Embedding Theory Research Articles

Associations between telomere length, glucocorticoid receptor gene DNA methylation, volume of stress-related brain structures, and academic performance in middle-school-age children

BackgroundThe biological embedding theory posits that early life experiences can lead to enduring physiological and molecular changes impacting various life outcomes, notably academic performance. Studying previously revealed and objective biomarkers of early life stress exposure, such as telomere length (TL), glucocorticoid receptor gene DNA methylation (DNAme), and the volume of brain structures involved in the regulation of HPA axis functioning (the hippocampus, the amygdala, and the medial prefrontal cortex), in relation to academic performance is crucial. This approach provides an objective measure that surpasses the limitations of self-reported early life adversity and reveals potential molecular and neurological targets for interventions to enhance academic outcomes. MethodsThe participants were 52 children of Mexican or Central American origin aged 11.6–15.6 years. DNA methylation levels and TL were analyzed in three cell sources: saliva, whole blood, and T cells derived from whole blood. ResultsOverall, the concordance across three systems of stress-related biomarkers (TL, DNAme, and the brain) was observed to some extent, although it was less pronounced than we expected; no consistency in different cell sources was revealed. Each of the academic domains that we studied was characterized by a unique and distinct complex of associations with biomarkers, both in terms of the type of biomarker, the directionality of the observed effects, and the cell source of biomarkers. Furthermore, there were biomarker-by-sex interaction effects in predicting academic performance measures. ConclusionsAssessed in an understudied youth sample, these preliminary data present new essential evidence for a deepened understanding of the biological mechanisms behind associations between exposure to early life stress and academic performance.

Research on the Fourteenth National Games Effect on Tennis Course Based on Social Embedding Theory

The Fourteenth Games in 2021 was successfully held in Shaanxi Province inside which many universities also played a more important role in the Fourteenth Games, and were affected by the Games in turn. This article, by adopting such research methods as the literature and data method, questionnaire survey method, interview method, logic analysis method, and comprehensive induction method, analyzes students’ insight into the Games and how they conduct physical exercises after the Games. And by using the theory of social embedding to study effects of the Games on tennis courses of colleges and universities. Through research, with the help of social embedding theory, the embedded subject of this article is the Effects of the Fourteenth National Games. The embedded object is P.E of Universities. The embedded content is the effects such as sports culture and sports incentives brought about by the Games. The subjects of behavior in embedding process are college students. The Games have exerted aspects of impact on college sports including the sports spirit such as the competition, the sports culture, and the hard work contained in the sports courses are embedded in the physical education courses. When this embedding process is stable and lasts long, the Games will have a profound impact on college physical education courses, and it will also affect the colleges and universities as well as their college sports courses, Students 'attitudes and behaviors have promoted the teaching of tennis curriculum, promoted students' post -school exercises, and achieved tennis popularization. It also helps to promote the construction of sports culture and sports spirit in colleges and universities.

Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients.

The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.

Neighborhood effect, virtual social networks, and farmers' social e‐commerce participation behavior

AbstractThe development of social e‐commerce can integrate the production, circulation, and sales of agricultural products; realize the digitalization of the agricultural production process; and promote farmers' savings and profits. On the basis of the stimulus–organism–response theory and the embedding theories, microsurvey data of 302 farmers regarding the winter jujube production area of the Dali facility in the Shaanxi Province were used to empirically test the impact of neighborhood effect (NE) and virtual social networks on farmers' participation in social e‐commerce, and the interaction effect of the two aspects. Additionally, we analyzed its mechanism under the framework of “social networks‐farmers' cognition‐social e‐commerce participation behavior (SEPB).” The research results are as follows. First, neighborhood participation, social software friends, and information release have a significant positive impact on farmers' SEPB, whereas information reception has a negative impact. Second, the empirical results considering the comprehensive effects of various variables show that NE, network communication, and network participation (NP) can all promote farmers' participation in social e‐commerce, and NP is complementary to NE. Third, mechanism analysis shows that NE and NP produce partial mediating effect and complete mediating effect, respectively, through self‐competence recognition (SR), which in turn positively impacts the SEPB. In the heterogeneity analysis, for farmers with a plantation area of less than or equal to 0.447 ha, SR has a partial mediating effect on the process of NE affecting SEPB, whereas the motivating factor is NP. In terms of labor force structure, only the percentage of nonagricultural workers exceeds 0.253, NE and NP affect SEPB through SR. This study can provide a reference for farmers to rationally use their social networks, and guide the formulation of social e‐commerce support policies at the national level.

Multivariate multiscale dispersion Lempel–Ziv complexity for fault diagnosis of machinery with multiple channels

Lempel–Ziv complexity (LZC), as a nonlinear feature in information science, has shown great promise in detecting correlations and capturing dynamic changes in single-channel time series. However, its application to multichannel data has been largely unexplored, while the complexity of real-world systems demands the utilization of data collected from multiple sensors or channels so as to extract distinguishable fault features for fault diagnosis. This paper proposes a novel method called multivariate multiscale dispersion Lempel–Ziv complexity (mvMDLZC) to extract the fault features hidden in multi-source information. First, multivariate embedding theory is applied to obtain multivariate embedded vectors and multivariate dispersion patterns, which can reflect the inherent relationships in the multichannel series. Second, by assigning labels to these patterns, the original multichannel time series can be transformed into a symbolic sequence with multiple symbols instead of the original binary conversion, enabling the accurate recovery of the system dynamics. Finally, the complexity counter value and normalized LZC are calculated for the complexity measure. Experimental results using synthetic and real-world datasets demonstrate that mvMDLZC outperforms existing LZC-based methods and multivariate dispersion entropy in recognizing different states of mechanical systems. Additionally, mvMDLZC exhibits robustness in handling challenges such as small sample datasets and noise interference, making it suitable for real industrial applications. These findings highlight the potential of mvMDLZC as a valuable approach for dissecting multichannel systems across various real-world scenarios.

Towards Early Dark Energy in string theory

Early Dark Energy (EDE) is a prominent model to resolve the Hubble tension, which employs a dynamical axion with a periodic potential. In this work, we take first steps towards the embedding of this model into stable compactifications of string theory. First, we provide a pedagogical review of the EDE scenario and its main challenges. Second, we construct a simple supergravity toy model using only minimal ingredients. Already at this level, we can understand the origin of the harmonics of the EDE scalar potential in terms of a delicate balance of the leading terms from separate non-perturbative effects. Third and final, we embed the model into a KKLT-type compactification, with the EDE scalar field realized by a two-form axion. We find that a successful embedding, with all moduli stabilized, requires restrictive assumptions, which are lacking at present a known string theory implementation mechanism, both on the Pfaffians and on the exponents of the non-perturbative terms responsible for the EDE dynamics. We point out that such non-generic conditions reflect well known challenges of the EDE model and further investigation might guide us towards a conclusive resolution. An alternative viewpoint suggests that rather than serving as the foundation for a string theory embedding, these conditions might instead indicate that EDE is, in fact, incompatible with string theory, at least in the realizations we study here. Further investigation will be needed to ascertain the status of EDE in string theory.

A Versatile Unitary Transformation Framework for an Optimal Bath Construction in Density-Matrix Based Quantum Embedding Approaches

The performance of embedding methods is directly tied to the quality of the bath orbital construction. In this paper, we develop a versatile framework, enabling the investigation of the optimal construction of the orbitals of the bath. As of today, in state-of-the-art embedding methods, the orbitals of the bath are constructed by performing a Singular Value Decomposition (SVD) on the impurity-environment part of the one-body reduced density matrix, as originally presented in Density Matrix Embedding Theory. Recently, the equivalence between the SVD protocol and the use of unitary transformation, the so-called Block-Householder transformation, has been established. We present a generalization of the Block-Householder transformation by introducing additional flexible parameters. The additional parameters are optimized such that the bath-orbitals fulfill physically motivated constraints. The efficiency of the approach is discussed and exemplified in the context of the half-filled Hubbard model in one-dimension.

Dark matter as a gravitational effect in the embedding theory approach

Dark matter as a gravitational effect in the embedding theory approach

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding.

The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

Structural embeddedness, entrepreneurial behavior, and firm performance in the industry network of small tourism enterprises: The moderating role of relational embeddedness and leadership self-efficacy

The survival and economic sustainability of small tourism enterprises (STEs) represent pressing industry issues that require attention. Drawing on network embedding theory, this paper proposes a conceptual framework that links the structural embeddedness of STEs' industry networks to entrepreneurial behavior and firm performance, while exploring the moderating roles of relational embeddedness and leadership self-efficacy. Empirical analysis using a sample of 420 STEs in China revealed several key findings: (1) STEs with a dominant position in the industry network tend to exhibit higher firm performance, and do so through timely and effective entrepreneurial behavior; (2) maintaining a dominant position in the industry network structure requires not only deep cooperation between business owners and other industry participants, but also the advisory role of family, relatives, and friends, who are close and responsible partners providing practical advice to small business owners that influence their entrepreneurial behavior; (3) however, the aforementioned benefits are conditional on entrepreneurs possessing a strong sense of leadership self-efficacy. Theoretical and practical implications are further discussed in this regard.

Photophysics of tz Adenine and tz Guanine fluorescent nucleobases embedded into DNA and RNA.

UV-VIS photoinduced events of tz A and tz G embedded into DNA and RNA are described by combining the Extended Multi-State Second-Order Perturbation Theory (XMS-CASPT2) and electrostatic embedding molecular mechanics methods (QM/MM). Our results point out that the S1 1 (ππ* La ) state is the bright state in both environments. After the photoexcitation to the S1 1 (ππ* La ) state, the electronic population evolves barrierless towards its minimum, from where the excess of energy can be dissipated by fluorescence. As the minimum energy crossing point structure between the ground and first bright states lies in a high-energy region, the direct internal conversion to the ground state is an unviable mechanism. Other spectroscopic properties (for instance, absorption and Stokes shifts) and comparisons with photochemical properties of canonical nucleobases are also provided.

A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation.

The equivalence in one-electron quantum baths between the practical implementation of density matrix embedding theory (DMET) and the more recent Householder-transformed density matrix functional embedding theory has been shown previously in the standard but special case where the reference full-size (one-electron reduced) density matrix, from which the bath is constructed, is idempotent [S. Yalouz et al., J. Chem. Phys. 157, 214112 (2022)]. We prove mathematically that the equivalence remains valid when the density matrix is not idempotent anymore, thus allowing for the construction of correlated (one-electron) quantum baths. A density-matrix functional exactification of DMET is derived within the present unified quantum embedding formalism. Numerical examples reveal that the embedding cluster can be quite sensitive to the level of density-matrix functional approximation used for computing the reference density matrix.

Embedding Nonrigid Solutes in an Averaged Environment: A Case Study on Rhodopsins.

Many simulation methods concerning solvated molecules are based on the assumption that the solvated species and the solvent can be characterized by some representative structures of the solute and some embedding potential corresponding to this structure. While the averaging of the solvent configurations to obtain an embedding potential has been studied in great detail, this hinges on a single solute structure representation. This assumption is re-examined and generalized for conformationally flexible solutes and tested on 4 nonrigid systems. In this generalized approach, the solute is characterized by a set of representative structures and the corresponding embedding potentials. The representative structures are identified by means of subdividing the statistical ensemble, which in this work is generated by a constant-temperature molecular dynamics simulation. The embedding potential defined in the Frozen-Density Embedding Theory is used to characterize the average effect of the solvent in each subensemble. The numerical examples concern the vertical excitation energies of protonated retinal Schiff bases in protein environments. It is comprehensively shown that subensemble averaging leads to huge computational savings compared with explicit averaging of the excitation energies in the whole ensemble while introducing only minor errors in the case of the systems examined.

In the context of mass entrepreneurship network embeddedness and entrepreneurial innovation performance of high-tech enterprises in Guangdong province

PurposeThe study aimed to analyze the influence of network embeddedness on the innovation performance of high-tech enterprises in Guangdong Province.Design/methodology/approachA conceptual model of the influence of network embeddedness on the innovation performance of high-tech enterprises in Guangdong province is established, which takes the business model as the mediating variable and political association as the moderating variable. Multivariate statistical analysis and the MacKinnon confidence interval method were used to analyze 418 questionnaires.FindingsThe results show that both relational embeddedness and structural embeddedness have significant positive effects on the innovation performance of high-tech enterprises in Guangdong Province. The business model has a partial mediating effect between relationship embeddedness, structure embeddedness, and innovation performance of high-tech enterprises in Guangdong Province, respectively. Political relevance has a significant negative moderating effect on the relationship between the relationship embeddedness and innovation performance of high-tech enterprises in Guangdong Province, but the moderating effect on structural embeddedness and innovation performance of high-tech enterprises in Guangdong province has not been verified.Research limitations/implicationsThe study of this paper also has some shortcomings: very few data research samples exist; the external factors affecting the performance of high-tech enterprises in Guangdong Province need to be further refined. The research scale needs further improvement.Practical implicationsIn this paper, embedding theory, transaction cost theory, resource dependence theory, rent-seeking theory, new institution theory and uncertainty management theory were integrated by system attempt to reveal the mediating and moderating roles of business model and political relevance, respectively, between network embeddedness behavior and entrepreneurial innovation performance of high-tech enterprises. The research conclusions expand the relevant research in the field of entrepreneurial innovation. At the same time, the research results provide theoretical support and reference for the innovative growth of high-tech enterprises and government behavior decision-making in Guangdong province.Originality/valueNetwork embeddedness will have a profound impact on the entrepreneurial innovation performance of high-tech enterprises. Existing research has overlooked discussing this issue from the perspective of internal and external influencing factors within the enterprise. Therefore, this study addresses this issue by (1) introducing the business model as the mediating variable from an internal perspective of the enterprise, (2) introducing political association as the moderating variable from an external perspective of the enterprise and (3) 418 original questionnaires of high-tech enterprises in Guangdong Province were used to test the effect of the study variables.

Embeddings of Decomposition Spaces

Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A decomposition space D ( Q , L p , Y ) \mathcal {D}(\mathcal {Q}, L^p, Y) is determined by a covering Q = ( Q i ) i ∈ I \mathcal {Q} = (Q_i)_{i \in I} of the frequency domain, an integrability exponent p p , and a sequence space Y ⊂ C I {Y \subset \mathbb {C}^I} . Given these ingredients, the decomposition space norm of a distribution g g is defined as ‖ g ‖ D ( Q , L p , Y ) = ‖ ( ‖ F − 1 ( φ i ⋅ g ^ ) ‖ L p ) i ∈ I ‖ Y , { \left \Vert g \right \Vert _{\mathcal {D}(\mathcal {Q}, L^p, Y)} = \left \Vert \left ( \left \Vert \mathcal {F}^{-1} \left ( \varphi _{i} \cdot \widehat {g} \right ) \right \Vert _{L^{p}} \right )_{i \in I} \right \Vert _{Y} } , where ( φ i ) i ∈ I (\varphi _i)_{i \in I} is a suitable partition of unity for Q \mathcal {Q} . We establish readily verifiable criteria which ensure the existence of a continuous inclusion (“an embedding”) D ( Q , L p 1 , Y ) ↪ D ( P , L p 2 , Z ) \mathcal {D}(\mathcal {Q},L^{p_1},Y) \hookrightarrow \mathcal {D}(\mathcal {P},L^{p_2},Z) , mostly concentrating on the case where Y = ℓ w q 1 ( I ) Y = \ell _{w}^{q_{1}} ( I ) and Z = ℓ v q 2 ( J ) Z = \ell _{v}^{q_{2}} (J) . Under suitable assumptions on Q , P \mathcal {Q}, \mathcal {P} , we will see that the relevant sufficient conditions are p 1 ≤ p 2 p_{1} \leq p_{2} and finiteness of a nested norm of the form \[ ‖ ( ‖ ( α i β j ⋅ v j / w i ) i ∈ I j ‖ ℓ t ) j ∈ J ‖ ℓ s , with I j = { i ∈ I : Q i ∩ P j ≠ ∅ } for j ∈ J . \left \Vert \left ( \left \Vert \left ( \alpha _{i} \beta _{j} \cdot v_{j} / w_{i} \right )_{ i \in I_{j}} \right \Vert _{\ell ^{t}} \right )_{j\in J} \right \Vert _{\ell ^{s}} \, , \quad \text {with} \quad I_{j} = \left \{ i \in I \,:\, Q_{i} \cap P_{j} \neq \varnothing \right \} \quad \text {for } j \in J \,. \] Like the sets I j I_j , the exponents t , s t, s and the weights α , β \alpha , \beta only depend on the quantities used to define the decomposition spaces. In a nutshell, in order to apply the embedding results presented in this article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings. These sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of p 1 , p 2 p_1, p_2 , our criteria yield a complete characterization for the existence of the embedding. The same holds for arbitrary values of p 1 , p 2 p_1, p_2 under more strict assumptions on the coverings. We also prove a rigidity result, namely that—for ( p 1 , q 1 ) ≠ ( 2 , 2 ) (p_{1}, q_{1}) \neq (2, 2) —two decomposition spaces D ( Q , L p 1 , ℓ w q 1 ) \mathcal {D}(\mathcal {Q}, L^{p_1}, \ell _w^{q_1}) and D ( P , L p 2 , ℓ v q 2 ) \mathcal {D}(\mathcal {P}, L^{p_2}, \ell _v^{q_2}) can only coincide if their “ingredients” are equivalent, that is, if p 1 = p 2 p_{1} = p_{2} and q 1 = q 2 q_{1} = q_{2} and if the coverings Q , P \mathcal {Q}, \mathcal {P} and the weights w , v w, v are equivalent in a suitable sense. The resulting embedding theory is illustrated by applications to α \alpha -modulation and Besov spaces. All known embedding results for these spaces are special cases of our approach; often, we improve considerably upon the state of the art.

Density Matrix Embedding Using Multiconfiguration Pair-Density Functional Theory.

We present a quantum embedding method for ground and excited states of extended systems that uses multiconfiguration pair-density functional theory (MC-PDFT) with densities provided by periodic density matrix embedding theory (pDMET). We compute local excitations in oxygen mono- and divacancies on a magnesium oxide (100) surface and find absolute deviations within 0.05 eV between pDMET using the MC-PDFT, denoted as pDME-PDFT, and the more expensive, nonembedded MC-PDFT approach. We further use pDME-PDFT to calculate local excitations in larger supercells for the monovacancy defect, for which the use of nonembedded MC-PDFT is prohibitively costly.

Solvent Dynamics Are Critical to Understanding Carbon Dioxide Dissolution and Hydration in Water.

Simulations of carbon dioxide (CO2) in water may aid in understanding the impact of its accumulation in aquatic environments and help advance technologies for carbon capture and utilization (via, e.g., mineralization). Quantum mechanical (QM) simulations based on static molecular models with polarizable continuum solvation poorly reproduce the energetics of CO2 hydration to form carbonic acid in water, independent of the level of QM theory employed. Only with density-functional-theory-based molecular dynamics and rare-event sampling, followed by energy corrections based on embedded correlated wavefunction theory (in conjunction with density functional embedding theory), can a close agreement between theory and experiment be achieved. Such multilevel simulations can serve as benchmarks for simpler, less costly models, giving insight into potential errors of the latter. The strong influence of sampling/averaging over dynamical solvent configurations on the energetics stems from the difference in polarity of both the transition state and product (both polar) versus the reactant (nonpolar). When a solute undergoes a change in polarity during reaction, affecting its interaction with the solvent, careful assessment of the energetic contribution of the solvent response to this change is critical. We show that static models (without structural sampling) that incorporate three explicit water molecules can yield far superior results than models with more explicit water molecules because fewer water molecules yield less configurational artifacts. Static models intelligently incorporating both explicit (molecules directly participating in the reaction) and implicit solvation, along with a proper QM theory, e.g., CCSD(T) for closed-shell systems, can close the accuracy gap between static and dynamic models.

Embedding theory of reservoir computing and reducing reservoir network using time delays

The dynamics of reservoir computing (RC), a compact recurrent neural network, is validated as a higher-dimensional embedding of the input nonlinear dynamics. Based on this rigorous validation, a delayed RC is established with a significantly reduced network size and a promoted memory capacity, which can achieve dynamics reconstruction even in the reservoir with a single neuron.

Ab initio quantum simulation of strongly correlated materials with quantum embedding

Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in the quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multifragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin-polarized states of a hydrogen chain (1D-H), the equation of state of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices.

Effective Reconstruction of Expectation Values from Ab Initio Quantum Embedding.

Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary "cluster" problems to exploit the locality of the correlated physics. In this work, we critically review approaches to recombine these fragmented solutions in order to compute nonlocal expectation values, including the total energy. Starting from the democratic partitioning of expectation values used in density matrix embedding theory, we motivate and develop a number of alternative approaches, numerically demonstrating their efficiency and improved accuracy as a function of increasing cluster size for both energetics and nonlocal two-body observables in molecular and solid state systems. These approaches consider the N-representability of the resulting expectation values via an implicit global wave function across the clusters, as well as the importance of including contributions to expectation values spanning multiple fragments simultaneously, thereby alleviating the fundamental locality approximation of the embedding. We clearly demonstrate the value of these introduced functionals for reliable extraction of observables and robust and systematic convergence as the cluster size increases, allowing for significantly smaller clusters to be used for a desired accuracy compared to traditional approaches in ab initio wave function quantum embedding.