The role of gentle algebras in higher homological algebra

We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra $\Lambda$ contains a $d$-cluster tilting subcategory for some $d \geq 2$, then $\Lambda$ is a radical square zero Nakayama algebra. This gives a complete classification of weakly $d$-representation finite gentle algebras. In the second part, we use a geometric model of the derived category to prove a similar result in the triangulated setup. More precisely, we show that if $\mathcal{D}^b(\operatorname{proj}\Lambda)$ contains a $d$-cluster tilting subcategory that is closed under $[d]$, then $\Lambda$ is derived equivalent to an algebra of Dynkin type $A$. In this case, our approach gives a geometric characterization of all $d$-cluster tilting subcategories of $\mathcal{D}^b(\Lambda)$ that are closed under $[d]$.Comment: 19 pages, comments welcom

Estimate of the Rigidity of Eclogite in the Lower Mantle From Waveform Modeling of Broadband S‐to‐P Wave Conversions

Broadband USArray recordings of the 21 July 2007 western Brazil earthquake (Mw=6.0; depth = 633 km) include high‐amplitude signals about 40 s, 75 s, and 100 s after the P wave arrival. They are consistent with S wave to P wave conversions in the mantle beneath northwestern South America. The signal at 100 s, denoted as S1750P, has the highest amplitude and is formed at 1,750 km depth based on slant‐stacking and semblance analysis. Waveform modeling using axisymmetric, finite difference synthetics indicates that S1750P is generated by a 10 km thick heterogeneity, presumably a fragment of subducted mid‐ocean ridge basalt in the lower mantle. The negative polarity of S1750P is a robust observation and constrains the shear velocity anomaly δVS of the heterogeneity to be negative. The amplitude of S1750P indicates that δVS is in the range from −1.6% to −12.4%. The large uncertainty in δVS is due to the large variability in the recorded S1750P amplitude and simplifications in the modeling of S1750P waveforms. The lower end of our estimate for δVS is consistent with ab initio calculations by Tsuchiya (2011), who estimated that δVS of eclogite at lower mantle pressure is between 0 and −2% due to shear softening from the poststishovite phase transition.Key PointsBroadband recordings of S‐P conversions allow for constraining compositional properties of deep Earth materialsStishovite is present in subducted eclogite and contributes to shear velocity softeningFragments of subducted oceanic crust are entrained in mantle flow and can be preserved at depths approaching 2,000 kmPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141104/1/grl56669_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141104/2/grl56642-sup-0002-supplementary.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141104/3/grl56642-sup-0001-supplementary.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141104/4/grl56669.pd

An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to emerge from - the data mining process. We will first validate this emergent space reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space discovery illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven spatial coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems

EMMPRIN is associated with S100A4 and predicts patient outcome in colorectal cancer

BACKGROUND: Proteolytic enzymes and their regulators have important biological roles in colorectal cancer by stimulating invasion and metastasis, which makes these factors attractive as potential prognostic biomarkers. METHODS: The expression of extracellular matrix metalloproteinase inducer (EMMPRIN) was characterised using immunohistochemistry in primary tumours from a cohort of 277 prospectively recruited colorectal cancer patients, and associations with expression of S100A4, clinicopathological parameters and patient outcome were investigated. RESULTS: One hundred and ninety-eight samples (72%) displayed positive membrane staining of the tumour cells, whereas 10 cases (4%) were borderline positive. EMMPRIN expression was associated with shorter metastasis-free, disease-specific and overall survival in both univariate and multivariate analyses. The prognostic impact was largely confined to TNM stage III, and EMMPRIN-negative stage III patients had an excellent prognosis. Furthermore, EMMPRIN was significantly associated with expression of S100A4, and the combined expression of these biomarkers conferred an even poorer prognosis. However, there was no evidence of direct regulation between the two proteins in the colorectal cancer cell lines HCT116 and SW620 in siRNA knockdown experiments. CONCLUSION: EMMPRIN is a promising prognostic biomarker in colorectal cancer, and our findings suggest that it could be used in the selection of stage III patients for adjuvant therapy

Molecular van der Waals fluids in cavity quantum electrodynamics

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. However, there are currently very limited approaches to manipulate van der Waals interactions. In this work, we demonstrate that strong light-matter coupling can be used to tune van der Waals interactions, and, thus, control the thermodynamic properties of many-molecule systems. Our analysis reveals orientation-dependent intermolecular interactions between van der Waals molecules (for example, H2) that depend on the distance between the molecules R as R−3 and R0. Moreover, we employ non-perturbative \textit{ab initio} cavity quantum electrodynamics calculations to develop machine learning-based van der Waals interaction potentials for molecules inside optical cavities. By simulating fluids of up to 1,000 H2 molecules, we demonstrate that strong light-matter coupling can tune the structural and thermodynamic properties of molecular fluids. In particular, we observe collective orientational order in many-molecule systems as a result of cavity-modified van der Waals interactions. These simulations and analyses demonstrate both local and collective effects induced by strong light-matter coupling and open new paths for controlling the properties of condensed phase systems

A model for optimal fleet composition of vessels for offshore wind farm maintenance

We present a discrete optimisation model that chooses an optimal fleet of vessels to support maintenance operations at Offshore Wind Farms (OFWs). The model is presented as a bi-level problem. On the first (tactical) level, decisions are made on the fleet composition for a certain time horizon. On the second (operational) level, the fleet is used to optimise the schedule of operations needed at the OWF, given events of failures and weather conditions

Effect of substrate thermal resistance on space-domain microchannel

In recent years, Fluorescent Melting Curve Analysis (FMCA) has become an almost ubiquitous feature of commercial quantitative PCR (qPCR) thermal cyclers. Here a micro-fluidic device is presented capable of performing FMCA within a microchannel. The device consists of modular thermally conductive blocks which can sandwich a microfluidic substrate. Opposing ends of the blocks are held at differing temperatures and a linear thermal gradient is generated along the microfluidic channel. Fluorescent measurements taken from a sample as it passes along the micro-fluidic channel permits fluorescent melting curves to be generated. In this study we measure DNA melting temperature from two plasmid fragments. The effects of flow velocity and ramp-rate are investigated, and measured melting curves are compared to those acquired from a commercially available PCR thermocycler

A Precious-Metal-Free Hybrid Electrolyzer for Alcohol Oxidation Coupled to CO2 -to-Syngas Conversion.

Electrolyzers combining CO2 reduction (CO2 R) with organic substrate oxidation can produce fuel and chemical feedstocks with a relatively low energy requirement when compared to systems that source electrons from water oxidation. Here, we report an anodic hybrid assembly based on a (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) electrocatalyst modified with a silatrane-anchor (STEMPO), which is covalently immobilized on a mesoporous indium tin oxide (mesoITO) scaffold for efficient alcohol oxidation (AlcOx). This molecular anode was subsequently combined with a cathode consisting of a polymeric cobalt phthalocyanine on carbon nanotubes to construct a hybrid, precious-metal-free coupled AlcOx-CO2 R electrolyzer. After three-hour electrolysis, glycerol is selectively oxidized to glyceraldehyde with a turnover number (TON) of ≈1000 and Faradaic efficiency (FE) of 83 %. The cathode generated a stoichiometric amount of syngas with a CO:H2 ratio of 1.25±0.25 and an overall cobalt-based TON of 894 with a FE of 82 %. This prototype device inspires the design and implementation of nonconventional strategies for coupling CO2 R to less energy demanding, and value-added, oxidative chemistry

2'-Alkynylnucleotides: A Sequence- and Spin Label-Flexible Strategy for EPR Spectroscopy in DNA.

Electron paramagnetic resonance (EPR) spectroscopy is a powerful method to elucidate molecular structure through the measurement of distances between conformationally well-defined spin labels. Here we report a sequence-flexible approach to the synthesis of double spin-labeled DNA duplexes, where 2'-alkynylnucleosides are incorporated at terminal and internal positions on complementary strands. Post-DNA synthesis copper-catalyzed azide-alkyne cycloaddition (CuAAC) reactions with a variety of spin labels enable the use of double electron-electron resonance experiments to measure a number of distances on the duplex, affording a high level of detailed structural information

The Stellar and Gaseous Contents of the Orion Dwarf Galaxy

We present new KPNO 0.9-m optical and VLA HI spectral line observations of the Orion dwarf galaxy. This nearby (D ~ 5.4 Mpc), intermediate-mass (M_dyn = 1.1x10^10 Solar masses) dwarf displays a wealth of structure in its neutral ISM, including three prominent "hole/depression" features in the inner HI disk. We explore the rich gas kinematics, where solid-body rotation dominates and the rotation curve is flat out to the observed edge of the HI disk (~6.8 kpc). The Orion dwarf contains a substantial fraction of dark matter throughout its disk: comparing the 4.7x10^8 Solar masses of detected neutral gas with estimates of the stellar mass from optical and near-infrared imaging (3.7x10^8 Solar masses) implies a mass-to-light ratio of ~13. New H alpha observations show only modest-strength current star formation (~0.04 Solar masses per year); this star formation rate is consistent with our 1.4 GHz radio continuum non-detection.Comment: Astronomical Journal, in press. Full-resolution version available from http://www.macalester.edu/~jcannon/pubs.htm