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Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
Partial derivatives of regular expressions, introduced by Antimirov, define an elegant algorithm for generating equivalent non-deterministic finite automata (NFA) with a limited number of states. Here we focus on runtime verification (RV)…
This work introduces TTS-Transducer - a novel architecture for text-to-speech, leveraging the strengths of audio codec models and neural transducers. Transducers, renowned for their superior quality and robustness in speech recognition, are…
Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…
Auto-regressive neural sequence models have been shown to be effective across text generation tasks. However, their left-to-right decoding order prevents generation from being parallelized. Insertion Transformer (Stern et al., 2019) is an…
In this paper we design a switching control law for the \'Cuk converter in the continuous conduction mode using piecewise linear Lyapunov functions. These Lyapunov functions can be constructed using different number of state variables…
The number of $n$-gaussoids is shown to be a double exponential function in $n$. The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$-minors and encoding the resulting combinatorial…
One of the important applications of Golay complementary sets (GCSs) is the reduction of peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM) systems. OFDM has played a major role in modern wireless…
Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those…
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…
Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper…
Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…
This article focuses on subset reachability in synchronizing automata. First, we provide families of synchronizing automata with subsets which cannot be reached with short words. These families do not fulfil Don's Conjecture about subset…
Gottschalk's surjunctivity conjecture states that for all group universes and finite alphabets, every equivariant and continuous selfmap of the full shift, known as cellular automaton, cannot be a strict embedding. Not all surjective…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal…
We propose a Recursive Polynomial Generic Construction (RPGC) of multiplication algorithms in any finite field $\mathbb{F}_{q^n}$ based on the method of D.V. and G.V. Chudnovsky specialized on the projective line. They are usual polynomial…