Related papers: Comparative analysis of the original and amplitude…
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…
The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which…
In this paper, we distinguish between two kinds of compositional data sets: elementary and aggregate. This fact will help us to decide the choice of the weights to use in log interaction analysis of aggregate compositional vectors. We show…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
A method for analyzing sequential data sets, similar to the permutation entropy one, is discussed. The characteristic features of this method are as follows: it preserves information about equal values, if any, in the embedding vectors; it…
Vector-space representations provide geometric tools for reasoning about the similarity of a set of objects and their relationships. Recent machine learning methods for deriving vector-space embeddings of words (e.g., word2vec) have…
A consistent and intuitive description of the twist-4 corrections to the hadron structure functions is presented in a QCD-improved parton model using time-ordered perturbative theory, where the collinear singularities are naturally…
A general calculational method is applied to investigate symmetry relations among divergent amplitudes in a free fermion model. A very traditional work on this subject is revisited. A systematic study of one, two and three point functions…
A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary…
In many causal inference problems, multiple action variables, such as factors, mediators, or network units, often share a common causal role yet lack a natural ordering. To avoid ambiguity, the scientific interpretation of a vector of…
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a…
We present an introductory investigation into continuous-space vector representations of sentences. We acquire pairs of very similar sentences differing only by a small alterations (such as change of a noun, adding an adjective, noun or…
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs,…
A suitable choice of the representation of candidate solutions is crucial for the efficiency of evolutionary algorithms and related metaheuristics. We focus on problems in permutation spaces, which are at the core of numerous practical…
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…
New approach to computing the amplitudes of multi-particle processes in renormalizable quantum field theories is presented. Its major feature is a separation of the renormalization from the computation. Within the suggested approach new…