Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions associated with symmetry classes of alternating sign matrices. These identities generalize those already found in our earlier paper, via the introduction of additional parameters. The left hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity. The right hand side of each identity is (one of the two factors present in) the partition function of the six-vertex model on a relevant domain.Comment: 34 pages, 14 figure

The shape of the urine stream — from biophysics to diagnostics

We develop a new computational model of capillary-waves in free-jet flows, and apply this to the problem of urological diagnosis in this first ever study of the biophysics behind the characteristic shape of the urine stream as it exits the urethral meatus. The computational fluid dynamics model is used to determine the shape of a liquid jet issuing from a non-axisymmetric orifice as it deforms under the action of surface tension. The computational results are verified with experimental modelling of the urine stream. We find that the shape of the stream can be used as an indicator of both the flow rate and orifice geometry. We performed volunteer trials which showed these fundamental correlations are also observed in vivo for male healthy volunteers and patients undergoing treatment for low flow rate. For healthy volunteers, self estimation of the flow shape provided an accurate estimation of peak flow rate (+-2%). However for the patients, the relationship between shape and flow rate suggested poor meatal opening during voiding. The results show that self measurement of the shape of the urine stream can be a useful diagnostic tool for medical practitioners since it provides a non-invasive method of measuring urine flow rate and urethral dilation

Discrete holomorphicity and quantized affine algebras

We consider non-local currents in the context of quantized affine algebras, following the construction introduced by Bernard and Felder. In the case of $U_q(A_1^{(1)})$ and $U_q(A_2^{(2)})$, these currents can be identified with configurations in the six-vertex and Izergin--Korepin nineteen-vertex models. Mapping these to their corresponding Temperley--Lieb loop models, we directly identify non-local currents with discretely holomorphic loop observables. In particular, we show that the bulk discrete holomorphicity relation and its recently derived boundary analogue are equivalent to conservation laws for non-local currents

Yang-Mills gravity in biconformal space

We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena for studying flat space Yang-Mills theories. By applying the biconformal extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theories and 4-dim, flat space gauge theories.Comment: 27 pages; paper emphasis shifted to focus on gravity; references adde

The public sphere and network democracy: Social movements and political change?

The article critically examines the democratic possibilities of technological innovations associated with Web 2.0 tools and in this context it address the first and second ‘waves’ of academic debates concerning the social media and the public sphere in the networked society. It argues that the initial optimism associated with a virtual public sphere has been replaced by doubts about whether this model was appropriate for the development of democratic values. It assesses whether the information communications networks have constructed a more personalised form of politics and it is concerned with the application of the networked power relations with reference to grassroots or social revolutionary movements. New communications environments were seen to be instrumental in forging the conditions for the ‘Arab Spring’ revolutions and the Turkish protests within Istanbul’s Taksim square during the summer of 2013. These Middle Eastern case examples are discussed along with the calls for political and economic change in Southern Europe within financially constrained countries of Spain and Greece. Based on such studies the article theorizes on the key question concerning whether the social media can contribute to democracy, revolution and expansion of the public sphere, or whether they remain instruments of control and power

Modern Political Communication and Web 2.0 in Representative Democracies

During the first two decades of the twenty-first century, the social media has facilitated interactive communications between the political elites and public. In the 2016 UK Referendum, the social media became a vehicle for contested political arguments and post-truth positions defined the Remain and Leave camps. For instance, it was claimed that the United Kingdom Independence Party former leader Nigel Farage’s anti-migrant tweets influenced many voters. In the 2016 US Presidential election, the victorious celebrity property tycoon Donald Trump maintained a controversial online presence. He posted tweets about his campaign and engaged in a blatantly hateful online discourse aimed at his political opponents. Therefore, does such a usage of the social media aid democratic representation or contribute to a greater destabilisation of modern politics

Effect of elevated CO2 and high temperature on seed-set and grain quality of rice

Hybrid vigour may help overcome the negative effects of climate change in rice. A popular rice hybrid (IR75217H), a heat-tolerant check (N22), and a mega-variety (IR64) were tested for tolerance of seed-set and grain quality to high-temperature stress at anthesis at ambient and elevated [CO2]. Under an ambient air temperature of 29 °C (tissue temperature 28.3 °C), elevated [CO2] increased vegetative and reproductive growth, including seed yield in all three genotypes. Seed-set was reduced by high temperature in all three genotypes, with the hybrid and IR64 equally affected and twice as sensitive as the tolerant cultivar N22. No interaction occurred between temperature and [CO2] for seed-set. The hybrid had significantly more anthesed spikelets at all temperatures than IR64 and at 29 °C this resulted in a large yield advantage. At 35 °C (tissue temperature 32.9 °C) the hybrid had a higher seed yield than IR64 due to the higher spikelet number, but at 38 °C (tissue temperature 34–35 °C) there was no yield advantage. Grain gel consistency in the hybrid and IR64 was reduced by high temperatures only at elevated [CO2], while the percentage of broken grains increased from 10% at 29 °C to 35% at 38 °C in the hybrid. It is concluded that seed-set of hybrids is susceptible to short episodes of high temperature during anthesis, but that at intermediate tissue temperatures of 32.9 °C higher spikelet number (yield potential) of the hybrid can compensate to some extent. If the heat tolerance from N22 or other tolerant donors could be transferred into hybrids, yield could be maintained under the higher temperatures predicted with climate change

Endothelial HO-1 induction by model TG-rich lipoproteins is regulated through a NOX4-Nrf2 pathway

Circulating levels of chylomicron remnants (CMRs) increase postprandially and their composition directly reflects dietary lipid intake. These TG-rich lipoproteins likely contribute to the development of endothelial dysfunction, albeit via unknown mechanisms. Here, we investigated how the FA composition of CMRs influences their actions on human aortic endothelial cells (HAECs) by comparing the effects of model CMRs—artificial TG-rich CMR-like particles (A-CRLPs)—containing TGs extracted from fish, DHA-rich algal, corn, or palm oils. HAECs responded with distinct transcriptional programs according to A-CRLP TG content and oxidation status, with genes involved in antioxidant defense and cytoprotection most prominently affected by n-3 PUFA-containing A-CRLPs. These particles were significantly more efficacious inducers of heme oxygenase-1 (HO-1) than n-6 PUFA corn or saturated FA-rich palm CRLPs. Mechanistically, HO-1 induction by all CRLPs requires NADPH oxidase 4, with PUFA-containing particles additionally dependent upon mitochondrial reactive oxygen species. Activation of both p38 MAPK and PPARβ/δ culminates in increased nuclear factor erythroid 2-related factor 2 (Nrf2) expression/nuclear translocation and HO-1 induction. These studies define new molecular pathways coupling endothelial cell activation by model CMRs with adaptive regulation of Nrf2-dependent HO-1 expression and may represent key mechanisms through which dietary FAs differentially impact progression of endothelial dysfunction

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra