Papers

We investigate the flavor structures of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) subject to non-invertible selection rules. In particular, we classify the flavor textures of all baryon-number-conserving dimension-six SMEFT operators and determine the resulting constraints on their Wilson coefficients. The selection rules determine not only the texture zeros but also the allowed tensor structures of the Wilson coefficients, which can be expressed analytically in terms of a reduced number of independent parameters. We also find that the flavor structures of higher-dimensional operators are not necessarily aligned with those of the Yukawa couplings, in contrast to the Minimal Flavor Violation hypothesis, in which the Yukawa couplings govern the flavor structure of higher-dimensional operators. It turns out that the resulting flavor and chirality patterns differ from those typically obtained in SMEFT with conventional flavor symmetries, providing characteristic predictions for $B$-meson observables and charged-lepton-flavor-violating radiative decays.

We study the superdiffusive behavior of random walks on the randomly oriented Manhattan lattice, i.e., the $d$-dimensional integer lattice $\mathbb{Z}^d$ where each axis-aligned line is independently assigned a random direction (forward or backward) with equal probability. The walker takes nearest-neighbor steps, choosing an axis randomly and moving along the assigned direction of that axis's line, with equal probabilities for each axis. We show that, in the critical dimension $d=3$, the diffusion coefficient of the random walk diverges in the Tauberian sense as $\sqrt{\log t}$ with a multiplicative correction $(\log\log t)^{\pm(2+\varepsilon)}$ as time $t\to\infty$. This gives an answer to a conjecture by Ledger, Tóth and Valkó (2018).

Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension $d=8$, storage falls by $\sim 10^7\times$ relative to the dense grid of $N^d$ points, and evolution wall-clock time falls by $\gtrsim 10^3\times$ against a baseline extrapolated from the measured $d\le 5$ scaling. We validate our pipeline by reproducing the $O(1/\sqrt{p_{\rm rare}})$ scaling of rare-event sampling.

We investigate the impact of charge regulation (CR) on the non-uniform swelling behavior of polyelectrolyte hydrogels. The Poisson-Boltzmann theory with electro-elastic coupling between the local polymer density and elastic deformation is considered. We investigate the spatial distributions of the elastic displacement and polymer density under different salt concentrations and compare charge-regulated gels with fixed-charge (non-CR) gels of the same net charge. Our results show that the CR induces spatially varying charge fractions, which strengthen the electro-elastic response and lead to stronger non-uniform swelling compared with non-CR gels. These findings provide a theoretical basis for understanding and controlling non-uniform swelling in responsive polyelectrolyte hydrogels.

Anomalous heat transport in strongly anharmonic crystalline solids poses both a fundamental challenge to the theoretical understanding and an opportunity for thermoelectric and thermal barrier coating applications. Although Green-Kubo theory reproduces experimental thermal conductivity ($\kappa$) at high temperatures, it lacks microscopic insight and neglects the Bose-Einstein statistics of lattice vibrations. On the other hand, the conventional Boltzmann transport equation (BTE) framework, based on a phonon-gas picture, fails due to strong anharmonicity-induced overdamped phonons. Herein, the thermal transport properties in TlAgSe, a metal chalcogenide, and Cs$_2$PbI$_2$C$_2$, an all-inorganic layered Ruddlesden-Popper perovskite, are investigated by explicitly accounting for temperature-dependent lattice dynamics through machine learning interatomic potentials and employing the Wigner transport equation (WTE) framework. Crucially, heat conduction is governed not only by higher-order phonon scattering-dominated populations' transport channel described within the BTE, but also by a coherences' channel in the WTE framework arising from wave-like interbranch coherence between eigenstates. Incorporating four-phonon scattering, WTE predicts average room-temperature $\kappa$ values of 0.31 Wm$^{-1}$K$^{-1}$ (TlAgSe) and 0.38 Wm$^{-1}$K$^{-1}$ (Cs$_2$PbI$_2$C$_2$), in excellent agreement with experiments. Phonon scattering-rate analysis reveals strong coherences' contributions and prevalent overdamped phonon modes, demonstrating the breakdown of the conventional BTE framework based on the phonon quasiparticle picture with only first-order anharmonic perturbation. This computational approach provides a unified description of heat transport in ultralow-$\kappa$ materials, offering a basis for the rational design of phononic and thermoelectric devices.

Representation quality is a central determinant of PINNs' performance, yet standard training leaves representations to emerge implicitly while fitting the final solution. We introduce representation curriculum, an ordered process in which representations are explicitly learned, transferred independently of their predictors, and progressively refined. We realize it with Staged Depth Training (SDT), which trains a shallow prefix under a temporary physics-informed head, discards the head, and freezes the learned prefix while adding depth, without equation-specific encodings or changes to the final architecture. Across the 20 default forward problems in PINNacle with three backbones, SDT improves 40 of 59 equal-budget problem–backbone cells by at least 5% and remains within that band in the rest, with a 32.8% geometric-mean error reduction on a PirateNet-style backbone. Mechanistic ablations suggest that the gain is not explained by optimizer restarts or shallow warm-starting alone. Representation visualizations and hyperparameter-basin analyses provide diagnostic evidence on representation geometry and local sensitivity to shared hyperparameters. On Poisson–Boltzmann 2D, SDT also more than doubles the fitted depth-scaling exponent for both backbones. These results support representation curriculum as a promising training strategy for improving PINNs while preserving the deployed architecture and inference cost.

Shannon–Rényi entropies probe the full measurement distribution of a quantum many-body state, but their microscopic evaluation remains difficult even in free-fermion systems. We show that the Born distribution of the critical transverse-field Ising chain is exactly the parity boundary of a weak inverse-square classical Ising model, a structure revealed by the Cauchy form of its probability kernel. The construction is exact at finite size for every real $n>0$ and isolates the long-distance sectors controlling the $n>1$ thermodynamics. Cutting a finite interval generates the universal $c\,n/[8(n-1)]$ logarithm directly from the missing $1/r^2$ interactions, with $c=1/2$ the Ising central charge. On the ring, the explicit finite-size factor has no constant term, while any additional noninteger singularity is confined to a residual cycle-only free energy. All explicit long-distance contributions become marginal only at $n=1$.

A quantum feedback loop that returns information from a forward simulation to an earlier internal time induces a completely positive trace-preserving map on a message register; iterating that map eventually destroys its ability to carry entanglement. The entanglement-breaking index N = n_EB(Phi), the round at which this happens, is studied along two axes, interaction and bath. On the interaction axis, strict contraction onto a full-rank fixed point forces N finite in every dimension, via an explicit separable ball around the limiting Choi state, and across 3997 sampled channels index and stability gap are one clock, N [1 - rho(A)] in [0.60, 1.50]. On the bath axis, a thermal ancilla at polarisation p = tanh(hbar omega / 2 k_B T) makes every channel quantity an exact quadratic in p, and one-sided certificates (no eigensolver) establish N = 3 at the reference circuit at every temperature. The infinite-temperature index is an architecture floor with closed form and exact measure (46.427% of circuits break entanglement in one round at infinite temperature). For exchange collisions (generalised amplitude damping) the index has a closed form and is monotone in p; for the loop the floor is not a bound: certified circuits dip below it in interior temperature windows, at a rate with Gaussian cutoff in epsilon = 1 - ||A_0||_2 (marginal exponent 2.02 [1.90, 2.16], 4.1 million circuits), and shallow-floor valleys survive to epsilon = 0.125. On a certified coupling-temperature surface, temperature moves the index by at most 3/2, the interaction by 1213/3. Applied to quantum-cognition proposals, a per-bath polarisation table at 310 K shows nuclear spins maximally hot and intramolecular vibrations frozen, and a four-input checklist replaces decoherence times by round budgets; Fisher's nuclear-spin proposal specifies its bath and storage coherence, not its processing interaction or rate.

The French Massif Central and the Eifel Volcanic Field represent two of the enigmatic features in France and Germany, respectively. Both areas have been affected by Cenozoic volcanism whose origin is still debated. Using 3-D numerical geodynamic modelling of recently developed solid-mechanical constitutive laws including viscoelastic-viscoplastic behaviour, we explored a new hypothesis to highlight the contribution of localised deformational (inelastic) heating towards the evolution of localised volcanism as being due to far-field-induced compressive stresses from the Africa-Eurasia convergence. Our simulations show that variations in crustal thicknesses can help localise inelastic strain near the Moho of relatively thicker crust, which leads to enhanced heating. Localised viscoplastic deformation above the brittle-ductile transition in the crust also formed conjugate deformation bands, resulting in localised changes in the topography which can be compared to present-day topography. The first-order picture that emerges from our simulations shows an association of elevated topography and tectonic structures that localise deformation, with a geothermal anomaly sufficient to explain the elevated heat flow and cause a potential localised zone for partial melting in hydrated or CO\textsubscript{2}-bearing mantle below the Moho.

For a channel $\Phi$ on $M_d$ written in the generalised Bloch parameterisation $r \mapsto Ar+c$, we prove that entanglement breaking implies $\|A\|_*^2 + \frac{d(d-1)}{2}\,|c|^2 \;\le\; (d-1)^2 ,$ where $\|\cdot\|_*$ denotes the nuclear norm. Read on the Choi state of the channel, the inequality is an instance of the covariance-matrix criterion of Gittsovich et al.; what is added here is an elementary proof in Holevo form and a complete description of the equality cases. Apart from the constant channel onto a pure state, which shows that the coefficient $d(d-1)/2$ cannot be increased, equality holds exactly for the measure-and-prepare channels with rank-one effects $\alpha_k|e_k\rangle\langle e_k|$ and pure outputs $|\psi_k\rangle\langle\psi_k|$ whose overlaps are an affine image of those of the measurement directions, $|\langle\psi_j|\psi_k\rangle|^2 = P + (1-P)\,(d|\langle e_j|e_k\rangle|^2 - 1)/(d-1)$ for a common $P = \mathrm{Tr}\,\Phi(\mathbf{1}/d)^2$. These include the completely dephasing channel, the re-preparation channel of every rank-one POVM, a one-parameter family interpolating between dephasing and the constant channel, and non-unital non-projective examples already at $d = 2$. The qubit case reads $\|A\|_*^2+|c|^2\le1$ and extends to full rank a rank-two condition of Ruskai. The proof sharpens Ruskai's bound $\|A\|_*\le1$ by retaining the POVM completeness relation $\sum_k f_k=0$, which her argument discards; this recentres $A$ from a second moment into a cross-covariance, and is the entire content of the improvement.

We investigate the joint effects of stochastic forcing and quenched structural heterogeneity on stochastic resonance (SR) and liquid-state computation in a small-world network of excitable FitzHugh–Nagumo neurons. Heterogeneity is introduced separately through coupling strengths and time delays drawn from Gaussian, bimodal, and shifted-exponential distributions. Weak periodic forcing resolves the stochastic-resonance landscape, whereas weak aperiodic driving probes noise-assisted signal encoding and Liquid State Machine (LSM) forecasting. Heterogeneity is not generically beneficial, but reorganizes the resonance landscape and computational performance in a distribution-dependent manner. Gaussian coupling disorder broadens the strong-response region, whereas bimodal disorder produces a more pronounced enhancement and shifts resonance toward weaker noise. Shifted-exponential coupling disorder behaves differently: increasing its scale broadens and shifts the coupling distribution toward less responsive regions. Time-delay heterogeneity can enhance or suppress SR depending on how the delay distribution samples the structured delay-response landscape. Under aperiodic forcing, stronger input–output coherence accompanies lower LSM prediction error, showing that SR can improve LSM performance and that suitable coupling heterogeneity can further enhance this computational benefit; Gaussian and bimodal coupling disorder shift the optimum toward weaker noise and reduce the noise-optimized root-mean-square prediction error, with the largest reduction obtained for the bimodal case. These results identify stochastic forcing and quenched heterogeneity as coupled control parameters and show that the computational enhancement of LSMs depends on disorder structure rather than magnitude alone.

Cold-to-hot heat transfer is a conspicuous non-equilibrium feature of rarefied cavity flows and is often used to judge whether a continuum closure captures higher-order transport. We examine what such agreement actually establishes. The exact heat-flux balance shows that the fourth-order contribution enters only through the divergence of the composite tensor (A_{ij}=R^{\mathrm{cl}}*{ij}+\Delta\delta*{ij}/3). A compactly supported Airy construction yields an infinite-dimensional family of symmetric divergence-free perturbations that preserve the flux-side wall trace. A two-dimensional-physical, three-dimensional-velocity (2D3V) description also leaves the transverse component (A_{zz}) unobserved. Heat flux therefore cannot uniquely identify the underlying fourth-order state. We test the consequences using direct simulation Monte Carlo (DSMC) ensembles and independent regularized 13-moment (R13) and regularized 26-moment (R26) solutions at two rarefaction levels. Counter-gradient transport and the dominant tensorial channel persist under changes in grid and particle number, whereas the local scalar fourth moment and the spatial organization of the counter-gradient region are more sensitive. A finite-particle-corrected fourth-moment audit shows that more than 95% of the resolved R26–DSMC composite-tensor discrepancy at the higher rarefaction lies in the discrete divergence-null space, whereas projected sampling noise hides only about half of its energy. R26 captures the circulation and heat-flux direction more closely than R13, yet the remaining differences concentrate in the wall and corner layers.

Fractional Laplacians encode anomalous scaling and covariant nonlocal response in quantum matter and holographic boundary systems. We place the corresponding scalar spectral theory on a dynamical closed worldsheet. A metric-dependent intertwiner maps the fractional quadratic form to that of $D$ free bosons, while its zeta Jacobian changes the matter determinant weight from $D$ to $sD$. The prime-determinant transformation includes the zero-mode area factor and determines both the moduli density and the Weyl coefficient $c_{\rm det}=sD$. Weyl cancellation therefore selects $D_\ast=26/s$. On the integer critical locus $1\leq D\leq26$, $N=26-D$ spectator bosons turn the residual determinant into a local critical CFT. Its fixed-area genus-$g$ vacuum measure is that of 26 free bosons, its torus trace is modular invariant, its plumbing channels are state resolved, and its BRST charge is nilpotent. The $D$ distinguished coordinates remain spectral composites; their pullback yields the Koba–Nielsen amplitudes and massless vertex conditions. Target backgrounds coupled to this distinguished sector retain the ordinary one-loop tensor beta functions, with dilaton deficit $sD-26$ and the corresponding string-frame action. Worldsheet gravity thus turns the fractional exponent into a quantum-geometric consistency parameter.

Discrete energy-level structures in Coulomb-like localized bound states are conventionally obtained by direct diagonalization of the Schrödinger equation or by semiclassical approximations that fail at low energies. Here we develop a geometric phase-space framework that recovers the exact discrete energy levels and shell degeneracy of three-dimensional Coulomb bound states from classical symplectic geometry and global boundary constraints, bypassing explicit operator diagonalization. Using Kustaanheimo–Stiefel regularization, we map negative-energy Kepler orbits to four-dimensional isotropic harmonic oscillators. The group composition law of the symplectic flow determines an integral kernel built from the classical two-point action and Van Vleck amplitude, whose infinitesimal generator satisfies an exact linear evolution equation—a property we term quadratic closure. Imposing three geometric constraints—decay at infinity, regularity at the origin, and fiber invariance under the Hopf fibration—we recover the exact $E_n/E_1=1/n^2$ scaling and $g_n=n^2$ degeneracy. The phase scale $\alpha$ sets the action unit; all spectral structural features are independent of its value. This framework offers a symmetry-transparent route to spectral data: for quadratic Hamiltonians, the classical kernel incurs zero semiclassical error even at ground-state energies, and the geometric constraints directly identify symmetry-protected degeneracies without diagonalization. We apply the method to shallow impurity states, moiré superlattices, and semiclassical transport, demonstrating how geometric screening rules simplify spectral analysis in condensed-matter environments.

As part of the Big Cross-Modal Attenuation Correction Challenge (BIC-MAC), we aimed to synthesise pseudo-CT images for PET/MR attenuation correction from whole-body non-attenuation-corrected PET (NAC-PET), Dixon MRI, and a two-dimensional topogram image. We developed a residual 3D U-Net in which a dedicated 2D topogram encoder provides bounded, multi-scale feature gating. The network was supervised jointly in CT and 511-keV attenuation-map space. Two complementary models, one emphasizing activity and cranial regions and one including a projection-domain attenuation-correction-factor regulariser, were combined by equal averaging in CT space. In controlled development experiments, the two training objectives yielded complementary error profiles. On the online BIC-MAC validation leaderboard, the ensemble achieved a mumap MAE of 0.005656, whole-body SUV MAE of 0.0356, organ bias of 2.65%, and brain outlier score of 0.0294. Topogram-gated multi-modal learning combines local volumetric information with global projected anatomy and provides a practical, physically informed approach to pseudo-CT synthesis for PET/MR.

We extend the discrete gauge rigidity of time-scaled intertwining cocycles to operator networks over a connected manifold M and classify the holonomy that the continuous setting admits. For dissipative semigroups $S_x(t)=e^{-tA_x}$ linked by transport operators $K_\gamma S_{\gamma(0)}(t)=S_{\gamma(1)}(\lambda(\gamma)t)K_\gamma$ along paths $\gamma$, we prove that the scaling field carries no monodromy: $\lambda(x,y)=\tau(x)/\tau(y)$ for a continuous positive function $\tau$, unique up to a multiplicative constant, with multiplicativity forced by the intertwining relation rather than assumed. For regular cocycles the transport defines a bounded operator connection on a Hilbert bundle over M; the holonomy of a closed loop is confined to the commutant of the generator and decomposes into spectral sectors, on each of which it is adiabatic (Berry-Wilczek-Zee) transport twisted by an independent commutant-valued sector potential; for flat unitary cocycles the holonomy is classified by unitary representations of $\pi_1(M)$ in the commutant. An explicit rotating network over $S^1$ exhibits holonomy equal to the parity operator while the Berry connection one-form of every level vanishes identically: the monodromy is carried by $\mathbb{Z}_2$ orientation classes of Moebius eigenline bundles.

The next-generation pressure standard is moving toward optical-based, field-deployable systems. However, most existing optical refractometry pressure standards rely on bulky ultra-low expansion (ULE) cavities and complex feedback locking, limiting their portability and on-site applicability. Here, we present a miniaturized, transportable optical pressure manometer based on a dual-channel Fabry-Perot cavity machined from a single block of common fused silica. By employing a differential measurement between an evacuated reference cavity and a gas-exposed measurement cavity, common-mode errors such as thermal expansion and pressure-induced deformation are largely canceled, enabling the use of low-cost fused silica to achieve performance comparable to ULE. Radio-frequency scanning with Lorentzian fitting replaces conventional feedback locking, simplifying the optical design and improving robustness. Calibrated against a piston manometer, the device demonstrates a measurement repeatability of 3.4~ppm and a total uncertainty of \(u = \sqrt{(10.6\times10^{-6}p)^2 + (5.4~\mathrm{mPa})^2}\). The system can resolve periodic pressure fluctuations originating from the piston manometer and exhibits superior response speed. With its small footprint, portability, and independence from external frequency references, this fused-silica dual-cavity manometer offers a practical route toward on-site, quantum-traceable pressure calibration.

This paper is a corrected English translation of an original Japanese work introducing "power geometry," a research programme centred on power transformations, deformations and dualities of functions in the sense of optimisation theory. Its two main motivations are the origin of probability distributions (via maximum-likelihood principles, rational-function parameters and ODEs linked to information geometry, the Pearson system and Schwarzian equations) and the construction of matrix dynamical systems that compute eigenvalues, singular values and principal or minor subspaces. Building on Brockett's double-bracket flows, the author extends these systems to rectangular matrices, flag manifolds and difference-of-convex potentials, and shows how a continuous power parameter can interpolate between largest- and smallest-eigenvalue problems. Dual potentials, topological distinctions between principal and minor subspace flows, and links via matrix Schwarzian–Riccati equations are examined, with a view toward design principles for classical and quantum information-processing algorithms.

We study relative entropy under gauge reduction in Whitney-discretized electromagnetism. The discrete Hodge decomposition separates exact gauge directions from harmonic and coexact physical degrees of freedom. For Gaussian distributions on the auxiliary potential space, relative entropy splits exactly into the relative entropy of the physical marginals and a nonnegative conditional gauge contribution. We express this contribution through Schur complements, conditional means, and physical–gauge correlations, and characterize equality between auxiliary and physical relative entropies. The physical divergence is also shown to be the minimum over all Gaussian auxiliary extensions. At the infinitesimal level, Fisher information admits an analogous decomposition. A two-variable model illustrates how statistically distinct auxiliary potentials may represent identical physical statistics. The construction provides an information-geometric interpretation of discrete gauge reduction without assigning physical significance to the eliminated gauge variables.

We provide a perspective into measuring the quantum information spreading by introducing N-operator correlators. Leveraging the idea from N-point correlation function from cosmology, we formulate a generalized Out-of-Time-Ordered Correlator (OTOC), called N-Operator Correlator (NOC). Such formulation can reduce the effect of restricted analysis associated with selecting only two operators for OTOC. NOC can take into account a larger set of measurement probes in measuring the degree of quantum information spreading. We demonstrate these concepts with two analytically tractable toy systems with computing thermal averages of operator time evolutions at a finite temperature: a single qubit in longitudinal field and XYZ two-qubit system. Our perspective serves as a basic introduction to generalized operator correlators in quantum mechanics.

We present a projected sensitivity study for hadronic mono-$Z$ dark-matter production using CMS Run~2015D HTMHT open data corresponding to 2.256382381~\invfb, from which 1{,}439{,}523 events satisfy the hadronic mono-$Z$ selection. Backgrounds are modelled with a conditional flow-matching continuous normalizing flow trained on the selected HTMHT events and evaluated on a held-out validation split reweighted to the full selected population. To mitigate artifacts from missing-object features and avoid in-sample scoring bias we apply sentinel imputation for undefined angular features, persist the train/validation split indices, and enforce a minimum reported background yield of 20 events when selecting the working point. A signal-side offline trigger proxy is applied to the simulated signal before scoring. Under this procedure the baseline analysis yields expected significances of 2.89$\sigma$, 7.62$\sigma$, and 7.41$\sigma$ for three simplified-model benchmarks. An ablation study that removes the detailed extra-jet kinematics reduces the expected significance by 53–71%, indicating that extra-jet topology carries substantial discriminating power in the hadronic mono-$Z$ channel. These results are projected sensitivities (no unblinding performed); the limitations and reproducibility of the study are discussed in Sections limitations and reproducibility.

With the observational accuracy of astrometric space telescopes such as Gaia, the Newtonian theoretical framework for positional astronomy is no longer appropriate. To model all effects relevant at the corresponding levels of accuracy, a more sophisticated description in the framework of General Relativity is required. It is generally known how various relativistic effects affect a given astrometric observation. In particular, the maximal light deflection of a given Solar System body can be easily estimated for a given observer. However, astrometric parameters for a given source are computed from a series of observations of that source. Depending on the relativistic effect, the fraction of observations affected, at some given level of accuracy, by that relativistic effect can vary and also be very small. Our goal is to investigate the impact of unaccounted relativistic effects on the astrometric parameters of a source observed by a Gaia-like astrometric telescope. The standard relativistic framework for Gaia is used to highlight such effects in some cases where they are most significant. Then, using the simulation tool AGISLab, we fit a set of Gaia-like observations of a given number of sources to the standard Gaia-like astrometric model for astrometric source parameters, but using different incomplete relativistic models. In this way we obtain the errors of the astrometric parameters if one were to drop different elements of the relativity model. A simplified analytical description of the errors is also provided and discussed. We demonstrate that, due to averaging over many observations per source, the errors in the astrometric parameters are drastically smaller than the corresponding relativistic effects in individual observations. This opens a way to potentially simplify the relativistic model for future astrometric projects aiming for higher accuracy than Gaia.

A composite structural index summarises a network in one number, and for a triangle-based index it is spectrally redundant: Tr(A^3) is the third moment of the adjacency spectrum. The non-redundant content sits one level down, in diag(A^3), which depends on eigenvectors and is not spectrally determined. A corollary in the theory paper predicted that the global scalar should tie sharpened spectral baselines rather than beat them, while the node-wise attribution should do better where the number of structural epicentres is unknown. We construct Omega-N by localizing each of the four factors. The direct localization is badly conditioned; two corrections from published practice fix it, a configuration-null excess per factor and a personalized-PageRank neighbourhood at several scales, giving ten interpretable features per node, with no attributes, training or embeddings. Against a recursive feature engine at five levels of recursion, Omega-N wins on three and ties on two of the six in-domain evaluations, the sixth a declared null where every arm returns chance, with ten features against its 28 to 252 before pruning. Two statistics from the graph and labels, not from performance, partition the eight benchmarks without error, and the two they exclude are the two on which it loses. The strongest application is drug-target prioritisation on protein interaction networks: +0.032 to +0.103 AUPRC over a six-feature centrality battery and +0.084 to +0.208 over the four-feature one, across three constructions, replicated on an independent AP-MS network and label source (degree-matched: +0.0723 on STRING, +0.0560 on BioPlex, p=0.00195). Adding Omega-N to centralities plus Node2Vec changes nothing. The claim is narrow and it is the point: ten named features, computed without training, match or beat hand-crafted centralities and a recursive engine, and do not touch learned representations.

We introduce the notion of universal quilt for toric CY3 singularities and construct examples when the universal quilts are themselves smooth Calabi-Yau threefolds. Such quilts are designed to contain all of the crepant resolutions of the given singularity. To obtain universal quilts we implement an algorithm that computes all triangulations for any given planar polygon. We also introduce the notion of quilt stack, to address the question of finding the most likely smooth configuration preceding a given singularity.

We construct helicity-conditioned statistical states for a Whitney-discretized electromagnetic field on a closed oriented three-manifold. The simplicial de Rham complex provides exact discrete gauge symmetry, while the Whitney inner product separates exact, harmonic, and coexact sectors. The spatial Abelian Chern–Simons functional is gauge invariant and depends only on the coexact potential. After fixing harmonic modes, we introduce a helicity-biased Gaussian ensemble on the reduced electromagnetic phase space and derive explicit formulas for its admissible parameters, partition function, mean helicity, relative entropy, and Fisher information. The distribution uniquely minimizes relative entropy under a prescribed mean-helicity constraint. Its helicity susceptibility equals the variance of the discrete Chern–Simons functional and controls the local distinguishability of neighboring statistical states. Because magnetic helicity is generally not conserved under unconstrained Maxwell dynamics, these states represent conditioned inference rather than dynamical equilibrium.

Accurate system-level prediction of cryogenic liquid storage remains challenging because reduced-order models rely on regime-dependent closures for unresolved heat and mass transfer, particularly under sloshing. We present a physics-integrated neural-network framework that combines a conservation-based zero-dimensional nodal model with data-driven closures for wall and interfacial heat transfer, phase change, pressurant quality, and liquid thermal-boundary-layer evolution. Thermal stratification and mixing within the liquid are represented through a first-order dynamical model for the boundary-layer thickness, while four operating-regime-specific neural networks infer the closure parameters for self-pressurization and relaxation, active pressurization, venting, and lateral sloshing. The framework was identified and evaluated using a dedicated database of 48 multi-stage cryogenic-tank experiments conducted in an optically accessible facility operated with liquid nitrogen. The experiments combine controlled wall heating, vapor injection and evacuation, and forced lateral sloshing, thereby covering both slowly evolving thermal states and strongly transient operating conditions. Generalization was assessed through experiment-level K-fold cross-validation, while an entropy-production penalty was included in the loss function to discourage violations of the second law of thermodynamics. Across the investigated cross-validation configurations, the global normalized root-mean-square error remained under 3%, with sloshing representing the most demanding regime. A final model trained on the complete database reconstructed the experiments with a global error of 1.6%. These results demonstrate that the proposed framework can extract physically interpretable and computationally efficient closure laws from a limited but information-rich experimental database.

Within the open quantum system formalism, using the Markovian process, we investigate the quantum speed limit time (QSLT) of a uniformly accelerated Unruh-DeWitt detector, interacting with the massless real scaler field. Three specific scenarios are being studied – the field is in Minkowski spacetime (i) without any reflecting boundary but at a finite temperature, (ii) presence of single boundary with the detector is accelerating parallel to the plane of it, and (iii) presence of two boundaries with the detector is moving between them along the parallel direction. Interestingly, the behavior of QSLT appears to be very distinctive around a particular value of $a$. For the first scenario QSLT shows very noticeable change around a specific $a$ and the required value of $a$ corresponding to this change decreases with the increase of field temperature. In the other two scenarios, QSLT starts to fluctuate after a critical value of $a$. If we further increase $a$, more vigorous fluctuation emerges. The value of $a$ required for the starting of the oscillation is much less for the double boundary case compared to the single boundary. Taking into account specific values of the distance between the boundaries and the detector's frequency, we estimate that the critical value of $a$ can be as low as $\sim 10^5 \text{m}/\text{s}^2$ for the double boundary situation. We argue that such a distinctive feature in QSLT can be a fruitful tool to diagnose the Unruh effect.

Conventional electrogastrography (EGG) analyses summarize gastric slow-wave activity using dominant frequency, power, or phase-based metrics, without explicitly modeling amplitude-dependent frequency dynamics. We developed a statistical nonlinear-dynamics framework that represents the gastric-band analytic EGG signal as a stochastic Stuart-Landau oscillator and estimate local effective phase-shear, $\beta_{\mathrm{eff}}$, a normalized measure of amplitude-frequency coupling. In overnight recordings from 60 healthy participants, effective phase-shear was consistently negative, generalized to held-out halves of each recording, and was abolished by amplitude surrogates that disrupted amplitude-phase alignment while preserving amplitude-series structure. We then applied the measure to fasted and fed recordings from 16 healthy participants and 24 participants with gastric dysfunction. Phase-shear magnitude differed between groups and classified dysfunction comparable to the strongest multielectrode phase-based traveling-wave measures. These findings establish amplitude-frequency coupling as a dynamical feature of gastric-band EGG that complements conventional spectral and spatial phase metrics, while motivating future multichannel observation models to determine its relationship to slow-wave propagation and gastric function.

Since the discovery of the Higgs particle in the LHC, numerous inflationary models utilize it as the inflaton. In this study, after establishing that Higgs inflation can be a viable model in the context of unimodular gravity, we address a scenario related to reheating, which plays a crucial role in connecting the inflationary era to a hot Big Bang universe. Also, we calculate essential parameters such as the temperature and the e-folds number according to the equation of the state parameter ($\omega_{re}$) in this regime of reheating. The physics behind the reheating process are extremely imprecise at present, and we have only a very limited range of acceptable values for $\omega_{re}$. We analyze the compatibility with Planck2018, BICEP/Keck2021, DESI2024, and ACT array bounds and find that within this model, $\omega_{re}$ is restricted to the range $ -1 \leq \omega_{re} \leq \frac{1}{6} $.

We investigate the observational viability of the linear Herglotz-type $f(R,T)$ gravity model, $f(R,T)=R+\alpha T$, which incorporates both geometry–matter coupling and non-conservative gravitational dynamics. Unlike previous analyses\cite{Wazny:2025jth} based on illustrative parameter choices, we perform a systematic Bayesian estimation of the four-dimensional parameter space $\{H_0,A,w,\Phi_0\}$, where $A$ characterizes the matter–geometry coupling, $w$ is the effective equation-of-state parameter, and $\Phi_0$ denotes the present-day Herglotz field. The background evolution is obtained by numerically integrating the coupled Herglotz cosmological equations at every point in the parameter space. We employ Cosmic Chronometer (CC), DESI DR2 baryon acoustic oscillation (BAO), and Union3 Type-Ia supernova data, both independently and in combination. The joint analysis yields $H_0=66.67^{+1.32}_{-1.28}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $A=1.57^{+0.66}_{-0.51}$, $w=-0.992^{+0.136}_{-0.119}$, and $\Phi_0=-0.062^{+0.185}_{-0.157}$ at $68\%$ credibility. The reconstructed Hubble expansion closely follows the flat $\Lambda$CDM prediction over the redshift range probed by the CC data. However, the deceleration parameter, effective equation of state, $Om(z)$ diagnostic, and statefinder $\{r,s\}$ trajectories exhibit appreciable departures from the concordance model, with the magnitude and redshift evolution depending on the observational dataset. These results demonstrate that Herglotz-type $f(R,T)$ gravity can provide an observationally viable description of the late-time expansion while retaining distinguishable cosmological signatures beyond the background Hubble history.