Related papers: Not All Multi-Valued Partial CFL Functions Are Ref…
Nonuniform families of polynomial-size finite automata and pushdown automata respectively have strong connections to nonuniform-NL and nonuniform-LOGCFL. We examine the behaviors of unambiguous and co-nondeterministic computations produced…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions $\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask…
We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in…
The existence of one-way functions is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf,…
Control Barrier Functions (CBFs) are a powerful tool for ensuring robotic safety, but designing or learning valid CBFs for complex systems is a significant challenge. While Hamilton-Jacobi Reachability provides a formal method for…
We consider the task of computing functions $f: \mathbb{N}^k\to \mathbb{N}$, where $ \mathbb{N}$ is the set of natural numbers, by finite teams of agents modelled as deterministic finite automata. The computation is carried out in a…
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…
Complex-valued neural networks (CVNNs) are a powerful modeling tool for domains where data can be naturally interpreted in terms of complex numbers. However, several analytical properties of the complex domain (e.g., holomorphicity) make…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common…
Control Barrier Functions (CBFs) offer a framework for ensuring set invariance and designing constrained control laws. However, crafting a valid CBF relies on system-specific assumptions and the availability of an accurate system model,…
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…
The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms…
In this paper, we propose a novel semi-supervised feature selection framework by mining correlations among multiple tasks and apply it to different multimedia applications. Instead of independently computing the importance of features for…
Real-world data consistently exhibits a long-tailed distribution, often spanning multiple categories. This complexity underscores the challenge of content comprehension, particularly in scenarios requiring Long-Tailed Multi-Label image…
We prove that every partial function with finite domain and range can be effectively simulated through sequential colorings of graphs. Namely, we show that given a finite set $S=\{0,1,\ldots,m-1\}$ and a number $n \geq \max\{m,3\}$, any…