NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks

The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a hard task. A typical application is the computation of a number of its eigenvalues and eigenvectors. Standard methods become infeasible as the number of nodes in the graph is too large. We propose the use of the fast summation based on the nonequispaced fast Fourier transform (NFFT) to perform the dense matrix-vector product with the graph Laplacian fast without ever forming the whole matrix. The enormous flexibility of the NFFT algorithm allows us to embed the accelerated multiplication into Lanczos-based eigenvalues routines or iterative linear system solvers and even consider other than the standard Gaussian kernels. We illustrate the feasibility of our approach on a number of test problems from image segmentation to semi-supervised learning based on graph-based PDEs. In particular, we compare our approach with the Nystr\"om method. Moreover, we present and test an enhanced, hybrid version of the Nystr\"om method, which internally uses the NFFT.Comment: 28 pages, 9 figure

Modification of Aluminium Surface Using Picosecond Laser for Printing Applications

Ultrafast picosecond laser pulses of wavelength of 1064nm have allowed the surface modification of anodised aluminium plate for potential industrial application. The interaction of the laser with the substrate created a hydrophilic surface, giving a contact angle of less than 10 degrees. On examination under a Scanning Electron Microscope (SEM), it was observed that these surfaces have an interesting ‘lotus-leaf’ like structure. It has been found that these laser processed hydrophilic surfaces revert with time. The potential for application in the printing industry is strong due to the reusability and sustainability of the process materials; initial trials confirm this. This technology would offer extra advantages as a non-chemical process without the need for developer, thereby reducing the overall cost and time of printin

Chromatic Polynomials for J(∏H)IJ(\prod H)I Strip Graphs and their Asymptotic Limits

We calculate the chromatic polynomials $P$ for $n$-vertex strip graphs of the form $J(\prod_{\ell=1}^m H)I$, where $J$ and $I$ are various subgraphs on the left and right ends of the strip, whose bulk is comprised of $m$-fold repetitions of a subgraph $H$. The strips have free boundary conditions in the longitudinal direction and free or periodic boundary conditions in the transverse direction. This extends our earlier calculations for strip graphs of the form $(\prod_{\ell=1}^m H)I$. We use a generating function method. From these results we compute the asymptotic limiting function $W=\lim_{n \to \infty}P^{1/n}$; for $q \in {\mathbb Z}_+$ this has physical significance as the ground state degeneracy per site (exponent of the ground state entropy) of the $q$-state Potts antiferromagnet on the given strip. In the complex $q$ plane, $W$ is an analytic function except on a certain continuous locus ${\cal B}$. In contrast to the $(\prod_{\ell=1}^m H)I$ strip graphs, where ${\cal B}$ (i) is independent of $I$, and (ii) consists of arcs and possible line segments that do not enclose any regions in the $q$ plane, we find that for some $J(\prod_{\ell=1}^m H)I$ strip graphs, ${\cal B}$ (i) does depend on $I$ and $J$, and (ii) can enclose regions in the $q$ plane. Our study elucidates the effects of different end subgraphs $I$ and $J$ and of boundary conditions on the infinite-length limit of the strip graphs.Comment: 33 pages, Latex, 7 encapsulated postscript figures, Physica A, in press, with some typos fixe

Singular Behaviour of the Potts Model in the Thermodynamic Limit

The self-duality transformation is applied to the Fisher zeroes near the critical point in the thermodynamic limit in the q>4 state Potts model in two dimensions. A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation. Conjecturing that all zeroes governing ferromagnetic critical behaviour satisfy the latter requirement, the full locus of Fisher zeroes is shown to be a circle. This locus, together with the density of zeroes is shown to be sufficient to recover the singular form of all thermodynamic functions in the thermodynamic limit.Comment: Contribution to Lattice 97, LaTeX, 3 pages, 0 figure

Electrical control of spins and giant g-factors in ring-like coupled quantum dots

Emerging theoretical concepts for quantum technologies have driven a continuous search for structures where a quantum state, such as spin, can be manipulated efficiently. Central to many concepts is the ability to control a system by electric and magnetic fields, relying on strong spin-orbit interaction and a large g-factor. Here, we present a new mechanism for spin and orbital manipulation using small electric and magnetic fields. By hybridizing specific quantum dot states at two points inside InAs nanowires, nearly perfect quantum rings form. Large and highly anisotropic effective g-factors are observed, explained by a strong orbital contribution. Importantly, we find that the orbital and spin-orbital contributions can be efficiently quenched by simply detuning the individual quantum dot levels with an electric field. In this way, we demonstrate not only control of the effective g-factor from 80 to almost 0 for the same charge state, but also electrostatic change of the ground state spin

RNAseq analysis reveals virus diversity within Hawaiian apiary insect communities

Deformed wing virus (DWV) is the most abundant viral pathogen of honey bees and has been associated with large-scale colony losses. DWV and other bee-associated RNA viruses are generalists capable of infecting diverse hosts. Here, we used RNAseq analysis to test the hypothesis that due to the frequency of interactions, a range of apiary pest species would become infected with DWV and/or other honey bee-associated viruses. We confirmed that DWV-A was the most prevalent virus in the apiary, with genetically similar sequences circulating in the apiary pests, suggesting frequent inter-species transmission. In addition, different proportions of the three DWV master variants as indicated by BLAST analysis and genome coverage plots revealed interesting DWV-species groupings. We also observed that new genomic recombinants were formed by the DWV master variants, which are likely adapted to replicate in different host species. Species groupings also applied when considering other viruses, many of which were widespread in the apiaries. In social wasps, samples were grouped further by site, which potentially also influenced viral load. Thus, the apiary invertebrate community has the potential to act as reservoirs of honey bee-associated viruses, highlighting the importance of considering the wider community in the apiary when considering honey bee health

Horizontal flows concurrent with an X2.2 flare in active region NOAA 11158

Horizontal proper motions were measured with local correlation tracking (LCT) techniques in active region NOAA 11158 on 2011 February 15 at a time when a major (X2.2) solar flare occurred. The measurements are based on continuum images and magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. The observed shear flows along the polarity inversion line were rather weak (a few 100 m/s). The counter-streaming region shifted toward the north after the flare. A small circular area with flow speeds of up to 1.2 km/s appeared after the flare near a region of rapid penumbral decay. The LCT signal in this region was provided by small-scale photospheric brigthenings, which were associated with fast traveling moving magnetic features. Umbral strengthening and rapid penumbral decay was observed after the flare. Both phenomena were closely tied to kernels of white-light flare emission. The white-light flare only lasted for about 15 min and peaked 4 min earlier than the X-ray flux. In comparison to other major flares, the X2.2 flare in active region NOAA 11158 only produced diminutive photospheric signatures.Comment: 6 pages, 4 figures, accepted for publication in Astronomische Nachrichten/A

Insect pollination reduces yield loss following heat stress in faba bean (Vicia faba L.)

Global food security, particularly crop fertilization and yield production, is threatened by heat waves that are projected to increase in frequency and magnitude with climate change. Effects of heat stress on the fertilization of insect-pollinated plants are not well understood, but experiments conducted primarily in self-pollinated crops, such as wheat, show that transfer of fertile pollen may recover yield following stress. We hypothesized that in the partially pollinator-dependent crop, faba bean (Vicia faba L.), insect pollination would elicit similar yield recovery following heat stress. We exposed potted faba bean plants to heat stress for 5 days during floral development and anthesis. Temperature treatments were representative of heat waves projected in the UK for the period 2021-2050 and onwards. Following temperature treatments, plants were distributed in flight cages and either pollinated by domesticated Bombus terrestris colonies or received no insect pollination. Yield loss due to heat stress at 30°C was greater in plants excluded from pollinators (15%) compared to those with bumblebee pollination (2.5%). Thus, the pollinator dependency of faba bean yield was 16% at control temperatures (18 to 26°C) and extreme stress (34°C), but was 53% following intermediate heat stress at 30°C. These findings provide the first evidence that the pollinator dependency of crops can be modified by heat stress, and suggest that insect pollination may become more important in crop production as the probability of heat waves increases

Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits

We calculate the chromatic polynomials $P((G_s)_m,q)$ and, from these, the asymptotic limiting functions $W(\{G_s\},q)=\lim_{n \to \infty}P(G_s,q)^{1/n}$ for families of $n$-vertex graphs $(G_s)_m$ comprised of $m$ repeated subgraphs $H$ adjoined to an initial graph $I$. These calculations of $W(\{G_s\},q)$ for infinitely long strips of varying widths yield important insights into properties of $W(\Lambda,q)$ for two-dimensional lattices $\Lambda$. In turn, these results connect with statistical mechanics, since $W(\Lambda,q)$ is the ground state degeneracy of the $q$-state Potts model on the lattice $\Lambda$. For our calculations, we develop and use a generating function method, which enables us to determine both the chromatic polynomials of finite strip graphs and the resultant $W(\{G_s\},q)$ function in the limit $n \to \infty$. From this, we obtain the exact continuous locus of points ${\cal B}$ where $W(\{G_s\},q)$ is nonanalytic in the complex $q$ plane. This locus is shown to consist of arcs which do not separate the $q$ plane into disconnected regions. Zeros of chromatic polynomials are computed for finite strips and compared with the exact locus of singularities ${\cal B}$. We find that as the width of the infinitely long strips is increased, the arcs comprising ${\cal B}$ elongate and move toward each other, which enables one to understand the origin of closed regions that result for the (infinite) 2D lattice.Comment: 48 pages, Latex, 12 encapsulated postscript figures, to appear in Physica

Subpoena, Marshall County, M.S, 2 December 1837

https://egrove.olemiss.edu/aldrichcorr_a/1081/thumbnail.jp