Combinatorial proofs on the joint distribution of descents and inverse descents

Let $A_{n,i,j}$ be the number of permutations on $[n]$ with $i-1$ descents and $j-1$ inverse descents. Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial and arithmetic properties of $A_{n,i,j}$, which contain a recurrence of $A_{n,i,j}$. Using the idea of balls in boxes, Petersen gave a combinatorial interpretation for the generating function of $A_{n,i,j}$, and obtained the same recurrence of $A_{n,i,j}$ from its generating function. Subsequently, Petersen asked whether there is a visual way to understand this recurrence. In this paper, after observing the internal structures of permutation grids, we present a combinatorial proof of the recurrence of $A_{n,i,j}$. Let $I_{n,k}$ and $J_{n,k}$ count the number of involutions and fixed-point free involutions on $[n]$ with $k$ descents, respectively. With the help of generating functions, Guo and Zeng derived two recurrences of $I_{n,k}$ and $J_{2n,k}$ that play an essential role in the proof of their unimodal properties. Unexpectedly, the constructive approach to the recurrence of $A_{n,i,j}$ is found to fuel the combinatorial interpretations of these two recurrences of $I_{n,k}$ and $J_{2n,k}$

The Critical Role of Point Defects In Improving the Specific Capacitance of δ-MnO2 Nanosheets

3D porous nanostructures built from 2D δ-MnO2 nanosheets are an environmentally friendly and industrially scalable class of supercapacitor electrode material. While both the electrochemistry and defects of this material have been studied, the role of defects in improving the energy storage density of these materials has not been addressed. In this work, δ-MnO2 nanosheet assemblies with 150 m2 g−1 specific surface area are prepared by exfoliation of crystalline KxMnO2 and subsequent reassembly. Equilibration at different pH introduces intentional Mn vacancies into the nanosheets, increasing pseudocapacitance to over 300 F g−1, reducing charge transfer resistance as low as 3 Ω, and providing a 50% improvement in cycling stability. X-ray absorption spectroscopy and high-energy X-ray scattering demonstrate a correlation between the defect content and the improved electrochemical performance. The results show that Mn vacancies provide ion intercalation sites which concurrently improve specific capacitance, charge transfer resistance and cycling stability

Publisher Correction: Copper adparticle enabled selective electrosynthesis of n-propanol.

An amendment to this paper has been published and can be accessed via a link at the top of the paper

A new version of the HBSC Family Affluence Scale - FAS III: Scottish qualitative findings from the International FAS Development Study

A critical review of the Family Affluence Scale (FAS) concluded that FAS II was no longer discriminatory within very rich or very poor countries, where a very high or a very low proportion of children were categorised as high FAS or low FAS respectively (Currie et al. 2008). The review concluded that a new version of FAS - FAS III - should be developed to take into account current trends in family consumption patterns across the European region, the US and Canada. In 2012, the FAS Development and Validation Study was conducted in eight countries - Denmark, Greenland, Italy, Norway, Poland, Romania, Slovakia and Scotland. This paper describes the Scottish qualitative findings from this study. The Scottish qualitative fieldwork comprising cognitive interviews and focus groups sampled from 11, 13 and 15 year-old participants from 18 of the most- and least- economically deprived schools. These qualitative results were used to inform the final FAS III recommendations.Publisher PDFPeer reviewe

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Phosphor-converted white light-emitting diodes for indoor illumination need to be warm-white (i.e., correlated color temperature \u3c4000 \u3eK) with good color rendition (i.e., color rendering index \u3e80). However, no single-phosphor, single-emitting-center-converted white light-emitting diodes can simultaneously satisfy the color temperature and rendition requirements due to the lack of sufficient red spectral component in the phosphors’ emission spectrum. Here, we report a new yellow Ba0.93Eu0.07Al2O4phosphor that has a new orthorhombic lattice structure and exhibits a broad yellow photoluminescence band with sufficient red spectral component. Warm-white emissions with correlated color temperature 80 were readily achieved when combining the Ba0.93Eu0.07Al2O4 phosphor with a blue light-emitting diode (440–470 nm). This study demonstrates that warm-white light-emitting diodes with high color rendition (i.e., color rendering index \u3e80) can be achieved based on single-phosphor, single-emitting-center conversion

Why do authoritarian regimes provide public goods? Policy communities, external shocks and ideas in China’s rural social policy making

Recent research on authoritarian regimes argues that they provide public goods in order to prevent rebellion. This essay shows that the ‘threat of rebellion’ alone cannot explain Chinese party-state policies to extend public goods to rural residents in the first decade of the twenty-first century. Drawing on theories of policy making, it argues that China’s one-party regime extended public goods to the rural population under the influence of ideas and policy options generated by policy communities of officials, researchers, international organisations and other actors. The party-state centre adopted and implemented these ideas and policy options when they provided solutions to external shocks and supported economic development goals. Explanations of policies and their outcomes in authoritarian political systems need to include not only ‘dictators’ but also other actors, and the ideas they generate

Fungi: Friend or Foe? A Mycobiome Evaluation in Children with Autism and Gastrointestinal Symptoms

Gastrointestinal (GI) symptoms often affect children with autism spectrum disorders (ASD) and GI symptoms have been associated with an abnormal fecal microbiome. There is limited evidence of Candida species being more prevalent in children with ASD. We enrolled 20 children with ASD and GI symptoms (ASD + GI), 10 children with ASD but no GI symptoms (ASD - GI), and 20 from typically developing (TD) children in this pilot study. Fecal mycobiome taxa were analyzed by Internal Transcribed Spacer sequencing. GI symptoms (GI Severity Index [GSI]), behavioral symptoms (Social Responsiveness Scale -2 [SRS-2]), inflammation and fungal immunity (fecal calprotectin and serum dectin-1 [ELISA]) were evaluated. We observed no changes in the abundance of total fungal species (alpha diversity) between groups. Samples with identifiable Candida spp. were present in 4 of 19 (21%) ASD + GI, in 5 of 9 (56%) ASD - GI, and in 4 of 16 (25%) TD children (overall P = 0.18). The presence of Candida spp. did not correlate with behavioral or GI symptoms (P = 0.38, P = 0.5, respectively). Fecal calprotectin was normal in all but one child. Finally, there was no significance in serum dectin-1 levels, suggesting no increased fungal immunity in children with ASD. Our data suggest that fungi are present at normal levels in the stool of children with ASD and are not associated with gut inflammation