Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Neural manifold analysis of brain circuit dynamics in health and disease

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as “neural manifolds”, and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioral performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, including principal component analysis (PCA), multi-dimensional scaling (MDS), Isomap, locally linear embedding (LLE), Laplacian eigenmaps (LEM), t-SNE, and uniform manifold approximation and projection (UMAP). We outline these methods under a common mathematical nomenclature, and compare their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behavior task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular cases where the behavioral complexity is greater, non-linear methods tend to find lower-dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimer’s Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology

Multiphoton minimal inertia scanning for fast acquisition of neural activity signals

Objective: Multi-photon laser scanning microscopy provides a powerful tool for monitoring the spatiotemporal dynamics of neural circuit activity. It is, however, intrinsically a point scanning technique. Standard raster scanning enables imaging at subcellular resolution; however, acquisition rates are limited by the size of the field of view to be scanned. Recently developed scanning strategies such as Travelling Salesman Scanning (TSS) have been developed to maximize cellular sampling rate by scanning only select regions in the field of view corresponding to locations of interest such as somata. However, such strategies are not optimized for the mechanical properties of galvanometric scanners. We thus aimed to develop a new scanning algorithm which produces minimal inertia trajectories, and compare its performance with existing scanning algorithms. Approach: We describe here the Adaptive Spiral Scanning (SSA) algorithm, which fits a set of near-circular trajectories to the cellular distribution to avoid inertial drifts of galvanometer position. We compare its performance to raster scanning and TSS in terms of cellular sampling frequency and signal-to-noise ratio (SNR). Main Results: Using surrogate neuron spatial position data, we show that SSA acquisition rates are an order of magnitude higher than those for raster scanning and generally exceed those achieved by TSS for neural densities comparable with those found in the cortex. We show that this result also holds true for in vitro hippocampal mouse brain slices bath loaded with the synthetic calcium dye Cal-520 AM. The ability of TSS to "park" the laser on each neuron along the scanning trajectory, however, enables higher SNR than SSA when all targets are precisely scanned. Raster scanning has the highest SNR but at a substantial cost in number of cells scanned. To understand the impact of sampling rate and SNR on functional calcium imaging, we used the Crame ́r-Rao Bound on evoked calcium traces recorded simultaneously with electrophysiology traces to calculate the lower bound estimate of the spike timing occurrence. Significance: The results show that TSS and SSA achieve comparable accuracy in spike time estimates compared to raster scanning, despite lower SNR. SSA is an easily implementable way for standard multi-photon laser scanning systems to gain temporal precision in the detection of action potentials while scanning hundreds of active cells

Sampling constrained probability distributions using Spherical Augmentation

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this paper, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called {Spherical Augmentation}, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.Comment: 41 pages, 13 figure

Phosphatidylinositol 4-kinase IIβ negatively regulates invadopodia formation and suppresses an invasive cellular phenotype

The type II PI 4-kinases enzymes synthesise the lipid phosphatidylinositol 4-phosphate (PI(4)P) which has been detected at the Golgi complex and endosomal compartments, and which recruits clathrin adaptors. Despite common mechanistic similarities between the isoforms, the extent of their redundancy is unclear.We found that depletion of PI4KIIα and PI4KIIβ using siRNA led to actin remodelling. Depletion of PI4KIIβ also induced the formation of invadopodia containing membrane type I matrix metalloproteinase (MT1-MMP).Depletion of PI4KII isoforms also differentially affected TGN pools of PI(4)P and post-TGN traffic. PI4KIIβ depletion caused increased MT1-MMP trafficking to invasive structures at the plasma membrane and was accompanied by reduced colocalisation of MT1-MMP with membranes containing the endosomal markers Rab5 and Rab7, but increased localisation with the exocytic Rab8. Depletion of PI4KIIβ was sufficient to confer an aggressive invasive phenotype on minimally invasive HeLa and MCF-7 cell lines. Mining oncogenomic databases revealed that loss of the PI4K2B allele and underexpression of PI4KIIβ mRNA is associated with human cancers. This finding supports the cell data and suggests that PI4KIIβ may be a clinically significant suppressor of invasion. We propose that PI4KIIβ synthesises a pool of PI(4)P that maintains MT1-MMP traffic in the degradative pathway and suppresses the formation of invadopodia

Comparison of Bond Character in Hydrocarbons and Fullerenes

We present a comparison of the bond polarizabilities for carbon-carbon bonds in hydrocarbons and fullerenes, using two different models for the fullerene Raman spectrum and the results of Raman measurements on ethane and ethylene. We find that the polarizabilities for single bonds in fullerenes and hydrocarbons compare well, while the double bonds in fullerenes have greater polarizability than in ethylene.Comment: 7 pages, no figures, uses RevTeX. (To appear in Phys. Rev. B.

Using games for teaching crisis communication in higher education and training

© 2016 IEEE. Terror actions and catastrophes are frequently described in media. As more and more countries experience terror actions and natural disasters, there has been a greater focus on learning how to handle and to manage them. In Norway on the 22nd of July 2011, Anders Behring Breivik placed a bomb in a car that exploded near the Governmental Offices killing 8 persons. He went on to an island where there was a political camp for youths killing another 67. The rescue operations unveiled an unprepared task force. The Gjrv-report provide a massive critique towards the call out services [1]. This kicked off a major work on updating safety routines in all municipalities. The municipalities are now obliged to have a plan for crisis preparedness [2]. This again triggered the need for education within the area of crisis preparedness, crisis training and crisis management. Hedmark University of Applied Science now offers different study programs, including a BA within these areas. It is, however, very expensive to train realistically and the need for different approaches regarding training has been discussed. One of the solutions that the University is currently working on, is the use of games. Game based learning, also called 'serious games', has become an academic genre and using games for learning and training has proven fruitful [3-12]. In the military, games have been used for simulation purposes [13] and spin offs from these have also reached a commercial market [14, 15]. Using games in education opens up a range of opportunities. One of them is within the area of Crisis Communication. Crisis Communication as a curriculum is about how to approach the area of crisis communication, understanding the key concepts and develop skills within the curriculum. Games that support communication between the gamers can for instance contribute towards a greater understanding of communication in a crisis situation. What is needed to communicate and how messages are received, in order to support handling a crisis, are amongst the concrete learning objectives one can attribute towards this type of training. To use games to support the hands on training can thus provide the learners with valuable know how, and support their learning outcome. The learning from this will be beneficial to the organizations they work in as they will have an experience that will aid them in the work on planning for and preparing for crisis in their own organizations

Dynamical chaos and power spectra in toy models of heteropolymers and proteins

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically non-chaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.Comment: 8 pages, 9 EPS figures, Phys. Rev. E (in press

Cardiac Biomarkers and Risk of Atrial Fibrillation in Chronic Kidney Disease: The CRIC Study.

Background We tested associations of cardiac biomarkers of myocardial stretch, injury, inflammation, and fibrosis with the risk of incident atrial fibrillation (AF) in a prospective study of chronic kidney disease patients. Methods and Results The study sample was 3053 participants with chronic kidney disease in the multicenter CRIC (Chronic Renal Insufficiency Cohort) study who were not identified as having AF at baseline. Cardiac biomarkers, measured at baseline, were NT-proBNP (N-terminal pro-B-type natriuretic peptide), high-sensitivity troponin T, galectin-3, growth differentiation factor-15, and soluble ST-2. Incident AF ("AF event") was defined as a hospitalization for AF. During a median follow-up of 8 years, 279 (9%) participants developed a new AF event. In adjusted models, higher baseline log-transformed NT-proBNP (N-terminal pro-B-type natriuretic peptide) was associated with incident AF (adjusted hazard ratio [HR] per SD higher concentration: 2.11; 95% CI, 1.75, 2.55), as was log-high-sensitivity troponin T (HR 1.42; 95% CI, 1.20, 1.68). These associations showed a dose-response relationship in categorical analyses. Although log-soluble ST-2 was associated with AF risk in continuous models (HR per SD higher concentration 1.35; 95% CI, 1.16, 1.58), this association was not consistent in categorical analyses. Log-galectin-3 (HR 1.05; 95% CI, 0.91, 1.22) and log-growth differentiation factor-15 (HR 1.16; 95% CI, 0.96, 1.40) were not significantly associated with incident AF. Conclusions We found strong associations between higher NT-proBNP (N-terminal pro-B-type natriuretic peptide) and high-sensitivity troponin T concentrations, and the risk of incident AF in a large cohort of participants with chronic kidney disease. Increased atrial myocardial stretch and myocardial cell injury may be implicated in the high burden of AF in patients with chronic kidney disease