The intersection type assignment system IT uses the formulas of the negative fragment of the predicate calculus (LJ) as types for the λ-terms. However, the deductions of IT only correspond to the proper sub-set of the derivations of LJ, obtained by imposing a metatheoretic condition about the use of the conjunction of LJ. This paper proposes a logical foundation for IT. This is done by introduc...

I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincaré dual of a submanifold 4 3. Smooth cycles and their intersections 8 4. Applications 14 5. The Euler class of an oriented rank two real vector bundle 18 References 20 1. TRANSVERSALITY AND TUBULAR NEIGHBORHOODS We need to introduce a bit of microlocal termino...

In this paper, a novel approach, called the Discrete-Time Occupancies Trajectory (DTOT), is proposed for intersection management of autonomous traffic in which all vehicles in the system are Autonomous Vehicles (AVs) and capable of wireless Vehicle-to-Intersection (V2I) communication. The main advantage of the proposed DTOT-based intersection management is that it enables us to utilize the spac...

This paper explores how autonomous driving agents drive through intersections in virtual urban environments. The knowledge about where a vehicle runs on an intersection is embedded in environment database. Control of how and when a vehicle runs through an intersection is provided by vehicle behaviors. Vehicle control for traversing an intersection is divided into cruising behavior, following be...

We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on ...

Let Bi be an (Ni, d)-fractional Brownian motion with Hurst index αi (i = 1,2), and let B1 and B2 be independent. We prove that, if N1 α1 + N2 α2 > d , then the intersection local times of B1 and B2 exist, and have a continuous version. We also establish Hölder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and int...

Several region connection calculi have been proposed for use in Qualitative Spatial Reasoning (QSR). Perhaps the most well-known model is RCC-8, which uses a 9-Intersection framework to identify the spatial relation between two regions. The calculation of the 9-Intersection matrix is particularly computationintensive in 3D. Herein we show that 9-Intersection calculations can be replaced with 2-...

In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We inves...

In this dissertation, we address a problem of safe and efficient intersection crossing traffic management of autonomous and connected ground traffic. Toward this objective, an algorithm that is called the Discrete-time occupancies trajectory based Intersection traffic Coordination Algorithm (DICA) is proposed. All vehicles in the system are Connected and Autonomous Vehicles (CAVs) and capable o...

INTRODUCTION For the assessment on medical response capacity for disaster in local area (such as rescue capacity, transport capacity and treatment capacity), it is necessary to assess it in peace time, and understand how many sufferers from disaster the hospital can respond to. Here the estimated formula of Hospital Treatment Capacity (hereinafter shortened to HTC), the maximum receivable numbe...