Related papers: $k$-Equivalence Relations and Associated Algorithm…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
In general terms, we establish algebraic relations that numbers must satisfy in order for their images to match after one or several transformations. Some groups associated with these relationships are identified, such as the Klein group.…
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…
We derive spin squeezing inequalities that generalize the concept of the spin squeezing parameter and provide necessary and sufficient conditions for genuine 2-, or 3- qubit entanglement for symmetric states, and sufficient condition for…
We show that there exists an atomic representable polyadic equality algebra of finite dimension n\geq 3, such that the cylindric reduct of its completion is not in SNr_n\CA_{n+4}, hence the result in the title. This solves an open problem…
We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
For a sequence of polynomials $\{p_k(t)\}$ in one real or complex variable, where $p_k$ has degree $k$, for $k\ge 0$, we find explicit expressions and recurrence relations for infinite matrices whose entries are the coefficients $d(n,m,k)$,…
We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.
Algebraic relations are established that determine the invariance of the transformed number after several transformations. The restrictions that determine the group structure of these relationships are analyzed, as is the case of the Klein…
Let $K$ be a field, fix an algebraic closure $\overline{K}$, and let $G$ be a subgroup of $\overline{K}^\times$. We are able to give a closed formula for the ratio between the degree $[K(G):K]$ and the index $|GK^\times:K^\times|$, provided…
In this paper, we define k-equivalence, a relation on graphs that relies on their associated cellular algebras. We show that a k-Boson quantum walk cannot distinguish pairs of graphs that are k- equivalent. The existence of pairs of…
Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$,…