Period Integrals of CY and General Type Complete Intersections

We develop a global Poincar\'e residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. Two important ingredients of our construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize our construction to CY and general type complete intersections. When $X$ is an algebraic manifold having a sufficiently large automorphism group $G$ and $V^*$ is a linear representation of $G$, we construct a holonomic D-module that governs the period integrals. The construction is based in part on the theory of tautological systems we have developed in the paper \cite{LSY1}, joint with R. Song. The approach allows us to explicitly describe a Picard-Fuchs type system for complete intersection varieties of general types, as well as CY, in any Fano variety, and in a homogeneous space in particular. In addition, the approach provides a new perspective of old examples such as CY complete intersections in a toric variety or partial flag variety.Comment: An erratum is included to correct Theorem 3.12 (Uniqueness of CY structure

An Interacting Multiple Model Approach for Target Intent Estimation at Urban Intersection for Application to Automated Driving Vehicle

Research shows that urban intersections are a hotspot for traffic accidents which cause major human injuries. Predicting turning, passing, and stop maneuvers against surrounding vehicles is considered to be fundamental for advanced driver assistance systems (ADAS), or automated driving systems in urban intersections. In order to estimate the target intent in such situations, an interacting multiple model (IMM)-based intersection-target-intent estimation algorithm is proposed. A driver model is developed to represent the driver’s maneuvering on the intersection using an IMM-based target intent classification algorithm. The performance of the intersection-target-intent estimation algorithm is examined through simulation studies. It is demonstrated that the intention of a target vehicle is successfully predicted based on observations at an individual intersection by proposed algorithms. Document type: Articl

The lattice of balanced equivalence relations of a coupled cell network

A coupled cell system is a collection of dynamical systems, or ‘cells’, that are coupled together. The associated coupled cell network is a labelled directed graph that indicates how the cells are coupled, and which cells are equivalent. Golubitsky, Stewart, Pivato and Török have presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of the concept of a ‘balanced equivalence relation’, which depends solely on the network architecture. In their approach the network is assumed to be finite. We prove that the set of all balanced equivalence relations on a network forms a lattice, in the sense of a partially ordered set in which any two elements have a meet and a join. The partial order is defined by refinement. Some aspects of the theory make use of infinite networks, so we work in the category of networks of ‘finite type’, a class that includes all locally finite networks. This context requires some modifications to the standard framework. As partial compensation, the lattice of balanced equivalence relations can then be proved complete. However, the intersection of two balanced equivalence relations need not be balanced, as we show by a simple example, so this lattice is not a sublattice of the lattice of all equivalence relations with its usual operations of meet and join. We discuss the structure of this lattice and computational issues associated with it. In particular, we describe how to determine whether the lattice contains more than the equality relation. As an example, we derive the form of the lattice for a linear chain of identical cells with feedback