A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube and the Crapo $\beta$-invariant of uniform matroids.Comment: 22 pages, 2 figures. Sections 6 and 7 of previous version simplified and condensed. Final version to appear in J. Combin. Theory Ser.

The Application of Flame Image Velocimetry to After-injection Effects on Flow Fields in a Small-Bore Diesel Engine

This study implements Flame Image Velocimetry (FIV), a diagnostic technique based on post-processing of high-speed soot luminosity images, to show the in-flame flow field development impacted by after-injection in a single-cylinder, small-bore optical diesel engine. Two after-injection cases with different dwell times between the main injection and after-injection, namely, close-coupled and long-dwell, as well as a main-injection-only case are compared regarding flow fields, flow vector magnitude, and turbulence intensity distribution. For each case, high-speed soot luminosity movies from 100 individual combustion cycles are recorded at a high frame rate of 45 kHz for FIV processing. The Reynolds decomposition using a spatial filtering method is applied to the obtained flow vectors so that bulk flow structures and turbulence intensity distributions can be discussed. The results show significant after-injection-induced flow structures as a group of vectors travelling back toward the center of the combustion chamber upon the jet impingement on the piston bowl wall and then jet-to-jet collision. Despite higher cyclic variations caused by the after-injection, increased bulk flow magnitude and turbulence intensity upon the after-injection event suggests locally enhanced mixing. Compared to the long-dwell after-injection, the close-coupled after-injection shows more significant turbulence enhancements

Comparing the Effects of Cognative Style, Subjective Emotion, and Physiological Phenomenon on the Accuracy of Intuitive Time-Series Forecasting Using an SONN: A Proposal

Self-organizing neural network (SONN) is known to be able to extract features in input samples [Kohonen, 1995]. By updating not only the weight vector of the winning neuron in the self-organizing layer but also those of its neighboring neurons, neighboring neurons would eventually become to respond similarly to a specific input vector. Then the distribution of winning neurons for a class may be distinguished from those for other classes. Luttrell proposed a SONN which can inherently use the correlation between input vectors of separate clusters and he called it self-supervised adaptive neural network [Luttrell, 1992]. In this report, we propose the use of the selfsupervised adaptive algorithm in analyzing the correlation between cognitive style and the accuracy of intuitive time-series forecasting, and suggest a way to compare the relative degree of correlation between each of cognitive style, subjective emotion and physiological phenomenon and the accuracy of intuitive time-series forecasting

Simplicial effective resistance and enumeration of spanning trees

A graph can be regarded as an electrical network in which each edge is a resistor. This point of view relates combinatorial quantities, such as the number of spanning trees, to electrical ones such as effective resistance. The second and third authors have extended the combinatorics/electricity analogy to higher dimension and expressed the simplicial analogue of effective resistance as a ratio of weighted tree enumerators. In this paper, we first use that ratio to prove a new enumeration formula for color-shifted complexes, confirming a conjecture by Aalipour and the first author, and generalizing a result of Ehrenborg and van Willigenburg on Ferrers graphs. We then use the same technique to recover an enumeration formula for shifted complexes, first proved by Klivans and the first and fourth authors. In each case, we add facets one at a time, and give explicit expressions for simplicial effective resistances of added facets by constructing high-dimensional analogues of currents and voltages (respectively homological cycles and cohomological cocycles).Comment: 27 pages, minor revisions from v

A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube

High resolution angle resolved photoemission studies on quasi-particle dynamics in graphite

We obtained the spectral function of the graphite H point using high resolution angle resolved photoelectron spectroscopy (ARPES). The extracted width of the spectral function (inverse of the photo-hole lifetime) near the H point is approximately proportional to the energy as expected from the linearly increasing density of states (DOS) near the Fermi energy. This is well accounted by our electron-phonon coupling theory considering the peculiar electronic DOS near the Fermi level. And we also investigated the temperature dependence of the peak widths both experimentally and theoretically. The upper bound for the electron-phonon coupling parameter is ~0.23, nearly the same value as previously reported at the K point. Our analysis of temperature dependent ARPES data at K shows that the energy of phonon mode of graphite has much higher energy scale than 125K which is dominant in electron-phonon coupling.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.

The Evolution of the Galaxy Stellar Mass Function at z= 4-8: A Steepening Low-mass-end Slope with Increasing Redshift

We present galaxy stellar mass functions (GSMFs) at $z=$ 4-8 from a rest-frame ultraviolet (UV) selected sample of $\sim$4500 galaxies, found via photometric redshifts over an area of $\sim$280 arcmin$^2$ in the CANDELS/GOODS fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data yet-to-date and the relatively large volume allow us to place a better constraint at both the low- and high-mass ends of the GSMFs compared to previous space-based studies from pre-CANDELS observations. Supplemented by a stacking analysis, we find a linear correlation between the rest-frame UV absolute magnitude at 1500 \AA\ ($M_{\rm UV}$) and logarithmic stellar mass ($\log M_*$) that holds for galaxies with $\log(M_*/M_{\odot}) \lesssim 10$. We use simulations to validate our method of measuring the slope of the $\log M_*$-$M_{\rm UV}$ relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over $z=$ 4-8, while the normalization of the trend exhibits a weak evolution toward lower masses at higher redshift. We combine the $\log M_*$-$M_{\rm UV}$ distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs, finding that the low-mass-end slope becomes steeper with increasing redshift from $\alpha=-1.55^{+0.08}_{-0.07}$ at $z=4$ to $\alpha=-2.25^{+0.72}_{-0.35}$ at $z=8$. The inferred stellar mass density, when integrated over $M_*=10^8$-$10^{13} M_{\odot}$, increases by a factor of $10^{+30}_{-2}$ between $z=7$ and $z=4$ and is in good agreement with the time integral of the cosmic star formation rate density.Comment: 27 pages, 17 figures, ApJ, in pres

A Versatile Assay for the Identification of RNA Silencing Suppressors Based on Complementation of Viral Movement

The cell-to-cell movement of Turnip crinkle virus (TCV) in Nicotiana benthamiana requires the presence of its coat protein (CP), a known suppressor of RNA silencing. RNA transcripts of a TCV construct containing a reporter gene (green fluorescent protein) (TCV-sGFP) in place of the CP open reading frame generated foci of three to five cells. TCV CP delivered in trans by Agrobacterium tumefaciens infiltration potentiated movement of TCV-sGFP and increased foci diameter, on average, by a factor of four. Deletion of the TCV movement proteins in TCV-sGFP (construct TCVΔ92-sGFP) abolished the movement complementation ability of TCV CP. Other known suppressors of RNA silencing from a wide spectrum of viruses also complemented the movement of TCV-sGFP when delivered in trans by Agrobacterium tumefaciens. These include suppressors from nonplant viruses with no known plant movement function, demonstrating that this assay is based solely on RNA silencing suppression. While the TCV-sGFP construct is primarily used as an infectious RNA transcript, it was also subcloned for direct expression from Agrobacterium tumefaciens for simple quantification of suppressor activity based on fluorescence levels in whole leaves. Thus, this system provides the flexibility to assay for suppressor activity in either the cytoplasm or nucleus, depending on the construct employed

Site-selective mapping of metastable states using electron-beam induced luminescence microscopy

Metastable states created by electron or hole capture in crystal defects are widely used in dosimetry and photonic applications. Feldspar, the most abundant mineral in the Earth crust (>50%), generates metastable states with lifetimes of millions of years upon exposure to ionizing radiation. Although feldspar is widely used in dosimetry and geochronometry, the creation of metastable states and charge transfer across them is poorly understood. Understanding such phenomena requires next-generation methods based on high-resolution, site-selective probing of the metastable states. Recent studies using site-selective techniques such as photoluminescence (PL), and radioluminescence (RL) at 7 K have revealed that feldspar exhibits two near-infrared (NIR) emission bands peaking at 880 nm and 955 nm, which are believed to arise from the principal electron-trapping states. Here, we map for the first time the electron-trapping states in potassium-rich feldspar using spectrally-resolved cathodoluminescence microscopy at a spatial resolution of around 6 to 22 micrometer. Each pixel probed by a scanning electron microscope provides us a cathodoluminescence spectrum (SEM-CL) in the range 600-1000 nm, and elemental data from energy-dispersive x-ray (EDX) spectroscopy. We conclude that the two NIR emissions are spatially variable and, therefore, originate from different sites. This conclusion contradicts the existing model that the two emissions arise from two different excited states of a principal trap. Moreover, we are able to link the individual NIR emission peaks with the geochemical variations (K, Na and Fe concentration), and propose a cluster model that explains the quenching of the NIR emission by Fe4+