We study a modification of the Hoppensteadt-Izhikevich canonical model for networks of class I neurons, in which the ‘pulse’ emitted by a neuron is smooth rather than a δ-function. We prove two types of results about synchronization and desynchronization of such networks, the first type pertaining to ‘pulse’ functions which are symmetric, and the other type in the regime in which each neuron is...

We develop a supersymmetric representation of the Hubbard operators which unifies the Slave Boson and Slave Fermion representations, allowing a second-quantized treatment of Hubbard operators with both symmetric and anti-symmetric character. We provide a simple example of the application of this method to the atomic limit of the Hubbard model and discuss its more general application to the infi...

These notes discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special emphasis on examples and explicit calculations. The notes are based on series of lectures given in Daejeon (March 2013), Rome (November-December 2015) and Guanajuat...

We present a complete pretopology semantics for a system of Intuitionistic Linear Logic (commutative or not) where the storage operator is split into a contraction and a weakening component and then recovered again from them. The semantics for weakening and contraction has been explored by Bart Jacobs 13] in a categorical setting. However, a completeness theorem is not given in 13] and the appr...

Add a stage of signal acquisition to a canonical model of portfolio choice. Under fully revealing asset price, investors’ information demand reflects their choice of transparency. In reducing uncertainty, financial transparency raises expected asset price and thus benefits holders of the risky asset. At a natural transparency limit, however, investors pay to inhibit further disclosure in order ...

We prove the Prym–Green conjecture on minimal free resolutions of paracanonical curves of odd genus. The proof proceeds via curves lying on ruled surfaces over an elliptic curve.

We present ongoing work into the systematic study of the use of dual adjunctions in coalgebraic modal logic. We introduce a category of internal models for a modal logic. These are constructed from syntax, and yield a generalised notion of canonical model. Further, expressivity of a modal logic is shown to be characterised by factorisation of its models via internal models and the existence of ...

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper we provide a rigorous toolkit for extending convex risk measures from L∞ to L, for p ≥ 1. Our main result is a one-to-one correspondence between law-invariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L. Some significant counterexamples illustrate the many pitfalls with convex ris...