Related papers: Newton trees for ideals in two variables and appli…
The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…
Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…
Decision tree is an important method for both induction research and data mining, which is mainly used for model classification and prediction. ID3 algorithm is the most widely used algorithm in the decision tree so far. In this paper, the…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in…
Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher…
Decision trees and decision rule systems play important roles as classifiers, knowledge representation tools, and algorithms. They are easily interpretable models for data analysis, making them widely used and studied in computer science.…
The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…
We propose a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph. The algorithm employs an inexact, preconditioned Newton…
Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel-fixed point, i.e. a point corresponding to a subscheme defined by…