Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Photoelectrochemical Behavior of Hierarchically Structured Si/WO_3 Core–Shell Tandem Photoanodes

WO_3 thin films have been deposited in a hierarchically structured core–shell morphology, with the cores consisting of an array of Si microwires and the shells consisting of a controlled morphology WO_3 layer. Porosity was introduced into the WO_3 outer shell by using a self-assembled microsphere colloidal crystal as a mask during the deposition of the WO_3 shell. Compared to conformal, unstructured WO_3 shells on Si microwires, the hierarchically structured core–shell photoanodes exhibited enhanced near-visible spectral response behavior, due to increased light absorption and reduced distances over which photogenerated carriers were collected. The use of structured substrates also improved the growth rate of microsphere-based colloidal crystals and suggests strategies for the use of colloidal materials in large-scale applications

A Note on (Meta)stable Brane Configurations in MQCD

We examine the M-theory version of SQCD which is known as MQCD. In the IIA limit, this theory appears to have a supersymmetry-breaking brane configuration which corresponds to the meta-stable state of N=1 SU(Nc) SQCD. However, the behavior at infinity of this non-supersymmetric brane construction differs from that of the supersymmetric ground state of MQCD. We interpret this to mean that it is not a meta-stable state in MQCD, but rather a state in another theory. This provides a concrete example of the fact that, while MQCD accurately describes the supersymmetric features of SCQD, it fails to reproduce its non-supersymmetric features (such as meta-stable states) not only quantitatively but also qualitatively.Comment: 30 pages, 7 figures, harvmac. v2 typo correcte

Determinants of Enrolment and Renewing of Community-Based Health Insurance in Households With Under-5 Children in Rural South-Western Uganda

Background: The desire for universal health coverage in developing countries has brought attention to community-based health insurance (CBHI) schemes in developing countries. The government of Uganda is currently debating policy for the national health insurance programme, targeting the integration of existing CBHI schemes into a larger national risk pool. However, while enrolment has been largely studied in other countries, it remains a generally under-covered issue from a Ugandan perspective. Using a large CBHI scheme, this study, therefore, aims at shedding more light on the determinants of households’ decisions to enrol and renew membership in these schemes. Methods: We collected household data from 464 households in 14 villages served by a large CBHI scheme in south-western Uganda. We then estimated logistic and zero-inflated negative binomial (ZINB) regressions to understand the determinants of enrolment and renewing membership in CBHI, respectively.Results: Results revealed that household’s socioeconomic status, husband’s employment in rural casual work (odds ratio [OR]: 2.581, CI: 1.104-6.032) and knowledge of health insurance premiums (OR: 17.072, CI: 7.027-41.477) were significant predictors of enrolment. Social capital and connectivity, assessed by the number of voluntary groups a household belonged to, was also positively associated with CBHI participation (OR: 5.664, CI: 2.927-10.963). More positive perceptions on insurance (OR: 2.991, CI: 1.273-7.029), access to information were also associated with enrolment and renewing among others. Burial group size and number of burial groups in a village, were all significantly associated with increased the likelihood of renewing CBHI. Conclusion: While socioeconomic factors remain important predictors of participation in insurance, mechanisms to promote inclusion should be devised. Improving the participation of communities can enhance trust in insurance and eventual coverage. Moreover, for households already insured, access to correct information and strengthening their social network information pathways enhances their chances of renewing

Sunflower & Flax Hybrid Performance and Variety Trial Archive

This report features the available sunflower and flax data from 2003-2017. Crop performance testing results are released annually through the activities of SDSU Extension and the South Dakota Agricultural Experiment Station at SDSU

Counting arithmetical structures on paths and cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag(d)-A)r = 0, where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag(d)-A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients C(2n-1,n-1), and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Scientific Reports / The tactile window to consciousness is characterized by frequency-specific integration and segregation of the primary somatosensory cortex

We recently proposed that besides levels of local cortical excitability, also distinct pre-stimulus network states (windows to consciousness) determine whether a near-threshold stimulus will be consciously perceived. In the present magnetoencephalography study, we scrutinised these pre-stimulus network states with a focus on the primary somatosensory cortex. For this purpose participants performed a simple near-threshold tactile detection task. Confirming previous studies, we found reduced alpha and beta power in the somatosensory region contralateral to stimulation prior to correct stimulus detection as compared to undetected stimuli, and stronger event-related responses following successful stimulus detection. As expected, using graph theoretical measures, we also observed modulated pre-stimulus network level integration. Specifically, the right primary somatosensory cortex contralateral to stimulation showed an increased integration in the theta band, and additionally, a decreased integration in the beta band. Overall, these results underline the importance of network states for enabling conscious perception. Moreover, they indicate that also a reduction of irrelevant functional connections contributes to the window to consciousness by tuning pre-stimulus pathways of information flow.Julia Natascha Frey, Philipp Ruhnau, Sabine Leske, Markus Siegel, Christoph Braun, Nathan Weis