相关论文: Proof of validity of first-order travel estimates

Extensive empirical studies show that the long distribution tail of travel time and the corresponding unexpected delay can have much more serious consequences than expected or moderate delay. However, the unexpected delay due to the…

We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

We show that H\"older continuity of the gradient is not only a sufficient condition, but also a necessary condition for the existence of a global upper bound on the error of the first-order Taylor approximation. We also relate this global…

In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. H\'ajek generalized this result to the first-order versions of \L ukasiewicz, G\"odel and…

This short note provides an explicit description of the Fr\'echet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fr\'echet derivatives of…

This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\'eka, Madar\'asz and N\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and…

The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is…

Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…

This paper is devoted to a new first order Taylor-like formula where the corresponding remainder is strongly reduced in comparison with the usual one which appears in the classical Taylor's formula. To derive this new formula, we introduce…

This paper is about the general disconnect that we see, both in practice and in literature, between the disciplines of travel demand modeling and causal inference. In this paper, we assert that travel demand modeling should be one of the…

In a recent paper, we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work, we kept only second order terms of the…

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

Getting insights on human mobility patterns and being able to reproduce them accurately is of the utmost importance in a wide range of applications from public health, to transport and urban planning. Still the relationship between the…

For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…

Uncertainty quantification in travel time estimation (TTE) aims to estimate the confidence interval for travel time, given the origin (O), destination (D), and departure time (T). Accurately quantifying this uncertainty requires generating…

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

We show that a complete first-order theory $T$ is distal provided it has a model $M$ such that the theory of the Shelah expansion of $M$ is distal.

We consider a first-order transport equation $\ppp_tu(x,t) + (H(x)\cdot\nabla u(x,t)) + p(x)u(x,t) = F(x,t)$ for $x \in \OOO \subset \R^d$, where $\OOO$ is a bounded domain and $0<t<T$. We prove a Carleman estimate for more generous…