Search for: All records

Abstract We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a$$\gamma$$fraction of the vertices classified correctly, where$$\gamma \in (0.5,1)$$depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017)Ann. Stat.45(1) 289–315.) for non-uniform HSBMs. Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest. 

Abstract Understanding psychology is an important task in modern society which helps predict human behavior and provide feedback accordingly. Monitoring of weak psychological and emotional changes requires bioelectronic devices to be stretchable and compliant for unobtrusive and high‐fidelity signal acquisition. Thin conductive polymer film is regarded as an ideal interface; however, it is very challenging to simultaneously balance mechanical robustness and opto‐electrical property. Here, a 40 nm‐thick film based on photolithographic double‐network conductive polymer mediated by graphene layer is reported, which concurrently enables stretchability, conductivity, and conformability. Photolithographic polymer and graphene endow the film photopatternability, enhance stress dissipation capability, as well as improve opto‐electrical conductivity (4458 S cm⁻¹@>90% transparency) through molecular rearrangement by π–π interaction, electrostatic interaction, and hydrogen bonding. The film is further applied onto corrugated facial skin, the subtle electromyogram is monitored, and machine learning algorithm is performed to understand complex emotions, indicating the outstanding ability for stretchable and compliant bioelectronics. 

Recent radiation-thermochemical-magnetohydrodynamic simulations resolved formation of quasar accretion disks from cosmological scales down to ~300 gravitational radii $R_g$, arguing they were ‘hyper-magnetized’ (plasma $\beta \ll 1$supported by toroidal magnetic fields) and distinct from traditional $\alpha$-disks. We extend these, refining to $\approx 3R_g$around a BH with multi-channel radiation and thermochemistry, and exploring a factor of 1000 range of accretion rates ( $\dot{m}\sim 0.01-20$). At smaller scales, we see the disks maintain steady accretion, thermalize and self-ionize, and radiation pressure grows in importance, but large deviations from local thermodynamic equilibrium and single-phase equations of state are always present. Trans-Alfvenic and highly-supersonic turbulence persists in all cases, and leads to efficient vertical mixing, so radiation pressure saturates at levels comparable to fluctuating magnetic and turbulent pressures even for $\dot{m}\gg 1$. The disks also become radiatively inefficient in the inner regions at high $\dot{m}$. The midplane magnetic field remains primarily toroidal at large radii, but at super-Eddington $\dot{m}$we see occasional transitions to a poloidal-field dominated state associated with outflows and flares. Large-scale magnetocentrifugal and continuum radiation-pressure-driven outflows are weak at $\dot{m}<1$, but can be strong at $\dot{m}\gtrsim 1$. In all cases there is a scattering photosphere above the disk extending to $\gtrsim 1000R_g$at large $\dot{m}$, and the disk is thick and flared owing to magnetic support (with $H/R$nearly independent of $\dot{m}$), so the outer disk is strongly illuminated by the inner disk and most of the inner disk continuum scatters or is reprocessed at larger scales, giving apparent emission region sizes as large as . 

Beyond lithium-ion technologies, lithium−sulfur batteries stand out because of their multielectron redox reactions and high theoretical specific energy (2500 Wh kg−1). However, the intrinsic irreversible transformation of soluble lithium polysulfides to solid short-chain sulfur species (Li2S2 and Li2S) and the associated large volume change of electrode materials significantly impair the long-term stability of the battery. Here we present a liquid sulfur electrode consisting of lithium thiophosphate complexes dissolved in organic solvents that enable the bonding and storage of discharge reaction products without precipitation. Insights garnered from coupled spectroscopic and density functional theory studies guide the complex molecular design, complexation mechanism, and associated electrochemical reaction mechanism. With the novel complexes as cathode materials, high specific capacity (1425 mAh g−1 at 0.2 C) and excellent cycling stability (80% retention after 400 cycles at 0.5 C) are achieved at room temperature. Moreover, the highly reversible all-liquid electrochemical conversion enables excellent low temperature battery operability (>400 mAh g−1 at −40 °C and >200 mAh g−1 at −60 °C). This work opens new avenues to design and tailor the sulfur electrode for enhanced electrochemical performance across a wide operating temperature range.