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Structured representations such as keypoints are widely used in pose transfer, conditional image generation, animation, and 3D reconstruction. However, their supervised learning requires expensive annotation for each target domain. We…
Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…
This thesis advances semantic representation learning to render language representations or models more semantically and geometrically interpretable, and to enable localised, quasi-symbolic, compositional control through deliberate shaping…
To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs…
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
The goal of this paper is to learn dense 3D shape correspondence for topology-varying objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
Automorphisms of structural matrix algebras in block upper triangular form has been studied recently in \cite{Akkurt E-M Barker 2}, and this work is a follow-up paper of that study. The aim of this paper is to explain the topic in a much…
Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…
Lie groups over local fields furnish prime examples of totally disconnected, locally compact groups. We discuss the scale, tidy subgroups and further subgroups (like contraction subgroups) for analytic endomorphisms of such groups. The text…
We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of…
One significant simplification in most previous work on robot learning is the closed-world assumption where the robot is assumed to know ahead of time a complete set of predicates describing the state of the physical world. However, robots…
With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data.…
A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for…
This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066