Related papers: Variants on the Berz sublinearity theorem

It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address…

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 give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

We study fragments of dependence logic defined either by restricting the number k of universal quantifiers or the width of dependence atoms in formulas. We find the sublogics of existential second-order logic corresponding to these…

We present a slightly different formulation of Zak's theorem on tangencies as well as some applications. In particular, we obtain a better bound on the dimension of the dual variety of a manifold and we classify extremal and…

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.

It is well-known that the central limit theorem holds for partial sums of a stationary sequence $(X_i)$ of $m$-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if…

We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several…

Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…

We develop an approach to choice principles and their contrapositive bar-induction principles as extensionality schemes connecting an ''intensional'' or ''effective'' view of respectively ill-and well-foundedness properties to an…

For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…

In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…

We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications…

We construct solution operators to the $\overline{\partial}$-equation that depend continuously on the domain. This is applied to derive a parameter version of Forstneri\v{c}'s splitting lemma: If both the maps and the domains they are…

The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with…

An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or "envariance" [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify…