Abstract We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein–Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza–Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the $$\Lambda $$ Λ CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the $$\Lambda $$ Λ CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.

One of the main problems in cosmology is to resolve the problem of accelerating expansion and cosmological coincidence problem of the late universe. Many models, such as the cosmological constant model, the scalar field model, and the holographic model proposed in Einstein’s tensor gravity theory, have solved many problems in explaining these problems. The Brans-Dicke (BD) scalar-tensor theory, proposed by Brans and Dicke in 1961, is a generalization of Einstein’s tensor theory of gravity. In this theory, the scalar field can be combined with gravity, and many scalar field models have been proposed, since the observational constraints of the coupling parameters are not clear. In general formalism for scalar fields, parameterization may be relevant in some sense. For example, parameterization of parameters such as dark matter-dark energy interaction coefficient, equation of state parameter, and holographic constant, which have been proposed to solve the problem of cosmological coincidence problem, has some significance. Therefore, in this paper, we have applied the well-known Jassal-Bagular-Padmanabhann (JBP) parameterization in cosmology to the scalar field to construct a holographic scalar field model, perform cosmological verification, and consider the problem of late cosmic acceleration expansion and cosmological coincidence problem. The model parameters obtained by minimizing the chi-square function have nonzero values, and the current values of the transition red shift, equation of state parameter, deceleration parameter, and coincidence parameter are in good agreement with previous studies. We also confirmed the validity of the model and finally obtained a limit on the rate of change of the gravitational constant.

A massive vector field is a highly promising candidate for dark matter in the Universe. A salient property of dark matter is its negligible or null coupling to ordinary matter, with the exception of gravitational interaction. This poses a significant challenge in producing the requisite amount of dark particles through processes within the Standard Model. In this study, we examine the production of a vector field during inflation due to its direct interaction with the inflaton field through kinetic and axionlike couplings as well as the field-dependent mass. The gradient-expansion formalism, previously proposed for massless Abelian gauge fields, is extended to include the longitudinal polarization of a massive vector field. We derive a coupled system of equations of motion for a set of bilinear functions of the vector field. This enables us to address the nonlinear dynamics of inflationary vector field production, including backreaction on background evolution. To illustrate this point, we apply our general formalism to a low-mass vector field whose kinetic and mass terms are coupled to the inflaton via the Ratra-type exponential function. The present study investigates the production of its transverse and longitudinal polarization components in a benchmark inflationary model with a quadratic inflaton potential. It has been demonstrated that pure mass coupling is able to enhance only the longitudinal components. By turning on also the kinetic coupling, one can get different scenarios. As the coupling function decreases, the primary contribution to the energy density is derived from the transverse polarizations of the vector field. Conversely, for an increasing coupling function, the longitudinal component becomes increasingly significant and rapidly propels the system into the strong backreaction regime.

The relevance of the article is determined by the problem of evaluating the effectiveness of developing human resource management systems in enterprises that distribute consumer goods, operating under complex conditions of high operational dynamism, seasonal demand fluctuations, digital transformation, and intensified market competition. It has been established that existing approaches to evaluating HR systems primarily cover certain aspects of personnel management and do not provide a comprehensive analysis necessary to improve the performance of distribution enterprises. The purpose of the study is to substantiate the theoretical and methodological foundations and to develop an integrated model for evaluating the effectiveness of developing human resource management systems in enterprises that distribute consumer goods. The research methodology is based on general scientific methods, including analysis, synthesis, formalization, and modeling. During the study, specific research methods were also applied, such as economic analysis, organizational diagnostics, HR analytics, benchmarking of HR indicators, the KPI method, and competency assessment. During the research, modern scientific methods for evaluating human resource management were analyzed, industry-specific features of distributors’ activities were identified, key HR challenges affecting the effectiveness of HR systems were systematized, and relevant analytical methods, including KPI and HR analytics, were evaluated. The result of the study is the development of an integrated evaluation model that includes operational-performance, strategic-developmental, and digital-analytical components, which, when combined, provide a comprehensive diagnosis of the enterprise’s HR system. The model enables the identification of the strengths and weaknesses of HR functions, the detection of structural imbalances, and the outlining of directions to improve the effectiveness of human resource management. Prospects for further research include adapting the developed model to evaluate the effectiveness of HR systems in distribution enterprises, accounting for different business scales, and developing digital tools for automated HR analytics to support managerial decision-making. Keywords: human resource management; HR system; effectiveness evaluation; distribution enterprises; integral model; KPI; HR analytics; HR Scorecard; human capital; digitalization of HR management.

We develop the quantization of a recently proposed model describing a totally antisymmetric rank- p tensor-spinor field (a fermionic p -form theory) in d -dimensional anti–de Sitter (AdS) space. The model provides a new nontrivial example of a reducible gauge theory, in which gauge transformations are linearly dependent and the degree of reducibility increases with p . It is well-known that in such cases the standard Faddeev-Popov-DeWitt prescription for the generating functional is not applicable. We quantize the fermionic p -form theory using the general Batalin-Vilkovisky formalism, employing two distinct gauge fermions associated with gauge-fixing functions of different admissible ranks, confirming the independence from the gauge choice. As a result, we obtain the quantum effective action in terms of a sequence of functional determinants corresponding to specific Dirac-like operators on AdS space.

This paper presents the complete axiomatic foundation of the Ze Vector Theory (ZVT), a unified framework for fundamental physics. ZVT posits a single ontological primitive—the Ze State—which inherently admits both a continuous (vector) and a discrete (counter) representation. From this basis, the theory derives space and time as antiparallel, co-equal projections of the State, rather than assuming them as a background manifold. Physical dynamics are defined as the norm-preserving redistribution of the State's measure, from which causality and quantum phenomena emerge naturally. Quantum discreteness is shown to be a consequence of the discrete substrate, while interference patterns arise from the superposition of statistical pathways for state transitions, eliminating the need for a physical collapse postulate. The theory intrinsically defines an observer as an autonomous subsystem capable of stable registration. Crucially, ZVT demonstrates that Special Relativity, General Relativity, standard Quantum Theory, and Causal Set Theory arise as specific limiting regimes of its general formalism. By deriving, rather than postulating, the core concepts of modern physics and seamlessly integrating the continuous and discrete, ZVT offers a coherent, monistic, and relational foundation for a unified description of reality.

A bstract We develop a general formalism to describe the Renormalization Group Flow of Schur indices and fusion algebras of BPS line defects in four-dimensional 𝒩 = 2 Supersymmetric Quantum Field Theories. The formalism includes and extends known results about the Seiberg-Witten description of these structures. Another application of the formalism is to describe the spectrum of BPS partices of 𝒩 = 2 gauge theories with matter in terms of the spectrum of pure 𝒩 = 2 gauge theories. Applications to the theory of quantum groups and to the quantization of cluster varieties are also discussed.

A bstract In this paper, we investigate the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix defined on a single Cauchy surface. We present the construction of the spacetime density matrix in general quantum systems and its representation via the Schwinger-Keldysh path integral. We further introduce a super-operator framework, within which the spacetime density matrix appears as a special case, and discuss possible generalizations from this perspective. We also show that the spacetime density matrix satisfies a Liouville-von Neumann type equation of motion. When considering subsystems, a reduced spacetime density matrix can be defined by tracing over complementary degrees of freedom. We study the general properties of its moments and, in particular, derive universal short-time behavior of the second moment. We find that coupling between subsystems plays a crucial role in obtaining nontrivial results. Assuming weak coupling, we develop a perturbative method to compute the moments systematically.

We introduce the concept of gauged Lagrangian 1-forms, extending the notion of Lagrangian 1-forms to the setting of gauge theories. This general formalism is applied to a natural geometric Lagrangian 1-form on the cotangent bundle of the space of holomorphic structures on a smooth principal G-bundle mathcal {P} over a compact Riemann surface C of arbitrary genus g, with or without marked points, in order to gauge the symmetry group of smooth bundle automorphisms of mathcal {P}. The resulting construction yields a multiform version of the 3d mixed BF action with so-called type A and B defects, providing a variational formulation of Hitchin’s completely integrable system over C. By passing to holomorphic local trivialisations and going partially on-shell, we obtain a unifying action for a hierarchy of Lax equations describing the Hitchin system in terms of meromorphic Lax matrices. The cases of genus 0 and 1 with marked points are treated in greater detail, producing explicit Lagrangian 1-forms for the rational Gaudin hierarchy and the elliptic Gaudin hierarchy, respectively, with the elliptic spin Calogero–Moser hierarchy arising as a special subcase.

Purpose. The objective of this study is to analyze the concept of digital twins as a technology integrating complexity theory and artificial intelligence, and to examine their applications across various fields. Particular emphasis is placed on mathematical approaches to the construction of digital twins, their distinctions from traditional mathematical models, and future development prospects. Methods. This research employs an interdisciplinary approach, incorporating an analysis of contemporary technologies such as physics-informed neural networks, reduced-order models, graph neural networks, and reservoir computing. A comparison of first-principles and data-driven modeling methods is conducted, with a focus on their integration for creating hybrid digital twins. Results. The findings demonstrate that digital twins possess unique characteristics, including dynamism, adaptability, and bidirectional interaction with physical objects. The key advantages and limitations of various mathematical approaches are identified, encompassing their applicability in industry, medicine, economics, and other domains. A general mathematical formalization of a digital twin, integrating traditional models and machine learning methods, is proposed. Conclusion. The prospects for the development of digital twins are outlined, including the creation of end-to-end ecosystems and the advancement of hybrid approaches for modeling complex nonlinear processes. The importance of further integration of complexity theory and artificial intelligence methods to enhance the accuracy and adaptability of virtual models is emphasized. Digital twins present new opportunities for the forecasting and management of complex systems under uncertainty, establishing them as a pivotal tool in science, industry, and society.

We present a comprehensive Floquet-Nambu theory to describe the time-dependent quantum transport in mesoscopic circuits involving superconductors. The central object of our framework is the first-order correlation function, which accounts for the excitations that are generated by a time-dependent voltage and their coherent scattering off the interface with a superconductor. We analyze the time-dependent current generated by periodic voltage pulses and how it depends on the excitation energies of the voltage drive compared to the gap of the superconductor. Our general formalism allows us to identify the conditions for the excitations that are scattered off the superconductor to become coherent electron-hole superpositions. To this end, we consider the purity of the outgoing states, which characterizes their ability to carry quantum information. To illustrate our formalism, we apply it to a system composed of chiral quantum Hall edge states connected to a superconductor, and we calculate the current in the outgoing lead and the purity of the outgoing states for Lorentzian and harmonic voltage drives. Our framework paves the way for systematic investigations of time-dependent scattering problems involving superconductivity, and it may help interpret future experiments in electron quantum optics with superconductors.

We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate. We derive a generic formula for a transversal T gate on color codes defined on general 3-manifolds, which acts as collective non-Clifford logical gates on any triplet of logical qubits with their logical- X membranes having a Z 2 triple intersection at a single point. The triple-intersection number is a topological invariant, which also arises in the path integral of the emergent higher symmetry operator in a topological quantum field theory (TQFT): the Z 2 3 gauge theory. Moreover, the transversal S gate of the color code corresponds to a higher-form symmetry in TQFT supported on a codimension-1 submanifold, giving rise to exponentially many addressable and parallelizable logical gates. A construction of constant-depth circuits of the above logical gates via cup-product cohomology operation is also presented for three copies of identical toric codes on arbitrary 3-manifolds. We have developed a generic formalism to compute the triple-intersection invariants for 3-manifolds, with the structure encoded into an interaction hypergraph which determines the logical gate property and also corresponds to the hypergraph magic state that can be injected into the code without distillation (“”). We also study the scaling of the Betti number and systoles with volume for various 3-manifolds, which translates to the encoding rate and distance. We further develop three types of LDPC codes supporting such logical gates: (1) A quasi-hyperbolic code from the product of 2D hyperbolic surface and a circle, with almost-constant rate k / n = O ( 1 / log  ( n ) ) and O ( log  ( n ) ) distance; (2) A homological fiber-bundle code from twisting the product by an isometry of the surface based on the construction by Freedman-Meyer-Luo, with O ( 1 / log 1 2  ( n ) ) rate and O ( log 1 2  ( n ) ) distance; (3) A specific family of 3D hyperbolic codes: the Torelli mapping-torus code, constructed from mapping tori of a pseudo-Anosov element in the Torelli subgroup, which has constant rate while the distance scaling is currently unknown. We then show a generic constant-overhead scheme for applying a parallelizable universal gate set with the aid of logical- X measurements.

General formalism for nondipole photoelectron angular distributions with arbitrary light polarization

Materialized views are essential for optimizing the performance of traditional databases and data warehouses by accelerating query responses. However, their substantial storage requirements and the impracticality of materializing all possible views raise the problem of selecting which views to persist, a fundamental physical design challenge. This article presents a rigorous formalization of this problem within the context of semantic databases. The methodology employed includes a comprehensive literature review aimed at identifying the variety of se-mantic database representations. This analysis revealed a significant diversity in data models and query languages used. Based on this analysis, a generic formalization framework is pro-posed. This framework enables the expression of various resolution approaches to the materialized view selection problem, taking into account the specificities of semantic databases. It offers broad applicability to any database management system, providing a common language to describe and compare view selection methods.

A theoretical formalism is developed for the dilatational viscoelastic modulus (ε) at fluid interfaces stabilized by mixtures of n soluble, nonionic surfactants. The model generalizes the diffusion–adsorption treatment by explicitly considering the coupling between the diffusive fluxes of each component and the dependence of the surface tension (σ) on the complete composition of the interfacial monolayer (Γi). An analytical expression for the complex modulus ε is derived regarding the equilibrium surface concentrations, diffusion coefficients, and the partial derivatives that define the interfacial equation of state and adsorption isotherms. It is rigorously demonstrated that this general formalism converges to established limiting cases in the literature: the Lucassen–van den Tempel model for a single surfactant and the models developed for binary mixtures by Jiang et al. and Joos. The framework is applied to analyze experimental data of the literature for a ternary mixture of ethoxylated alcohols (C10EO5/C12EO5/C14EO8) by Fainerman et al. The analysis reveals that the predictive fidelity of the formalism is critically dependent on the suitability of the selected thermodynamic adsorption model, underscoring that an accurate description of the interfacial equation of state and adsorption isotherms is an indispensable prerequisite for the quantitative implementation of the dynamic theory.

Abstract Often, when a molecular simulation of a complex mixture is to be performed, one runs into the issue of converting complex, experimentally prepared formulations into mole fractions of individual molecular entities. Conversely, in fields such as organic chemistry, there is often a need to convert mole fractions into other compositional units. In common practice, those conversions are performed manually, requiring the writing of the appropriate material balances every time. This work addresses both issues simultaneously by introducing a general matrix formalism that enables conversion between any combination of IUPAC-recognized composition units through the resolution of a simple linear system. The framework can also be used in the reverse direction to convert mole fractions back into any other desired unit of composition. Recursion (i.e., mixtures of mixtures) and the decomposition of complexes into individual molecules or ions are handled consistently. A Python library to perform these calculations is available at https://github.com/TheophileGaudin/chemcalc-lib and can be added to a Python environment with pip install chemcalc_lib .

Digital quantum simulation (DQS) has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Such systems, like many-particle bosonic systems and intricate optical experimental setups, pose significant challenges for classical simulation methods. In this paper, we utilize a general formalism for the DQS of bosonic systems, which consists of mapping bosonic operators to Pauli operators using the Gray code, in order to simulate interferometric variants of Afshar’s experiment—an intricate optical experiment—on IBM’s quantum computers. We investigated experiments analogous to Afshar’s double-slit experiment performed by Unruh and Pessoa Júnior, exploring discussions on the apparent violation of Bohr’s complementarity principle when considering the entire experimental setup. Based on the aforementioned experiments, we construct a variation of a delayed-choice setup. We also explore another experiment starting with a two-photon initial state. Finally, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of Quantum Mechanics.

A unified electromagnetic response theory has been formulated in terms of quasi-energy derivatives within the nonrelativistic single-determinant framework. The formalism is applicable to any type of optical response, without restriction to monochromatic fields. Electromagnetic properties are expressed through quasi-energy derivatives, providing a consistent and general description under arbitrary static or dynamic perturbations. Magnetic properties obtained from this framework are inherently gauge-invariant, since a gauge transformation of the electromagnetic potentials corresponds to a unitary phase transformation acting on both the Hamiltonian and molecular orbitals. The present theory thus offers a comprehensive foundation for evaluating (hyper)polarizabilities, (hyper)magnetizabilities, and other related response properties.

As information plays an ever more central role across disciplines, the lack of a precise and reusable definition of state impedes comparison, measurement, and verification. Building on Objective Information Theory (OIT), this paper proposes a logic-based framework that defines the state of an object or system at a time point (or interval) as the semantic valuation of a set of well-formed formulas over a given domain and interpretation. Within first-order and higher-order logic—extended to infinitary logic when needed—we show how finite and broad classes of infinite structures can be characterized, drawing on core results from model theory. We then instantiate the framework in economics, sociology, computer science, and natural language, demonstrating that logic provides a unifying language for representing, reasoning about, and relating states across domains. Finally, we refine OIT by supplying a universal state representation that supports cross-domain exchange, measurement, and verification.

Localized orbital-based quantum embedding, as originally formulated in the context of density matrix embedding theory (DMET), is revisited from the perspective of lattice density functional theory (DFT). An in-principle exact (in the sense of full configuration interaction) formulation of the theory, where the occupations of the localized orbitals play the role of the density, is derived for any (model or ab initio) electronic Hamiltonian. From this general formalism we deduce an exact relation between the local Hartree-exchange-correlation (Hxc) potential of the full-size Kohn-Sham (KS) lattice-like system and the embedding chemical potential that is adjusted on each embedded fragment, individually, such that both KS and embedding cluster systems reproduce the exact same local density. When well-identified density-functional approximations (that find their justification in the strongly correlated regime) are applied, a practical self-consistent local potential functional embedding theory (LPFET), where the local Hxc potential becomes the basic variable, naturally emerges from the theory. LPFET differs from previous density embedding approaches by its fragment-dependent embedding chemical potential expression, which is a simple functional of the Hxc potential. Numerical calculations on prototypical systems show the ability of such an ansatz to improve substantially the description of density profiles (localized orbitals occupation numbers in this context) in strongly correlated systems.