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Conformal symplectic and relativistic optimization
TLDR
This work proposes a new algorithm based on a dissipative relativistic system that normalizes the momentum and may result in more stable/faster optimization, and generalizes both Nesterov and heavy ball.
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Nonextensivity in geological faults
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On the zeros of L-functions
We generalize our recent construction of the zeros of the Riemann $\zeta$-function to two infinite classes of $L$-functions, Dirichlet $L$-functions and those based on level one modular forms. More…
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On dissipative symplectic integration with applications to gradient-based optimization
TLDR
A generalization of symplectic integrators to non-conservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error, enabling the derivation of ‘rate-matching’ algorithms without the need for a discrete convergence analysis.
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A Dynamical Systems Perspective on Nonsmooth Constrained Optimization
TLDR
This work introduces two new ADMM variants, one based on Nesterov's acceleration and the other inspired by Polyak's heavy ball method, and derives differential inclusions modelling these algorithms in the continuous-time limit.
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How is Distributed ADMM Affected by Network Topology
TLDR
A full characterization of the convergence of distributed over-relaxed ADMM for the same type of consensus problem in terms of the topology of the underlying graph is provided and a proof of the aforementioned conjecture is shown it is valid for any graph, even the ones whose random walks cannot be accelerated via Markov chain lifting.
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Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular $L$-functions
We consider the non-trivial zeros of the Riemann $\zeta$-function and two classes of $L$-functions; Dirichlet $L$-functions and those based on level one modular forms. We show that there are an…
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Statistical and other properties of Riemann zeros based on an explicit equation for the $n$-th zero on the critical line
We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers $n=1,2,\dotsc$, whose ordinates can be obtained as the solution of a new…
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Some Riemann Hypotheses from random walks over primes
The aim of this paper is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of [Formula: see text]-functions,…
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Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive…
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