Inertia of partial transpose of positive semidefinite matrices

We show that the partial transpose of $9\times 9$ positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in "LINEAR AND MULTILINEAR ALGEBRA, Changchun Feng et al, 2022". We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of $12\times 12$ positive semidefinite matrices.Comment: 20 pages, comments are welcom

Local dynamics and thermal activation in the transverse-field Ising chain

There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the NMR $1/T_2^{\prime}$ relaxation rate to be half of that for the $1/T_1$ relaxation rate. Our findings reveal a new surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.Comment: 17 pages, 5 figure

Active beam steering enabled by photonic crystal surface emitting laser

Emitting light towards on-demand directions is important for various optoelectronic applications, such as optical communication, displaying, and ranging. However, almost all existing directional emitters are assemblies of passive optical antennae and external light sources, which are usually bulky, fragile, and with unendurable loss of light power. Here we theoretically propose and experimentally demonstrate a new conceptual design of directional emitter, by using a single surface-emitting laser source itself to achieve dynamically controlled beam steering. The laser is built on photonic crystals that operates near the band edges in the continuum. By shrinking laser sizes into tens-of-wavelength, the optical modes quantize in three-dimensional momentum space, and each of them directionally radiates towards the far-field. Further utilizing the luminescence spectrum shifting effect under current injection, we consecutively select a sequence of modes into lasing action and show the laser maintaining in single mode operation with linewidths at a minimum of $1.8$ MHz and emitting power of $\sim$ ten milliwatts, and we demonstrate fast beam steering across a range of $3.2^\circ \times 4^\circ$ in a time scale of $500$ nanoseconds. Our work proposes a novel method for on-chip active beam steering, which could pave the way for the development of automotive, industrial, and robotic applications.Comment: 23 pages, 5 figure

Super-resolution microscopy and its applications in neuroscience

Optical microscopy promises researchers to see most tiny substances directly. However, the resolution of conventional microscopy is restricted by the diffraction limit. This makes it a challenge to observe subcellular processes happened in nanoscale. The development of super-resolution microscopy provides a solution to this challenge. Here, we briefly review several commonly used super-resolution techniques, explicating their basic principles and applications in biological science, especially in neuroscience. In addition, characteristics and limitations of each technique are compared to provide a guidance for biologists to choose the most suitable tool

Experimental study on microwave propagation characteristics of different coal-gangue mixtures

The problem of coal-gangue identification is one of the technical problems that have not been effectively solved for a long time in the coal industry. By analyzing the characteristics and limitations of existing coal-gangue identification methods, the feasibility of coal-gangue identification based on microwave detection technology is discussed. Firstly, the electromagnetic parameters of different coals and gangues are measured and analyzed to provide a basis for the subsequent analysis of sample test results. Then, in order to explore the influence of coal gangue size parameters on microwave propagation, the propagation law of coal gangue dielectric samples with different thickness and cross-sectional area on different frequency bands is studied. Because the coal-gangue mixture is a multi-scale medium composed of coal, gangue and air, the volume and shape are different, and the spatial distribution and mixing form are complex and changeable. The scattering effect in the microwave irradiation area is very complex, resulting in obvious differences in the transmission characteristics of electromagnetic waves in different coal-gangue mixtures. Finally, in order to explore the variation law of microwave propagation characteristics in different coal-gangue media, some microwave detection experiments of coal-gangue mixture under different microwave frequency bands, different particle sizes and different gangue contents are carried out. The results show that: the electromagnetic parameters, thickness and sectional area have obvious influence on the propagation law of microwave in the media. Different particle size and gangue rate have certain influence on microwave propagation in coal-gangue mixture. When microwave with frequency greater than 4 GHz irradiates the coal gangue mixture, the increase of particle size will gradually increase the intensity values of S11 and S21 and the amplitude of O21 signal. When the electromagnetic parameters of coal and gangue in the mixed medium are quite different, after the frequency is greater than 3.5 GHz, the increase of particle size reduces the S21 intensity from −35.3 dB to −38.2 dB, and the O21 signal amplitude from 1.6 mV to 1.26 mV, with certain time delay characteristics. Through the experimental analysis, the differences of the transmitted wave signal intensity value, the time-domain transmitted wave signal amplitude and the transmitted wave signal delay at the sensitive frequency points can be mastered, so as to provide a new idea and method for accurate identification of coal and gangue in top coal caving face

LyricWhiz: Robust Multilingual Zero-shot Lyrics Transcription by Whispering to ChatGPT

We introduce LyricWhiz, a robust, multilingual, and zero-shot automatic lyrics transcription method achieving state-of-the-art performance on various lyrics transcription datasets, even in challenging genres such as rock and metal. Our novel, training-free approach utilizes Whisper, a weakly supervised robust speech recognition model, and GPT-4, today's most performant chat-based large language model. In the proposed method, Whisper functions as the "ear" by transcribing the audio, while GPT-4 serves as the "brain," acting as an annotator with a strong performance for contextualized output selection and correction. Our experiments show that LyricWhiz significantly reduces Word Error Rate compared to existing methods in English and can effectively transcribe lyrics across multiple languages. Furthermore, we use LyricWhiz to create the first publicly available, large-scale, multilingual lyrics transcription dataset with a CC-BY-NC-SA copyright license, based on MTG-Jamendo, and offer a human-annotated subset for noise level estimation and evaluation. We anticipate that our proposed method and dataset will advance the development of multilingual lyrics transcription, a challenging and emerging task.Comment: 9 pages, 2 figures, 5 tables, accepted by ISMIR 202

Hydrochemical Evolution Mechanisms of Shallow Groundwater and Its Quality Assessment in the Estuarine Coastal Zone: A Case Study of Qidong, China

Identification of geochemical characters and the influence of river and seawater on coastal areas are of significant impact on water resources management in coastal areas globally. Thus, it requires careful investigation of the hydrochemical evolution mechanisms and assessment of the quality of shallow groundwater. The study specifically focused on the estuarine coastal zone of Qidong, China, a city located on the Yangtze estuary. Thirty shallow groundwater samples and five surface water samples were collected during a field investigation, and 25 water quality indexes were analyzed. Methods including mathematical statistics, Gibbs figure, Piper diagram, and ionic rations were used to analyze the hydrochemical characteristics and evolution mechanisms. The spatial distribution of key parameters was assessed using a GIS-based spatial gridding technique. Results showed that the shallow groundwater in this estuarine coastal zone is weakly alkaline. The major hydrochemical parameters, including total dissolved solids (TDS), Na+ and Cl−, Mg2+, and SO42−, displayed similar spatial distributions; the distributions of Ca2+ and Mg2+ were irregular; the distributions of SO42− and HCO3− shared a similar trend, increasing gradually from the southern to northern regions of the study zone; and the values of NO3− and NH4+ were generally low in the study area. The hydrochemistry of the groundwater consists of HCO3-CaMg type and HCO3-Na, with HCO3·Cl-Na type and Cl-Na being the dominant constituents toward the coastal strip. The coastal aquifers are subjected to the ongoing influence of seawater intrusion, ion exchange processes, freshwater infiltration, and mineral (carbonate and silicate) dissolution, which impact groundwater evolution. Most of the groundwater samples are unsuitable for drinking purposes, but more than 90% of samples have irrigation suitability, based on the WHO standards and the classifications of sodium absorption ratio (SAR), soluble-sodium percentage (SSP)

Experimental Investigations and Numerical Simulations of the Vibrational Performance of Wood Truss Joist Floors with Strongbacks

This paper provides an experimental study and computer modeling analysis of vibration performance of full-scale wood truss joist floors, related to the static deflection and vibration mode/frequency and single-person-induced vibration. The vibration behavior of full-scale truss joist floors was investigated and the influences of the strongbacks on the vibration behavior were assessed. The results showed that the simulated predictions agreed well with the measured results. Strongbacks do not significantly affect the fundamental frequency of the truss joist floors but influence the second and third modal frequencies. The use of strongback rows at mid-span effectively decreased the maximum deformation of point loading at floor center. The effect of adding strongbacks at one-third of each span on decreasing maximum deformation at the floor center was minimal. The case of walking parallel to the joist produced higher acceleration response at the floor center than that of walking perpendicular to the joist. The closer the placements of strongbacks were to the mid-span, the more significant reduction of the vibration at floor center was. Two strongback rows at mid-span performed the best effect on reduction of vibration response at floor center. However, the use of strongbacks had limits of reduction peak acceleration of the sheathing between the joists. The study provides a valuable guide for future vibration serviceability study and design optimization of wood truss joist floors

Accelerometer-derived physical activity and mortality in individuals with type 2 diabetes

Abstract Physical activity (PA) has been shown to reduce diabetes mortality, but largely based on imprecise self-reported data, which may hinder the development of related recommendations. Here, we perform a prospective cohort study of 19,624 individuals with type 2 diabetes (T2D) from the UK Biobank with a median follow-up of 6.9 years. Duration and intensity of PA are measured by wrist-worn accelerometers over a 7-day period. We observe L-shaped associations of longer duration of PA, regardless of PA intensity, with risks of all-cause and cancer mortality, as well as a negatively linear association with cardiovascular disease mortality. 12.7%, 15.8%, and 22.3% of deaths are attributable to the lowest level of light-intensity, moderate-intensity PA, and vigorous-intensity PA, respectively. Collectively, our findings provide insights for clinical guidelines that should highlight the potential value of adherence to greater intensity and duration of PA for patients with T2D

Two-photon focal modulation microscopy for high-resolution imaging in deep tissue

Two-photon microscopy (2PM) is one of the most widely used tools for in vivo deep tissue imaging. However, the spatial resolution and penetration depth are still limited due to the strong scattering background. Here we demonstrate a two-photon focal modulation microscopy. By utilizing the modulation and demodulation techniques, background rejection capability is enhanced, thus spatial resolution and imaging penetration depth are improved. Compared with 2PM, the transverse resolution is increased by 70%, while the axial resolution is increased to 2-fold. Furthermore, when applied in conventional 2PM mode, it can achieve inertial-free scanning in either transverse or axial direction with in principle unlimited scanning speed. Finally, we applied 2PFMM in thick scattering samples to further examine the imaging performance. The results show that the signal-to-background ratio of 2PFMM can be improved up to five times of 2PM at the depth of 500 μm. Fluorescent imaging in the mouse brain tissue. 3D Thy1-GFP hippocampal neurons imaged by (A) 2PM compared with (B) 2PFMM; (C-H) xy maximum-intensity projection imaged by 2PM compared with 2PFMM. Scale bar 50 μm