Search Results (714)

The Stueckelberg–Horwitz–Piron (SHP) formalism describes particles and fields traced out as spacetime events functionally dependent on an external evolution parameter $\tau$. This approach addresses a number of difficulties associated with the problem of time. In SHP general relativity, the state of the unconstrained phase space variables $\{x^{\mu }\left(\tau \right),p_{\nu }\left(\tau \right)\}$ specifies a 4D block spacetime $\mathcal{M}\left(\tau \right)$ that evolves to an infinitesimally close 4D block spacetime $\mathcal{M}(\tau +\delta \tau )$ under a scalar Hamiltonian. As the configuration of matter and energy evolves with $\tau$ it induces changes in the spacetime metric ${\gamma }_{\mu \nu }(x,\tau )$, leading to $\tau$-dependent geodesic equations for the phase space variables. The 4+1 approach in gravitation generalizes the 3+1 formalism of Arnowitt, Deser, and Misner (ADM) to construct $\tau$-dependent Einstein field equations, a canonical Hamiltonian formalism, and an initial value problem for ${\gamma }_{\mu \nu }(x,\tau )$. To conform to known gravitational phenomenology, we must respect the 5D symmetries associated with the free fields—the geometrical constructs relevant to $\mathcal{M}\left(\tau \right)$ as an embedded hypersurface—and the O(3,1) symmetries of 4D matter. The 4+1 formalism has been discussed in a series of publications. The goal of this paper is to provide a systematic review of the subject, make a few corrections and some significant additions, and present the theory in a concise and orderly fashion. Full article

This paper is a contribution to Einstein’s general relativity theory and is mostly a review of known work. It concentrates attention on four fourth-order tensors which arise on the space-time manifold describing this theory and which are very useful. These are the (Riemann) curvature tensor, the Weyl conformal tensor, the “E” tensor and the Weyl projective tensor. The first of these, the curvature tensor, plays an important role in the formulation and interpretation of Einstein’s theory. Next, the Weyl conformal tensor is introduced and its conformal properties described and with it, the Petrov classification of gravitational fields which arises from this tensor. This, in turn, gives rise to the Bel criteria for distinguishing Petrov types at a point by an alignment of certain null directions at that point. The third of these tensors, the “E” tensor, is an important tensor in calculations due to its close connection to the Ricci tensor. The fourth tensor, the Weyl projective tensor, is then described together with its properties relating to the geodesic structure of space-time. As examples of the combined usefulness of these tensors, pp-waves and generalised pp-waves are discussed and related, and a review of the geodesic structure of vacuum metrics is given. Full article

The present paper is aimed at studying the convergence of the Yamabe flow in the case of noncompact solitons. The more specified example of locally conformally flat noncompact solitons is addressed with the aim to newly analyse the qualities of the Ricci scalar. The particular case of noncompact pseudo-Riemannian solitons is studied; moreover, in the instances of Schwarzschild and Generalized-Schwarzschild geometries, rescalings of spherically symmetric weights are performed. For this purpose, new results are achieved as far as the considered structures are concerned. The Myers Theorem is upgraded as the new Myers paradigm of spacetime-dimensional manifolds, where the Einstein Field Equations can now be taken into account. In particular, the Myers Theorems are studied here as far as their new implementation in General Relativity Theory is concerned. As a first important result, the Myers mean curvature is found to coincide with the Ricci scalar in General Relativity Theory, where the 4-position of the observer, from which the 4-velocity 4-vector is calculated from, is taken as that of the observer solidal with the reference frame of the photon. The following results are also of relevance. In more detail, the umbilicity conditions are applied. At a further step, the role of the umbilicity conditions in GR after the Myers Theorems are studied for weighted manifolds and specific new implications of weighted manifolds are developed. The description of the weighted Schwarzschild manifolds and that of the weighted Generalized-Schwarzschild manifolds are newly studied as follows: as a new finding, the Birkhoff Theorem is newly reconciled with the rotational ansatz of the metrised solitons, and the comparison with the previous results about the Brendle non-metrised solitons is accomplished with the outcome stressing the new roles of the new rescalings of the metric tensor with respect to the previous known results of the scaling of the metric tensor of the non-metrised solitons. In the present framework, these procedures allow one to prove the reconciliation of the EFEs with the Yamabe flow. The flow on the tipping lightcones is newly written. The umbilicity condition is studied in General Relativity after the upgrade of the Myers Theorems as far as the sectional curvatures are concerned; as a result, the Calabi–Bernstein description is implemented in General Relativity, as well as the Chen–Yau requirements, and the cases of weighted manifolds are taken into account. More specifically, the equal-time 2-dimensional space surfaces are studied analytically, onto which the weighted General-Relativistic solitons which satisfy the Einstein field equations after the Yamabe flow are projected due to the rotational ansatz. As an accessory introductory result, the class of Wu non-metrised solitons are proven to be discarded in several aspects of the Wu description as the conditions provided after the work of Wu are not compatible with metrisation. Full article

This paper presents a detailed re-examination of the conformalcompactification $\overline{\mathbb{M}}$ of Minkowski space $\mathbb{M}$, constructed as the projective null cone of the six-dimensional space ${\mathbb{R}}^{4,2}$. We provide an explicit and basis-independent formulation, emphasizing geometric clarity. A central result is the explicit identification of $\overline{\mathbb{M}}$ with the unitary group $U\left(2\right)$ via a diffeomorphism, offering a clear matrix representation for points in the compactified space. We then systematically construct and analyze the action of the full conformal group $\mathrm{O}(4,2)$ and its connected component ${\mathrm{SO}}_0(4,2)$ on this manifold. A key contribution is the detailed study of the double cover, $\tilde{\mathbb{M}}$, which is shown to be diffeomorphic to $S^3\times S^1$. This construction resolves the non-effectiveness of the $\mathrm{SO}(4,2)$ action on $\overline{\mathbb{M}}$, yielding an effective group action on the covering space. A significant portion of our analysis is devoted to a precise and novel geometric characterization of the conformal infinity. Moving beyond the often-misrepresented “double cone” description, we demonstrate that the infinity of the double cover, ${\tilde{\mathbb{M}}}_{\infty }$, is a squeezed torus (specifically, a horn cyclide), while the simple infinity, ${\overline{\mathbb{M}}}_{\infty }$, is a needle cyclide. We provide explicit parametrizations and graphical representations of these structures. Finally, we explore the embedding of five-dimensional constant-curvature spaces, whose boundary is the compactified Minkowski space. The paper aims to clarify long-standing misconceptions in the literature and provides a robust, coordinate-free geometric foundation for conformal compactification, with potential implications for cosmology and conformal field theory. Full article

Pseudomonas aeruginosa causes severe healthcare-associated infections, yet no vaccine has been licenced. To circumvent the antigenic variability of classical surface antigens, we evaluated LolB—an essential outer-membrane lipoprotein whose periplasmic orientation favours T-cell-dominant mechanisms with potential antibody access via outer-membrane vesicles (OMVs) or bacteriolysis. An integrative in silico pipeline combined multi-strain conservation (20 isolates), epitope discovery (B- and T-cell), safety filters, physicochemical profiling, de novo/refined 3D modelling, molecular dynamics (MD), and docking to TLR4/MD-2. LolB was highly conserved (95–100% identity) under strong purifying selection (dN/dS = 0.15). A conformational B-cell hotspot centred on Q72 mapped to a solvent-accessible flexible loop. Two class II epitopes—LAAQNSPLT and FLGSAAAVS—showed predicted high affinity (IC₅₀ < 10 nM), non-toxicity, and broad coverage, with the pooled set achieving 98.6% global HLA coverage in silico. The final 119-aa construct (N-terminal hBD-3 adjuvant; GPGPG linkers) was compact and tractable (MW = 12.7 kDa; instability index < 40; near-neutral GRAVY) and scored higher for antigenicity than native LolB (VaxiJen 0.82 vs. 0.41). MD supported thermal stability up to 350 K, linker RMSF < 1.5 Å, and a stable 18.2 ± 2.8 Å interdomain spacing. Docking predicted a 1420 Ų interface and ΔG = −10.2 kcal·mol⁻¹ (Kd = 28 nM) with reproducible polar contacts, suggesting productive TLR4/MD-2 engagement. A conservative R42A/K variant is proposed to temper IFN-γ bias. This work therefore suggests an essentiality-anchored LolB-derived multi-epitope construct as a computational vaccine candidate against multidrug-resistant P. aaeruginosa and defines specific experimentally testable hypotheses for future in vitro/in vivo assessment. Essentiality-anchored epitope selection plus adjuvant-surface engineering yielded a structurally coherent, immunologically rational LolB-derived multi-epitope vaccine warranting experimental validation. Full article

We develop a local, patchwise geometric framework that embeds a broad class of potential Hamiltonian dynamical systems into a family of Riemannian Hamilton patches built over an underlying Gutzwiller manifold. We adopt a conformal (Jacobi) ansatz and a frame-adapted reconstruction procedure, through which we construct, on each patch, a pulled-back metric, along with a reduced (truncated) connection (not a metric-compatible connection) and a corresponding dynamical curvature tensor governing geodesic deviation in the Hamilton coordinates. Then, using the Poisson–Hodge reconstruction, we reconstruct coordinate potentials, enforcing harmonic obstructions, and along with exactness and Jacobian nondegeneracy conditions, we obtain explicit elliptic bounds that control the connection and curvature residuals. On the basis of this construction, we formalize the notion of a Hamilton manifold such that reparametrized geodesics approximate Newton trajectories with controlled acceleration and tolerances. As a generalized structural framework, to promote the local Jacobi reconstructions to a coherent dynamical evolution and provide a dynamical closure, we introduce a patchwise hyperbolic geometric flow for the pullback metric coupled to a kinetic (Vlasov) closure that controls reconstruction and curvature residuals. Under natural regularity, ellipticity, and overlap-tolerance assumptions, together with precise estimates that control the reconstruction and curvature errors, we establish short-time well-posedness of the coupled Vlasov–hyperbolic geometric flow that defines the patchwise Hamilton manifold. Motivated by this construction of the Hamilton manifold with atlas-dependent time, we propose convergence and stability conjectures for dissipative and conservative (non-dissipative) hyperbolic geometric flows. On a single patch, these conjectures characterize local orbital stability (in the sense of coercivity modulo symmetry) and identify local linear instability when unstable linear modes are present. On a finite atlas (the Hamilton manifold with atlas-dependent time), we state conjectures under which local stability propagates to global stability, provided that overlap residuals remain uniformly sufficiently small. The framework identifies the geometric origin of local instability diagnostics used in Hamiltonian mechanics and outlines a practical strategy for verifying stability or instability, numerically or analytically, on finite coverings of configuration space (the Hamilton manifold). Full article

The structural characterization of GG-rich DNA sequences in presence of metal ions provides essential insight into quadruplex stability and ion-dependent conformational specifics. We report the crystal structure of the GG-quadruplex formed by the sequence GGGGTTTTGGGG in the presence of Zn²⁺, K⁺, and Na⁺. It was deposited in the RCSB Protein Data Bank under the accession code 9FTA. The structure was determined by single-crystal X-ray diffraction at a resolution of 2.49 Å in the space group P2₁2₁2₁. It reveals a parallel-stranded, two-G-tetrad stabilized by K⁺ ions within the central channel, while Na⁺ and Zn²⁺ occupy peripheral and groove-associated sites. Zn²⁺ ions are engaged in noncanonical coordination interactions with phosphate oxygens and structured water molecules, contributing to lattice stabilization and subtle adjustments in groove dimensions. The T4 loop forms a compact, ordered motif that contributes to crystal packing rather than intramolecular G4 stabilization. The presence of mixed cations produces a sole lattice architecture mediated by ions that provides structural insight into how bivalent and monovalent metals mutually modulate G-quadruplex topology. These results suggest a basis for understanding the specific ion effects on G4 structures and may direct the design of metal open DNA architectures. Full article

Non-covalent molecular self-assembly serves as a distinctive strategy for enhancing the mechanical performance of lignin-based composite hydrogels. Nevertheless, the self-assembly process can be significantly influenced, leading to alterations in the nanostructure of the hydrogel, because of the diverse conformational reorganizations of lignin in different solvents. In this research, a solvent exchange process was employed to generate a phase-separated structure comprising hydrophobic lignin domains and hydrophilic poly(N,N-dimethylacrylamide) (PDMA) domains through the aggregation of lignin, thereby forming tough lignin/PDMA hydrogels. By adjusting the solvent composition, the hydrogels exhibit distinct nanostructural transformations that are precisely correlated with the changes in Hansen Solubility Parameters (HSPs) of the solvent mixtures. Balanced HSPs facilitates the formation of small-scale lignin domains with high-domain density, which act as crosslinking points for the establishment of a reinforced network. Remarkably, lignin/PDMA hydrogels prepared at a boundary solvation condition unexpectedly induced the formation of large and highly condensed lignin domains, which displayed a radius of gyration (Rg) of 7.7 nm and an inter-domain distance (d-spacing) of 98.1 nm within the hydrogel network. These unique nanostructural features further contribute to its superior mechanical performance, including excellent tensile strength of 3.2 MPa, Young’s modulus of 5.7 MPa, and fracture energy of 41.2 kJ m⁻², which outperforms most reported lignin hydrogels. Additionally, it offers a strong adhesion and rapid drying approach, rendering the hydrogel more suitable for applications as hydrogel coatings. Full article

The crystal structure of proteins is generally considered static due to the constraints imposed by crystal packing. We determined the crystal structure of rice NADP-malic enzyme 2 (OsNADP-ME2), an oxidative decarboxylase that converts malic acid to pyruvate and provides NADPH to generate reactive oxygen species. The OsNADP-ME2 is crystallized as a tetramer in the space group of P2₁. In the crystal, all the crystal packing interactions are made through the NADP-binding domain of the enzyme. Interestingly, a protomer shows a conformational change, with a 7.4° tilt in the NADP-binding domain. Basically, the crystal packing consists of a horizontal arrangement of vertically parallel P2₁ screw axes. In the vertical direction, a protomer (Mol A) is tightly sandwiched by two protomers (Mol C) of nearby tetramers and vice versa. In the horizontal direction, two protomers (Mol B and D) of a tetramer are parallelly bound to nearby tetramers, of which one protomer (Mol B) has tighter interactions than the other protomer (Mol D). The protomer Mol D, with the least interaction surface in the crystal packing, adopts an open conformation of the NADP-binding domain, which may be the flexible part of the enzyme for NADP+ cofactor binding. Crystallization can provide valuable information for protein structure. Full article

In this paper, we extend some existing models of the Ebola virus disease through a hybrid impulsive conformable approach. The base of the introduced model is a class of partial differential equations that incorporate diffusion terms to describe the development of the Ebola virus disease in time and space. In the extended model, we have considered impulsive effects at fixed moments of time, which is of high significance in investigating opportunities for impulsive vaccination strategies and impulsive control drug treatment on disease evolution. In addition, conformable setting is proposed, which provides modeling flexibility without the complications inherent in classical fractional derivatives. Instead of studying the global stability of an equilibrium, the more general notion of stability of sets is introduced and analyzed. The main stability of sets results are obtained by using the impulsive conformable Lyapunov technique and comparison principle. The proposed framework, concepts and techniques may serve as effective tools for analyzing numerous phenomena in medicine and biology. Full article

Via constructing an explicit Lagrangian for which the perturbation equations are analogs of a scalar field propagating in a planar black-hole space–time, it is found that all planar black holes conformal to a Painlevé–Gullstrand-type line element can be realized as analog metrics. We also introduce the concept of holographic entanglement entropy for planar black-hole space–times. This is valid for an arbitrary choice of conformal and blackening factor, thereby vastly extending the number of known examples of explicitly known analog metrics. Full article

This paper investigates biharmonic conformal immersions of surfaces into a conformally flat 3-space. We first establish a characterization of such immersions of totally umbilical surfaces into a generic 3-manifold. It is then proved that any biharmonic conformal immersion of a totally umbilical surface into a nonpositively curved 3-manifold is necessarily a conformal minimal immersion. We further examine the biharmonicity of conformal immersions of totally umbilical planes into a conformally flat 3-space and construct explicit examples of such immersions from a 2-sphere (minus a point) into a conformally flat 3-sphere. Finally, the study is extended to biharmonic conformal immersions of Hopf cylinders associated with a Riemannian submersion. Full article

Injection molding is widely used for plastic parts, but its performance is limited by the cooling stage, which dominates cycle time and affects dimensional stability and energy consumption. Conformal cooling channels, which can be manufactured using additive technologies, improve thermal efficiency but introduce a high-dimensional design problem. This work proposes an integrated methodology for optimizing injection molds with conformal cooling channels that combines parametric CAD (Computer-Aided Drawing), simulation, non-linear principal component analysis, artificial neural network, and multi-objective evolutionary optimization. The workflow is applied to a case study with five cooling layouts. An initial set of 36 metrics related to temperature gradients, warpage, shrinkage, and energy is reduced to a small number of latent objectives, simplifying the search space while preserving the main physical trends. Artificial neural networks surrogates accurately reproduce numerical results, enabling exploration of the design space at a fraction of the computational cost. The optimization yields diverse Pareto-optimal solutions that balance cycle time, dimensional stability, and energy consumption, assisting the design of more sustainable injection molds. Sensitivity analysis identifies mold temperature and channel position/diameter as key design levers. The proposed methodology reduces dependence on expensive simulations and is readily transferable to industrial mold design. Full article

Professors, students, and researchers from universities around the world use software distributed under licenses for numerical simulation purposes, which requires a computer with considerable hardware capabilities. This implies a high cost of simulations in engineering applications that require dynamic modeling using numerical methods, particularly in robotics and nonlinear control. This article compares and analyzes the performance of a frugal simulation scheme based on the use of low-cost, free, and open-source technology, specifically a low-power, single-board minicomputer (Raspberry Pi) in conjunction with GNU-Octave software. The benchmark is a numerical simulation of trajectory tracking control in the joint space of a Selective Conformal Assembly Robot Arm (SCARA). To perform this task, a system of coupled nonlinear differential equations is solved in matrix form using a numerical method known as an ODE solver. This solution includes the control law and the dynamic system model derived from Euler–Lagrange formalism. The time complexity and accuracy are analyzed to compare the performance of the frugal simulation tool with that of a conventional simulation setup consisting of a personal computer and MATLAB^TM running the same simulation code. The analysis shows minimal deviations in the numerical solutions and reasonable time complexity. Moreover, the frugality score of this approach and the low acquisition cost of the simulation tool enable the creation of simulation laboratories at universities with limited budgets for education and research. Full article

The Hodgkin–Huxley equations have successfully described neuronal excitability for over seventy years, yet their mathematical structure remains empirically justified rather than theoretically explained. Why are gating variables bounded between 0 and 1? Why does sodium conductance depend on m³h rather than other combinations? Why does potassium depend on n⁴? Why do all rate functions contain exponential voltage dependencies? Why are the kinetics first-order? We demonstrate that these structural features arise naturally from three fundamental physical symmetries governing ion channel dynamics: the compactness of conformational state space, the scaling invariance of membrane conductance, and temporal translation invariance. Using Lie group theory, we show that these symmetries uniquely determine a mathematical structure in which: (1) gating variables are necessarily bounded, (2) voltage dependencies must be exponential, (3) exponents must be integers, and (4) kinetics must be first-order. The Hodgkin–Huxley equations, rather than mere empirical fits, emerge from fundamental symmetry principles. This framework establishes that neural electrophysiology obeys the same theoretical principles as modern physics, where symmetries constrain the form of dynamical equations. It further provides a principled basis for interpreting deviations from classical behavior as manifestations of additional symmetries or symmetry breaking. Full article