Related papers: Dependence and Isolated Extensions
We point out that a field \phi charged under a global U(1) symmetry generally allows for a starred localized extension with the transformation rule, \phi\to U_L\star\phi\star U_R^{-1}. This results in a double gauging of the global U(1)…
We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We study when a map between two subsets of a Boolean domain W can be extended to an automorphism of W. Under many hypotheses, if the underlying Boolean algebra is complete or if the sets are finite or Boolean domains, the necessary and…
Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…
We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and $\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and secondary…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
In dependent type theory, being able to refer to a type universe as a term itself increases its expressive power, but requires mechanisms in place to prevent Girard's paradox from introducing logical inconsistency in the presence of…
We call an abelian variety over a finite field $\mathbb{F}_q$ super-isolated if its ($\mathbb{F}_q$-rational) isogeny class contains a single isomorphism class. In this paper, we use the Honda-Tate theorem to characterize super-isolated…
In this short note, using results of Bourgain, Fremlin, and Talagrand \cite{BFT}, we show that for a countable structure $M$, a saturated elementary extension $M^*$ of $M$ and a formula $\phi(x,y)$ the following are equivalent: (i)…
Let $\xi$ be an algebraic number and let $\alpha,\beta\in \mathbb Q[\xi]$. An explicit formula for the coordinates of the product $\alpha\beta$ is given in terms of the coordinates of $\alpha$ and $\beta$ and the companion matrix of the…
Refining a constructive combinatorial method due to MacLane and Schilling, we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree. If the value group of the…
Within dependently typed languages, such as Idris, types can depend on values. This dependency, however, can limit the collection of items in standard containers: all elements must have the same type, and as such their types must contain…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the…