Constrained Energy Minimization Research Articles

GraphPPL.jl: A Probabilistic Programming Language for Graphical Models

This paper presents GraphPPL.jl, a novel probabilistic programming language designed for graphical models. GraphPPL.jl uniquely represents probabilistic models as factor graphs. A notable feature of GraphPPL.jl is its model nesting capability, which facilitates the creation of modular graphical models and significantly simplifies the development of large (hierarchical) graphical models. Furthermore, GraphPPL.jl offers a plugin system to incorporate inference-specific information into the graph, allowing integration with various well-known inference engines. To demonstrate this, GraphPPL.jl includes a flexible plugin to define a Constrained Bethe Free Energy minimization process, also known as variational inference. In particular, the Constrained Bethe Free Energy defined by GraphPPL.jl serves as a potential inference framework for numerous well-known inference backends, making it a versatile tool for diverse applications. This paper details the design and implementation of GraphPPL.jl, highlighting its power, expressiveness, and user-friendliness. It also emphasizes the clear separation between model definition and inference while providing developers with extensibility and customization options. This establishes GraphPPL.jl as a high-level user interface language that allows users to create complex graphical models without being burdened with the complexity of inference while allowing backend developers to easily adopt GraphPPL.jl as their frontend language.

Recognition and Scoring Physical Exercises via Temporal and Relative Analysis of Skeleton Nodes Extracted from the Kinect Sensor

Human activity recognition is known as the backbone of the development of interactive systems, such as computer games. This process is usually performed by either vision-based or depth sensors. So far, various solutions have been developed for this purpose; however, all the challenges of this process have not been completely resolved. In this paper, a solution based on pattern recognition has been developed for labeling and scoring physical exercises performed in front of the Kinect sensor. Extracting the features from human skeletal joints and then generating relative descriptors among them is the first step of our method. This has led to quantification of the meaningful relationships between different parts of the skeletal joints during exercise performance. In this method, the discriminating descriptors of each exercise motion are used to identify the adaptive kernels of the Constrained Energy Minimization method as a target detector operator. The results indicated an accuracy of 95.9% in the labeling process of physical exercise motions. Scoring the exercise motions was the second step after the labeling process, in which a geometric method was used to interpolate numerical quantities extracted from descriptor vectors to transform into semantic scores. The results demonstrated the scoring process coincided with the scores derived by the sports coach by a 99.5 grade in the R2 index.

Advanced exploration of rare metal mineralization through integrated remote sensing and geophysical analysis of structurally-controlled hydrothermal alterations

Fusing multi-source (remote sensing and geophysical) data and diverse approaches validation in targeting hydrothermal alteration and structural anomalies enhances the potential for accurately detecting and characterizing mineralization zones. Sentinel 2 data and ASTER were processed for lithological and hydrothermal alteration mapping in the rare metal-rich Umm Naggat area (Egypt). Different image processing techniques were implemented, including false color composites, minimum noise fraction, band rationing, band math, mineral indices, relative absorption band depth, and constrained energy minimization. The rare metal-bearing Umm Naggat younger granite (NYG) pluton was lithologically discriminated and intra-differentiated to mafic-rich biotite granites, mafic-poor alkali feldspar granites, and albitized granites. Extensive hydrothermal alterations, such as albitization, ferrugination, propylitization, argillization, and phyllitization, overprint the NYG pluton. Normalized standard deviation, automatic lineament extractions, and trend analysis highlighted the key structural directions (NW, NNW, NNE, and NE) and distinguished the NYG pluton as a moderate to high structural density zone. The high structural density and intensive alteration zones are spatially associated and more localized within the NYG pluton than the surrounding rocks. Spatial overlay analysis confirmed that the hydrothermal alterations and fluid circulation systems are structurally-controlled. Furthermore, the hydrothermal alteration mapping and structural analysis outcomes were verified by combining fieldwork, slab polishing, petrographic investigations, and mineral chemistry through semi-quantitative scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS) and quantitative electron probe microanalysis (EPMA) analysis. As a result, the hydrothermal genesis of rare metal-bearing minerals (Nb-rutile, Nb-ilmenite, and columbite) close to or incorporated within alteration minerals (chlorite, muscovite, and hematite) is confirmed from the alteration zones (propylitic, phyllic, and ferruginated). In addition, biotite muscovitization and chloritization significantly contribute to the secondary rare metal enrichment. The current study emphasizes the extensive distribution of secondary rare metal-bearing minerals within the entire NYG pluton (not only limited to the northern albitized granite as depicted by previous studies), which might shed light on these hydrothermally-altered younger granites as a new potential source for Nb and Ta in Egypt.

Coastline target detection based on UAV hyperspectral remote sensing images

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.

Joint spatial constrained energy minimization for gas identification in hyperspectral imaging

Hyperspectral gas identification plays a crucial role in a variety of applications ranging from environmental monitoring to national security. Constrained Energy Minimization (CEM) constitutes a pivotal approach in hyperspectral gas target identification, emphasizing the enhancement of target signal output energy and the suppression of background signal output energy through the design of specialized filters. However, conventional CEM algorithms present notable deficiencies, notably their failure to fully exploit spatial information in hyperspectral image target recognition and their ineffectiveness in detecting targets over extensive areas. To address these challenges, a hyperspectral gas identification method named Joint Spatial Constrained Energy Minimization (JSCEM) was introduced. This method incorporates adaptive weight constraints and employs “pseudo background spectrum” techniques, integrating spatial data to improve target discernment and refining the estimation accuracy of the background autocorrelation matrix. Experimental validations involving both simulated and manual data have shown that the JSCEM method offers marked improvements in the detection of large-area gas targets within hyperspectral image. Simulation data indicate that the detection performance of the JSCEM method is significantly enhanced compared to various existing CEM algorithms. Furthermore, measured data confirm that the JSCEM algorithm accurately identifies large gas targets in hyperspectral images, offering a precise approach to gas detection. This advancement is expected to be valuable in industries requiring accurate and efficient gas identification.

Riemannian Newton Methods for Energy Minimization Problems of Kohn–Sham Type

This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn–Sham models. In particular, we introduce Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates their supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes.

Integrating remote sensing and geophysical data for mapping potential gold mineralization localities at Abu Marawat area, central Eastern Desert, Egypt

Abu Marawat area in the Central Eastern Desert of Egypt is a very promising mineralization district located in the Golden Triangle area. The current study provides an integrated approach from multisource datasets including; remote sensing, airborne geophysical spectrometry and magnetic data supported by field studies and spectroscopic analyses for delineating potential mineralization localities. Several remote sensing techniques were adopted including; Band Ratios, Relative Band Depth, Mineralogical Indices, Spectral Angle Mapper, and Constrained Energy Minimization. These techniques showed that the alteration mineral assemblage is mainly, kaolinite, sericite, and iron oxides, with less abundant chlorite, epidote, and carbonates. In addition, the radiometry data were processed to map the localities with the highest possibility of potassic alteration abundance by integrating the potassium distribution, K/eTh ratio, and the F-parameter maps. The surface and subsurface linear structural features were also mapped using Digital Elevation Model (DEM) and aeromagnetic data, respectively. The surface linear structures were found exhibiting E-W and NE-SW trends, while, the subsurface structures showed dominant NW–SE trend. All the depicted fault trends match well with the local and regional geological and tectonic setting of the study area suggesting structural control on the mineralization in this area. Integration between the results obtained from both the remote sensing and the geophysical data was conducted by a GIS weighted overlay model. The obtained mineralization potentiality map highlights eight potential localities for mineralization. The accuracy of the adopted methodology was demonstrated through fieldwork and spectral analyses; several alteration indicators were observed, including quartz veins, iron oxides, kaolinite, malachite, montmorillonite, chlorite, talc, and sericite alteration indicator minerals. The adopted remote sensing-geophysical approach showed being very effective for mapping the hydrothermal gold-related alteration zones, and is recommended for other similar investigations.

Delineating the uranium anomalous zones using remote sensing and radiometric data: a case study from Gabal Umm Tinassib area, North Eastern Desert, Egypt

AbstractRemote sensing (RS) and airborne gamma-ray spectrometric (AGS) methods are utilized to delineate significant uranium zones and altered mineralization areas in Gabal Umm Tinassib and its surrounding region, situated in the northern section of the Egyptian Eastern Desert. AGS serves as a valuable tool for mapping surface geology and conducting mineral exploration. It assesses the concentrations of radioactive elements such as potassium (K), equivalent uranium (eU), and equivalent thorium (eTh). The concentration of radioelements exhibits measurable and significant variation according to lithology. On the other hand, several processing steps are employed for the RS data to generate high-quality images for geological mapping and to identify the mineralized alteration zones. The analysis of RS and AGS data in this study led to insightful conclusions. The utilization of False Color Composite (FCC) with the three best bands derived from the Optimum Index Factor (OIF), Principal Component Analysis (PCA) to extract two highly informative datasets, and the application of two band ratios contributed to accurate geological mapping. These band ratios notably identified identical alteration locations on both younger and older granite basement rocks. Additionally, the constrained energy minimization (CEM) technique effectively pinpointed alterations across these strata. The statistical analysis of AGS data revealed that radioactivity levels in the region range from 1.3 to 19.3 Ur for the total-count (TC), 0.2–3.6% for K, 0.09–11.6 ppm for eU, and 1.1–30.0 ppm for eTh. The estimated coefficient of variability (CoV) demonstrated that the three radio-elements exhibited normal distribution patterns across different rock units, with CoV values of less than 100%, except for K in the Malha Formation. High radiometric readings are observed in the outcroppings of younger and older granites. However, the lowest readings are recorded over undifferentiated Upper-Cretaceous sediments, Abu Rimth Formation, Galala Formation, and some parts of Quaternary sediments. The derived ternary radio-elements map highlights significant radiometric and related uranium anomalous zones as bright white regions. A strong correlation was found between high radiometric anomalous zones and the presumed occurrence of alteration zones in the study area.

ASTER data processing and fusion for alteration minerals and silicification detection: Implications for cupriferous mineralization exploration in the western Anti-Atlas, Morocco

Alteration minerals and silicification are typically associated with a variety of ore mineralizations and could be detected using multispectral remote sensing sensors as indicators for mineral exploration. In this investigation, the Visible Near-Infra-Red (VNIR), Short-Wave Infra-Red (SWIR), and Thermal Infra-Red (TIR) bands of the ASTER satellite sensor derived layers were fused to detect alteration minerals and silicification in east the Kerdous inlier for cupriferous mineralization exploration. Several image processing techniques were executed in the present investigation, namely, Band Ratio (BR), Selective Principal Component Analysis (SPCA) and Constrained Energy Minimization (CEM) techniques. Initially, the BR and SPCA processing results revealed several alteration zones, including argillic, phyllic, dolomitization and silicification as well as iron oxides and hydroxides. Then, these zones were mapped at sub-pixel level using the CEM technique. Pyrophyllite, kaolinite, dolomite, illite, muscovite, montmorillonite, topaz and hematite were revealed displaying a significant distribution in relation with the eastern Amlen region lithological units and previously detected mineral potential zones using HyMap imaging spectroscopy. Mainly, a close spatial association between iron oxides and hydroxide minerals, argillic, and phyllic alteration was detected, as well as a strong silicification was detected around doleritic dykes unit in Jbel Lkest area. A weighted overlay approach was used in the integration of hydrothermal alteration minerals and silicification, which allowed the elaboration of a new mineral alteration map of study area with five alteration intensities. ASTER and the various employed processing techniques allowed a practical and cost effective mapping of alteration features, which corroborates well with field survey and X-ray diffraction analysis. Therefore, ASTER data and the employed processing techniques offers a practical approach for mineral prospection in comparable settings.

Modeling remote-sensing and geophysical data to delineate the favorable mineralization localities at Semna area, Central Eastern Desert, Egypt

Semna area is located within the Golden Triangle district in the Central Eastern Desert of Egypt. The study maintains using multisource datasets of remote sensing, aero-spectrometry, aero-magnetic, and field investigations for unraveling the ambiguities associated with the alteration zones at the targeted area. Three remote sensing mapping techniques including; constrained energy minimization, linear spectral unmixing, and mineral indices, were adopted to delineate the alteration zones. The γ-ray spectrometry data of K (%), K/eTh, K/eU, and F-parameter enabled mapping the potassium-enriched localities as indication on possible potassic alteration zones. The surface and subsurface linear structural features were delineated from the digital elevation model and aero-magnetic data, respectively. The outcomes of all the implemented datasets were integrated using GIS overlay modeling, producing an integrated mineralization favorability/potentiality map. Eighteen localities with high potential for mineralization were highlighted. A field study was conducted to the investigated area during which, several alteration indicators were observed, including quartz veins, iron oxides staining, kaolinite, malachite, carbonate, and muscovite (sericite) alteration indicator minerals.

Massively parallel implementation of iterative eigensolvers in large-scale plane-wave density functional theory

The Kohn-sham density functional theory (DFT) is a powerful method to describe the electronic structures of molecules and solids in condensed matter physics, computational chemistry and materials science. However, large and accurate DFT calculations within plane waves process a cubic-scaling computational complexity, which is usually limited by expensive computation and communication costs. The rapid development of high performance computing (HPC) on leadership supercomputers brings new opportunities for developing plane-wave DFT calculations for large-scale systems. Here, we implement parallel iterative eigensolvers in large-scale plane-wave DFT calculations, including Davidson, locally optimal block preconditioned conjugate gradient (LOBPCG), projected preconditioned conjugate gradient (PPCG) and the Chebyshev subspace iteration (CheFSI) algorithms, and analyze the performance of these algorithms in massively parallel plane-wave computing tasks. We adopt a two-level parallelization strategy that combines the message passing interface (MPI) with open multi-processing (OpenMP) parallel programming to handle data exchange and matrix operations in the construction and diagonalization of large-scale Hamiltonian matrix within plane waves. Numerical results illustrate that these iterative eigensolvers can scale up to 42,592 processing cores with high peak performance of 30% on leadship supercomputers to study the electronic structures of bulk silicon systems containing 10,648 atoms. Program summaryProgram Title: Plane wave density functional theory (PWDFT)CPC Library link to program files:https://doi.org/10.17632/c8v2mx5vn4.1Developer's repository link:https://bitbucket.org/berkeleylab/scalesLicensing provisions: BSD 3-clauseProgramming language: C++Nature of problem: PWDFT is used for electronic structure calculations based on Kohn-Sham density functional theory. The key challenge to address is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem. MPI/OpenMP-based approaches are employed to provide multi-core acceleration for the study of the chemical and material properties of larger-scale molecules and solids.Solution method: PWDFT implements self-consistent field (SCF) iterations and direct constrained minimization algorithms with various acceleration strategies. It is written in C++ and offers parallel acceleration based on MPI/OpenMP.

Lineaments Characterization and their Tectonic Significance in Mineralization using Landsat TM Data and Field Studies along Mambilla Plateau, Northeast, Nigeria

Lineament characterization and their tectonic significance in mineralization using Landsat TM data and field studies Along the Mambilla Plateau and environs, northeast Nigeria .The area forms part of the mineralized shear zone of the Northeastern, part of the Basement Complex. The Basement Complex rocks underlie more than two-thirds of the plateau and date back to the Precambrian to early Paleozoic eras. While the remaining part of the plateau and its surroundings are made up of volcanic rocks of the upper Cenozoic to Tertiary and Quaternary ages. Remote sensing imagery data and field measurements were integrated for mapping the structural elements and hydrothermal alteration zones related to mineralization. Tectonically the lineaments trends NE-SW, NNW-SSE, NW-SE, and NS, are the main trends controlling mineralization in the area based on data from remote sensing and field measurements. On the other hand, applying band ratios and the constrained energy minimization (CEM) technique to Landsat-8 data pointed out alteration minerals associated with the hydrothermal fluids. Silica, sericite, and chlorite are the common alteration minerals detected, while goethite and epidote are less common in the alteration zones of the area under study. A combination of CET structural complexity, circular features, and alteration zones produced a potential mineralization map, pointing out numerous prospective zones for mineralization that are proximate to areas where artisanal mining activities are carried out. The predictive map was validated by projecting the known prospect zones in the study area, reflecting an agreement between the known occurrences and the higher classes of the predictive zone. The techniques in the current research can be adopted as a direct indicator for structural mapping and detecting alteration zones related to mineralization elsewhere.

Constrained Energy Minimization (CEM) for Hyperspectral Target Detection: Theory and Generalizations

Constrained Energy Minimization (CEM) for Hyperspectral Target Detection: Theory and Generalizations

Hyperspectral target detection based on constrained energy minimization variational autoencoder

Hyperspectral target detection based on constrained energy minimization variational autoencoder

Stain Detection Based on Unmanned Aerial Vehicle Hyperspectral Photovoltaic Module

Solar power generation has great development potential as an abundant and clean energy source. However, many factors affect the efficiency of the photovoltaic (PV) module; among these factors, outdoor PV modules are inevitably affected by stains, thus reducing the power generation efficiency of the PV panel. This paper proposes a framework for PV module stain detection based on UAV hyperspectral images (HSIs). The framework consists of two stain detection methods: constrained energy minimization (CEM)-based and orthogonal subspace projection (OSP)-based stain detection methods. Firstly, the contaminated PV modules are analyzed and processed to enhance the data’s analytical capability. Secondly, based on the known spectral signature of the PV module, stain detection methods are proposed, including CEM-based stain detection and OSP-based stain detection for PV modules. The experimental results on real data illustrate that, in comparison with contrasting methods, the proposed method achieves stain detection results that closely align with known stain percentages. Additionally, it exhibits a fitting curve similar to the more maturely developed electroluminescence-based methods currently in use.

Ice Identification with Error-Accumulation Enhanced Neural Dynamics in Optical Remote Sensing Images

Arctic sea ice plays an important role in Arctic-related research. Therefore, how to identify Arctic sea ice from remote sensing images with high quality in an unavoidable noise environment is an urgent challenge to be solved. In this paper, a constrained energy minimization (CEM) method is applied for Arctic sea ice identification, which only requires the target spectrum. Moreover, an error-accumulation enhanced neural dynamics (EAEND) model with strong noise immunity and high computing accuracy is proposed to aid with the CEM method for Arctic sea ice identification. With the theoretical analysis, the proposed EAEND model possesses a small steady-state error in noisy environments. Finally, compared with other existing models, the proposed EAEND model can not only complete sea ice identification in excellent fashion, but also has the advantages of high efficiency and noise immunity.

Mapping and discrimination of the mineralization potential in granitoids from Banyo area (Adamawa, Cameroon), using Landsat 9 OLI, ASTER images and field observations

The Banyo area is situated in the west Cameroon domain of the Central African Fold Belt. In this study, field data and remote sensing conventional mapping techniques including Red-Green-Blue (RGB) colour combination, principal component analysis (PCA), Crosta-PCA, Band Ratios (BR), Constrained Energy Minimization (CEM), Minimum Noise Fraction (MNF), Spectral Angle Mapper (SAM) classification and Linear Spectral Unmixing (LSU) algorithms were used to process Landsat 9 OLI and ASTER data in order to discriminate various rock units such as biotite-amphibole granites, hornblende-biotite orthogneiss and map associated mineral deposits (e.g., iron-oxide, hydroxyl and corundum minerals). In addition, it was found that RGB combination (743) of OLI bands, PCA of OLI bands (PC123), BR of OLI bands (4/2, 6/7, 6/5), BR of ASTER (4/2, 7/6, 8/9), Crosta-PCA of OLI bands, MNF (123) of OLI bands, SAM, and LSU techniques applied to ASTER bands ascertain potential locations of granitoids and gneisses bearing iron and hydroxyl minerals. On the other hand, this study also revealed that corundum deposits are detected by applying the CEM method to OLI band ratio 6/7 highlighting red tones and processing SAM classification algorithm both using laboratory reference spectra. Automatic (using PCI Geomatica line tool) and manual extractions of lineaments revealed three major trends (N-S, E-W, and WNW-ESE to NW-SE) and an accessory trend (NE-SW to ENE-WSW) that surround hydrothermally altered rocks recognized as containing iron oxide, hydroxyl, and corundum mineral deposits. In the field, these lineaments may group to the tree deformation phases. The D1 phase (NW-SE); the D2 phase (NE-SW to ENE-WSW) and the D3 phase (N-S). Maximum Likelihood Calssification (MLC) and SAM classification methods showed to be more effective in discriminating rocks bearing Iron-oxide, hydroxyl and corundum minerals in the study area.This result permits to confirm that, the combination of remote sensing (Landsat 9 OLI and ASTER data in this case) and field data constitute a useful tool for mineral exploration in the shear zone. However, the accuracy assessment was relied on comparing the different maps produced from Landsat 9 OLI and ASTER data with the ground truth sample points and also, with the earliest geological map of Banyo area. Thus, quantitatively the results were accurate at 99%.

Nonlinear RNN with noise-immune: A robust and learning-free method for hyperspectral image target detection

While the recurrent neural network (RNN) has achieved remarkable performance on dynamic and control tasks, its applications to image processing, particularly target detection are limited. Challenges arise from differences between the two domains, such as the way for merging time information into static problems and variances of dynamic and static solving methods. To this end, we first extend the existing constrained energy minimization (CEM)-based detection scheme to a dynamic version, e.g. dynamic reinforced CEM (DRCEM), which injects the dynamic information. After that, aided by the rigorous mathematical derivation and optimization theory, the DRCEM is merged into the RNN solution framework. To enhance the robustness and convergence of the existing RNN solutions for improving DRCEM performance, the nonlinear and bounded-constraint RNN (NBCRNN) is designed by developing a novel nonlinear activation function, then applying the proposed model to implement the DRCEM scheme. The corresponding theorem results reveal the proposed model possesses global convergence and enhanced robustness. Compared to state-of-the-art works, the DRCEM solved by the NBCRNN model detection method achieves better detection accuracy, with 1.82% improvement in terms of the Kappa coefficient, and reduces the residual error from 10−4 to 10−7. Furthermore, our detection method is able to preserve the detection accuracy in presence of noise perturbated. To the best of our knowledge, it is the first work to develop the zeroing-type RNN for hyperspectral image target detection. The code and models are publicly available at Github DRCEM_NBCRNN Code Implementation.

A continuum theory for stripe-shaped magnetic domains in thin films

Starting from a potential-based kinematical description of continuously distributed stripe-shaped domain walls, a mesoscopic potential is derived through an averaging procedure. The resulting mesoscopic theory is formulated in terms of a few fields with physically meaningful microscopic interpretation. Based on a phenomenological closure-domain extension, a constrained energy minimization principle is introduced. A monolithic finite-element based numerical solution algorithm is proposed. Based on a consistent linearization of the numerical algorithm, quadratic convergence is obtained for the nonlinear solution procedure. A first simple examination of the theory is undertaken by simulating a thin film with spatially and temporally non-constant effective anisotropy. The results are found to be consistent with analytical predictions.

The geochemistry, origin, and hydrothermal alteration mapping associated with the gold-bearing quartz veins at Hamash district, South Eastern Desert, Egypt

Integrating diverse techniques and datasets, significantly enhances the accurate identification of various mineral deposits. This work aims to determine different types of mineral deposits in the Hamash district (Southern Eastern Desert, Egypt) by combining structural features (derived from ALOS PALSAR DEM), alteration zones (detected using ASTER and Sentinel-2), and ore mineralogy. Multispectral imaging, such as ASTER and Sentinel-2 satellite data, provides a cost-effective and efficient tool for lithological and hydrothermal alteration mapping utilizing selective band ratios (SBR), directed principal component analysis (DPCA), feature-oriented false-color composites (FFCC), and constrained energy minimization (CEM). The deductions drawn from the analysis of ASTER and Sentinel 2 satellite data are solidly corroborated through meticulous investigations of pre-existing lithological maps in the study area, on-site validation via fieldwork, and robust laboratory analysis, attesting to reliable results. Validation of remote sensing results was performed through field observations, petrographic investigations, X-ray diffraction technique (XRD), and SEM–EDX analyses. Based on ore mineralogy derived from XRD and SEM results the quartz-vein-associated ore minerals in the Hamash district include chalcopyrite, pyrite, hematite, goethite, bornite, covellite, and gold. According to the present paragenesis, the mineralization in the study area is classified into three types: sulfide mineralized zone, transitional zone, and supergene zone. Using an ore microscope, our studies identified that the alteration zones include gold-bearing sulfide minerals as well as the minerals goethite and malachite. In gold-bearing quartz samples, the concentrations of Cu, As, Ag, and Sb are positively correlated with Au at the degree of shear deformation. According to data gathered from the fire assay results, Au content varied from 0.027 to 57.20 ppm, along with Cu (10–6484 ppm), Ag (0.5–20.5 ppm), As (5–2046 ppm), Zn (3–1095 ppm), Pb (2–1383 ppm), and Sb (5–23). Our results confirmed that the Hamash region is one of the most important gold-bearing sites, with gold concentrations ranging from 0.027 up to 57.20 ppm. Furthermore, the current contribution highlighted four stages in the paragenetic sequence of the recorded ores, including magmatic, metamorphic, hydrothermal, and supergene by origin, indicating a considered similarity with the known Egyptian gold sites regarding host rocks, mineralization style, alteration assemblage, and several ore mineral conditions.