Related papers: Syntactic Structure, Quantum Weights
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
Classical and quantum mechanical descriptions of motion are fundamentally different. The universality of free fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum…
This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
We develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise…
Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an…
We study function fields of curves over a base field $K$ which is either a global field or a large field having a separable field extension of degree divisible by $4$. We show that, for any such function field, Hilbert's 10th Problem has a…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
Spin foam models, an approach to defining the dynamics of loop quantum gravity, make use of the Plebanski formulation of gravity, in which gravity is recovered from a topological field theory via certain constraints called simplicity…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…