Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for the general d-dimensional hyper-cubic lattice, where the parameter J determines the width of the distributions. We explain in detail how the expansions are calculated. The analysis, using the Dlog-Pad\'e approximation and the techniques known as M1 and M2, leads to estimates for the critical threshold (J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for \gamma agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.Comment: 13 figure

Tensor decomposition and homotopy continuation

A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness sets via numerical elimination theory, we develop computational methods for computing ranks and border ranks of tensors along with decompositions. More generally, we present our approach using joins of any collection of irreducible and nondegenerate projective varieties $X_1,\ldots,X_k\subset\mathbb{P}^N$ defined over $\mathbb{C}$. After computing ranks over $\mathbb{C}$, we also explore computing real ranks. Various examples are included to demonstrate this numerical algebraic geometric approach.Comment: We have added two examples: A Coppersmith-Winograd tensor, Matrix multiplication with zeros. (26 pages, 1 figure

Kelvin probe characterization of buried graphitic microchannels in single-crystal diamond

In this work, we present an investigation by Kelvin Probe Microscopy (KPM) of buried graphitic microchannels fabricated in single-crystal diamond by direct MeV ion microbeam writing. Metal deposition of variable-thickness masks was adopted to implant channels with emerging endpoints and high temperature annealing was performed in order to induce the graphitization of the highly-damaged buried region. When an electrical current was flowing through the biased buried channel, the structure was clearly evidenced by KPM maps of the electrical potential of the surface region overlying the channel at increasing distances from the grounded electrode. The KPM profiling shows regions of opposite contrast located at different distances from the endpoints of the channel. This effect is attributed to the different electrical conduction properties of the surface and of the buried graphitic layer. The model adopted to interpret these KPM maps and profiles proved to be suitable for the electronic characterization of buried conductive channels, providing a non-invasive method to measure the local resistivity with a micrometer resolution. The results demonstrate the potential of the technique as a powerful diagnostic tool to monitor the functionality of all-carbon graphite/diamond devices to be fabricated by MeV ion beam lithography.Comment: 21 pages, 5 figure

Slow breathing and hypoxic challenge: cardiorespiratory consequences and their central neural substrates

Controlled slow breathing (at 6/min, a rate frequently adopted during yoga practice) can benefit cardiovascular function, including responses to hypoxia. We tested the neural substrates of cardiorespiratory control in humans during volitional controlled breathing and hypoxic challenge using functional magnetic resonance imaging (fMRI). Twenty healthy volunteers were scanned during paced (slow and normal rate) breathing and during spontaneous breathing of normoxic and hypoxic (13% inspired O2) air. Cardiovascular and respiratory measures were acquired concurrently, including beat-to-beat blood pressure from a subset of participants (N = 7). Slow breathing was associated with increased tidal ventilatory volume. Induced hypoxia raised heart rate and suppressed heart rate variability. Within the brain, slow breathing activated dorsal pons, periaqueductal grey matter, cerebellum, hypothalamus, thalamus and lateral and anterior insular cortices. Blocks of hypoxia activated mid pons, bilateral amygdalae, anterior insular and occipitotemporal cortices. Interaction between slow breathing and hypoxia was expressed in ventral striatal and frontal polar activity. Across conditions, within brainstem, dorsal medullary and pontine activity correlated with tidal volume and inversely with heart rate. Activity in rostroventral medulla correlated with beat-to-beat blood pressure and heart rate variability. Widespread insula and striatal activity tracked decreases in heart rate, while subregions of insular cortex correlated with momentary increases in tidal volume. Our findings define slow breathing effects on central and cardiovascular responses to hypoxic challenge. They highlight the recruitment of discrete brainstem nuclei to cardiorespiratory control, and the engagement of corticostriatal circuitry in support of physiological responses that accompany breathing regulation during hypoxic challenge

River, delta and coastal morphological response accounting for biological dynamics

Abstract. Management and construction can increase resilience in the face of climate change, and benefits can be enhanced through integration of biogenic materials including shells and vegetation. Rivers and coastal landforms are dynamic systems that respond to intentional and unintended manipulation of critical factors, often with unforeseen and/or undesirable resulting effects. River management strategies have impacts that include deltas and coastal areas which are increasingly vulnerable to climate change with reference to sea level rise and storm intensity. Whereas conventional assessment and analysis of rivers and coasts has relied on modelling of hydrology, hydraulics and sediment transport, incorporating additional biological factors can offer more comprehensive, beneficial and realistic alternatives. Suitable modelling tools can provide improved decision support. The question has been whether current models can effectively address biological responses with suitable reliability and efficiency. Since morphodynamic evolution exhibits its effects on a large timescale, the choice of mathematical model is not trivial and depends upon the availability of data, as well as the spatial extent, timelines and computation effort desired. The ultimate goal of the work is to set up a conveniently simplified river morphodynamic model, coupled with a biological dynamics plant population model able to predict the long-term evolution of large alluvial river systems managed through bioengineering. This paper presents the first step of the work related to the application of the model accounting for stationary vegetation condition. Sensitivity analysis has been performed on the main hydraulic, sedimentology, and biological parameters. The model has been applied to significant river training in Europe, Asia and North America, and comparative analysis has been used to validate analytical solutions. Data gaps and further areas for investigation are identified