The eta invariant of the Dirac operator over a noncompact cofinite quotient of PSL(2,R) is defined through a regularized trace following Melrose. It reduces to the standard definition in terms of eigenvalues in the case of a totally nontrivial spin structure. When the S1-fibers are rescaled, the metric becomes of nonexact fibred-cusp type near the ends. We completely describe the continuous spe...

We extend the notion of exact completion on a category with weak finite limits to Lawvere’s elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, t...

A duality transform for the coalgebra of the free difference quotient derivationmultiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic functions endowed with yet another generalization of the difference quotient derivation.

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main observation of this paper is that, over the field of complex numbers, the Chow quotient admits symplectic and other topological interpretations, namely, symplectically, the moduli spaces of stable orbits with prescribed momentum charges; and topologically, the moduli space of s...

In humans, oxytocin (OT) enhances prosocial behaviour. However, it is still unclear how the prosocial effects of OT are modulated by emotional features and/or individuals' characteristics. In a placebo-controlled design, we tested 20 healthy male volunteers to investigate these behavioural and neurophysiological modulations using magnetoencephalography. As an index of the individuals' character...

This thesis presents a method to semi-automate the reasoning about network bounds, namely the backlog and delay. Network Calculus offers a rich theory for modeling network elements. Using the modeling techniques of network calculus, network elements are represented by discrete-time systems whose dynamics are linear in min-plus algebra. From the state-space representation of a min-plus linear (M...

A lift of a given network is a network that admits the first network as quotient. Assuming that a bifurcation occurs for a coupled cell system consistent with the structure of a regular network (in which all cells have the same type and receive the same number of inputs and all arrows have the same type), it is well known that some lifts exhibit new bifurcating branches of solutions. In this wo...

This paper deals with structurally constrained periodic control design for interconnected systems. It is assumed that the system is linear time-invariant (LTI), observable and controllable, and that its modes are distinct and nonzero. It is shown that the notions of quotient fixed mode (QFM) and structured decentralized fixed mode (SDFM) are equivalent for this class of systems. Then, it is pro...