On the mean values of L-functions in orthogonal and symplectic families

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L-functions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with orthogonal & symplectic symmetry. Specifically, we establish formulae for real quadratic Dirichlet L-functions and for the L-functions associated with primitive Hecke eigenforms of weight 2 in terms of partial Euler and Hadamard products. We then prove asymptotic formulae for some moments of these partial products and make general conjectures based on results for the moments of characteristic polynomials of random matrices

On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class

We establish the equivalence of conjectures concerning the pair correlation of zeros of $L$-functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston & Montgomery [7] and Montgomery & Soundararajan [11] for the Riemann zeta-function to other $L$-functions in the Selberg class. Our approach is based on the statistics of the zeros because the analogue of the Hardy-Littlewood conjecture for the auto-correlation of the arithmetic functions we consider is not available in general. One of our main findings is that the variances of sums of these arithmetic functions over primes in short intervals have a different form when the degree of the associated $L$-functions is 2 or higher to that which holds when the degree is 1 (e.g. the Riemann zeta-function). Specifically, when the degree is 2 or higher there are two regimes in which the variances take qualitatively different forms, whilst in the degree-1 case there is a single regime

Model Counting for Formulas of Bounded Clique-Width

We show that #SAT is polynomial-time tractable for classes of CNF formulas whose incidence graphs have bounded symmetric clique-width (or bounded clique-width, or bounded rank-width). This result strictly generalizes polynomial-time tractability results for classes of formulas with signed incidence graphs of bounded clique-width and classes of formulas with incidence graphs of bounded modular treewidth, which were the most general results of this kind known so far.Comment: Extended version of a paper published at ISAAC 201

Geospatial analysis of regional climate impacts to accelerate cost-efficient direct air capture deployment

Carbon dioxide (CO2) removal from the atmospheric will be essential if we are to achieve net-zero emissions targets. Direct air capture (DAC) is a CO2 removal method with the potential for large-scale deployment. However, DAC operational costs, and thus deployment potential, is dependent on performance, which can vary under different climate conditions. Here, to further develop our understanding of the impact of regional climate variation on DAC performance, we use high-resolution hourly based global weather profiles between 2016 and 2020 and weighted average capital costs to obtain DAC regional performance and levelized cost of DAC (LCOD). We found that relatively cold and drier regions have favorable DAC performance. Moreover, approximately 25% of the world’s land is potentially unsuitable due to very cold ambient temperatures for a substantial part of the year. For the remaining regions, the estimated LCOD is $320–$540 per tCO2 at an electricity cost of $50 MWh−1. Our results improve the understanding of regional DAC performance, which can provide valuable insights for sustainable DAC deployment and effective climate action

Beyond 90% capture: Possible, but at what cost?

© 2020 Elsevier Ltd Carbon capture and storage (CCS) will have an essential role in meeting our climate change mitigation targets. CCS technologies are technically mature and will likely be deployed to decarbonise power, industry, heat, and removal of CO2 from the atmosphere. The assumption of a 90% CO2 capture rate has become ubiquitous in the literature, which has led to doubt around whether CO2 capture rates above 90% are even feasible. However, in the context of a 1.5 °C target, going beyond 90% capture will be vital, with residual emissions needing to be indirectly captured via carbon dioxide removal (CDR) technologies. Whilst there will be trade-offs between the cost of increased rates of CO2 capture, and the cost of offsets, understanding where this lies is key to minimising the dependence on CDR. This study quantifies the maximum limit of feasible CO2 capture rate for a range of power and industrial sources of CO2, beyond which abatement becomes uneconomical. In no case, was a capture rate of 90% found to be optimal, with capture rates of up to 98% possible at a relatively low marginal cost. Flue gas composition was found to be a key determinant of the cost of capture, with more dilute streams exhibiting a more pronounced minimum. Indirect capture by deploying complementary CDR is also assessed. The results show that current policy initiatives are unlikely to be sufficient to enable the economically viable deployment of CCS in all but a very few niche sectors of the economy

Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II

Let $K$ be a quadratic number field and $\zeta_K(s)$ be the associated Dedekind zeta-function. We show that there are infinitely many normalized gaps between consecutive zeros of $\zeta_K(s)$ on the critical line which are greater than $2.866$ times the average spacing.Comment: 12 pages; to appear in the Quarterly Journal of Mathematic

Electrical conductivity beyond linear response in layered superconductors under magnetic field

The time-dependent Ginzburg-Landau approach is used to investigate nonlinear response of a strongly type-II superconductor. The dissipation takes a form of the flux flow which is quantitatively studied beyond linear response. Thermal fluctuations, represented by the Langevin white noise, are assumed to be strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid and marginalize the effects of the vortex pinning by inhomogeneities. The layered structure of the superconductor is accounted for by means of the Lawrence-Doniach model. The nonlinear interaction term in dynamics is treated within Gaussian approximation and we go beyond the often used lowest Landau level approximation to treat arbitrary magnetic fields. The I-V curve is calculated for arbitrary temperature and the results are compared to experimental data on high-$T_{c}$ superconductor YBa$_{2}$Cu$_{3}$O$$.Comment: 8 pages, 3 figure

Between Treewidth and Clique-width

Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set that are all FPT parameterized by treewidth but none of which can be FPT parameterized by clique-width unless FPT = W[1], as shown by Fomin et al [7, 8]. We therefore seek a structural graph parameter that shares some of the generality of clique-width without paying this price. Based on splits, branch decompositions and the work of Vatshelle [18] on Maximum Matching-width, we consider the graph parameter sm-width which lies between treewidth and clique-width. Some graph classes of unbounded treewidth, like distance-hereditary graphs, have bounded sm-width. We show that MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set are all FPT parameterized by sm-width