arXiv research

The study shows conditions for thermostats to have no conjugate points.

The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.

In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.

Smooth orbit equivalence proves metric equivalence for geodesic flows.

We show a Hopf type rigidity for thermostats without conjugate points on a 2-torus

Guillarmou extends X-ray transform to magnetic and thermostat flows.

In this paper, we will recover Hamilton's Harnack inequality for the Ricci flow from the view point of Hyperbolic thermostat.

Researchers study injectivity of magnetic and thermostatic nonabelian ray transforms on compact surfaces.

Improved stability for large-scale Bayesian sampling.

Alternative construction of quasi-Fuchsian flows using vortex equations.

RL applied to TCLs for power consumption control.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) a…

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian $2$-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow induced by the Hilbert metric on the quotient surface of divisible convex sets. We …

We propose a new sampling method, the thermostat-assisted continuously-tempered Hamiltonian Monte Carlo, for Bayesian learning on large datasets and multimodal distributions. It simulates the Nosé-Hoover dynamics of a continuously-tempered Hamiltonian system built on the distribution of interest. A significant advantag…

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distrib…

We consider a general family of curves $Γ$ on a compact oriented Finsler surface $(M,F)$ with boundary $\partial M$. Let $\varphi\in C^{\infty}(M)$ and $ω$ a smooth 1-form on $M$. We show that $\int_{γ(t)}\{\varphi(γ(t))+ω_{γ(t)}(\dotγ(t))\}\,dt=0$ holds for every $γ\inΓ$ whose endpoints belong to $\partial M$, $γ(a)…

Recent studies have shown that the aggregated dynamic flexibility of an ensemble of thermostatic loads can be modeled in the form of a virtual battery. The existing methods for computing the virtual battery parameters require the knowledge of the first-principle models and parameter values of the loads in the ensemble.…

We use online convex optimization (OCO) for setpoint tracking with uncertain, flexible loads. We consider full feedback from the loads, bandit feedback, and two intermediate types of feedback: partial bandit where a subset of the loads are individually observed and the rest are observed in aggregate, and Bernoulli feed…

Study proves uniqueness for ray transform on surfaces with obstacles.

Study resonant forms for dissipative Anosov flows on 3-manifolds.

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian modeling and predictive strengths of max-margin learning. However, Monte Carlo sampli…

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the …

A new hierarchy quantifies agency in systems based on information processing.

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…

Proposes a method to handle missing inputs in Bayesian optimization.