Deconstructing graviphoton from mass-deformed ABJM

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two-sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is $U(N)\times U(N-1)$. We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang -Mills coupling constant to the value which corresponds to M5 brane compactified on \mb{R}^ {1,2} \times S^3/{\mb{Z}_k}. The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.Comment: 26 page

Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Finite-time Lyapunov exponents of deep neural networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.Comment: 6 pages, 4 figure

ggtranscript: an R package for the visualization and interpretation of transcript isoforms using ggplot2

MOTIVATION: The advent of long-read sequencing technologies has increased demand for the visualisation and interpretation of transcripts. However, tools that perform such visualizations remain inflexible and lack the ability to easily identify differences between transcript structures. Here, we introduce ggtranscript, an R package that provides a fast and flexible method to visualize and compare transcripts. As a ggplot2 extension, ggtranscript inherits the functionality and familiarity of ggplot2 making it easy to use. AVAILABILITY: ggtranscript is an R package available at https://github.com/dzhang32/ggtranscript (DOI: https://doi.org/10.5281/zenodo.6374061) via an open-source MIT license. Further is available at https://dzhang32.github.io/ggtranscript/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online

Constructing Self-Dual Strings

We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.Comment: 1+19 pages, presentation improved, minor corrections, published versio

ADAMTS1 alters blood vessel morphology and TSP1 levels in LNCaP and LNCaP-19 prostate tumors

<p>Abstract</p> <p>Background</p> <p>Decreased expression of the angiogenesis inhibitor ADAMTS1 (ADAM metallopeptidase with thrombospondin type 1 motif, 1) has previously been reported during prostate cancer progression. The aim of this study was to investigate the function of ADAMTS1 in prostate tumors.</p> <p>Methods</p> <p>ADAMTS1 was downregulated by shRNA technology in the human prostate cancer cell line LNCaP (androgen-dependent), originally expressing ADAMTS1, and was upregulated by transfection in its subline LNCaP-19 (androgen-independent), expressing low levels of ADAMTS1. Cells were implanted subcutaneously in nude mice and tumor growth, microvessel density (MVD), blood vessel morphology, pericyte coverage and thrombospondin 1 (TSP1) were studied in the tumor xenografts.</p> <p>Results</p> <p>Modified expression of ADAMTS1 resulted in altered blood vessel morphology in the tumors. Low expression levels of ADAMTS1 were associated with small diameter blood vessels both in LNCaP and LNCaP-19 tumors, while high levels of ADAMTS1 were associated with larger vessels. In addition, TSP1 levels in the tumor xenografts were inversely related to ADAMTS1 expression. MVD and pericyte coverage were not affected. Moreover, upregulation of ADAMTS1 inhibited tumor growth of LNCaP-19, as evidenced by delayed tumor establishment. In contrast, downregulation of ADAMTS1 in LNCaP resulted in reduced tumor growth rate.</p> <p>Conclusions</p> <p>The present study demonstrates that ADAMTS1 is an important regulatory factor of angiogenesis and tumor growth in prostate tumors, where modified ADAMTS1 expression resulted in markedly changed blood vessel morphology, possibly related to altered TSP1 levels.</p

Super-Yang-Mills and M5-branes

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $\eta^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $\eta^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE

Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra

In this paper, we study the equations of motion for non-Abelian N=(2,0) tensor multiplets in six dimensions, which were recently proposed by Lambert and Papageorgakis. Some equations are regarded as constraint equations. We employ a loop extension of the Lorentzian three-algebra (3-algebra) and examine the equations of motion around various solutions of the constraint equations. The resultant equations take forms that allow Lagrangian descriptions. We find various (5+d)-dimensional Lagrangians and investigate the relation between them from the viewpoint of M-theory duality.Comment: 44+1 pages, reference added, typos corrected, and several discussions added; v3, reference added, many typos corrected, the language improved; v4, some typos and references corrected, final version to appear in J. Phys.

Energy and flux variations across thin auroral arcs

Two discrete auroral arc filaments, with widths of less than 1 km, have been analysed using multi-station, multi-monochromatic optical observations from small and medium field-of-view imagers and the EISCAT radar. The energy and flux of the precipitating electrons, volume emission rates and local electric fields in the ionosphere have been determined at high temporal (up to 30 Hz) and spatial (down to tens of metres) resolution. A new time-dependent inversion model is used to derive energy spectra from EISCAT electron density profiles. The energy and flux are also derived independently from optical emissions combined with ion-chemistry modelling, and a good agreement is found. A robust method to obtain detailed 2-D maps of the average energy and number flux of small scale aurora is presented. The arcs are stretched in the north-south direction, and the lowest energies are found on the western, leading edges of the arcs. The large ionospheric electric fields (250 mV m?1) found from tristatic radar measurements are evidence of strong currents associated with the region close to the optical arcs. The different data sets indicate that the arcs appear on the boundaries between regions with different average energy of diffuse precipitation, caused by pitch-angle scattering. The two thin arcs on these boundaries are found to be related to an increase in number flux (and thus increased energy flux) without an increase in energ