THE SPECTRALITY DECISION PROBLEM

An efficient algorithm for deciding whether a given integer vector is the spectrum of some Boolean function is presented. The algorithm performs a step-by-step spectral decomposition of the input vector and checks at each step a set of necessary conditions for spectrality for the resulting vectors. The algorithm concludes that the input vector cannot lead to a valid Boolean function as soon as a vector not satisfying the conditions is found, which, as proved in the paper, for almost all cases happens after the first step of the decomposition.

The Spectrality of a Class of Fractal Measures on R^(n)

Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.

Spectrality of planar self-affine measures with two-element digit set

The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.

Spectrality of a class of self-affine measures with decomposable digit sets

The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.

Determination of liquid viscosity based on dual-frequency-bandparticle tracking

An optical-tweezers-based dual-frequency-band particle tracking system was designed and fabricated for liquid viscositydetection. On the basis of the liquid viscosity dependent model of the particle’s restricted Brownian motion with theFax´en correction taken into account, the liquid viscosity and optical trap stiffness were determined by fitting the theoreticalprediction with the measured power spectral densities of the particle’s displacement and velocity that were derived from thedual-frequency-band particle tracking data. When the SiO2 beads were employed as probe particles in the measurements ofdifferent kinds of liquids, the measurement results exhibit a good agreement with the reported results, as well as a detectionuncertainty better than 4.6%. This kind of noninvasive economical technique can be applied in diverse environments forboth in situ and ex situ viscosity detection of liquids.

一种用于大视场成像和偏振光谱探测的微型可重构超构光学系统

Wide-angle imaging and spectral detection play vital roles in tasks such as target tracking,object classification,and anti-camouflage.However,limited by their intrinsically different architectures,as determined by frequency dispersion requirements,their simultaneous implementation in a shared-aperture system is difficult.Here,we propose a novel concept to realize reconfigurable dual-mode detection based on electrical-control tunable metasurfaces.As a proof-of-concept demonstration,the simultaneous implementation of wide-angle imaging and polarization-spectral detection in a miniature sharedaperture meta-optical system is realized for the first time via the electrical control of cascaded catenary-like metasurfaces.The proposed system supports the imaging(spectral)resolution of approximately 27.8 line-pairs per millimeter(lp·mm^(-1);~80 nm)for an imaging(spectral)mode from 8 to 14 μm.This system also bears a large field of view of about 70°,enabling multi-target recognition in both modes.This work may promote the miniaturization of multifunctional optical systems,including spectrometers and polarization imagers,and illustrates the potential industrial applications of meta-optics in biomedicine,security,space exploration,and more.

从H1N1血凝素序列提取的沙门氏菌传递的COBRA-HA1抗原对甲型流感亚型产生广谱保护作用

A universal vaccine is in high demand to address the uncertainties of antigenic drift and the reduced effectiveness of current influenza vaccines.In this study,a strategy called computationally optimized broadly reactive antigen(COBRA)was used to generate a consensus sequence of the hemagglutinin globular head portion(HA1)of influenza virus samples collected from 1918 to 2021 to trace evolutionary changes and incorporate them into the designed constructs.Constructs carrying different HA1regions were delivered into eukaryotic cells by Salmonella-mediated bactofection using a Semliki Forest virus RNA-dependent RNApolymerase(RdRp)-based eukaryotic expression system,pJHL204.Recombinant protein expression was confirmed by Western blot and immunofluorescence assays.Mice immunized with the designed constructs produced a humoral response,with a significant increase in immunoglobulin G(IgG)levels,and a cell-mediated immune response,including a 1.5-fold increase in CD4^(+) and CD8^(+)T cells.Specifically,constructs #1 and #5 increased the production of interferon-γ(IFN-γ)producing CD4^(+)and CD8^(+)T cells,skewing the response toward the T helper type 1 cell(Th1)pathway.Additionally,interleukin-4(IL-4)-producing T cells were upregulated 4-fold.Protective efficacy was demonstrated,with up to 4-fold higher production of neutralizing antibodies and a hemagglutination inhibition titer>40 against the selected viral strains.The designed constructs conferred a broadly protective immune response,resulting in a notable reduction in viral titer and minimal inflammation in the lungs of mice challenged with the influenza A/PR8/34,A/Brisbane/59/2007,A/California/07/2009,KBPV VR-92,and NCCP 43021 strains.This discovery revolutionizes influenza vaccine design and delivery;Salmonella-mediated COBRA-HA1 is a highly effective in vivo antigen presentation strategy.This approach can effectively combat seasonal H1N1 influenza strains and potential pandemic outbreaks.

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

Experimental investigation of spectral evolution in flash radiation by hypervelocity impact on aluminum plates

In this study,a series of hypervelocity impact tests were carried out based on a two-stage light gas gun,and the sequence spectrum and radiation evolution data of the impact products under different impact conditions were obtained.The diameter of the projectile is 3-5 mm,the impact velocity is 3.13-6.58 km/s,and the chamber pressure is 0.56-990 Pa.The spectrum of ejected debris cloud in the 250-310 nm band were obtained using a transient spectral measurement system and a multi-channel radiometer measurement system.The test results reveal that the flash radiation intensity increases as a power function with the kinetic energy of the impact.Furthermore,the peak value of the line spectrum decreases as the chamber vacuum degree increases,while the radiation width gradually expands.The line spectrum in the spectral characterization curve corresponds to the ejected debris clouds splitting phase,which does not produce significant line spectrum during material fragmentation and is dominated by the continuum spectrum produced by blackbody radiation.There will appear one or three characteristic peaks in the flash radiation time curve,the first and second peaks correspond to the penetration phase and the third peak corresponds to the expansion phase of the ejected debris clouds on the time scale,the first and second peaks are more sensitive to the chamber vacuum degree,and when the pressure is higher than 99 Pa,the first and second characteristic peaks will disappear.The radiant heat attenuation of the flash under different impact conditions is significantly different,the attenuation exponent has a power function relationship with the impact velocity and the chamber vacuum degree,while the attenuation exponent has a linear relationship with the diameter of the projectile,the specific expression of the attenuation exponent is obtained by fitting.The findings from this research can serve as a valuable reference for remote diagnostic technologies based on flash radiation characteristics.

Comparison of a Spectral Bin and Two Multi-Moment Bulk Microphysics Schemes for Supercell Simulation:Investigation into Key Processes Responsible for Hydrometeor Distributions and Precipitation

There are more uncertainties with ice hydrometeor representations and related processes than liquid hydrometeors within microphysics parameterization(MP)schemes because of their complicated geometries and physical properties.Idealized supercell simulations are produced using the WRF model coupled with“full”Hebrew University spectral bin MP(HU-SBM),and NSSL and Thompson bulk MP(BMP)schemes.HU-SBM downdrafts are typically weaker than those of the NSSL and Thompson simulations,accompanied by less rain evaporation.HU-SBM produces more cloud ice(plates),graupel,and hail than the BMPs,yet precipitates less at the surface.The limiting mass bins(and subsequently,particle size)of rimed ice in HU-SBM and slower rimed ice fall speeds lead to smaller melting-level net rimed ice fluxes than those of the BMPs.Aggregation from plates in HU-SBM,together with snow–graupel collisions,leads to a greater snow contribution to rain than those of the BMPs.Replacing HU-SBM’s fall speeds using the formulations of the BMPs after aggregating the discrete bin values to mass mixing ratios and total number concentrations increases net rain and rimed ice fluxes.Still,they are smaller in magnitude than bulk rain,NSSL hail,and Thompson graupel net fluxes near the surface.Conversely,the melting-layer net rimed ice fluxes are reduced when the fall speeds for the NSSL and Thompson simulations are calculated using HU-SBM fall speed formulations after discretizing the bulk particle size distributions(PSDs)into spectral bins.The results highlight precipitation sensitivity to storm dynamics,fall speed,hydrometeor evolution governed by process rates,and MP PSD design.

Joint alignment and steering to manage interference

In wireless communication networks,mobile users in overlapping areas may experience severe interference,therefore,designing effective Interference Management(IM)methods is crucial to improving network performance.However,when managing multiple disturbances from the same source,it may not be feasible to use existing IM methods such as Interference Alignment(IA)and Interference Steering(IS)exclusively.It is because with IA,the aligned interference becomes indistinguishable at its desired Receiver(Rx)under the cost constraint of Degrees-of-Freedom(DoF),while with IS,more transmit power will be consumed in the direct and repeated application of IS to each interference.To remedy these deficiencies,Interference Alignment Steering(IAS)is proposed by incorporating IA and IS and exploiting their advantages in IM.With IAS,the interfering Transmitter(Tx)first aligns one interference incurred by the transmission of one data stream to a one-dimensional subspace orthogonal to the desired transmission at the interfered Rx,and then the remaining interferences are treated as a whole and steered to the same subspace as the aligned interference.Moreover,two improved versions of IAS,i.e.,IAS with Full Adjustment at the Interfering Tx(IAS-FAIT)and Interference Steering and Alignment(ISA),are presented.The former considers the influence of IA on the interfering user-pair's performance.The orthogonality between the desired signals at the interfered Rx can be maintained by adjusting the spatial characteristics of all interferences and the aligned interference components,thus ensuring the Spectral Efficiency(SE)of the interfering communication pairs.Under ISA,the power cost for IS at the interfered Tx is minimized,hence improving SE performance of the interfered communication-pairs.Since the proposed methods are realized at the interfering and interfered Txs cooperatively,the expenses of IM are shared by both communication-pairs.Our in-depth simulation results show that joint use of IA and IS can effectively manage multiple disturbances from the same source and improve the system's SE.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Estimating wheat spike-leaf composite indicator(SLI)dynamics by coupling spectral indices and machine learning

The contribution of spike photosynthesis to grain yield(GY)has been overlooked in the accurate spectral prediction of yield.Thus,it’s essential to construct and estimate a yield-related phenotypic trait considering spike photosynthesis.Based on field and spectral reflectance data from 19 wheat cultivars under two nitrogen fertilization conditions in two years,our objectives were to(i)construct a yield-related phenotypic trait(spike–leaf composite indicator,SLI)accounting for the contribution of the spike to photosynthesis,(ii)develop a novel spectral index(enhanced triangle vegetation index,ETVI3)sensitive to SLI,and(iii)establish and evaluate SLI estimation models by integrating spectral indices and machine learning algorithms.The results showed that SLI was sensitive to nitrogen fertilizer and wheat cultivar variation as well as a better predictor of yield than the leaf area index.ETVI3 maintained a strong correlation with SLI throughout the growth stage,whereas the correlations of other spectral indices with SLI were poor after spike emergence.Integrating spectral indices and machine learning algorithms improved the estimation accuracy of SLI,with the most accurate estimates of SLI showing coefficient of determination,root mean square error(RMSE),and relative RMSE values of 0.71,0.047,and 26.93%,respectively.These results provide new insights into the role of fruiting organs for the accurate spectral prediction of GY.This high-throughput SLI estimation approach can be applied for wheat yield prediction at whole growth stages and may be assisted with agronomical practices and variety selection.

Decoupling of temporal/spatial broadening effects in Doppler wind LiDAR by 2D spectral analysis

Pulse echo accumulation is commonly employed in coherent Doppler wind LiDAR(light detection and ranging)under the assumption of steady wind.Here,the measured spectral data are analyzed in the time dimension and frequency dimension to cope with the temporal wind shear and achieve the optimal accumulation time.A hardware-efficient algorithm combining the interpolation and cross-correlation is used to enhance the wind retrieval accuracy by reducing the frequency sampling interval and then reduce the spectral width calculation error.Moreover,the temporal broadening effect and spatial broadening effect are decoupled according to the strategy we developed.

Power Allocation for SE Maximization in Uplink Massive MIMO System Under Minimum Rate Constraint

In this paper,we optimize the spectrum efficiency(SE)of uplink massive multiple-input multiple-output(MIMO)system with imperfect channel state information(CSI)over Rayleigh fading channel.The SE optimization problem is formulated under the constraints of maximum power and minimum rate of each user.Then,we develop a near-optimal power allocation(PA)scheme by using the successive convex approximation(SCA)method,Lagrange multiplier method,and block coordinate descent(BCD)method,and it can obtain almost the same SE as the benchmark scheme with lower complexity.Since this scheme needs three-layer iteration,a suboptimal PA scheme is developed to further reduce the complexity,where the characteristic of massive MIMO(i.e.,numerous receive antennas)is utilized for convex reformulation,and the rate constraint is converted to linear constraints.This suboptimal scheme only needs single-layer iteration,thus has lower complexity than the near-optimal scheme.Finally,we joint design the pilot power and data power to further improve the performance,and propose an two-stage algorithm to obtain joint PA.Simulation results verify the effectiveness of the proposed schemes,and superior SE performance is achieved.

A research on the effect of plasma spectrum collection device on LIBS spectral intensity

Only a small amount of spectral information is collected because the collection solid angle of the optical fiber probe and lens is very limited when collecting spectral information.To overcome this limitation,this study presents a novel method for acquiring plasma spectral information from various spatial directions.A parabolic-shaped plasma spectral collection device(PSCD)is employed to effectively collect more spectral information into the spectrometer,thereby enhancing the overall spectral intensity.The research objects in this study were soil samples containing different concentrations of heavy metals Pb,Cr,and Cd.The results indicate that the PSCD significantly enhances the spectral signal,with an enhancement rate of up to 45%.Moreover,the signal-to-noise ratio also increases by as much as 36%.Simultaneously,when compared to the absence of a device,it is found that there is no significant variation in plasma temperature when the PSCD is utilized.This observation eliminates the impact of the spatial effect caused by the PSCD on the spectral intensity.Consequently,a concentrationspectral intensity relationship curve is established under the PSCD.The results revealed that the linear fitting R^(2)for Pb,Cr,and Cd increased by 0.011,0.001,and 0.054,respectively.Additionally,the limit of detection(LOD)decreased by 0.361 ppm,0.901 ppm,and 0.602 ppm,respectively.These findings indicate that the spectral enhancement rate elevates with the increase in heavy metal concentration.Hence,the PSCD can effectively enhance the spectral intensity and reduce the detection limit of heavy metals in soil.

Prediction of impurity spectrum function by deep learning algorithm

By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.

Response of InSight resonance modes to environmental factors on Mars

The InSight(Interior Exploration using Seismic Investigations,Geodesy,and Heat Transport)mission has recorded continuous ambient noise signals with many spectral peaks since its landing in 2018.The majority of these peaks are modes produced by instrumental vibrations and are associated with environmental factors,such as temperature and wind energy fluctuations.Understanding how these modes react under various conditions is crucial because it aids in identifying their origins.In this study,we analyzed the three-component spectra of InSight recordings from sols 184–738 and obtained the horizontal-to-vertical spectral ratio(HVSR,also known as H/V)curves for different time intervals.The primary modes,such as those at 3.3 and 4.1 Hz,exhibited different behaviors,suggesting diverse origins.Some modes were sensitive to low temperature and some were sensitive to high temperature.Additionally,we investigated the influence of wind and temperature on the H/V curve.The peak frequency was mainly affected by temperature,whereas the H/V value was not associated with the temperature or wind only.Characterizing these modes and elucidating their origins are significant for processing signals from InSight and can provide valuable guidance for designing future planetary seismometers.

Single-station microtremor surveys for site characterization:A case study in Erzurum city,eastern Turkey

The single-station microtremor method is one of the fastest,most reliable,and cheapest methods used to identify dynamic soil properties.This study utilizes 49 single-station microtremor measurements to identify the dynamic soil properties of the Hilalkent quarter of the Yakutiye district in Erzurum.Soil dominant frequency and the amplification factor were calculated by using the Nakamura horizontal/vertical spectral ratio(H/V)method.While the soil dominant frequency values varied between 0.4 Hz and 10 Hz,the soil amplification factor changed between 1 and 10.Higher H/V values were acquired with lower frequency values.The vulnerability index(K_(g))and shear strain parameters that are utilized to estimate the damage that may be caused by an earthquake were mapped.Especially in the west side of the study area,higher K_(g) values were observed.The shear strain map was created with 0.25 g,0.50 g and 0.75 g bedrock accelerations,and soil types that lost elasticity during an earthquake were identified.The average shear wave velocity for the first 30 m(V_(s30))was calculated.Finally,it was observed that the western part of the study area,which resulted in a higher period and higher H/V,higher K_(g) and lower V_(s30) values,presents a higher risk of damage during an earthquake.