Search Results (12)

We propose Phase-Adaptive Federated Learning (PAFL), a novel framework for privacy-preserving personalized travel itinerary generation that dynamically balances privacy and utility through a phase-dependent aggregation mechanism inspired by phase-change materials. (1) PAFL’s primary objective is to dynamically optimize the privacy–utility trade-off in federated travel recommendation systems through phase-adaptive anonymization. The phase parameter φ ∈ [0, 1] operates as a tunable control variable that continuously adjusts the latent space geometry between differentially private (φ→1) and utility-optimized (φ→0) representations via a thermodynamic-inspired transformation. Conventional federated learning approaches often rely on static privacy-preserving techniques, which either degrade recommendation quality or inadequately protect sensitive user data; PAFL addresses this limitation through three key innovations: a latent-space phase transformer, a differential privacy-gradient inverter with mathematically provable reconstruction bounds (εt ≤ 1.0), and a lightweight sequential transformer. (2) PAFL’s core innovation lies in its phase-adaptive mechanism that dynamically balances privacy preservation through differential privacy and utility maintenance via gradient inversion, governed by the tunable phase parameter φ. Experimental results demonstrate statistically significant improvements, with 18.7% higher HR@10 (p < 0.01) and 62% lower membership inference risk compared to state-of-the-art methods, while maintaining εtotal < 2.3 over 100 training rounds. The framework advances federated learning for sensitive recommendation tasks by establishing a new paradigm for adaptive privacy–utility optimization. Full article

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes. Full article

Classical thermodynamics employs the state of thermodynamic equilibrium, characterized by maximal disorder of the constituent particles, as the reference frame from which the Second Law is formulated and the definition of entropy is derived. Non-equilibrium thermodynamics analyzes the fluxes of matter and energy that are generated in the course of the general tendency to achieve equilibrium. The systems described by classical and non-equilibrium thermodynamics may be heuristically useful within certain limits, but epistemologically, they have fundamental problems in the application to autopoietic living systems. We discuss here the paradigm defined as a relational biological thermodynamics. The standard to which this refers relates to the biological function operating within the context of particular environment and not to the abstract state of thermodynamic equilibrium. This is defined as the stable non-equilibrium state, following Ervin Bauer. Similar to physics, where abandoning the absolute space-time resulted in the application of non-Euclidean geometry, relational biological thermodynamics leads to revealing the basic iterative structures that are formed as a consequence of the search for an optimal coordinate system by living organisms to maintain stable non-equilibrium. Through this search, the developing system achieves the condition of maximization of its power via synergistic effects. Full article

A model has been developed and implemented in the software package BoilFAST that allows for reliable calculations of the self-pressurization and boil-off losses for liquid hydrogen in different tank geometries and thermal insulation systems. The model accounts for the heat transfer from the vapor to the liquid phase, incorporates realistic heat transfer mechanisms, and uses reference equations of state to calculate thermodynamic properties. The model is validated by testing against a variety of scenarios using multiple sets of industrially relevant data for liquid hydrogen (LH2), including self-pressurization and densification data obtained from an LH₂ storage tank at NASA’s Kennedy Space Centre. The model exhibits excellent agreement with experimental and industrial data across a range of simulated conditions, including zero boil-off in microgravity environments, self-pressurization of a stored mass of LH₂, and boil-off from a previously pressurized tank as it is being relieved of vapor. Full article

The knowledge of nanoscale mechanical properties of montmorillonite (MMT) with various compensation cations upon hydration is essential for many environmental engineering-related applications. This paper uses a Molecular Dynamics (MD) method to simulate nanoscale elastic properties of hydrated Na-, Cs-, and Ca-MMT with unconstrained system atoms. The variation of basal spacing of MMT shows step characteristics in the initial crystalline swelling stage followed by an approximately linear change in the subsequent osmotic swelling stage as the increasing of interlayer water content. The water content of MMT in the thermodynamic stable-state conditions during hydration is determined by comparing the immersion energy and hydration energy. Under this stable hydration state, the nanoscale elastic properties are further simulated by the constant strain method. Since the non-bonding strength between MMT lamellae is much lower than the boning strength within the mineral structure, the in-plane and out-of-plane strength of MMT has strong anisotropy. Simulated results including the stiffness tensor and linear elastic constants based on the assumption of orthotropic symmetry are all in good agreement with results from the literature. Furthermore, the out-of-plane stiffness tensor components of C₃₃, C₄₄, and C₅₅ all fluctuate with the increase of interlayer water content, which is related to the formation of interlayer H-bonds and atom-free volume ratio. The in-plane stiffness tensor components C₁₁, C₂₂, and C₁₂ decrease nonlinearly with the increase of water content, and these components are mainly controlled by the bonding strength of mineral atoms and the geometry of the hydrated MMT system. Young’s modulus in all three directions exhibits a nonlinear decrease with increasing water content. Full article

Transcription factors are proteins lying at the endpoint of signaling pathways that control the complex process of DNA transcription. Typically, they are structurally disordered in the inactive state, but in response to an external stimulus, like a suitable ligand, they change their conformation, thereby activating DNA transcription in a spatiotemporal fashion. The observed disorder or fuzziness is functionally beneficial because it can add adaptability, versatility, and reversibility to the interaction. In this context, mimetics of the basic region of the GCN4 transcription factor (Tf) and their interaction with dsDNA sequences would be suitable models to explore the concept of conformational fuzziness experimentally. Herein, we present the first example of a system that mimics the DNA sequence-specific recognition by the GCN4 Tf through the formation of a non- covalent tetra-component complex: peptide–azoβ-CyD(dimer)–peptide–DNA. The non-covalent complex is constructed on the one hand by a 30 amino acid peptide corresponding to the basic region of GCN4 and functionalized with an adamantane moiety, and on the other hand an allosteric receptor, the azoCyDdimer, that has an azobenzene linker connecting two β-cyclodextrin units. The azoCyDdimer responds to light stimulus, existing as two photo-states: the first thermodynamically stable with an E:Z isomer ratio of 95:5 and the second obtained after irradiation with ultraviolet light, resulting in a photostationary state with a 60:40 E:Z ratio. Through electrophoretic shift assays and circular dichroism spectroscopy, we demonstrate that the E isomer is responsible for dimerization and recognition. The formation of the non-covalent tetra component complex occurs in the presence of the GCN4 cognate dsDNA sequence (′5-..ATGA cg TCAT..-3′) but not with (′5-..ATGA c TCAT..-3′) that differs in only one spacing nucleotide. Thus, we demonstrated that the tetra-component complex is formed in a specific manner that depends on the geometry of the ligand, the peptide length, and the ds DNA sequence. We hypothesized that the mechanism of interaction is sequential, and it can be described by the polymorphism model of static fuzziness. We argue that chemically modified peptides of the GCN4 Tf are suitable minimalist experimental models to investigate conformational fuzziness in protein–DNA interactions. Full article

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics. Full article

We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann’s constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state. Full article

Urban morphology and increasing building density play a key role in the overall use of energy and promotion of environmental sustainability. The urban environment causes a local increase of temperature, a phenomenon known as Urban Heat Island (UHI). The purpose of this work is the study of the possible formation of an UHI and the evaluation of its magnitude, in the context of a small city, carried out with the ENVI-met^® software. For this purpose, a simulation was needed, and this simulation is preparatory for a monitoring campaign on site, which will be held in the immediate future. ENVI-met^® simulates the temporal evolution of several thermodynamics parameters on a micro-scale range, creating a 3D, non-hydrostatic model of the interactions between building-atmosphere-vegetation. The weather conditions applied simulate a typical Italian summer heat wave. Three different case-studies have been analyzed: Base Case, Cool Case and Green Case. Analysis of the actual state in the Base Case shows how even in an area with average building density, such as the old town center of a small city, fully developed UHI may rise with strong thermal gradients between built areas and open zones with plenty of vegetation. These gradients arise in a really tiny space (few hundreds of meters), showing that the influence of urban geometry can be decisive in the characterization of local microclimate. Simulations, carried out considering the application of green or cool roofs, showed small relevant effects as they become evident only in large areas heavily built up (metropolis) subject to more intense climate conditions. Full article

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of “Information Geometry” theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean “Moment map” by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. We will synthetize the analogies between both Koszul and Souriau models, and will reduce their definitions to the exclusive Cartan “Inner Product”. Interpreting Legendre transform as Fourier transform in (Min,+) algebra, we conclude with a definition of Entropy given by a relation mixing Fourier/Laplace transforms: Entropy = (minus) Fourier_(Min,+) o Log o Laplace_(+,X). Full article

From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein–Yang–Mills black holes in arbitrary spacetime dimensions D ≥ 5. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological extremal Einstein–Yang–Mills black holes. Full article

We study thermodynamic state-space geometry of the black holes in string theory and M-theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and subensemble theory. We extend our analysis for the black brane foams and bubbling black brane solutions in M-theory. We discuss the nature of state-space correlations of various black brane configurations, and show that the notion of state-space manifolds describes the associated coarse-grained interactions of the corresponding microscopic CFT data. Full article