Thermal feedback in Si JFETs operating at low temperatures

Thermal feedback theory for silicon junction FET operating at low temperature

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio

Steinberg modules and Donkin pairs

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.Comment: 16 pages; proof of Brundan's conjecture adde

Energy-conserving physics for nonhydrostatic dynamics in mass coordinate models

Motivated by reducing errors in the energy budget related to enthalpy fluxes within the Energy Exascale Earth System Model (E3SM), we study several physics–dynamics coupling approaches. Using idealized physics, a moist rising bubble test case, and the E3SM's nonhydrostatic dynamical core, we consider unapproximated and approximated thermodynamics applied at constant pressure or constant volume. With the standard dynamics and physics time-split implementation, we describe how the constant-pressure and constant-volume approaches use different mechanisms to transform physics tendencies into dynamical motion and show that only the constant-volume approach is consistent with the underlying equations. Using time step convergence studies, we show that the two approaches both converge but to slightly different solutions. We reproduce the large inconsistencies between the energy flux internal to the model and the energy flux of precipitation when using approximate thermodynamics, which can only be removed by considering variable latent heats, both when computing the latent heating from phase change and when applying this heating to update the temperature. Finally, we show that in the nonhydrostatic case, for physics applied at constant pressure, the general relation that enthalpy is locally conserved no longer holds. In this case, the conserved quantity is enthalpy plus an additional term proportional to the difference between hydrostatic pressure and full pressure.</p

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Three disks in a row: A two-dimensional scattering analog of the double-well problem

We investigate the scattering off three nonoverlapping disks equidistantly spaced along a line in the two-dimensional plane with the radii of the outer disks equal and the radius of the inner disk varied. This system is a two-dimensional scattering analog to the double-well-potential (bound state) problem in one dimension. In both systems the symmetry splittings between symmetric and antisymmetric states or resonances, respectively, have to be traced back to tunneling effects, as semiclassically the geometrical periodic orbits have no contact with the vertical symmetry axis. We construct the leading semiclassical ``creeping'' orbits that are responsible for the symmetry splitting of the resonances in this system. The collinear three-disk-system is not only one of the simplest but also one of the most effective systems for detecting creeping phenomena. While in symmetrically placed n-disk systems creeping corrections affect the subleading resonances, they here alone determine the symmetry splitting of the 3-disk resonances in the semiclassical calculation. It should therefore be considered as a paradigm for the study of creeping effects. PACS numbers: 03.65.Sq, 03.20.+i, 05.45.+bComment: replaced with published version (minor misprints corrected and references updated); 23 pages, LaTeX plus 8 Postscript figures, uses epsfig.sty, espf.sty, and epsf.te

January 31, 2019

The Breeze is the student newspaper of James Madison University in Harrisonburg, Virginia

Microscopic Origin of Quantum Chaos in Rotational Damping

The rotational spectrum of $^{168}$Yb is calculated diagonalizing different effective interactions within the basis of unperturbed rotational bands provided by the cranked shell model. A transition between order and chaos taking place in the energy region between 1 and 2 MeV above the yrast line is observed, associated with the onset of rotational damping. It can be related to the higher multipole components of the force acting among the unperturbed rotational bands.Comment: 7 pages, plain TEX, YITP/K-99

Complex Periodic Orbits and Tunnelling in Chaotic Potentials

We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is applicable whenever the tunnelling is dominated by isolated orbits, a situation which applies to chaotic systems but also to certain near-integrable ones. It is used to analyse a specific two-dimensional potential with chaotic dynamics. Mean behaviour of the splittings is predicted by an orbit with imaginary action. Oscillations around this mean are obtained from a collection of related orbits whose actions have nonzero real part

Bayesian Network Enhanced with Structural Reliability Methods: Methodology

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems