapped environment. This is done by implementing a probabilistic algorithm to filter noisy sensor measurements and track the robot's position and orientation. This paper…
The class PLS (Polynomial Local Search) captures the complexity of finding a solution that is locally optimal and has proven to be an important concept in the theory of local search. It has been shown that local search versions of various…
The k-nearest-neighbor method performs classification tasks for a query sample based on the information contained in its neighborhood. Previous studies into the k-nearest-neighbor algorithm usually achieved the decision value for a class by…
Every finite local principal ideal ring is the homomorphic image of a discrete valuation ring of a number field, and is determined by five invariants. We present an action of a group, non-commutative in general, on the set of Eisenstein…
We present a novel approach to place recognition well-suited to environments with many dynamic objects--objects that may or may not be present in an agent's subsequent visits. By incorporating an object-detecting preprocessing step, our…
We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation…
This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…