Related papers: Well-Orderedness of the Bashicu Matrix System
In this paper, we proposed a new efficient sorting algorithm based on insertion sort concept. The proposed algorithm called Bidirectional Conditional Insertion Sort (BCIS). It is in-place sorting algorithm and it has remarkably efficient…
We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…
In this paper, we introduce PSI-LinUCB, a scalable variant of LinUCB that enables efficient training, inference, and memory usage by representing the inverse regularized design matrix as a sum of a diagonal matrix and low-rank correction.…
We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.
A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically…
This paper considers the order estimation problem of stochastic autoregressive exogenous input (ARX) systems by using quantized data. Based on the least squares algorithm and inspired by the control systems information criterion (CIC), a…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
We investigate the descriptive complexity of order convergence in separable Banach lattices. While uniform convergence is Borel and $\sigma$-order convergence is known to be ${\bf \Delta}^1_2$, it is unclear in general when $\sigma$-order…
A four index notation (e.g. (10-11) is often used to denote reciprocal lattice vectors or crystal faces of hexagonal crystals. The purposes of this notation have never been fully explained. This note clarifies the underlying mathematics of…
We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.
The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine learning and statistics, and the design of…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
We show that a system of unstable higher Toda brackets can be defined inductively.
We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary. We define the…
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
Using techniques introduced by H. Thomas and N. Williams in "Cyclic Symmetry of the Scaled Simplex," we prove that modular sweep maps are bijective. We construct the inverse of the modular sweep map by passing through an intermediary set of…