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Language models lack the notion of interchangeable tokens: symbols that are semantically equivalent yet distinct, such as bound variables in formal logic. This limitation prevents generalization to larger vocabularies and hinders the…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only…
Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best.…
An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over…
Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…
We provide a new algorithm for evaluating the gamma function at any (rational) point and a new infinite product representation free from the presence of Euler and Mascheroni constant.Formulae and inequalities seemingly new are obtained as…
The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…
Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
Typical iterated filters, such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF), and iterated posterior linearization filter (IPLF), have been developed to improve the linearization point (or density)…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…
Several effective preprocessing techniques for Boolean formulas with and without quantifiers use unit propagation to simplify the formula. Among these techniques are vivification, unit propagation look-ahead (UPLA), and the identification…
The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Pl\"ucker relations for the quantum linear transformations, and then use them to…
The class of Unambiguous Star-Free Regular Languages (UL) was defined by Schutzenberger as the class of languages defined by Unambiguous Polynomials. UL has been variously characterized (over finite words) by logics such as TL[X_a,Y_a],…