Error bounds and normalising constants for sequential monte carlo samplers in high dimensions

In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. TheSMCsamplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using theSMCsampler and the exact asymptotic relative L2-error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd2). © Applied Probability Trust 2014

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This new working group (WG) was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted; alongside the changed nature of the classroom interactions between the humans (teachers and students) and the chosen technologies. Starting with the assumption that technology resources are being used, the WG explored the nature of these tools and their affordances for the mathematical teaching and learning. The work was framed by the following three pedagogic activities, which are proving to be particularly challenging: introducing and developing understanding of new mathematical topics; managing interaction and communication in mathematics; and assessing mathematics, both formatively and summatively. Three case studies of teachers’ practices were presented to initiate discussions with respect to these challenges and to highlight some existing theoretical and methodological frames

Pinning potential in highly performant CaKFe4As4 superconductor from DC magnetic relaxation and AC multi-frequency susceptibility studies

We have investigated the pinning potential of high-quality single crystals of superconducting material CaKFe4As4 having high critical current density and very high upper critical field using both magnetization relaxation measurements and frequency-dependent AC susceptibility. Preliminary studies of the superconducting transition and of the isothermal magnetization loops confirmed the high quality of the samples, while temperature dependence of the AC susceptibility in high magnetic fields show absolutely no dependence on the cooling conditions, hence, no magnetic history. From magnetization relaxation measurements were extracted the values of the normalized pinning potential U*, which reveals a clear crossover between elastic creep and plastic creep. The extremely high values of U*, up to 1200 K around the temperature of 20 K lead to a nearly zero value of the probability of thermally-activated flux jumps at temperatures of interest for high-field applications. The values of the creep exponents in the two creep regimes resulted from the analysis of the magnetization relaxation data are in complete agreement with theoretical models. Pinning potentials were also estimated, near the critical temperature, from AC susceptibility measurements, their values being close to those resulted (at the same temperature and DC field) from the magnetization relaxation data

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This working group (WG), which met for the second time in June 2021, was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted as a result of the COVID-19 pandemic. Following a brief introduction to the aims for the WG, we offer three further case studies of teachers’ practices and an emerging synthesis of the cases according to three pedagogic activities that are proving to be particularly challenging

A lagged particle filter for stable filtering of certain high-dimensional state-space models

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with the dimension of the hidden state. Inspired by lag-approximation methods for the smoothing problem, we introduce a lagged approximation of the smoothing distribution that is necessarily biased. For certain classes of SSMs, particularly those that forget the initial condition exponentially fast in time, the bias of our approximation is shown to be uniformly controlled in the dimension and exponentially small in time. We develop a sequential Monte Carlo (SMC) method to recursively estimate expectations with respect to our biased filtering distributions. Moreover, we prove for a class of class of SSMs that can contain dependencies amongst coordinates that as the dimension $d\rightarrow\infty$ the cost to achieve a stable mean square error in estimation, for classes of expectations, is of $\mathcal{O}(Nd^2)$ per-unit time, where $N$ is the number of simulated samples in the SMC algorithm. Our methodology is implemented on several challenging high-dimensional examples including the conservative shallow-water model

Electron-fluctuation interaction in a non-Fermi superconductor

We studied the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the 2D Anderson non-Fermi system. The classical fluctuations give a temperature dependence in the pseudogap induced in the fermionic excitations.Comment: revtex fil

Information geometric nonlinear filtering

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with the quadratic variation of the process of posterior distributions in this metric. Apart from providing a suitable setting in which to study such information-theoretic properties, the Hilbert manifold has an appropriate topology from the point of view of multi-objective filter approximations. A general class of finite-dimensional exponential filters is shown to fit within this framework, and an intrinsic evolution equation, involving Amari's -1-covariant derivative, is developed for such filters. Three example systems, one of infinite dimension, are developed in detail

Runx1+ vascular smooth muscle cells are essential for hematopoietic stem and progenitor cell development in vivo

Hematopoietic stem cells (HSCs) produce all essential cellular components of the blood. Stromal cell lines supporting HSCs follow a vascular smooth muscle cell (vSMC) differentiation pathway, suggesting that some hematopoiesis-supporting cells originate from vSMC precursors. These pericyte-like precursors were recently identified in the aorta-gonad-mesonephros (AGM) region; however, their role in the hematopoietic development in vivo remains unknown. Here, we identify a subpopulation of NG2 +Runx1 + perivascular cells that display a sclerotome-derived vSMC transcriptomic profile. We show that deleting Runx1 in NG2 + cells impairs the hematopoietic development in vivo and causes transcriptional changes in pericytes/vSMCs, endothelial cells and hematopoietic cells in the murine AGM. Importantly, this deletion leads also to a significant reduction of HSC reconstitution potential in the bone marrow in vivo. This defect is developmental, as NG2 +Runx1 + cells were not detected in the adult bone marrow, demonstrating the existence of a specialised pericyte population in the HSC-generating niche, unique to the embryo. </p