Spectral Sum Research Articles

Graph theoretical descriptors differentiate d-Mannose isomers in the principal component proposed feature space: A computational approach

The intricate nature of carbohydrates, particularly monosaccharides, stems from the existence of several chiral centers within their tertiary structures. Predicting and characterizing the molecular geometries and electrostatic landscapes of these substances is difficult due to their complex electrical properties. Moreover, these structures can display a substantial degree of conformational flexibility due to the presence of many rotatable bonds. Moreover, identifying and distinguishing between D and L enantiomers of monosaccharides presents a significant analytical obstacle since there is a need for empirically measurable properties that can distinguish them. This work uses Principal Component Analysis (PCA) to explore the chemical information included in 3D descriptors in order to comprehend the conformational space of d-Mannose stereoisomers. The isomers may be discriminated by utilizing 3D matrix-based indices, geometrical descriptors, and RDF descriptors. The isomers can be distinguished by descriptors, such as the Harary-like index from the reciprocal squared geometrical matrix (H_RG), Harary-like index from Coulomb matrix (H_Coulomb), Wiener-like index from Coulomb matrix (Wi_Coulomb), Wiener-like index from geometrical matrix (Wi_G), Graph energy from Coulomb matrix (SpAbs_Coulomb), Spectral absolute deviation from Coulomb matrix (SpAD_Coulomb), and Spectral positive sum from Coulomb matrix (SpPos_Coulomb). Among these descriptors, the first two, H_RG and H_Coulomb, perform the best in differentiation among the 3D-Matrix-Based Descriptors (3D-MBD) class. The results obtained from this study provide a significant chemical insight into the structural characteristics of the compounds inside the graph theoretical framework. These findings are likely to serve as the basis for developing new methods for analytical experiments.

Some remarks on compositeness of * *Supported in part by the National Nature Science Foundations of China (12335002, 12375078, 11975028). H.Q. Zheng and Z. Xiao are also Supported by "the Fundamental Research Funds for the Central Universities"

Recently, the LHCb experimental group found an exotic state from the process. A key question is whether it is just a molecule or may have a confined tetraquark ingredient. To investigate this, different methods were used, including a two-channel ( and ) K-matrix unitarization and a single-channel Flatté-like parametrization method analyzed utilizing the pole counting rule and spectral density function sum rule. These analyses demonstrated that is a molecular state, although the possibility that there may exist an elementary ingredient cannot be excluded, according to an approximate analysis of its production rate.

Formula omitted] from QCD Laplace sum rule

We present a review of our recent works on heavy-light exotic states, with new compact integrated expressions of the spectral functions at lowest order (LO) of perturbative (PT) QCD and up to d=6 condensates of the Operator Product Expansion (OPE). Including higher order (HO) PT corrections, which we have estimated by assuming the factorization of the molecule/four-quark spectral functions, we evaluate masses and couplings with the Laplace sum rules (LSR) and finite energy (FESR) QCD spectral sum rules (QSSR) approaches. Our optimal results based on stability criteria are summarized and compared with experimental candidates and some LO QSSR results. We conclude that, our predicted spectra, do not confirm that the X(5568) is a pure molecule or a four-quark state. The masses of the XZ observed states are compatible with (almost) pure JPC=1+±,0++ molecule or/and four-quark states. The SU3 corrections on the meson masses are tiny: ≤10% (respectively ≤3%) for the c (respectively b)-quark channel but can be large for the couplings (≤20%). We expect that the resonance near the D−K+ threshold can be originated from the 0+(D−K+) molecule and/or D−K+ scattering. The X0(2900), XJ(3150) (if J = 0), X1(2900) and the XJ(3350) (if J = 1) can emerge from a minimal mixing model between tetramoles and first radial excitation. The Zc(3900,4025,4040,4430) and Zcs(3983) spectra are well reproduced by the molecules and tetramoles candidates, or radial excitation.

A Deep Reinforcement Learning Scheme for Sum Rate and Fairness Maximization Among D2D Pairs Underlaying Cellular Network With NOMA

Device-to-device (D2D) communication is an emerging technology in 5G and upcoming 6G networks due to its properties to enhanced spectral efficiency (SE), energy-efficiency (EE), and sum rate. Despite these advantages, co-channel and cross-channel interference, and ultra-massive connectivity are major issues which can deteriorate performance of any implemented solution in this environment. To address these issues, in this paper, we integrated the power domain non-orthogonal multiple access techniques (PD-NOMA) on the base station (BS). NOMA serves more than one user using the same resource block (RB) and reduces the effect of interference at CUs due to the presence of successive interference cancellation (SIC). The problem is formulated as a mixed-integer non-linear programming (MINLP) with associated resources and power constraints of the BS and DDPs with an aim to maximize the sum rate and fairness among the NOMA-enabled CUs and D2D pairs (DDPs). We firstly used the centralized deep deterministic policy gradient (DDPG) and arithmetic-geometric mean approximation (AGMA) technique to reduce cross-channel interference (CR-CI) and control the power. Then, to provide fairness to all the users, we transformed the proposed solution into distributed deep deterministic policy gradient (D3PG). Also, the successive convex approximation technique is then integrated into the D3PG to mitigate the effect of co-channel (CO-CI) interference among DDPs. The experimental results show that the proposed scheme has superior performance with respect to sum rate and fairness. Also, the results reveal that the proposed scheme has 21.05%, 34.21%, and 49.8% higher sum rate in comparison to DDPG, Deep dueling, and DQN scheduling.

Reinforcement Learning Based Efficient Power Control and Spectrum Utilization for D2D Communication in 5G Network

There are billions of inter-connected devices by the help of Internet-of-Things (IoT) that have been used in a number of applications such as for wearable devices, e-healthcare, agriculture, transportation, etc. Interconnection of devices establishes a direct link and easily shares the information by utilizing the spectrum of cellular users to enhance the spectral efficiency with low power consumption in an underlaid Device-to-Device (D2D) communication. Due to reuse of the spectrum of cellular devices by D2D users causes severe interference between them which may impact on the network performance. Therefore, we proposed a Q-Learning based low power selection scheme with the help of multi-agent reinforcement learning to detract the interference that helps to increase the capacity of the D2D network. For the maximization of capacity, the updated reward function has been reformulated with the help of a stochastic policy environment. With the help of a stochastic approach, we figure out the proposed optimal low power consumption techniques which ensures the quality of service (QoS) standards of the cellular devices and D2D users for D2D communication in 5G Networks and increase the utilization of resources. Numerical results confirm that the proposed scheme improves the spectral efficiency and sum rate as compared to Q-Learning approach by 14% and 12.65%.

On the nature of X(3960)

A near-threshold enhancement in the D^{+}_{s}D^{-}_{s} system, dubbed as X(3960), is observed by the LHCb collaboration recently. A combined analysis on chi _{c0}(3930)~(rightarrow D^+ D^-), X(3960)~(rightarrow D^{+}_{s}D^{-}_{s}), and X(3915)~(rightarrow J/psi omega ) is performed using both a K-matrix approach of D_{(s)}bar{D}_{(s)} four-point contact interactions and a model of Flatté-like parameterizations. The use of the pole counting rule and spectral density function sum rule indicate, under current statistics, that this D^{+}_{s}D^{-}_{s} near-threshold state has probably the mixed nature of a cbar{c} confining state and D^{+}_{s}D^{-}_{s} continuum.

X(6900) peak could be a molecular state

The analyses of the LHCb data on $X(6900)$ found in di-$J/\psi$ and $J/\psi \psi(3686)$ systems are performed using a momentum-dependent {Flatt\'{e}}-like parameterization. The use of the pole counting rule and spectral density function sum rule give consistent conclusions that $X(6900)$ may not be a molecule of $J/\psi \psi(3686)$. Nevertheless it is still possible that $X(6900)$ be a molecule of higher states, such as $J/\psi\psi(3770)$, $\chi_{c0}\chi_{c2}$, etc.

Cumulant expansion in the Holstein model: Spectral functions and mobility

We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law $\ensuremath{\mu}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ in the limit of weak coupling and $\ensuremath{\mu}\ensuremath{\propto}{T}^{\ensuremath{-}3/2}$ for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.

Euler-Heisenberg Lagrangian under an axial gauge field

Augmentations to the Euler-Heisenberg Lagrangian (QED one-loop effective action in homogeneous electromagnetic fields) under a constant background axial gauge are examined. Two special configurations admit an exact eigendecomposition, and hence effective action as a spectral sum, of the augmented Dirac operator: one with a magnetic field with chiral chemical potential, and the other with an electric field with spatial axial gauge, which resembles an emergent vorticity. An enhancement to Schwinger pair production is found for the latter, which is more fully analyzed using the worldline instanton formalism. There it is found the overall enhancement is due to the spatial axial gauge serving as a negative mass shift. Finally, we remark on the exactly solvable massless case for arbitrary electromagnetic and axial gauges.

QCD spectral sum rules 2022

We present a compact review of the status of QCD spectral sum rules until 2022. We emphasize the recent progresses for determining the QCD input parameters (αs, running quark masses, quark and gluon condensates) where their correlations have been taken into account. Some selected phenomenological uses of the sum rules in different channels (light and heavy quarks, gluonia/glueballs, hybrids and four-quark states) are briefly reviewed and commented. The estimate of the 1−+ light hybrid mass is revised which confirms the hybrid nature of the π1(1600) but not the π1(2050).

0+ XTZ states from QCD spectral sum rules

We review our results in [1] for the masses and couplings of Tccqq′ (JP=0+) states from (inverse) QCD Laplace sum rule (LSR), their ratios R and double ratio of sum rules (DRSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections and Lowest Order (LO) QCD condensates up to 〈G3〉. We show that combining R and DRSR can provide more precise results. Calibrated to the observed Xc(3872) and Tcc1+(3875), R combined with DRSR lead to a more precise prediction of MTcc0+=3883(3)MeV. In a similar way, calibrated to the new prediction of Tcc0+R⊕DRSR lead to the improved mass predictions: MTccs¯u¯0+=3927(6)MeV and MTccs¯s¯0+=3993(11)MeV. We extend our analysis to the bottom sector and compare our results with the ones from different LSR predictions and some other determinations (lattice, quark and potential models, …) in the literature.

Conformational preferences of DNA from the promoter regions of the c-MYC, VEGF, and Bcl-2 oncogenes.

We characterized the conformational preferences of DNA in an equimolar mixture of complementary G-rich and C-rich strands from the promoter regions of the c-MYC, VEGF, and Bcl-2 oncogenes. Our CD-based approach presupposes that the CD spectrum of such a mixture is the spectral sum of the constituent duplex, G-quadruplex, i-motif, and coiled conformations. Spectra were acquired over a range of temperatures at different pH and concentrations of KCl. Each spectrum was unmixed in terms of the predetermined spectra of the constituent conformational states to obtain the corresponding weighting factors for their fractional contributions to the total population of DNA. The temperature-dependences of those contributions then were analyzed in concert according to a model based on a thermodynamic representation of the underlying equilibria. Comparison of the conformational data on the c-MYC, VEGF, and Bcl-2 DNA reveals that the distribution of conformational states depends on the specific DNA sequence and is modulated by environmental factors. Under the physiological conditions of room temperature, neutral pH, and elevated concentrations of potassium ions, the duplex conformation coexists with the G-quadruplex conformation in proportions that depend on the sequence. This observed conformational diversity has biological implications suggesting a novel, thermodynamically controlled mechanism for the regulation of gene expression. In that hypothesis, a specific distribution of duplex and tetraplex conformations in a promoter region is fine-tuned to maintain the healthy level of gene expression. Any deviation from a healthy distribution of conformational states may result in pathology stemming from up- or downregulation of the gene.

Nonequilibrium spectral moment sum rules of the Holstein–Hubbard model

We derive a general procedure for evaluating the nth derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green’s function and self-energy for a system described by the Holstein–Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.

Performance analysis of NOMA in Rayleigh and Nakagami Fading channel

Cellular connectivity is expanding rapidly in the modern world. The multiple access strategy is one of the highly used methods for allocating the range of users in cellular network. Spectrum allocation is a crucial element to take into account since cellular communication is becoming more and more popular. NOMA is a channel access mechanism used in 5G mobile communication. It is also known as non-orthogonal multiple access. NOMA is a potential strategy for enhancing spectral efficiency and sum rate. Using the NOMA method, we evaluated the BER versus transmitted power of two users in rayleigh and nakagami fading channels. In this NOMA setup, a single antenna is shared by two users. Two users can accept the same frequency using 5G NOMA technology, but at different power levels. The results of the MATLAB simulation show that the two user NOMA in the Nakagami channel performs better than the Rayleigh channel in terms of Bit Error Rate vs. Transmitted Power.

Research on frequency band sparse optimization algorithm in health index of rolling bearing

SummaryThe construction of health indicators of rolling bearing is significant for the monitoring of its health condition and residual life prediction. The main work is based on the frequency band sparse optimization algorithm in the rolling bearing health index. On the one hand, the index construction method based on machine learning model has poor interpretability; on the other hand, there are many interference components in the original vibration signal, extracting statistical features directly based on the original signal as a poor health indicator. For the above problems, this paper proposes a rolling bearing health index construction method based on sparse frequency band characterization. First, the signal including each independent sub‐band has been obtained by wavelet packet decomposition. Second, a sparse model is constructed by combining the sub‐band amplitudes and matrices decomposed by the wavelet packet in the fault state and the normal state, so as to select the frequency band sensitive to the fault information. Thereafter, the spectral amplitude sum of sensitive frequency band (SASSFB) is calculated as a health indicator that reflects the degradation information during the complete life operation of the rolling bearing. Finally, the effectiveness of the method is verified by utilizing the published bearing accelerated life experimental data set.

The prime geodesic theorem for PSL2(ℤ[i]) and spectral exponential sums

This work addresses the Prime Geodesic Theorem for the Picard manifold $\mathcal{M} = \mathrm{PSL}_{2}(\mathbb{Z}[i]) \backslash \mathfrak{h}^{3}$, which asks for the asymptotic evaluation of a counting function for the closed geodesics on $\mathcal{M}$. Let $E_{\Gamma}(X)$ be the error term in the Prime Geodesic Theorem. We establish that $E_{\Gamma}(X) = O_{\varepsilon}(X^{3/2+\varepsilon})$ on average as well as many pointwise bounds. The second moment bound parallels an analogous result for $\Gamma = \mathrm{PSL}_{2}(\mathbb{Z})$ due to Balog et al. and our innovation features the delicate analysis of sums of Kloosterman sums with an explicit manipulation of oscillatory integrals. The proof of the pointwise bounds requires Weyl-strength subconvexity for quadratic Dirichlet $L$-functions over $\mathbb{Q}(i)$. Moreover, an asymptotic formula for a spectral exponential sum in the spectral aspect for a cofinite Kleinian group $\Gamma$ is given. Our numerical experiments visualise in particular that $E_{\Gamma}(X)$ obeys a conjectural bound of size $O_{\epsilon}(X^{1+\varepsilon})$.

DK and BK-like spectra from Laplace sum rule at NLO

Encouraged by the agreement, with the recent LHCb data on the D−K+ invariant mass from B→D+D−K+ decay, of our results for the masses of the 0+ and 1− open charm (c¯d¯)(us) tetraquarks and molecules states from QCD spectral sum rules within stability criteria, which we review here, we extend our analysis to the b-quark channel. We find, in the 0+ case the lowest mass MBK=5195(15)MeV with fBK=8.3(2.4)keV and three (almost) degenerate states having respectively the masses MSS=5702(60)MeV, MAA=5661(75)MeV and MB⁎K⁎=5720(71)MeV and couplings fSS=22.2(2.3)keV, fAA=30.1(3.1)keV and fB⁎K⁎=26.5(2.8)keV, from which we can associate a scalar tetramole with MTM0=5694(69)MeV and fTM0=26.5(2.7)keV. In the spin 1 case, we find four (almost) degenerate states associated with a tetramole having MTM1=5700(81)MeV and fTM1=16.2(2.6)keV. For the first radial excitation of the BK molecule, we have M(BK)1=6265(146)MeV and f(BK)1=22.8(3.2)keV. For the remaining states, we associate a scalar and vector tetramoles having respectively M(TM0)1=7439(314)MeV, f(TM0)1=74.7(8.4)keV and M(TM1)1=7544(345)MeV, f(TM1)1=33.0(6.7)keV.

Spectral exponential sums on hyperbolic surfaces

We study an exponential sum over Laplacian eigenvalues of Maaß forms on $$\varGamma \backslash {\mathbb {H}}$$ , where $$\varGamma $$ is a congruence subgroup of $${{\,\mathrm{SL}\,}}_{2}({\mathbb {Z}})$$ and $${\mathbb {H}}$$ is the upper half-plane. The goal is to establish an asymptotic formula that expresses the spectral exponential sum in terms of an oscillatory main term, the von Mangoldt function and the Selberg zeta function.

Quantitative analysis of the main components in ceramic raw materials based on the desktop LIBS analyzer

The concentrations of SiO2, Al2O3, K2O, Na2O, CaO, MgO, Fe2O3 and TiO2, and loss on ignition (L.O.I.) are the main inorganic components of geological samples. Concentrations of the eight oxides and L.O.I. are also the main indicators of concern in the production of building ceramics. Quantitative analysis of the eight oxides and L.O.I. was performed using fiber-laser-based laser-induced breakdown spectroscopy (LIBS). A combination of continuous background deduction, full width at half maximum (FWHM) intensity integral and spectral sum normalization was proposed for data processing. After the data processing combined the continuous background deduction, FWHM intensity integral and spectral sum normalization, the mean absolute errors (MAEs) of the calibration of L.O.I., SiO2, Al2O3, K2O, Na2O, CaO, MgO, Fe2O3 and TiO2 was reduced from 2.03%, 12.06%, 4.84%, 1.10%, 0.69%, 0.31%, 0.11%, 0.20% and 0.10% to 1.80%, 9.48%, 2.12%, 0.36%, 0.58%, 0.11%, 0.08%, 0.19% and 0.05%, respectively. This multivariate method was further introduced and discussed to improve the analysis performance. The MAEs of L.O.I., SiO2, Al2O3, K2O and Na2O were further reduced to 1.12%, 2.07%, 1.38%, 0.35% and 0.43%, respectively. The results show that the overall prediction error can meet the requirements for the production of building ceramics. The LIBS desktop analyzer has great potential in detection applications on geological samples.

Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems.

We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.