Related papers: Polyregular Functions
A parking function is a function $\pi:[n]\to [n]$ whose $i$th-smallest output is at most $i,$ corresponding to a parking procedure for $n$ cars on a one-way street. We refine this concept by introducing preference-restricted parking…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
We consider two non-linear generalizations of fractal interpolating functions generated from iterated function systems. The first corresponds to fitting data using a Kth-order polynomial, while the second relates to the freedom of adding…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain…
We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}^n. This result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
Prox-regularity is a generalization of convexity that includes all C2, lower-C2, strongly amenable and primal-lower-nice functions. The study of prox-regular functions provides insight on a broad spectrum of important functions.…
Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output…
For conformal maps defined in the unit disk one can define a certain Poisson bracket that involves the harmonic moments of the image domain. When this bracket is applied to the conformal map itself together with its conformally reflected…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this article regular noncommutative rational functions $r$ are characterized via the…
We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions,…
The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials