Related papers: Identify Equivalent Frames
This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
It is well known that two finite sequences of vectors in inner product spaces are unitarily equivalent if and only if their respective inner products (Gram matrices) are equal. Here we present a corresponding result for the projective…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
A finite word $f$ is Hamming-isometric if for any two word $u$ and $v$ of same length avoiding $f$, $u$ can be transformed into $v$ by changing one by one all the letters on which $u$ differs from $v$, in such a way that all of the new…
We consider a problem that involves finding similar elements in a collection of sets. The problem is motivated by applications in machine learning and pattern recognition. We formulate the similar elements problem as an optimization and…
The pattern matching problem with swaps is to find all occurrences of a pattern in a text while allowing the pattern to swap adjacent symbols. The goal is to design fast matching algorithm that takes advantage of the bit parallelism of…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
Four dimensional scalar-tensor theory is considered within two conformal frames, the Jordan frame (JF) and the Einstein frame (EF). The actions for the theory are equivalent and equations of motion can be obtained from each action. It is…
A robotic system continuously measures its own motions and the external world during operation. Such measurements are with respect to some frame of reference, i.e., a coordinate system. A nontrivial robotic system has a large number of…
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…
We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the clique width of a graph is bounded in terms of its rank width, we also obtain a polynomial time isomorphism test…
Alias analysis, which determines whether two expressions in a program may reference to the same object, has many potential applications in program construction and verification. We have developed a theory for alias analysis, the "alias…
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…