Energy Variance Research Articles

Acoustic Emission simulation: assessing the influence of AE source modeling and addressing the issue of dimensionality in the propagation medium

A thorough understanding of simulating Acoustic Emission (AE) requires the source modeling and propagation medium to be considered respectively. Crack initiation and propagation simulation as an AE source can be performed by the Successive Node Release (SNR) method and the Direct Node Release (DNR) method. Both are compared to show how the source model affects the AE signals. The SNR method is commonly used to simulate the crack initiation and propagation. It is necessary to consider the influence of the crack velocity profile on the crack initiation [1]. However, for the DNR method, all nodes are instantaneously released once the critical crack length is attained. Hence, it is not necessary to consider the velocity profile. Instead, it is sufficient to define the average crack velocity. However, the kinetic energy varies when employing different methods, leading to a variance in the source energy. We thus assess the suitable conditions to apply the DNR method to represent crack initiation and investigate the influence of the node release methods on the AE signals. Secondly, a comparative assessment of the Pencil-lead Break test on PMMA plates is conducted using both two-dimensional (2D) and three-dimensional (3D) finite element simulations. This analysis is valuable for understanding the deficiencies and constraints of the 2D simulation. However, there is a significant difference in the AE signals between 2D and 3D simulations, suggesting that the 2D simulation is unable to capture the AE information during wave propagation, in spite of its lower computational cost. Therefore, to obtain extensive and precise information from the PLB test, it is crucial to have an extensive understanding of the limits of the 2D simulation. This understanding should take into account factors such as the distance between the sensor and the source, as well as the descriptors chosen to characterize the AE.

Identification of quantitative trait loci and candidate genes for pod shatter resistance in Brassica carinata

BackgroundUnderstanding the genetic control of pod shatter resistance and its association with pod length is crucial for breeding improved pod shatter resistance and reducing pre-harvest yield losses due to extensive shattering in cultivars of Brassica species. In this study, we evaluated a doubled haploid (DH) mapping population derived from an F1 cross between two Brassica carinata parental lines Y-BcDH64 and W-BcDH76 (YWDH), originating from Ethiopia and determined genetic bases of variation in pod length and pod shatter resistance, measured as rupture energy. The YWDH population, its parental lines and 11 controls were grown across three years for genetic analysis.ResultsBy using three quantitative trait loci (QTL) analytic approaches, we identified nine genomic regions on B02, B03, B04, B06, B07 and C01 chromosomes for rupture energy that were repeatedly detected across three growing environments. One of the QTL on chromosome B07, flanked with DArTseq markers 100,046,735 and 100,022,658, accounted for up to 27.6% of genetic variance in rupture energy. We observed no relationship between pod length and rupture energy, suggesting that pod length does not contribute to variation in pod shatter resistance. Comparative mapping identified six candidate genes; SHP1 on B6, FUL and MAN on chromosomes B07, IND and NST2 on B08, and MAN7 on C07 that mapped within 0.2 Mb from the QTL for rupture energy.ConclusionThe results suggest that favourable alleles of stable QTL on B06, B07, B08 and C01 for pod shatter resistance can be incorporated into the shatter-prone B. carinata and its related species to improve final seed yield at harvest.

Neuro‐fuzzy‐based cluster formation scheme for energy‐efficient data routing in IOT‐enabled WSN

SummaryInternet of things–enabled wireless sensor networks face challenges like inflexibility, poor scalability, suboptimal cluster head selection, and energy inefficiencies. This is due to the faster data transmission rates between cluster nodes during data packet routing. This creates unnecessary energy consumption burdens for those actively transmitting nodes. Conceptually, an effective cluster formation phase supports better data routing mechanisms, while sustaining the energy efficiency of individual nodes. This paper proposes a Neuro‐Fuzzy based Cluster Formation (NFCF) scheme to facilitate adaptive and energy‐efficient cluster topologies. NFCF utilizes fuzzy logic and neural networks to identify optimal super nodes for flexible cluster formations. This approach enables configurable cluster sizes along with inclusion/exclusion criteria for member nodes based on energy thresholds. Parameters evaluated for node selection include the degree of super node, expected energy per cluster, energy variance, and residual energy. Nodes not meeting the thresholds are excluded. The neural network updates fuzzy rules to guide optimal clustering decisions based on anticipated energy dynamics under different conditions. The performance of the proposed NFCF scheme is evaluated based on objective function changes related to data transmission, individual node energy variation, energy variance before and after transmissions, and averaged end‐to‐end delay across transmission cycles. Results are compared against genetic fuzzy clustering, fuzzy energy‐aware clustering, fuzzy‐based distributed clustering, fuzzy logic‐based multi‐hop clustering, and fuzzy weighted k‐means clustering.

Using Experiments, 3D Scanning, and CFD to Analyze the Variance in Energy Losses Through Pipe Elbows

Pipe bends, or elbows, cause energy loss in pipelines due to the flow conditions they create. This energy loss has traditionally been approximated based on published minor loss coefficients, known as k-factors. However, the energy losses of elbows can vary based on geometric characteristics, which may not be accounted for in the published k-factors. The purpose of this research was to quantify the variance in energy loss resulting from elbows with geometric differences and to determine appropriate methods for approximating these variances using computational fluid dynamics (CFD). Eight polyvinyl chloride (PVC) elbows were physically tested in a hydraulic laboratory to determine the individual loss coefficients. The resulting data show that the minor loss coefficient k for two short-radius elbows of the same nominal size can vary by up to 51%. The same tests on two of the elbows were repeated using CFD, in which they were modeled two different ways: 1) using the ideal geometry and 2) using the actual geometry. The actual geometry was captured using 3D scanning. Each geometry was used in a series of simulations, and the results were compared to the experimental data. The CFD simulations were able to reproduce similar variances between the two elbows as displayed in the physical tests, although they were unable to reproduce the same k-factors. When compared to the experimental k-factor data, using the actual geometries captured by 3D scanning was not consistently more accurate than using idealized geometries.

Energy criterion for synchronization of neuron populations

Energy regulates the neuron activities, including inter-neuronal communication, biorhythm, and brain function. In this paper, we propose the energy criterion for the synchronization of neuron populations, and neurons tend to be synchronous if the energy variance approaches zero. Furthermore, we investigate the energy distribution of neuron population. The individual energy groups, two or three groups, expand until they merge into a uniform energy group with the increasing of the coupling intensity. Then, the uniform energy group tends to be a Normal distribution when the neuron population is synchronized. The energy criterion and energy distribution for synchronization are confirmed in the chain network, small world network and the scale free network composed by the FithzHugh-Nagumo (FHN) neurons. These results advance the understanding of the role played by the energy in neuron populations.

Multi-Objective Optimized GPSR Intelligent Routing Protocol for UAV Clusters

Unmanned aerial vehicle (UAV) clusters offer significant potential in civil, military, and commercial fields due to their flexibility and cooperative capabilities. However, characteristics such as dynamic topology and limited energy storage bring challenges to the design of routing protocols for UAV networks. This study leverages the Deep Double Q-Learning Network (DDQN) algorithm to optimize the traditional Greedy Perimeter Stateless Routing (GPSR) protocol, resulting in a multi-objective optimized GPSR routing protocol (DDQN-MTGPSR). By constructing a multi-objective routing optimization model through cross-layer data fusion, the proposed approach aims to enhance UAV network communication performance comprehensively. In addition, this study develops the above DDQN-MTGPSR intelligent routing algorithm based on the NS-3 platform and uses an artificial intelligence framework. In order to verify the effectiveness of the DDQN-MTGPSR algorithm, it is simulated and compared with the traditional ad hoc routing protocols, and the experimental results show that compared with the GPSR protocol, the DDQN-MTGPSR has achieved significant optimization in the key metrics such as the average end-to-end delay, packet delivery rate, node average residual energy variance and percentage of node average residual energy. In high dynamic scenarios, the above indicators were optimized by 20.05%, 12.72%, 0.47%, and 50.15%, respectively, while optimizing 36.31%, 26.26%, 8.709%, and 69.3% in large-scale scenarios, respectively.

Hyperuniformity in Ashkin–Teller model

We show that equilibrium systems inddimension that obey the inequalitydν>2,known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example ind = 2 where the correlation length exponentνvaries continuously with the inter-spin interaction strengthλand exceeds the valued2set by Harris criterion whenλis negative; there, the variance of the subsystem energy across a length scalelvaries asld-αwith hyperuniformity exponentα=2(1-ν-1).Point configurations constructed by assigning unity to the sites which has coarse-grained energy beyond a threshold value also exhibit suppressed number fluctuation and hyperuniformiyty with same exponentα.

Generalized Spin in the Variance-Based Wave Function Optimization Method within the Doubly Occupied Configuration Interaction Framework.

In this work, we implement a generalized spin formulation of the doubly occupied configuration interaction methodology using the energy variance of the N-electron Hamiltonian. We perform the optimization of the N-electron wave functions and calculate their corresponding energies, using a unified variational treatment for ground and excited states based on the energy variance, which allows us to describe the entire energy spectra on an equal footing. We analyze the effects produced by the breakdown of the Ŝ2 and Ŝz symmetries in the spectra of model hydrogenic clusters in terms of energies and spin-related quantities, arising from the restricted, unrestricted, and generalized spin methods. The results are compared with other related methods as well as full configuration interaction.

Longwave Radiative Feedback Due To Stratiform and Anvil Clouds

AbstractStudies have implicated the importance of longwave (LW) cloud‐radiative forcing (CRF) in facilitating or accelerating the upscale development of tropical moist convection. While different cloud types are known to have distinct CRF, their individual roles in driving upscale development through radiative feedback is largely unexplored. Here we examine the hypothesis that CRF from stratiform regions has the greatest positive effect on upscale development of tropical convection. We do so through numerical model experiments using convection‐permitting ensemble WRF (Weather Research and Forecasting) simulations of tropical cyclone formation. Using a new column‐by‐column cloud classification scheme, we identify the contributions of five cloud types (shallow, congestus, and deep convective; and stratiform and anvil clouds). We examine their relative impacts on longwave radiation moist static energy (MSE) variance feedback and test the removal of this forcing in additional mechanism‐denial simulations. Our results indicate the importance stratiform and anvil regions in accelerating convective upscale development.

MRI Radiomics Data Analysis for Differentiation between Malignant Mixed Müllerian Tumors and Endometrial Carcinoma.

The objective of this study was to compare the quantitative radiomics data between malignant mixed Müllerian tumors (MMMTs) and endometrial carcinoma (EC) and identify texture features associated with overall survival (OS). This study included 61 patients (36 with EC and 25 with MMMTs) and analyzed various radiomic features and gray-level co-occurrence matrix (GLCM) features. These variables and patient clinicopathologic characteristics were compared between EC and MMMTs using the Wilcoxon Rank sum and Fisher's exact test. The area under the curve of the receiving operating characteristics (AUC ROC) was calculated for univariate analysis in predicting EC status. Logistic regression with elastic net regularization was performed for texture feature selection. This study showed that skewness (p = 0.045) and tumor volume (p = 0.007) significantly differed between EC and MMMTs. The range of cluster shade, the angular variance of cluster shade, and the range of the sum of squares variance were significant predictors of EC status (p ≤ 0.05). The regularized Cox regression analysis identified the "256 Angular Variance of Energy" texture feature as significantly associated with OS independently of the EC/MMMT grouping (p = 0.004). The volume and texture features of the tumor region may help distinguish between EC and MMMTs and predict patient outcomes.

Matrix product state approximations to quantum states of low energy variance

We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that produces matrix product states whose energy variance decreases as the bond dimension increases. Our results imply that variances as small as ∝1/log⁡N can be achieved with polynomial bond dimension. With this, we prove that there exist states with a very narrow support in the bulk of the spectrum that still have moderate entanglement entropy, in contrast with typical eigenstates that display a volume law. Our main technical tool is the Berry-Esseen theorem for spin systems, a strengthening of the central limit theorem for the energy distribution of product states. We also give a simpler proof of that theorem, together with slight improvements in the error scaling, which should be of independent interest.

Machine learning prediction model for gray-level co-occurrence matrix features of synchronous liver metastasis in colorectal cancer.

Synchronous liver metastasis (SLM) is a significant contributor to morbidity in colorectal cancer (CRC). There are no effective predictive device integration algorithms to predict adverse SLM events during the diagnosis of CRC. To explore the risk factors for SLM in CRC and construct a visual prediction model based on gray-level co-occurrence matrix (GLCM) features collected from magnetic resonance imaging (MRI). Our study retrospectively enrolled 392 patients with CRC from Yichang Central People's Hospital from January 2015 to May 2023. Patients were randomly divided into a training and validation group (3:7). The clinical parameters and GLCM features extracted from MRI were included as candidate variables. The prediction model was constructed using a generalized linear regression model, random forest model (RFM), and artificial neural network model. Receiver operating characteristic curves and decision curves were used to evaluate the prediction model. Among the 392 patients, 48 had SLM (12.24%). We obtained fourteen GLCM imaging data for variable screening of SLM prediction models. Inverse difference, mean sum, sum entropy, sum variance, sum of squares, energy, and difference variance were listed as candidate variables, and the prediction efficiency (area under the curve) of the subsequent RFM in the training set and internal validation set was 0.917 [95% confidence interval (95%CI): 0.866-0.968] and 0.09 (95%CI: 0.858-0.960), respectively. A predictive model combining GLCM image features with machine learning can predict SLM in CRC. This model can assist clinicians in making timely and personalized clinical decisions.

Satellite-Based Estimation of the Role of Cloud-Radiative Interaction in Accelerating Tropical Cyclone Development

Abstract Recent modeling studies have suggested a potentially important role of cloud-radiative interactions in accelerating tropical cyclone (TC) development, but there has been only limited investigation of this in observations. Here, we investigate this by performing radiative transfer calculations based on cloud property retrievals from the CloudSat Tropical Cyclone (CSTC) dataset. We examine the radius–height structure of radiative heating anomalies, compute the resulting radiatively driven circulations, and use the moist static energy variance budget to compute radiative feedbacks. We find that inner-core midlevel ice water content and anomalous specific humidity increase with TC intensification rate, resulting in enhanced inner-core deep-layer longwave warming anomalies and shortwave cooling anomalies in rapidly intensifying TCs. This leads to a stronger radiatively driven deep in-up-and-out overturning circulation and inner-core radiative feedback in rapidly intensifying TCs. The longwave-driven circulation provides radially inward momentum fluxes and upward moisture fluxes, which benefit TC development, while the shortwave-driven circulation suppresses TC development. The longwave anomalies, which dominate the inner-core positive radiative feedback, are mainly generated from cloud-radiative interactions, with ice particles dominating the deep-layer circulation and liquid droplets and water vapor contributing to the shallow circulation. Moreover, the variability in ice water content, as opposed to the variability in liquid water content and the effective radii of ice particles and liquid droplets, dominates the uncertainty in TC-radiative interaction. These results provide observational evidence for the importance of cloud-radiative interactions in TC development and suggest that the amount and spatial structure of ice water content are critical for determining the strength of this interaction. Significance Statement The limited investigation of tropical cyclone (TC)-radiative interaction in observations impedes our understanding of TC development. This study aims to quantitatively show the spatial variation in radiation in TCs and their effect on TC development by using a set of satellite-based observations. We relate TC-radiative interaction to TC intensification and emphasize the inner-core features. Moreover, we quantitatively demonstrate the relative contribution from clouds, liquid droplets, ice particles, and water vapor to TC-radiative interaction as well as the source of the variation in radiative properties. These results provide an additional observational foundation for the importance of cloud-radiative interactions in TC development and support a quantitative validation for numerical modeling.

Partitioning among-animal variance of energy utilization in lactating Jersey cows

Animals vary in the way in which they utilize energy due to diet, genetics, and management. Energy consumed by the animal supports milk production, but considerable variation among-animals in energy utilization is thought to exist. The study objective was to estimate the among-animal variance in energy utilization in data collected from Jersey cows using indirect calorimetry. Individual animal-period data from 15 studies (n = 560) were used. The data set included 115 animals from 44 to 410 DIM producing 11.5 to 39.1 kg/d of milk. On average, the 63 treatments in the data set ranged 14.8 to 19.5% CP, 21.4 to 43.0% NDF, 16.2 to 33.3% starch, and 2.21 to 6.44% crude fat. Data were analyzed with the Glimmix procedure of SAS (9.4) with random effects of cow, treatment nested within period, square, and experiment. The percentage of among-animal, dietary treatment, and experimental variance was calculated as the variance associated with each fraction divided by the sum of variance from animal, dietary treatment, experiment, and residual which was considered the total variance. The percentage of among-animal variance was characterized as high or low when the value was greater than or less than the mean value of 29.2%. Among-animal variance explained approximately 29.3 - 42.5% of the total variance in DM intake (DMI), gross energy (GE), digestible energy (DE), metabolizable energy (ME), and net energy of lactation (NEL) in Mcal/d. When energetic components of feces, urine, and heat in Mcal/d were expressed per unit of DMI the among-animal variance decreased by 20.4, 4.82, and 9.55% units, respectively. However, among-animal variance explained 4.80, 8.78, and 5.02% units more of the total variation for methane energy, lactation energy, and tissue energy in Mcal/d when expressed per unit of DMI. Variance in energetic efficiencies of DE/GE, ME/GE, and ME/DE were explained to a lesser extent by among-animal variance (averaging 17.8 ± 1.95%). The among-animal contribution to total variance in milk energy was 28.8%. Milk energy was a large proportion of the energy efficiency calculation which included milk energy plus corrected tissue energy over net energy intake which likely contributed to the 22.2% of total among-animal variance in energy efficiency. Results indicate that among-animal variance explains a large proportion of the total variation in DMI. This contributes to the variance observed for energy fractions as well as energy components when expressed in Mcal/d. Variation in energetic loss associated with methane was primarily explained by differences among-animals and was increased when expressed per unit of DMI highlighting the role of inherent animal differences in these losses.

Enhancing image security via chaotic maps, Fibonacci, Tribonacci transformations, and DWT diffusion: a robust data encryption approach

In recent years, numerous image encryption schemes have been developed that demonstrate different levels of effectiveness in terms of robust security and real-time applications. While a few of them outperform in terms of robust security, others perform well for real-time applications where less processing time is required. Balancing these two aspects poses a challenge, aiming to achieve efficient encryption without compromising security. To address this challenge, the proposed research presents a robust data security approach for encrypting grayscale images, comprising five key phases. The first and second phases of the proposed encryption framework are dedicated to the generation of secret keys and the confusion stage, respectively. While the level-1, level-2, and level-2 diffusions are performed in phases 3, 4, and 5, respectively, The proposed approach begins with secret key generation using chaotic maps for the initial pixel scrambling in the plaintext image, followed by employing the Fibonacci Transformation (FT) for an additional layer of pixel shuffling. To enhance security, Tribonacci Transformation (TT) creates level-1 diffusion in the permuted image. Level-2 diffusion is introduced to further strengthen the diffusion within the plaintext image, which is achieved by decomposing the diffused image into eight-bit planes and implementing XOR operations with corresponding bit planes that are extracted from the key image. After that, the discrete wavelet transform (DWT) is employed to develop secondary keys. The DWT frequency sub-band (high-frequency sub-band) is substituted using the substitution box process. This creates further diffusion (level 3 diffusion) to make it difficult for an attacker to recover the plaintext image from an encrypted image. Several statistical tests, including mean square error analysis, histogram variance analysis, entropy assessment, peak signal-to-noise ratio evaluation, correlation analysis, key space evaluation, and key sensitivity analysis, demonstrate the effectiveness of the proposed work. The proposed encryption framework achieves significant statistical values, with entropy, correlation, energy, and histogram variance values standing at 7.999, 0.0001, 0.0156, and 6458, respectively. These results contribute to its robustness against cyberattacks. Moreover, the processing time of the proposed encryption framework is less than one second, which makes it more suitable for real-world applications. A detailed comparative analysis with the existing methods based on chaos, DWT, Tribonacci transformation (TT), and Fibonacci transformation (FT) reveals that the proposed encryption scheme outperforms the existing ones.

Performance evaluation of ten numerical methods for Weibull distribution parameter estimation applied to Nigerian wind speed data

Utilizing wind energy necessitates a thorough understanding of wind profiles as well as a precise forecast of wind speed at a study location. In this study, ten Numerical Methods (NEMs), which include the Empirical Method of Lysen (EML), Percentile Method (PCM), Maximum Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM), Empirical Method of Justus (EMJ), Alternative Moment Method (AMM), Median and Quartiles Method (MQM), Probability Weighted Moments Based on Power Density Method (PWMBPM), Method of Mabchour (MOMAB) and Energy Variance Method (EVM) were applied to estimate the two- parameter (k and c) Weibull (Wbl) distribution in five locations (Jos, Kano, Maiduguri, Abuja, and Akure) in Nigeria. The performance of these NEMs was assessed using five different metrics and the most effective NEM was determined for each studied location. Daily wind speed data spanning 11 years for the studied locations were sourced from the Meteorological Agency in Nigeria and used in this study. The k and c parameters range from 2.91 to 5.46 and 9.95 to 10.26 (Kano); 2.31 to 4.50 and 5.63 to 6.20 (Maiduguri); 3.19 to 7.61 and 12.16 to 12.99 (Jos); 2.18 to 6.77 and 4.99 to 5.50 (Abuja), and 1.84 to 3.18 and 3.83 to 3.90 (Akure). Findings revealed that the best methods for estimating Wbl parameters for the Kano, Maiduguri, Jos, Abuja, and Akure locations were MMLM, MMLM, MQM, MQM, and EMJ, EML, and AMM, respectively, as MOMAB remained the least performing NEM for all the studied locations. The results also showed that the Vms , Vmps , and V emax varied from 3.47 m/s to 11.63 m/s, 3.40 m/s to 11.90 m/s, and 4.58 m/s to 12.59 m/s, respectively, with the most recorded for Jos. The PWPD augmented from 36.45 W/m2 (Akure) to 1000.06 W/m2 Jos), at a hub height of 10 m.Based on these results Jos was the best location for installing wind turbines while Kano was an excellent place for integrating the grid. Additionally, the Maiduguri location was determined to be suitable for a stand-alone application while Abuja and Akure were considered to be unsuitable for wind energy applications.

A variance-based optimization for determining ground and excited N-electron wave functions within the doubly occupied configuration interaction scheme.

This work describes optimizations of N-electron system wave functions by means of the simulated annealing technique within the doubly occupied configuration interaction framework. Using that technique, we minimize the energy variance of a Hamiltonian, providing determinations of wave functions corresponding to ground or excited states in an identical manner. The procedure that allows us to determine electronic spectra can be performed using treatments of restricted or unrestricted types. The results found in selected systems, described in terms of energy, spin, and wave function, are analyzed, showing the performance of each method. We also compare these results with those arising from more traditional approaches that minimize the energy, in both restricted and unrestricted versions, and with those obtained from the full configuration interaction treatment.

Precise control of hole transport layer integration on PDTS-DTTFBT: PC71BM organic solar cells

Efforts to enhance the commercial viability of organic solar cells (OSCs) prioritize high power conversion efficiency(PCE). This study proposes precision tuning of the photoactive layer thickness in the nanoscale as an innovative method to boost efficiency. Utilizing PDTS-DTTFBT: PC71BM, an organic blend, as the active layer aims to capture a broad photon range while addressing optical losses due to low-energy photons rather than mere absorption. The study integrates PEDOT: PSS and molybdenum trioxide (MoO3) as hole transport layers, alongside C60, PC60BM, and ZnO electron transport layers. Meticulous analysis of their photon absorption, reflectance, charge carrier generation, and localized energy variance emphasizes their impact on the efficiency of PDTS-DTFFBT: PC71BM active films. Notably, incorporating MoO3 as the hole transport layer significantly mitigated losses and altered localized energy, culminating in an impressive 17.69% efficiency at an optimized blend thickness of 120 nm. Augmenting blend thickness directly boosts PCE and current density until reaching optimal thickness, while diminishing fill factor, with minimal effect on open-circuit voltage. These results highlight the efficacy of this methodology in enhancing the performance of organic solar cells.

Folded Spectrum VQE: A Quantum Computing Method for the Calculation of Molecular Excited States.

The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.

Long-term X-ray temporal and spectral study of a Seyfert galaxy Mrk 6

ABSTRACT We present a long-term X-ray study of a nearby Active Galactic Nucleus Mrk 6, utilizing observations from XMM–Newton, Suzaku, Swift, and NuSTAR observatories, spanning 22 years from 2001 to 2022. From timing analysis, we estimated variance, normalized variance, and fractional rms amplitude in different energy bands.The temporal study shows fractional rms amplitude (Fvar) below 10 per cent for the shorter time-scale (∼60 ks) and above 20 per cent for the longer time-scale (∼weeks). A complex correlation is observed between the soft (0.5–3.0 keV) and hard (3.0–10.0 keV) X-ray bands of different epochs of observations. This result prompts a detailed investigation through spectral analysis, employing various phenomenological and physical models on the X-ray spectra. Our analysis reveals a heterogeneous structure of the obscuring material surrounding Mrk 6. A partially ionized absorber exhibits a rapid change in location and extends up to the narrow-line regions or torus. In contrast, another component, located far from the central engine, remained relatively stable. During the observation period, the source luminosity in the 3.0–10.0 keV range varies between (3–15) × 1042 erg s−1.