Relative Invariants Research Articles

Equivariant 𝒟-modules on 2×2×𝓃 hypermatrices

We study D \mathcal {D} -modules and related invariants on the space of 2 × 2 × n 2\times 2\times n hypermatrices for n ≥ 3 n\geq 3 , which has finitely many orbits under the action of G = G L 2 ( C ) × G L 2 ( C ) × G L n ( C ) G=GL_2(\mathbb {C}) \times GL_2(\mathbb {C}) \times GL_n(\mathbb {C}) . We describe the category of coherent G G -equivariant D \mathcal {D} -modules as the category of representations of a quiver with relations. We classify the simple equivariant D \mathcal {D} -modules, determine their characteristic cycles and find special representations that appear in their G G -structures. We determine the explicit D \mathcal {D} -module structure of the local cohomology groups with supports given by orbit closures. As a consequence, we calculate the Lyubeznik numbers and intersection cohomology groups of the orbit closures. All but one of the orbit closures have rational singularities: we use local cohomology to prove that the one exception is neither normal nor Cohen–Macaulay. While our results display special behavior in the cases n = 3 n=3 and n = 4 n=4 , they are completely uniform for n ≥ 5 n\geq 5 .

On the Stability of Planetary Motions During Stellar Approaches

The problem of the spatial motion of a passively gravitating body during an to the central body of a perturbing body – a test star – is considered. Using the exact expression of the force function, an integral invariant relationship – a quasi-integral – was found. Due to the quasi-integral, the regions of possible motion of the passively gravitating body, the surfaces of minimal energy (a generalization of the zero velocity surfaces), and the singular points of these surfaces were determined. The stability of planetary motion according to Hill during the approach of a test star to the Solar System was investigated. Criteria for the possibility, as well as the impossibility of capturing the passively gravitating body by the test star, were established. According to the Hill stability criteria, critical values of the orbital parameters of the test star were established, at which the planets of the Solar System either become satellites of the test star or leave the bounds of the Solar System.

A generalization of the shock invariant relationship

Shock invariant relationship, which was conceived for inert shock waves to derive the 4th power relationship between shock pressure and maximum strain rate, is generalized for reactive shock waves such as Chapman–Jouget detonation and shock-induced vaporization. The generalization, based on the first-order reaction models, is a power function relationship between overall dissipated energy (Δedis) and reaction time Δτ such that ΔedisΔτ1/α=constant, where the power coefficient α is found to be in the range of 2/3–4. Experimental data, though scarce, are consistent with the generalization. Implication of the generalization for inert shocks is also considered and suggests a broad range of the 4th power coefficient including an inequality equation that constrains the shock and particle velocity relationship.

Automated extrinsic calibration of solid-state frame LiDAR sensors with non-overlapping field of view for monitoring indoor stockpile storage facilities

Several industrial and commercial bulk material management applications rely on accurate, current stockpile volume estimation. Proximal imaging and LiDAR sensing modalities can be used to derive stockpile volume estimates in outdoor and indoor storage facilities. Among available imaging and LiDAR sensing modalities, the latter is more advantageous for indoor storage facilities due to its ability to capture scans under poor lighting conditions. Evaluating volumes from such sensing modalities requires the pose (i.e., position and orientation) parameters of the used sensors relative to a common reference frame. For outdoor facilities, a Global Navigation Satellite System (GNSS) combined with an Inertial Navigation System (INS) can be used to derive the sensors’ pose relative to a global reference frame. For indoor facilities, GNSS signal outages will not allow for such capability. Prior research has developed strategies for establishing the sensor position and orientation for stockpile volume estimation while relying on multi-beam spinning LiDAR units. These approaches are feasible due to the large range and Field of View (FOV) of such systems that can capture the internal surfaces of indoor storage facilities.The mechanical movement of multi-beam spinning LiDAR units together with the harsh conditions within indoor facilities (e.g., excessive humidity, wide range of temperature variation, dust, and corrosive environment in deicing salt storage facilities) limit the use of such systems. With the increasing availability of solid-state LiDAR units, there is an interest in exploring their potential for stockpile volume estimation. Despite their higher robustness to harsh conditions, solid-state LiDAR units have shorter distance measurement range and limited FOV when compared with multi-beam spinning LiDAR. This research presents a strategy for the extrinsic calibration (i.e., estimating the relative pose parameters) of installed solid-state LiDAR units inside stockpile storage facilities. The extrinsic calibration is made possible using deployed spherical targets and a complete, reference scan of the facility from another LiDAR sensing modality. The proposed research introduces strategies for: 1) automated extraction of the spherical targets; 2) automated matching of these targets in the solid-state LiDAR and reference scans using invariant relationships among them; and 3) coarse-to-fine estimation of the calibration parameters. Experimental results in several facilities have shown the feasibility of using the proposed methodology to conduct the extrinsic calibration and volume evaluation with an error percentage less than 3.5% even with occlusion percentages reaching up to 50%.

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Sequential parametrized topological complexity and related invariants

Sequential parametrized topological complexity and related invariants

Probing the structure of water in individual living cells

Water regulates or even governs a wide range of biological processes. Despite its fundamental importance, surprisingly little is known about the structure of intracellular water. Herein we employ a Raman micro-spectroscopy technique to uncover the composition, abundance and vibrational spectra of intracellular water in individual living cells. In three different cell types, we show a small but consistent population (~3%) of non-bulk-like water. It exhibits a weakened hydrogen-bonded network and a more disordered tetrahedral structure. We attribute this population to biointerfacial water located in the vicinity of biomolecules. Moreover, our whole-cell modeling suggests that all soluble (globular) proteins inside cells are surrounded by, on average, one full molecular layer (about 2.6 Angstrom) of biointerfacial water. Furthermore, relative invariance of biointerfacial water is observed among different single cells. Overall, our study not only opens up experimental possibilities of interrogating water structure in vivo but also provides insights into water in life.

Numerical Calculations of Adiabatic Invariants From MHD‐Driven Magnetic Fields

AbstractThe adiabatic invariants (M, J, Φ) and the related invariants (M, K, L*) have been established as effective coordinate systems for describing radiation belt dynamics at a theoretical level, and through numerical techniques, can be paired with in situ observations to order phase‐space density. To date, methods for numerical techniques to calculate adiabatic invariants have focused on empirical models such the Tsyganenko models TS05, T96, and T89. In this work, we develop methods based on numerical integration and variable step size iteration for the calculation of adiabatic invariants, applying the method to the Lyon‐Fedder‐Mobarry (LFM) global magnetohydrodynamics (MHD) simulation code, with optional coupling to the Rice Convection Model (RCM). By opening the door to adiabatic invariant modeling with MHD magnetic fields, the opportunity for exploratory modeling work of radiation belt dynamics is enabled. Calculations performed using LFM are cross‐referenced with the same code applied to the T96 and TS05 Tsyganenko models evaluated on the LFM grid. Important aspects of the adiabatic invariant calculation are reviewed and discussed, including (a) sensitivity to magnetic field model used, (b) differences in the problem between quiet and disturbed geomagnetic states, and (c) the selection of key parameters, such as the magnetic local time step size for drift shell determination. The rigorous development and documentation of this algorithm additionally acts as preliminary step for future thorough reassessment of in situ phase‐space density results using alternative magnetic field models.

Assessing nanobody interaction with SARS-CoV-2 Nsp9.

The interaction between SARS-CoV-2 non-structural protein Nsp9 and the nanobody 2NSP90 was investigated by NMR spectroscopy using the paramagnetic perturbation methodology PENELOP (Paramagnetic Equilibrium vs Nonequilibrium magnetization Enhancement or LOss Perturbation). The Nsp9 monomer is an essential component of the replication and transcription complex (RTC) that reproduces the viral gRNA for subsequent propagation. Therefore preventing Nsp9 recruitment in RTC would represent an efficient antiviral strategy that could be applied to different coronaviruses, given the Nsp9 relative invariance. The NMR results were consistent with a previous characterization suggesting a 4:4 Nsp9-to-nanobody stoichiometry with the occurrence of two epitope pairs on each of the Nsp9 units that establish the inter-dimer contacts of Nsp9 tetramer. The oligomerization state of Nsp9 was also analyzed by molecular dynamics simulations and both dimers and tetramers resulted plausible. A different distribution of the mapped epitopes on the tetramer surface with respect to the former 4:4 complex could also be possible, as well as different stoichiometries of the Nsp9-nanobody assemblies such as the 2:2 stoichiometry suggested by the recent crystal structure of the Nsp9 complex with 2NSP23 (PDB ID: 8dqu), a nanobody exhibiting essentially the same affinity as 2NSP90. The experimental NMR evidence, however, ruled out the occurrence in liquid state of the relevant Nsp9 conformational change observed in the same crystal structure.

A lifespan study of the confidence-accuracy relation in working memory and episodic long-term memory.

The relation between an individual's memory accuracy and reported confidence in their memories can indicate self-awareness of memory strengths and weaknesses. We provide a lifespan perspective on this confidence-accuracy relation, based on two previously published experiments with 320 participants, including children aged 6-13, young adults aged 18-27, and older adults aged 65-77, across tests of working memory (WM) and long-term memory (LTM). Participants studied visual items in arrays of varying set sizes and completed item recognition tests featuring 6-point confidence ratings either immediately after studying each array (WM tests) or following a long period of study events (LTM tests). Confidence-accuracy characteristic analyses showed that accuracy improved with increasing confidence for all age groups and in both WM and LTM tests. These findings reflect a universal ability across the lifespan to use awareness of the strengths and limitations of one's memories to adjust reported confidence. Despite this age invariance in the confidence-accuracy relation, however, young children were more prone to high-confidence memory errors than other groups in tests of WM, whereas older adults were more susceptible to high-confidence false alarms in tests of LTM. Thus, although participants of all ages can assess when their memories are weaker or stronger, individuals with generally weaker memories are less adept at this confidence-accuracy calibration. Findings also speak to potential different sources of high-confidence memory errors for young children and older adults, relative to young adults. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Invariant Charge Carrier Dynamics Using a Non-Planar Non-Fullerene Acceptor across Multiple Processing Solvents.

Conventional non-fullerene acceptors (NFAs) typically have planar structures that can enable improved electron mobility and produce more efficient organic photovoltaic devices. A relatively simple A-D-A'-D-A type NFA specifically designed to match with poly(3-hexylthiophene-2,5-diyl) (P3HT) for green-absorbing agrivoltaic applications has been examined using a variety of techniques: microsecond transient absorption spectroscopy, atomic force microscopy, and photoluminescence. Relatively invariant charge carrier decay dynamics are observed in the blend films across a variety of processing solvents. Raman spectroscopy in conjunction with computational studies reveals that this NFA is non-planar and that multiple conformations are present in films, while preserving the crystalline nature of P3HT. The non-planarity of the NFA therefore creates a dispersive acceptor environment, irrespective of processing solvent, and this leads to the observed relative invariance in charge carrier decay dynamics and high tolerance to morphological variation. The findings presented in this work highlight the potential of non-planar materials as acceptors in organic photovoltaic devices.

BPKEM: A biometric-based private key encryption and management framework for blockchain.

The fundamental technology behind bitcoin, known as blockchain, has been studied and used in a variety of industries especially in finance. The security of blockchain is extremely important as it will affects the assets of the clients as well as it is the lifeline feature of the entire system that needs to be guaranteed. Currently, there is a lack of a methodical approach to guarantee the security and dependability of the private key during its whole life. Furthermore, there is no quick, easy, or secure way to create the encryption key. A biometric-based private key encryption and management framework (BPKEM) for blockchain is proposed not only to solve the private key lifecycle manag- ement problem, but also it maintains compatibility with existing blockchain systems. For the problem of private key encryption, a biometric-based stable key generation method is proposed. By using the relative invariance between facial and fingerprint feature points, this measure can convert feature points into stable and distinguishable descriptors, then using a reusable fuzzy extractor to create a stable key. The correct- ness and efficiency of the newly proposed biometric-based blockchain encryption tech- nique in this paper has been validated in the experiments.

The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map

Given a smooth log Calabi–Yau pair (X, D), we use the intrinsic mirror symmetry construction to define the mirror proper Landau–Ginzburg potential and show that it is a generating function of two-point relative Gromov–Witten invariants of (X, D). We compute certain relative invariants with several negative contact orders, and then apply the relative mirror theorem of Fan et al. (Sel Math (NS) 25(4): Art. 54, 25, 2019. https://doi.org/10.1007/s00029-019-0501-z) to compute two-point relative invariants. When D is nef, we compute the proper Landau–Ginzburg potential and show that it is the inverse of the relative mirror map. Specializing to the case of a toric variety X, this implies the conjecture of m Gräfnitz et al. (2022) that the proper Landau–Ginzburg potential is the open mirror map. When X is a Fano variety, the proper potential is related to the anti-derivative of the regularized quantum period.

Rate-dependent damage sequence interaction model for predicting the mechanical property of in-service aluminum alloy 6005A-T6

Engineering structures and materials will undergo fatigue, aging, and other degradation behaviors during long-term service under the combined influence of complex boundary conditions. These service damages make the materials and structures no longer meet the initial design requirements and pose a potential risk to the service system. This study proposes a material mesoscopic model to decouple the microstructure into a system composed of matrix and void phases. The matrix phase has an invariant constitutive relationship as an ideally undamaged material, and the different evolutionary behaviors of the void phase are described as damage evolution functions and lead to different stress–strain behaviors of the actual material. First, the damage described by different definitions is proposed, and a nonlinear function of damage evolution consistent with the Weibull distribution characteristic of microstructural continuity is derived. Then, an experimental–numerical method is improved to accurately identify the accelerated damage evolution behavior under various strain rates. Finally, the ideally undamaged constitutive of the matrix phase and the damage evolution function of the void phase are established, which can cover the void nucleation, growth, and aggregation process. Besides, the damage sequence interaction model is established in conjunction with the mesoscopic physical mechanism, and the total damage evolution function for materials containing prior service damage in subsequent ductile deformation is achieved by measuring the apparent elastic modulus of the material only. Finally, the ideally undamaged constitutive and damage evolution function are calibrated for aluminum alloy 6005A-T6, commonly used in the car body structure of rail vehicles, and verified with damaged specimens that experienced certain service loads. The material's damage sequence interaction mode is determined, and the rate-dependent residual strength is predicted.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.

Discovering causally invariant features for out-of-distribution generalization

Out-of-distribution (OOD) generalization aims to generalize a model trained on source domains to unseen target domains. Recently, causality-based generalization methods have focused on learning invariant causal relationships around the label variable, as causal mechanisms are robust across different domains. However, these methods would yield an inaccurate causal variable set due to the lack of heterogeneous domain data or a prior causal structure, which severely weakens their generalization capacity. To address this problem, we propose a Causally Invariant Features Discovery (CIFD) framework, which combines causal structure discovery and causal effect estimation for selecting a high-quality causal variable set and realizing better OOD generalization. Specifically, CIFD first identifies all potential causal variables by learning a double-layer-based local causal structure around the label variable. Secondly, CIFD uses a double-layer causal effect estimator for estimating the causality of potential causal variables and obtaining true causal variables. The comprehensive experiments on both regression and classification tasks clearly demonstrate the superiority of our framework over the state-of-art methods.

Log‐based anomaly detection for distributed systems: State of the art, industry experience, and open issues

AbstractDistributed systems have been widely used in many safety‐critical areas. Any abnormalities (e.g., service interruption or service quality degradation) could lead to application crashes or decrease user satisfaction. These things may cause serious economic losses. Among the various quality assurance approaches for distributed systems, log‐based anomaly detection (LAD) has become a popular research topic. Its popularity relates to system logs being able to record and reveal important run‐time information. This paper presents a general LAD framework for distributed systems. Log grouping and feature‐pattern mining are two crucial LAD components that impact on the anomaly‐detection effectiveness. We also present a systematic survey of techniques in these two directions; propose classification frameworks for log grouping and feature patterns; and summarize four log‐grouping techniques and five feature patterns (which refer to invariant relationships among logs that can be used for anomaly detection). To evaluate their applicability, we report on the findings when applying existing techniques to Ray, a popular industrial distributed system. Based on these findings, several open issues are identified, which provide potential guidance for future research and development.

Marked relative invariants and GW/PT correspondences

We introduce marked relative Pandharipande-Thomas (PT) invariants for a pair (X,D) of a smooth projective threefold and a smooth divisor. These invariants are defined by integration over the moduli space of r-marked stable pairs on (X,D), and appear naturally when degenerating diagonal insertions via the Li-Wu degeneration formula. We propose a Gromov-Witten (GW) / PT correspondence for marked relative invariants. We show compatibility of the conjecture with the degeneration formula and a splitting formula for relative diagonals. The results provide new tools to prove GW/PT correspondences for varieties with vanishing cohomology.As an application we prove the GW/PT correspondence for:(i)all Fano complete intersections, and(ii)the reduced theories of (S×C,S×{z1,…,zN}) where S is a K3 surface and C is a curve, for all curve classes which have divisibility at most 2 over the K3 surface.In the appendix we introduce a notion of higher-descendent invariants which can be seen as an analogue of the nodal Gromov-Witten invariants defined by Argüz, Bousseau, Pandharipande and Zvonkine in [3]. We show that the higher-descendent invariants reduce to marked relative invariants with diagonal insertions.

КОНЦЕПЦІЯ ГЕНЕТИЧНОГО ЯДРА В СТРУКТУРНІЙ ОРГАНІЗАЦІЇ І ЕВОЛЮЦІЇ СКЛАДНИХ ЕЛЕКТРОМЕХАНІЧНИХ СИСТЕМ

The interdisciplinary aspect in the study of the core concept in complex genetically organized systems of natural and anthropogenic origin is analyzed. The purpose of the article is scientific substantiation of the nature and essence of the genetic core of the electromechanical system. Based on the provisions of the theory of genetic evolution of electromechanical systems, the information essence of the genetic core as a carrier of genetic information of the primary source of the electromagnetic field is revealed. The analysis of the invariant relationships of the genetic nucleus with the structure of groups, subgroupsand small periods, the generative system was carried out. An invariant connection between the core concept and the processes of evolutionary speciation and the main taxonomic categories of electromechanical systems has been established. Based on the results of the system-genetic analysis, a definition of the concept of the genetic core is proposed. The relationship between genetic and energy cores in the hierarchy of levels of complexity of electromechanical systems is studied. The principles of genetic structuring of complex systems of themultinuclear type are revealed. According to the results of the system-genetic analysis of the conception of the genetic core of electro-mechanical systems, its main properties are summarized. The im-portance of the obtained research results for the spreadof genetic prediction technology and interdisciplinary synthesis to complex electromechanical complexes with nuclei of different physical nature is emphasized

(Digital Presentation) Unraveling of the Morphology and Chemistry Dynamics in the FEC-Generated Silicon Anode SEI across Delithiated and Lithiated States

The silicon solid electrolyte interphase (SEI) faces cyclical cracking and reconstruction due to the ~350% volume expansion of Si which leads to shortened cell life during electrochemical cycling. Understanding the SEI morphology/chemistry and more importantly its dynamic evolution from delithiated and lithiated states is paramount to engineering a stable Si anode. Fluoroethylene carbonate (FEC) is a preferred additive with widely demonstrated enhancement of the Si cycling. Thus, insights into the effects of FEC on the dynamics of the resulting SEI may provide hints toward engineering the Si interface. Herein, ATR-FTIR, AFM, tip IR, and XPS probing all show pronounced relative invariance of the FEC-generated SEI compared to the FEC-free SEI between adjacent lithiated and delithiated states beyond the formation cycles. The SEI of Si thin film model surfaces in the baseline 1 M LiPF6 in EC:EMC (1:1) undergoes major morphological and chemical speciation swings between half-cycles while comparatively the SEI upon addition of FEC displays far less dynamic evolution. This morphology and chemistry stability of the FEC-SEI supports the enhanced cycling stability of silicon anodes in FEC-containing electrolytes. The experimental evidence gathered suggests that the FEC-SEI invariance is enabled by an elastomeric polycarbonate matrix that preserves the SEI integrity against the expansion of silicon upon lithiation. In turn, less electrolyte-consuming reconstruction occurs which manifests as and high LiF content from one half-cycle to the next. This work provides critical insights to enhance the silicon anode stability via targeted SEI engineering, namely that LiF protected by an elastomeric protective matrix may be key to buffering the unavoidable mechanical disruption. Figure 1