Related papers: Some results on $\mathbb{R}$-computable structures
Many real-world systems can be usefully represented as sets of interacting components. Examples include computational systems, such as query processors and compilers, natural systems, such as cells and ecosystems, and social systems, such…
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
We study the existence of uncountable first-order structures that are homogeneous with respect to their finitely generated substructures. In many classical cases this is either well-known or follows from general facts, for example, if the…
We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…
We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown…
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…
The best empirical research in political science clearly defines substantive parameters of interest, presents a set of assumptions that guarantee its identification, and uses an appropriate estimator. We argue for the importance of…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Part 2 of 3 from master's thesis: Modeling Compact Objects with Effective Field Theory. Using the Effective Field Theory framework for extended objects, we build the effective theory of a binary system made up of the most general compact…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…