Papers

We relate the properties of bivariate-bicycle-surface (BBS) codes, constructed from a pair of bivariate polynomials over a finite field, to the number and location of their common roots in the extension field. The number of roots $(x,y)$ with finite, non-zero coordinates – counted with algebraic multiplicity – determines the dimension of the codes. This dimension is invariant under monomial automorphisms of the Laurent polynomial ring. Conversely, roots with zero or infinite $x$- or $y$-coordinates indicate that specialized generators are required near the corresponding boundary (e.g., the left or right boundary for a root where $x$ is zero or infinite, respectively). These roots can appear or disappear under monomial transformations, which reveals the structure of tilted boundaries. Based on these results, we formulate a prescription for constructing BBS codes that works for regions with rectangular, diagonal, and arbitrarily tilted boundaries. A key advantage of this approach is that no corner corrections are needed, provided the polynomials satisfy orientation-specific edge conditions.

We study the post-inflationary open-string Hagedorn phase in perturbatively moduli stabilized brane-antibrane inflation. In this class of models, the volume modulus is stabilized by perturbative corrections rather than by non-perturbative effects to the superpotential, thereby avoiding the standard brane-antibrane $\eta$-problem. Since inflation ends through tachyon condensation and brane-antibrane annihilation, the endpoint is intrinsically stringy and need not be described immediately by an ordinary radiation bath. We analyze whether the energy released at annihilation can drive the visible sector into an open-string Hagedorn phase, and study the consequences for dark radiation. If the Standard Model (SM) branes lie in the same throat as where the annihilation occurs, we find that a modest fraction of the released energy deposited into surviving visible open strings is sufficient to enter the Hagedorn regime and can suppress the effective number of relativistic species $\Delta N_{\rm eff}$ below current observational bounds. If the SM lies in a different throat, the result depends on inter-throat energy transfer: prompt or delayed transfer can still yield a visible Hagedorn phase. However, the mechanism is most efficient when the local string scale in the SM throat is lower than or comparable to that in the annihilation throat.

Fluid injection into the Earth's subsurface, performed for energy extraction, waste disposal, and resource development, is known to reactivate gouge-filled faults and induce seismicity, a key hazard in modern geotechnical operations. Nevertheless, the role of injection rate in controlling fault-gouge failure remains poorly understood. Here we present both an analytical theory and coupled fluid–granular (discrete element) numerical simulations to explain this rate dependence. Assuming a pre-stressed gouge-filled fault subject to fluid injection, we derive a pore-pressure diffusion equation with a dilative sink. Its solution predicts a rate-dependent failure criterion, arising from pressure heterogeneity within the layer: slow injection allows pressure to diffuse uniformly throughout the layer, promoting uniform weakening, whereas rapid injection produces strong gradients, leaving distal regions stronger. The numerical simulations confirm the theory and reproduce experimental observations not captured by classical, uniform-pressure effective-stress theory. The framework links grain-scale physics to fault-scale failure and provides quantitative guidance for the design of injection protocols in geotechnical operations involving granular geomaterials.

We apply the mesoscopic coarse-graining framework of~\cite{OsanoMeso,OsanoExtensivity,OsanoPerturbation} to three problems in Cosmological Perturbation Theory and the backreaction debate. (i)~A non-perturbative lower bound on the kinematic backreaction $\QD$ in the Buchert equations, derived from the Gibbs–Bogoliubov inequality: $\QD$ cannot be suppressed below its linear-perturbation-theoryvalue, regardless of the degree of non-linearity, provided the system satisfies stability and temperedness. (ii)~The radius of convergence of the mesoscopic cumulant expansion equals $O(\kNL^{-1})$, the non-linear scale of the matter power spectrum, providing a KAM-theorem explanation for why standard perturbation theory fails at $k>\kNL$. (iii)~For a Gaussian matter field, the inter-cell mutual information is exactly $I(i,j)=-\tfrac{1}{2}\ln(1-r_{ij}^2)$, gauge-invariant at linear order and computable directly from the observed $P(k)$; for $\Lambda$CDM at $\ell=50\,\mathrm{Mpc}\,h^{-1}$, $I_{\rm NN}\approx 0.10$.The total mutual information gives a data-computable measure of the backreaction correction to the FRW free energy. The gauge proof holds at linear order; the KAM identification is exact; the backreaction bound rests on a stated conjecture.

Polymer chain scission is a key mechanism for fracture of soft materials. It is well known from single-molecule force spectroscopy experiments that the critical condition for chain scission depends on the loading rate and other environmental effects (e.g., temperature and solvent). Common approaches to describing the kinetics of chain scission often assume force-controlled conditions, that is, when a polymer chain is stretched by a prescribed force. As a result of this assumption, chain scission is irreversible, excluding the possibility of healing. In many soft materials, however, self-healing has been observed after fracture, suggesting possibly reversible chain scission. Here, we show that reversible chain scission is possible under displacement-controlled conditions, that is, when a polymer chain is stretched with a prescribed end-to-end distance. We present a breakable freely-jointed chain model, assuming that a polymer chain breaks when one of its links breaks while the other links remain nearly rigid. At a prescribed end-to-end distance, the free energy of the chain has two local minima and a local maximum (the transition state), giving rise to energy barriers for chain scission and healing. As the prescribed displacement increases, the energy barrier decreases for scission but increases for healing, depending on the chain length (number of links) and the potential energy of the link. With the energy barriers, we adopt a kinetic approach to predict the statistics and kinetics of a single polymer chain under tension, first by integrating the rate equation and then by kinetic Monte Carlo simulations. Notably, the present model predicts rate-dependent chain scission, with a lower bound for the rupture force that could be several orders of magnitude lower than the upper bound (which is close to the theoretical strength of the covalent bonds).

Tensor networks and quantum circuits are structural objects whose meaning depends on connectivity, indices, contraction order, gate placement, measurements, and related design choices. They are often easier to reason about visually than as code, yet in Python they are frequently constructed, transformed, and checked through backend-specific objects or compact symbolic expressions. This can make structural mistakes hard to notice during development, debugging, and communication. This paper presents three complementary packages: Tensor-Network-Visualization for visual debugging and structural inspection of supported tensor-network and traced einsum workflows; Tensor-Network-Editor for visual-to-code authoring, backend code generation, JSON preservation, export, and design-level analysis; and Quantum Circuit Drawer for clear circuit rendering, inspection, and complementary comparison of circuits or documented result distributions. The packages form a visual authoring and inspection layer around existing tensor-network libraries, array-based scientific Python workflows, and quantum SDKs. They are not simulators: they do not implement new contraction algorithms, execute quantum circuits, or guarantee full semantic equivalence across arbitrary backends. Their contribution is to make structural artifacts visible, editable, inspectable, comparable, exportable, and reproducible within those ecosystems.

We have demonstrated Laser Induced Fluorescence (LIF) in a Capacitively Coupled Plasma (CCP) discharge to directly measure the most crucial ion properties at a discharge regime suitable for a broad range of plasma research related to plasma processing and dusty plasma investigations that has been impossible for many years. The ion flow measurements in the presence and absence of dust particles show that ions move much faster directionally than expected from thermal motion, with reductions observed in the presence of dust particles. Ion temperatures are also found to exceed room temperature, contrary to a common assumption in the dusty plasma community. These findings represent a significant advancement in experimental plasma research, providing vital information to refine ion-driven process models with insights that span multiple research fields.

To utilize quantum error-correcting codes, a decoder must infer the logical sector from the measured syndrome. Beyond a hard logical decision, some decoders provide soft information estimating its reliability. For minimum-weight perfect matching (MWPM), a common confidence measure is the complementary, or logical, gap. Neural-network decoders trained with binary cross entropy naturally output a different score, the logit, whose relation to the matching gap remains unclear. Here, we test whether the logit of a graph neural network (GNN) decoder behaves as a learned proxy for the logical gap. Using a pretrained GNN for the rotated surface code under uniform circuit-level noise [PRR, 7(2):023181, 2025], we compare its logit with the MWPM gap shot by shot on identical syndromes. The native GNN decoder-logit pair yields a lower post-selected logical error rate than the native MWPM decoder-gap pair over the operationally relevant range of acceptance rates. Exchanging the scores between decoders isolates score discrimination from hard-decision accuracy and shows that both contribute to the advantage. At larger distances each score best ranks failures of its own decoder, whereas at small distance, where the bounded matching gap saturates, the learned confidence better discriminates MWPM failures than the gap itself. Finally, GNN confidence is substantially better described by the posterior logistic form implied by an ideal log-likelihood ratio, while the MWPM gap shows systematic departures. Thus, a neural-network decoder trained only on syndromes and logical labels learns a gap-like confidence proxy whose native scale more closely follows the expected posterior calibration form, supporting learned soft output when MWPM gap estimates are unavailable, costly, or insufficiently expressive.

Altermagnets combine compensated collinear magnetic order with momentum-dependent spin splitting in the electronic band structure. Here, we show that rolling a two-dimensional (2D) $d$-wave altermagnet into a nanotube converts this momentum dependence into chiral-angle-controlled one-dimensional (1D) spin splitting through dimensional projection. A minimal tight-binding model reveals a characteristic nodal–antinodal dependence on the chiral angle $\theta$, with the central circumferential subband exhibiting a $\cos(2\theta)$ scaling and the projected spin splitting vanishing for the nodal orientation and reversing sign between orthogonal antinodal orientations. First-principles calculations for V$_2$O and representative symmetric and Janus systems demonstrate that this nodal–antinodal selection rule persists despite curvature-induced structural asymmetry and magnetic moment imbalance. We further show that the projected electronic structure produces chiral-angle-controlled spin-polarized transport: antinodal nanotubes exhibit spin-polarized transmission, whereas the nodal nanotube remains conducting with identical spin-channel transmission. These results demonstrate how dimensional projection can translate the momentum-space spin splitting of a 2D altermagnet into geometrically controlled electronic and transport properties in nanotubes.

We investigate how quantum resource constraints affect deep thermalization, the emergence of universal local wavefunction distributions from partial measurements of a quantum many-body state. Quantum resources, such as non-stabilizerness (magic), coherence, asymmetry, imaginarity, and non-Gaussianity, are essential for quantum information processing, and constraints on their global abundance can reshape these emergent distributions. To address this question, we develop a unified framework for deep thermalization within general quantum resource theories (QRTs). Our central result is that QRTs fall into two classes: “smoothly localizable” (SL) QRTs, where the resource content of local post-measurement states changes continuously with the global resource density, set by the initial state and measurement basis, yielding continuously tunable wavefunction distributions; and “threshold localizable” (TL) QRTs, where the local resource content jumps discontinuously from minimal to near-maximal past a critical global resource threshold, producing a sharp transition between a resourceless, “deep-ergodicity breaking” distribution and a resourceful, maximally random one. We trace this SL-TL dichotomy to an information-theoretic mechanism, block sharpening: by viewing each QRT as coherence between blocks in Hilbert space, we show that the local resource content depends on the measurement's ability to collapse an initial superposition into a single resourceless block. Our theory is analytically tractable and quantitatively predicts the phase boundaries across all studied QRTs, which we validate with extensive numerical simulations. Finally, we highlight two consequences: a novel magic transition in zero-rate quantum error-correcting codes–previously believed to occur only at finite rates–and new implications for quantum resource certification protocols based on post-measurement state ensembles.

We investigate the spectral properties of tight-binding quantum Hamiltonians defined on the bipartite Levi graphs of finite geometric configurations. In Part I, we analyze the $10_3$ Desargues and Kantor configurations, demonstrating how deterministic spatial deformations induced by real planar embeddings ($\mathbb{R}\mathbb{P}^2$) destroy translational symmetry, leading to structural wave localization. We show how embedding in the complex projective plane ($\mathbb{C}\mathbb{P}^2$) restores Bloch wave propagation via synthetic gauge phases. In Part II, we evaluate the Schläfli double six ($12_5, 30_2$) and the Cremona-Richmond ($15_3$) configurations in $\mathbb{R}^3$. We analytically derive their exact spectral decompositions, confirming the existence of macroscopic zero-energy flat bands ($E=0$) driven entirely by geometric frustration. In Part III, we establish a formal structural isomorphism between these discrete tight-binding networks and the flavor symmetry sector of the Standard Model. We map the Schläfli graph to the $SU(6)$ flavor multiplets, where the flat band corresponds to the kinematic freezing of ultra-heavy baryons. Finally, we discuss the complementary Cremona-Richmond $15_3$ topology, demonstrating how its distinct geometric nature (based on tritangent planes rather than point intersections) provides a purely algebraic, topological completion to the $W(E_6)$ symmetry of the 27 lines.

We report multi-wavelength studies of the transient EP250916a, detected by the Einstein Probe on 2025 September 16. Located at low Galactic latitude, the source exhibited a rapid X-ray brightening, reaching an unabsorbed 0.5–10 keV flux of $(6.4 \pm 0.1) \times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$, followed by a plateau and a two-stage decay lasting over 40 days. Swift/XRT monitoring shows a persistently hard spectrum ($\Gamma \approx 1.6$–2.2) with only modest softening during decay, while a NuSTAR observation confirms a hard-state continuum extending up to 70 keV. Timing analysis of XMM-Newton data reveals a weak quasi-periodic oscillation (QPO) at $\sim$13 Hz. No other coherent pulsations or thermonuclear bursts are detected. Broadband spectral modeling favors a nonthermal power-law continuum with partial-covering absorption, and shows no significant thermal disk component. Optical imaging obtained with NOT/ALFOSC, LCO, and GaiaDR3 identifies two faint sources within the 2 arcsec Swift/XRT positional uncertainty. A MeerKAT observation at 1.28 GHz yielded no radio counterpart, with a 3$\sigma$ upper limit of 60 $\mu$Jy beam$^{-1}$. The combination of a long-lasting outburst, a hard nonthermal X-ray spectrum, a weak QPO detection, the absence of coherent timing features, and faint potential optical counterparts disfavors a stellar-flare or extragalactic origin and supports an accreting compact-object scenario. Comparisons with similar faint, hard-state transients place EP250916a within a growing population of low-luminosity, hard-state black hole X-ray binary candidates.

We present a unified theoretical framework for the mapping between diffusive and wave-like dynamics, formulated as a spectral integral operator acting on temporal fields. By introducing an analytic continuation in the complex frequency plane, we establish an explicit correspondence between thermal diffusion and a virtual wave field governed by a hyperbolic equation. This mapping is shown to define a causal, compact Fredholm operator that acts as a nonstationary low-pass filter, thereby revealing the intrinsic information loss of diffusive processes and the fundamental ill-posedness of the inverse reconstruction. Within this operator framework, we demonstrate that commonly used excitation schemes-including pulse, lock-in, chirped, and coded excitations-emerge as distinct projections onto subspaces of a single underlying transformation, corresponding to different sampling strategies of its spectral structure. This unifies previously disparate virtual wave formulations and provides a systematic interpretation of excitation design in terms of operator sampling and information encoding. The framework further generalizes to matrix-valued systems and suggests a spectral-geometric interpretation of temporal evolution across diffusive and propagative regimes.

Wave resistance is the drag generated by the wave radiation that a source moving at a fluid interface sustains. Under stochastic trajectories, the mean drag is controlled by the ensemble-averaged surface profile built from the trajectory history. We show that the result is a finite resistance below the deterministic radiation threshold and a regularization of the singular response at the minimum phase velocity of the capillary-gravity waves. We derive explicit scaling laws for drifted Brownian trajectories, including a universal high-diffusivity decay. For drifted Lévy flight, we find the mean wave resistance in closed-form, extending wave-drag theory to non-Gaussian trajectories.

We propose a theoretical mechanism to indirectly detect the small parity-violating energy difference (PVED) between chiral enantiomers through a macroscopic enantiomeric excess observed in an ultracold gas. We consider that chiral molecules are formed resonantly via ultracold collisions of achiral diatomic molecules, with PVED inducing a slight asymmetry in the resonance energies of right- and left-handed configurations. After formation, chiral molecules evolve within a Bose-Einstein condensate (BEC), incorporating nonlinear interactions, tunneling between enantiomeric states, intrinsic PVED, and thermal conversion rates. These collective dynamics enable amplification of the microscopic bias into a global population imbalance. Using coupled rate equations, we show that, under realistic regimes, a complete enantiomeric excess can be achieved even for extremely small intrinsic asymmetries. We illustrate the model with concrete examples (HSOH, H$_2$Se$_2$, H$_2$Te$_2$), predicting observable enantiomeric excesses under plausible experimental conditions. We also consider non-PVED effects that could be amplified under the proposed mechanism, including electric and magnetic fields as well as thermal fluctuations, the latter being illustrated through the aforementioned molecular examples. Overall, our results suggest that ultracold physics could provide a new pathway to probe molecular parity violation, a fundamental weak effect that remains experimentally undetected.

We make use of the free data formalism developed in \cite{CK25} to construct solutions of the Einstein vacuum constraint equations by integrating in the forward direction. This, together with a new gauge condition based on effective uniformization, allows us to construct general solutions with limited decay at spacelike infinity. In particular, we construct solutions with minimal and even borderline decay, as considered in \cite{Shen23}, \cite{Shen24} in connection with the stability of the Minkowski space. In a forthcoming paper, we make use of the techniques we develop here to identify and construct a general class of short-pulse Cauchy data that lead to the formation of trapped surfaces, extending the well-known result of \cite{LiYu}.

Predicting the output of quantum circuits is a central bottleneck for verifying quantum processors because a generic wavefunction grows exponentially with system size. We introduce a neural statebank that learns this wavefunction along the circuit trajectory. Each layer is stored as an autoregressive Transformer checkpoint trained from local gate updates to the preceding checkpoint, producing a compact neural representation that can evaluate amplitudes and generate independent samples. On long-range circuits combining entanglement, magic, and non-diagonal branching, a 0.3-million-parameter statebank reaches $\sim 10^{-2}$ infidelity at 34 qubits, outperforming the other tested approximate simulators while using far less memory than exact state-vector evolution. The same architecture accurately simulates quantum approximate optimization, Clifford+$T$, and Clifford circuits.

These lecture notes are based on the lectures on Statistical Mechanics of Random Matrices delivered at the Spring College on the Physics of Complex Systems, held at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, from 19 February to 15 March 2024. Their aim is to present a statistical-mechanics route to the spectral theory of sparse and diluted random matrices, with emphasis on cavity and replica methods, resolvent techniques, population dynamics, typical spectral densities, spectral-count fluctuations and large deviations, conditioned spectra, and non-Hermitian extensions. The written form of the notes has been deliberately expanded beyond the material actually covered during the lectures. This is partly because a set of lecture notes can afford a more systematic development than a sequence of blackboard lectures, and partly because several natural continuations of the material become clearer once the central methods have been introduced. Consequently, not every topic discussed here was presented during the College. The additional material is included to give a more coherent account of the subject and to indicate directions that, hopefully, can be covered in greater detail in future lectures or schools. Since these are lecture notes rather than a state-of-the-art review, the choice of topics is necessarily selective and is naturally tilted towards the author's own work and collaborations on this subject. I have nevertheless tried, within the limits of this format, to place the material in contact with the broader literature and to represent the surrounding state of the art as fairly as possible. Inevitably, some relevant contributions may be missing or treated too briefly; such omissions are unintentional and reflect the pedagogical scope of the notes rather than a judgement on their importance.

We develop a regularised arbitrary-gauge formulation of nonrelativistic quantum electrodynamics and use it to compare Coulomb and multipolar descriptions with a Lorentzian form factor. We analyse the effect of regularisation in perturbation theory, including alternative partitions of the Hamiltonian into free and interaction parts, and the limits of the electric dipole approximation. The regularised multipolar gauge exhibits a cut-off-dependent trade-off between the strength of individual interaction terms and the localisation of material subsystems that suppresses direct inter-atomic interactions. We discuss the implications of the framework for short-range phenomena, including Dicke criticality.

For over four decades, Gribov's no-pole condition has been almost exclusively explored in Euclidean space, where the elliptic nature of the Faddeev-Popov operator provides a clear spectral boundary. In physical Minkowski spacetime, however, this operator becomes a hyperbolic wave operator, and the Euclidean positivity criterion collapses. We show that the natural Lorentzian replacement is a real-time boundary-value problem: a gauge configuration remains inside the first Gribov region as long as the Faddeev-Popov wave equation admits no source-free solutions obeying the Feynman boundary condition. For backgrounds localized in time, this condition translates to the injectivity of the negative-frequency block of the classical ghost scattering map. For stationary backgrounds, it becomes a spatial bound-state or threshold-resonance problem under Fourier transformation. Using a Wronskian identity, we prove that pure frequency mixing in stable self-adjoint time-dependent channels is structurally protected and cannot by itself produce the obstruction. While static chromomagnetic backgrounds reproduce the familiar zero-frequency horizon crossing, static chromoelectric potentials reach the horizon at finite, non-vanishing frequency - a uniquely Lorentzian phenomenon arising because $A_0$ couples directly to the ghost time derivative. We also cast the condition in Fredholm form and show that the exact restriction is a functional determinant, which the naive local continuation of the Gribov-Zwanziger action fails to reproduce, leaving the construction of a genuine local real-time action as the central open problem.

We investigate entanglement transfer in a multi-giant-atom waveguide system. By tailoring chiral spontaneous emission and exploiting dark-state dynamics, the setup enables perfect, unidirectional sequential or selective transfer of quantum states and their associated entanglement. The distance between two entangled atoms, i.e., the entanglement length, can be dynamically adjusted, allowing robust conversion between long-range and short-range entanglement during propagation. The system inherently converges to a dark state, guaranteeing high-fidelity directional transfer. When the additional phase is modulated as a periodic piecewise function, spatially separated giant atoms exhibit stable, nearly lossless state exchange and maintain steady entanglement even under non-Markovian conditions. This behavior mimics conventional braided architectures without suffering from propagation delays or spatial restrictions. Our proposal offers a scalable pathway for continuous long-distance entanglement transport and resilient state exchange in quantum networks.

Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization. Hence, a successful reconstruction is direct evidence for a latent mean-field theory and the microscopic parameters of that theory can be read off the trained decoder. We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters, recovering the full Hopfield pattern matrix from equilibrium samples alone. We find that, when applied to Salamander retinal recordings, a two-latent VAE reproduces the population statistics with only two effective collective variables allowing us to recover the `stored patterns' of the neural population and write a generalized Hopfield model which correctly models the experimental data.

Optimization of continuous-variable objectives on standard gate-based quantum computers via variational algorithms such as QAOA is typically approached by first discretizing each decision variable into a finite binary representation. This increases qubit requirements and restricts solution precision through fixed-resolution encodings. We propose a qubit-efficient variational framework for continuous optimization that instead encodes each decision variable into the squared amplitude or equivalently, the measurement probability of a single qubit state. This removes explicit discretization from the variable representation while remaining entirely within the standard qubit circuit model unlike methods like CV-QAOA employing qumode based hardware to achieve the same. To read out encoded variables, we propose using amplitude estimation rather than naive sampling or tomographic reconstruction, with the goal of improving precision scaling for continuous-value recovery. We outline how amplitude-estimation error propagates to decision-variable error and then to objective-value error under standard regularity assumptions, suggesting a distinct width-versus-precision tradeoff relative to discretized approaches. In particular, the framework replaces the logarithmic increase in qubits needed for finer binary precision with a constant cost of one qubit per decision variable, while shifting accuracy requirements into the estimation procedure. We position this approach relative to traditional discretized variational formulations, and argue that it provides a promising new direction for continuous optimization on standard qubit architectures.

Dynamical mean-field theory (DMFT) reduces dense high-dimensional disordered dynamics to a self-consistent effective stochastic process. For sparse and heterogeneous networks, however, local fields contain finitely many strong inputs, so the Gaussian closure mechanisms of dense DMFT need not apply. We develop a continuous-time cavity derivation of sparse-network DMFT at the level of path measures for stochastic dynamics with general pairwise interactions on sparse random graphs. The cavity equations are exact on trees and yield the finite-time thermodynamic description on locally tree-like graphs. They show explicitly how reciprocity changes dynamical closure: fully directed graphs recover the sparse directed path-probability equation, whereas reciprocal or bidirected edges require conditional path kernels driven by the imposed history of the receiving node. Ensemble averaging gives laws over path-probability messages, with barycenters and higher-message moments closing by multilinearity and independence of incoming branches. A causal discrete-time derivation yields the corresponding population-dynamics representation, distinguishing trajectory populations for directed graphs from conditional branch-law or finite-depth tree populations for reciprocal graphs. We also formulate finite-memory numerical closures and test them in an additive-input recurrent neural network specialization. Finally, high-connectivity limits are obtained as projections of the sparse path-measure theory, clarifying when dense drift, noise, and response channels reduce to standard low-dimensional DMFT and when path-level descriptions remain essential.

The phase prediction of chemically disordered alloys poses a significant computational challenge due to the combinatorial complexity of such materials. The high-throughput compositional exploration of chemically disordered alloys, including high-entropy alloys, requires an approach to efficiently explore the potential energy landscape of such complex materials. Additionally, a metric to quantify the potential energy landscape explored for phase prediction of the compositions needs to be defined. We propose an information-theoretic approach to phase prediction in chemically disordered alloys in the present work. We demonstrate the applicability of alchemical Monte Carlo sampling using an efficient Graph Convolutional Neural Network-Based machine learning model. We additionally demonstrate the applicability and limitations of the Bond Disproportion Vector (BDV) as a low-computational-cost descriptor and benchmark it against the state-of-the-art Smooth Overlap of Atomic Positions (SOAP) descriptor. We show the applicability of an information entropy-based metric for the phase prediction of binary (CoNi, MoW, FeNi and TaW), ternary (CoCrNi, CrFeNi), quaternary (CoCrFeNi) and quinary ($\mathrm{Al_x(CoCrFeNi)_{1-x}}$) alloys. Information entropy-based phase prediction can be applicable in challenging cases where conventional approaches are not feasible.

Muography, commonly known as muon tomography, is a passive, non-destructive imaging technique that utilizes naturally occurring cosmic-ray muons to visualize the internal density structures of large, static, or inaccessible objects. In course of developing a small prototype muography system for material identification that relies upon the multiple Coulomb scattering of muons in matter, we explored the possible use of Thick-GEM detector as muon tracking device. It is a 5-20 fold scaled-up version of traditional GEM technology, that has become increasingly popular in recent years, owing to its mechanical robustness, cost-effective production, and excellent position sensing capabilities. A few prototypes of this detector of dimension $40\,\mathrm{mm} \times 48\,\mathrm{mm}$ with variation in other design parameters, were manufactured from a local industry. Subsequent to conditioning, detailed characterization of the detectors was performed to validate their suitability in muography applications. To identify the optimal operating region, gain variation was studied under various voltage configurations for both single and double-stage configurations. Experimental measurement of muon detection efficiency across the entire operating range yielded a maximum efficiency of 99.5% in both cases. Using a collimated Fe$^{55}$-source, the best spatial resolution was determined to be 30 $\mu$m for both single and double-stage operation.

Since its classical origin, Hamilton's principle has been formulated under an exact closure condition: admissible variations vanish at the boundaries of the variational domain. This condition removes the boundary term in the first variation of the action and yields the Euler–Lagrange equation. Although natural for isolated deterministic systems, fixed boundary admissibility is usually treated as a technical condition rather than as a physical closure hypothesis. Here we ask what follows when this hypothesis is made explicit and relaxed. We introduce variational openness as the retention of the boundary contribution in the variational balance. The retained term defines a boundary-openness density, which must be projected onto admissible variations before it becomes a dynamical source. In this formulation, the classical Euler–Lagrange equation is recovered as the exact-closure limit of an open variational balance; the source term is therefore identified with incomplete variational closure rather than with an externally imposed force. The framework is illustrated through three elementary examples: an open harmonic oscillator, a finite-compliance boundary, and a delayed oscillator with memory. These examples show how boundary openness can produce forcing, partial closure, history dependence, and non-Markovian structure while preserving standard mechanics in the closed limit. The resulting perspective suggests that Hamiltonian mechanics may be understood as the mechanics of variationally closed systems and motivates an open Hamilton–Jacobi theory in which admissibility itself becomes dynamical.

Routine full-disk EUV imaging has been available only since the modern era, such as SOHO and SDO. To extend EUV coronal context into earlier periods, we leverage the multi-decade availability of full-disk \HeI{} observations, whose absorption is modulated by coronal irradiance and magnetic topology and is widely used as a proxy for open-field regions. We present a diffusion-based conditional image translation framework, Coronal Hole-aware Diffusion Model Translator (CH-aware DMT), to reconstruct synthetic SDO/AIA 193 Å EUV images from \HeI{} inputs. The model is trained on temporally co-aligned SOLIS \HeI{} and AIA 193 Å pairs spanning 2011–2015 using a month-based split, where January–October are used for training, November is used for validation, and December for testing. On the held-out test set, the reconstructions preserve dominant full-disk EUV morphology (CC=0.92) and recover CH-related low-intensity structure (CC=0.84). We further assess historical applicability by (1) comparing reconstructed AIA 193 Å morphology with SOHO/EIT 195 Å over 2005–2015; (2) comparing reconstructed AIA 193 Å images generated from KPVT \HeI{} inputs against Yohkoh/SXT soft X-ray observations; and (3) evaluating long-term reconstructed disk-integrated emission statistics against observational EUV series and independent solar activity proxies (sunspot number and F10.7 radio flux over 1974–2015). These results indicate that CH-aware DMT conditioned on \HeI{} can provide a physically plausible synthetic AIA 193 Å coronal proxy for historical studies, supporting multi-decade analyses of large-scale coronal evolution before the direct EUV imaging was available.

The ability to predict protein three-dimensional structures from amino acid sequences is a landmark achievement in molecular biology, where recent deep learning approaches such as AlphaFold are the culmination of decades of work. Yet, the quantitative understanding of how protein sequences give rise to dynamic conformational changes and higher-order assemblies remains unsolved. Folding and conformational states are dynamic, stochastic processes, shaped by sequence, energy, co-translational constraints, chaperone machineries, and the physicochemical conditions of the cellular environment. Recent advances now position the field to move beyond static structural endpoints toward a mechanistic understanding of folding dynamics in living systems. Single-molecule techniques enable time-resolved observation of folding trajectories and intermediate states hitherto hidden by traditional structural biology approaches, while computational innovations and data-driven approaches offer new ways to integrate heterogeneous data across scales. In this Roadmap, we review the current conceptual landscape of protein folding, examine the experimental and theoretical gaps that remain, and discuss emerging strategies that integrate high-resolution measurements with multiscale modeling. We outline a roadmap toward a quantitative and predictive science of protein folding dynamics, conformational kinetics, and macromolecular self-assembly. Realizing this vision would transform our understanding of the dynamics of molecular self-organization, from the folding of individual polypeptides to the emergence of dynamic macromolecular complexes. This will enable rational control of folding and misfolding in health and disease, extend protein engineering principles beyond static structural design, and establish a mechanistic foundation for predictive and personalized interventions in proteostasis-related disorders.

We look at Bell inequalities from the lens of information structures in stochastic teams. We consider the usual Clauser-Horne-Shimony-Holt (CHSH) game and a dynamic variant of the same to study how various classes of strategies, classical, projective and quantum, behave under team theoretic solution concepts. We endow players with a fixed quantum state that we take as the Bell state, and allow variation of the measurement strategies. In the static game, projective strategies (where each player performs projective measurements) are team optimal for all parameter values and are closed under best response. In the dynamic game these properties fail: projective strategies may be strictly outperformed by classical ones, best responses to projective strategies need not be projective, and, beyond a sharp threshold on the channel noise, team optimal projective strategies cease to be person-by-person optimal, even though person-by-person optimal projective pairs always exist. These results shed light on the delicate interplay of information structure in quantum strategies and the fragility, under a change of information structure, of structural properties that are taken for granted in the static setting.