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Abstract The quantum conductance and its classical wave analogue, the transmittance, are given by the sum of the eigenvalues of the transmission matrix. However, neither measurements nor theoretical analysis of the transmission eigenchannels have been carried out to explain the dips in conductance found in simulations as new channels are introduced. Here, we measure the microwave transmission matrices of random waveguides and find the spectra of all transmission eigenvalues, even at dips in the lowest transmission eigenchannel that are orders of magnitude below the noise in the transmission matrix. Transmission vanishes both at topological transmission zeros, where the energy density at the sample output vanishes, and at crossovers to new channels, where the longitudinal velocity vanishes. Zeros of transmission pull down all the transmission eigenvalues and thereby produce dips in the transmittance. These dips and the ability to probe the characteristics of even the lowest transmission eigenchannel are due to correlation among the eigenvalues. The precise tracking of dips in the conductance by peaks in the density of states points to a further correlation between zeros and poles of the transmission matrix. The conductance approaches Ohm’s law as the sample width increases in accord with the correspondence principle. 

Abstract The diffusion model is used to calculate both the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered samples, such as a layer of paint or a tissue sample, the flux transmitted through the sample may be dramatically enhanced or suppressed relative to predictions of diffusion theory when the sample is excited by a waveform corresponding to a transmission eigenchannel. Even so, it is widely assumed that the velocity of waves is irretrievably randomized in scattering media. Here we demonstrate in microwave measurements and numerical simulations that the statistics of velocity of different transmission eigenchannels are distinct and remains so on all length scales and are identical on the incident and output surfaces. The interplay between eigenchannel velocities and transmission eigenvalues determines the energy density within the medium, the diffusion coefficient, and the dynamics of propagation. The diffusion coefficient and all scattering parameters, including the scattering mean free path, oscillate with the width of the sample as the number and shape of the propagating channels in the medium change. 

Abstract BackgroundAnthropogenic activities have increased the inputs of atmospheric reactive nitrogen (N) into terrestrial ecosystems, affecting soil carbon stability and microbial communities. Previous studies have primarily examined the effects of nitrogen deposition on microbial taxonomy, enzymatic activities, and functional processes. Here, we examined various functional traits of soil microbial communities and how these traits are interrelated in a Mediterranean-type grassland administrated with 14 years of 7 g m⁻²year⁻¹of N amendment, based on estimated atmospheric N deposition in areas within California, USA, by the end of the twenty-first century. ResultsSoil microbial communities were significantly altered by N deposition. Consistent with higher aboveground plant biomass and litter, fast-growing bacteria, assessed by abundance-weighted average rRNA operon copy number, were favored in N deposited soils. The relative abundances of genes associated with labile carbon (C) degradation (e.g.,amyAandcda) were also increased. In contrast, the relative abundances of functional genes associated with the degradation of more recalcitrant C (e.g.,mannanaseandchitinase) were either unchanged or decreased. Compared with the ambient control, N deposition significantly reduced network complexity, such as average degree and connectedness. The network for N deposited samples contained only genes associated with C degradation, suggesting that C degradation genes became more intensely connected under N deposition. ConclusionsWe propose a conceptual model to summarize the mechanisms of how changes in above- and belowground ecosystems by long-term N deposition collectively lead to more soil C accumulation. 

Networks are vital tools for understanding and modeling interactions in complex systems in science and engineering, and direct and indirect interactions are pervasive in all types of networks. However, quantitatively disentangling direct and indirect relationships in networks remains a formidable task. Here, we present a framework, called iDIRECT (Inference of Direct and Indirect Relationships with Effective Copula-based Transitivity), for quantitatively inferring direct dependencies in association networks. Using copula-based transitivity, iDIRECT eliminates/ameliorates several challenging mathematical problems, including ill-conditioning, self-looping, and interaction strength overflow. With simulation data as benchmark examples, iDIRECT showed high prediction accuracies. Application of iDIRECT to reconstruct gene regulatory networks in Escherichia coli also revealed considerably higher prediction power than the best-performing approaches in the DREAM5 (Dialogue on Reverse Engineering Assessment and Methods project, #5) Network Inference Challenge. In addition, applying iDIRECT to highly diverse grassland soil microbial communities in response to climate warming showed that the iDIRECT-processed networks were significantly different from the original networks, with considerably fewer nodes, links, and connectivity, but higher relative modularity. Further analysis revealed that the iDIRECT-processed network was more complex under warming than the control and more robust to both random and target species removal ( P < 0.001). As a general approach, iDIRECT has great advantages for network inference, and it should be widely applicable to infer direct relationships in association networks across diverse disciplines in science and engineering. 

ABSTRACT Tundra ecosystems are typically carbon (C) rich but nitrogen (N) limited. Since biological N 2 fixation is the major source of biologically available N, the soil N 2 -fixing (i.e., diazotrophic) community serves as an essential N supplier to the tundra ecosystem. Recent climate warming has induced deeper permafrost thaw and adversely affected C sequestration, which is modulated by N availability. Therefore, it is crucial to examine the responses of diazotrophic communities to warming across the depths of tundra soils. Herein, we carried out one of the deepest sequencing efforts of nitrogenase gene ( nifH ) to investigate how 5 years of experimental winter warming affects Alaskan soil diazotrophic community composition and abundance spanning both the organic and mineral layers. Although soil depth had a stronger influence on diazotrophic community composition than warming, warming significantly ( P <  0.05) enhanced diazotrophic abundance by 86.3% and aboveground plant biomass by 25.2%. Diazotrophic composition in the middle and lower organic layers, detected by nifH sequencing and a microarray-based tool (GeoChip), was markedly altered, with an increase of α-diversity. Changes in diazotrophic abundance and composition significantly correlated with soil moisture, soil thaw duration, and plant biomass, as shown by structural equation modeling analyses. Therefore, more abundant diazotrophic communities induced by warming may potentially serve as an important mechanism for supplementing biologically available N in this tundra ecosystem. IMPORTANCE With the likelihood that changes in global climate will adversely affect the soil C reservoir in the northern circumpolar permafrost zone, an understanding of the potential role of diazotrophic communities in enhancing biological N 2 fixation, which constrains both plant production and microbial decomposition in tundra soils, is important in elucidating the responses of soil microbial communities to global climate change. A recent study showed that the composition of the diazotrophic community in a tundra soil exhibited no change under a short-term (1.5-year) winter warming experiment. However, it remains crucial to examine whether the lack of diazotrophic community responses to warming is persistent over a longer time period as a possibly important mechanism in stabilizing tundra soil C. Through a detailed characterization of the effects of winter warming on diazotrophic communities, we showed that a long-term (5-year) winter warming substantially enhanced diazotrophic abundance and altered community composition, though soil depth had a stronger influence on diazotrophic community composition than warming. These changes were best explained by changes in soil moisture, soil thaw duration, and plant biomass. These results provide crucial insights into the potential factors that may impact future C and N availability in tundra regions.