Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure

A sticky HDP-HMM with application to speaker diarization

We consider the problem of speaker diarization, the problem of segmenting an audio recording of a meeting into temporal segments corresponding to individual speakers. The problem is rendered particularly difficult by the fact that we are not allowed to assume knowledge of the number of people participating in the meeting. To address this problem, we take a Bayesian nonparametric approach to speaker diarization that builds on the hierarchical Dirichlet process hidden Markov model (HDP-HMM) of Teh et al. [J. Amer. Statist. Assoc. 101 (2006) 1566--1581]. Although the basic HDP-HMM tends to over-segment the audio data---creating redundant states and rapidly switching among them---we describe an augmented HDP-HMM that provides effective control over the switching rate. We also show that this augmentation makes it possible to treat emission distributions nonparametrically. To scale the resulting architecture to realistic diarization problems, we develop a sampling algorithm that employs a truncated approximation of the Dirichlet process to jointly resample the full state sequence, greatly improving mixing rates. Working with a benchmark NIST data set, we show that our Bayesian nonparametric architecture yields state-of-the-art speaker diarization results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS395 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Infant cortex responds to other humans from shortly after birth

A significant feature of the adult human brain is its ability to selectively process information about conspecifics. Much debate has centred on whether this specialization is primarily a result of phylogenetic adaptation, or whether the brain acquires expertise in processing social stimuli as a result of its being born into an intensely social environment. Here we study the haemodynamic response in cortical areas of newborns (1–5 days old) while they passively viewed dynamic human or mechanical action videos. We observed activation selective to a dynamic face stimulus over bilateral posterior temporal cortex, but no activation in response to a moving human arm. This selective activation to the social stimulus correlated with age in hours over the first few days post partum. Thus, even very limited experience of face-to-face interaction with other humans may be sufficient to elicit social stimulus activation of relevant cortical regions

Control over Multi-Scale Self-Organization-Based Processes under the Extreme Tribological Conditions of Cutting through the Application of Complex Adaptive Surface-Engineered Systems

This paper features a comprehensive analysis of various multiscale selforganization processes that occur during cutting. A thorough study of entropy production during friction has uncovered several channels of its reduction that can be achieved by various selforganization processes. These processes are (1) self-organization during physical vapor deposition PVD coating deposition on the cutting tool substrates; (2) tribofilm formation caused by interactions with the environment during operation, which consist of the following compounds: thermal barriers; Magnéli phase tribo-oxides with metallic properties at elevated temperatures, tribo-oxides that transform into a liquid phase at operating temperatures, and mixed action tribo-oxides that serve as thermal barriers/lubricants, and (3) multiscale selforganization processes that occur on the surface of the tool during cutting, which include chip formation, the generation of adhesive layers, and the buildup edge formation. In-depth knowledge of these processes can be used to significantly increase the wear resistance of the coated cutting tools. This can be achieved by the application of the latest generation of complex adaptive surface-engineered systems represented by several state-of-the-art adaptive nano-multilayer PVD coatings, as well as high entropy alloy coatings (HEAC)

Low temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, though consistent with universality.Comment: 14 pages, LaTeX with IOP style files (ioplppt.sty), epic.sty and eepic.sty. To appear in J. Phys.

Late-Time Circumstellar Interaction in a Spitzer Selected Sample of Type IIn Supernovae

Type IIn supernovae (SNe IIn) are a rare (< 10%) subclass of core-collapse SNe that exhibit relatively narrow emission lines from a dense, pre-existing circumstellar medium (CSM). In 2009, a warm Spitzer survey observed 30 SNe IIn discovered in 2003 - 2008 and detected 10 SNe at distances out to 175 Mpc with unreported late-time infrared emission, in some cases more than 5 years post-discovery. For this single epoch of data, the warm-dust parameters suggest the presence of a radiative heating source consisting of optical/X-ray emission continuously generated by ongoing CSM interaction. Here we present multi-wavelength follow-up observations of this sample of 10 SNe IIn and the well-studied Type IIn SN 2010jl. A recent epoch of Spitzer observations reveals ongoing mid-infrared emission from nine of the SNe in this sample. We also detect three of the SNe in archival WISE data, in addition to SNe 1987A, 2004dj, and 2008iy. For at least five of the SNe in the sample, optical and/or X-ray emission confirms the presence of radiative emission from ongoing CSM interaction. The two Spitzer nondetections are consistent with the forward shock overrunning and destroying the dust shell, a result that places upper limits on the dust-shell size. The optical and infrared observations confirm the radiative heating model and constrain a number of model parameters, including progenitor mass-loss characteristics. All of the SNe in this sample experienced an outburst on the order of tens to hundreds of years prior to the SN explosion followed by periods of less intense mass loss. Although all evidence points to massive progenitors, the variation in the data highlights the diversity in SN IIn progenitor evolution. While these observations do not identify a particular progenitor system, they demonstrate that future, coordinated, multi-wavelength campaigns can constrain theoretical mass-loss models.Comment: 10 pages, 6 figures, accepted to AJ (with comments

Interface-Induced Plasmon Nonhomogeneity in Nanostructured Metal-Dielectric Planar Metamaterial

Transformations of the electronic structure in thin silver layers in metal-dielectric (TiAlN/Ag) multilayer nanocomposite were investigated by a set of electron spectroscopy techniques. Localization of the electronic states in the valence band and reduction of electron concentration in the conduction band was observed. This led to decreasing metallic properties of silver in the thin films. A critical layer thickness of 23.5 nm associated with the development of quantum effects was determined by X-ray photoelectron spectroscopy. Scanning Auger electron microscopy of characteristic energy losses provided images of plasmon localization in the Ag layers. The nonuniformity of plasmon intensities distribution near the metal-nitride interfaces was assessed experimentally

The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index 1<α≤2\bf 1<\alpha \leq 2

We study fundamental properties of the fractional, one-dimensional Weyl operator $\hat{\mathcal{P}}^{\alpha}$ densely defined on the Hilbert space $\mathcal{H}=L^2({\mathbb R},dx)$ and determine the asymptotic behaviour of both the free Green's function and its variation with respect to energy for bound states. In the sequel we specify the Birman-Schwinger representation for the Schr\"{o}dinger operator $K_{\alpha}\hat{\mathcal{P}}^{\alpha}-g|\hat{V}|$ and extract the finite-rank portion which is essential for the asymptotic expansion of the ground state. Finally, we determine necessary and sufficient conditions for there to be a bound state for small coupling constant $g$.Comment: 16 pages, 1 figur

Functional Approach to Stochastic Inflation

We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.Comment: 20 pages, Preprint BROWN-HET-960, uses phyzz