Generalized entropy measures are widely used to characterize localization and multifractality, and the regime \(q>1\) is often empirically found to exhibit improved numerical stability and cleaner scaling behavior. Here, we develop a fluctuation-stability framework for generalized entropy diagnostics and show that weak-amplitude spectral fluctuations are amplified for \(q<1\) and suppressed for \(q>1\), thereby providing a theoretical basis for the physically robust \(q>1\) regime. A thermodynamic scaling analysis further identifies an asymptotically stable regime beyond a critical threshold. As an application, we introduce the entropy-gradient susceptibility \(χ_q\) as a coarse-grained probe of spectral heterogeneity. Using the Aubry-André and generalized Aubry-André models, we demonstrate that \(χ_q\) sharply distinguishes homogeneous localization transitions from mobility-edge coexistence regimes. Our results establish fluctuation stability as a guiding principle for generalized entropy diagnostics in quasiperiodic systems.

Gene regulatory networks (GRNs) are high-value targets for therapeutic and synthetic-biology control. Classical Hill models carry a structural defect: the production term vanishes when the activator is absent, causing loss of controllability under multiplicative actuation and a collapse of network coupling under additive actuation -- precisely where biological operation is most common. Building on logistic functions as robust Hill alternatives, we develop an additive state-feedback framework for logistic-based GRNs, with two companion scalar results. A feedforward-plus-proportional law turns any positive setpoint into a closed-loop equilibrium, regardless of the uncontrolled dynamics. We prove local exponential stability under a Gershgorin gain bound and, via a common quadratic Lyapunov function built on the logistic sector bound, global exponential stability under the explicit condition $(γ_1+K_1)(γ_2+K_2)>κ_1κ_2λ^2/64$, with a closed-form rate. A diagonal Lyapunov certificate $P=\mathrm{diag}(B,A)$ yields an explicit settling-time bound (within $1\%$ of simulation) and an ISS ultimate-bound estimate. We further establish a parameter-uniform monostabilization budget $K^{*}=κλ/4-γ$ for bistable self-activation switches, and a Halanay-type delay-uniform global exponential stability theorem under $γ+K>κλ/4$, with two-sided closed-form rate bounds. Numerical comparison with the Hill counterpart confirms robust tracking in the nominal range while exposing the structural divergence near the boundary of the positive orthant: the Hill coupling $|[J_f]_{21}|=Θ(x_{d,1}^{n-1})\to0$ as $x_{d,1}\to0$, whereas the logistic coupling stays strictly positive.

Finite element (FE) methods are the benchmark for solid mechanics simulations, yet their computational cost becomes prohibitive for problems with localised nonlinearities, fine-scale features, or long-time dynamic evolution. In our earlier FE-neural operator (FE-NO) hybrid framework [1], physics-informed deep operator networks were coupled with FE solvers through overlapping domain decomposition with Dirichlet-Dirichlet interface exchange, accelerating intensive subdomains while preserving FE fidelity elsewhere. Two limitations remained: the overlapping formulation required redundant interface computations that increased inner Schwarz iteration counts, and the convolutional feature extractor restricted the NO subdomain to structured grids, precluding irregular geometries. A non-overlapping Schwarz alternating method with Neumann-Dirichlet interface exchange replaces it, transmitting traction from the NO to FE rather than displacement. This eliminates the overlap layer and reduces inner Schwarz iterations while maintaining bounded error accumulation across all tested time horizons. For arbitrarily shaped subdomains, a Point-DeepONet operates on unstructured FE point clouds without interpolation, extending it to non-convex and irregular geometries. Strain and stress operators are derived analytically from the displacement operators via kinematic equations, rather than as independent networks, reducing trainable parameter sets while enforcing mechanical consistency by construction. The framework is validated on three benchmarks: static linear elasticity, quasi-static hyperelasticity, and elastodynamics with regular and irregular geometries. These results establish a non-overlapping FE-NO coupling paradigm that is geometry-flexible, parameter-efficient, and convergence-stable, providing a pathway for hybrid physics-based and operator-learning solvers in large-scale dynamic solid mechanics.

Adaptive variational quantum algorithms like ADAPT-VQE construct tailored ansätze by iteratively selecting operators from a pool using gradient-based criteria. While this avoids oversized parameter spaces, repeatedly scanning the full pool incurs a classical cost that scales linearly with pool size-a major bottleneck for systems with long-range interactions or large operator sets. Here, we reformulate adaptive operator selection as a graph-based decision problem and introduce a graph neural network (GNN) policy that predicts the next entangling operator directly from the interaction graph and state-dependent observables. Training data are generated from exact simulations of disordered long-range spin chains, using gradient magnitudes as supervision signals. The learned policy accurately reproduces the dominant structure of the greedy gradient-based selection rule, significantly outperforming heuristics based solely on interaction strength. Integrated into a variational quantum eigensolver (VQE) workflow, this GNN-VQE approach achieves energy errors close to standard ADAPT-VQE while drastically reducing full-pool gradient evaluations. To test transferability beyond spin models, we evaluate the policy on small active-space molecular benchmarks (LiH and BeH_$2$). We find the GNN is highly effective as a shortlist generator: exact rescoring over just a few GNN-proposed candidates recovers near-oracle rollout behavior while searching only a small fraction of the pool. These results demonstrate that adaptive circuit construction contains learnable structure that can be exploited to accelerate variational quantum algorithms.

As it is well known, solutions of equations of nonlinear elastodynamics, representing extremals of the action functional, can form shocks. We adapt the classical approach of Emmy Noether to such singular extremals and derive the appropriately generalized integral relations within Calculus of Variations. We apply them to elastodynamical extremals with shocks, obtaining new integral relations involving kinetic and elastic energies. For the extremals representing thermodynamically admissible (entropy) solutions of the corresponding hyperbolic Euler-Lagrange equations, the classical equalities, characterizing the variational approach of Noether, expectedly transform into ineqalities. We show that, rather remarkably, despite the crucial role of material velocity in the fully inertial energy redistribution processes, the corresponding kinetic energy can be completely eliminated from the expression for the dynamically stored elastic energy, even in the presence of shocks.

We investigate connected sequential geometric structures in correlated neutral meson systems within the framework of Bargmann invariants. Building upon previously developed third- and fourth-order rephasing-invariant geometric structures involving decay-projected conditional states, we introduce a connected sequential fourth-order Bargmann invariant in which the decay-projected states associated with two decay channels are linked through a direct overlap between the corresponding projected states. This construction incorporates explicit projection-projection correlations within the cyclic overlap chain. The connected sequential invariant encodes the geometric relation between decay-projected states, thereby extending the geometric correlation framework developed for correlated neutral meson systems. To characterize the resulting geometric structures, we define rephasing-invariant ratios that quantify connected sequential correlations and provide a direct comparison with the previously studied disconnected geometric correlations. The behavior of these quantities is analyzed in the regime of small CP violation using the standard rephasing-invariant interference parameters together with a small-asymmetry expansion. We show that the connected sequential ratios exhibit characteristic scaling behaviors governed by both mixing asymmetry and relative interference-phase alignment, leading to geometric scaling properties distinct from those of the disconnected structures. We further discuss the geometric interpretation of the connected sequential invariants and their possible relevance to correlated neutral meson systems. The resulting framework extends the hierarchy of Bargmann invariant geometric correlations associated with neutral meson mixing and decay, providing a complementary geometric perspective on CP-sensitive interference phenomena.

Signed networks consist of both positive and negative relations, and structural balance theory provides an important conceptural framework for understanding their global tension structure. While existing statistical methods mainly focus on assessing empirical evidence of balance in a single observed network, many real-world signed relations evolve over time. This paper develops nonparametric inference for the population degree of structural balance at specified time points in dynamic signed networks, where the target time may or may not coincide with an observed snapshot. We consider a dynamic signed graphon model in which both edge formation and sign generation are governed by smoothly time-varying graphon functions. To exploit temporal smoothness, we construct a kernel-smoothed estimator that borrows information from snapshots near the target time point. Our theoretical analysis establishes a studentized inference procedure and a higher-order distributional approximation based on Edgeworth expansion, showing that temporal smoothing improves inference in sparse networks by reducing variance of observation noise, up to smoothing bias and time-discretization errors. We demonstrate the finite-sample performance and practical usefulness of the proposed method through extensive simulation studies and an application to a dynamic international relation network in political science.

An external magnetic field is applied to the classical hydrogen atom treated in classical electromagnetic theory including classical electromagnetic zero-point radiation. In an earlier article, it was shown that the average value of each of the electron's action variables appears as a discrete value, corresponding to a representation of the rotation group, because of resonance between the periodic orbit of the electron and the random classical zero-point radiation. Here it is shown that, in the presence of a magnetic field and because of resonance, the classical orbital motion of the electron is in resonance with random classical zero-point radiation only for orientations of the orbit which take integer values for the angle made with the direction of the magnetic field, but excluding the m=0 orientation where the magnetic field is parallel to the orbital plane of the electron. Classical electromagnetic explanations are given for the Stern-Gerlach result, and for the Zeeman effect.

We study the problem of implementing a quantum channel using a small ancilla with classical randomization and postselection on an output failure flag. The simulation is probabilistic, but exact conditioned on success. We prove that any unital channel on a $d$-dimensional system can be simulated with ancilla dimension $k$ and success probability $Ω(\frac{k}{\log d})$. Equivalently, every unital channel on $n$ qubits can be simulated with constant success probability using only $O(\log n)$ ancillary qubits. We show that this tradeoff is best possible by constructing a family of channels which cannot be simulated with success probability better than $O(\frac{k}{\log d})$. We also show that the class of \textit{highly noncommutative} channels, which includes random channels, admits constant-success simulation with just a single ancillary qubit. We further show that this model of simulation necessarily fails for strongly non-unital channels and discuss possible extensions involving adaptivity. On the technical side we rely on a partition-based protocol and matrix concentration inequalities, including the recent refinement of noncommutative Khintchine inequalities due to Bandeira, Boedihardjo and van Handel.

We investigate UV absorption lines tracing cool gas in eight bright ($-21.9<M_\mathrm{UV}<-20.5$) galaxies at $z=7.2-10.6$ using deep JWST/NIRSpec medium-resolution spectra homogeneously selected from archival data. We identify multiple absorption lines of low-ionization species (LIS) in five galaxies, while the remaining three show only one or no significant detections. The average LIS equivalent widths $\mathrm{EW_{LIS}}$ indicate weaker absorption lines in compact ($r_\mathrm{e}\lesssim 100$ pc) galaxies with high $L_\mathrm{Hβ}/L_\mathrm{UV}$ and $Σ_\mathrm{SFR}$, suggestive of absorption-line suppression due to intense star formation or nuclear activity. We simultaneously fit multiple LIS lines, accounting for both covering fraction $C_f$ and column density $N$, and find that the five galaxies follow the local $C_f$-$N$ relation. Through the LIS-line fitting, we derive chemical abundance ratios. The five galaxies have abundance ratios similar to those of damped Ly$α$ (DLA) systems in the [Si/O]-[C/O] and [Fe/Si]-[Al/Si] planes, suggesting that their absorbing gas is similar to that of DLAs. We find that two galaxies at $z\sim 7$ are already highly Fe-enriched, with $\mathrm{[Fe/Si]}\simeq -0.2$, near the solar abundance ratio. While the high Fe enrichment may originate from early Type-Ia supernovae (SNe Ia) or pair-instability supernovae (PISNe), these two galaxies also show $\mathrm{[Al/Si]}\sim0$, with no signature of the strong odd-even effect expected from PISNe, favoring SNe Ia.

Systematic surveys of filaments have been conducted to study their properties and their relationship to the process of star formation. In this paper, we use synthetic Herschel observations derived from 3D numerical simulations to compute column density maps, then use the \texttt{FILFINDER} algorithm to identify filaments. We obtain a large sample of 8,832 filaments that we further decompose into 110,193 branches. We characterize the physical properties of these filamentary structures and explore their correlations with embedded clumps. Furthermore, we directly compare our synthetic results with an observational catalogue of 32,059 filaments from the Herschel Infrared Galactic Plane Survey (Hi-GAL). Our results show that filaments are central to the star formation process, hosting $94\%$ of clumps from synthetic observations and $93\%$ of stars from our 3D numerical simulation. Filaments that host clumps have higher median column densities ($1.1\times10^{21}\,\rm{cm}^{-2}$) than those without ($3.8\times10^{20}\,\rm{cm}^{-2}$). We find power-law distributions for our synthetic filament masses and lengths, with power-law indexes of $α_{\rm M}=-0.86$ and $α_{\rm L} = -1.71$, respectively. We also find that the relation between the density of filaments and the background density is $N_{\rm{fs}} \propto N_{\rm{bs}}^{0.78}$. The measured properties of the filaments from the 2D synthetic observations are qualitatively consistent with those of the filaments from the Hi-GAL survey.

We study the quantitative approximation of certain stochastic integrals, where we use discrete time approximations under initial enlargement of filtration. It turns out that the approximation rate is in general the same as in the case of no additional information, however, the asymptotic constant improves.

Optical intelligent reflecting surfaces (OIRS) can improve the coverage of indoor visible light communication (VLC) systems, however, practical deployment requires a finite offline codebook to avoid repeated real-time optimisation of mirror orientations. A uniform codebook with fixed angular steps does not provide uniform coverage on the user plane, because the mapping from steering angles to reflection locations on the user plane is nonlinear. To address this problem, this paper proposes a geometric-optics-based non-uniform codebook design for OIRS-assisted VLC systems. The proposed method constructs an individual codebook for each IRS element according to its geometric position, so that the reflected beams are distributed more uniformly over the user plane. The codebook accuracy is evaluated using the Frobenius norm of the channel error matrix. Simulation results show that the proposed design provides more uniform spatial mapping with fewer codewords than the uniform codebook, and that the sweep-angle resolution has a stronger effect on the codebook accuracy than the tilt-angle resolution.

We report the discovery of 11 X-ray flares from 7 M dwarfs previously unknown to exhibit flaring activity, by cross-matching eROSITA observations of bright, nearby M dwarfs with the Chandra telescope archive. To analyze the properties of these flares in a broader context, we compile the sample of all reported X-ray flares from the 15 M dwarfs identified as flaring in the literature. We use this combined sample to derive constraints on the X-ray flare frequency distributions of M0-M6 stars. The average flare occurrence rate we measure is $\sim 10^{-1}\,\rm ks^{-1}$ (corresponding to $\sim 9$ flares per day). The X-ray flares in this sample span energies from $10^{29}\,\rm erg$ to $10^{33}\,\rm erg$ and exhibit a strong correlation between flare strength and duration. The flare properties we characterize include their durations, flux and temperature enhancements, and temporal asymmetries. Using these results and recent simulations of flare-driven atmospheric escape, we derive an upper limit on the time required for habitable Earth-like planets orbiting these M dwarfs to completely lose their atmospheres: 0.5-30 Myr.

The meet of two points in $\mathbb{Z}^d$ is their coordinatewise minimum. We show that every finite antichain $A$ in $\mathbb{Z}^d$ has at least $c_d |A|^{d/(d-1)}$ distinct pairwise meets, where $c_d > 0$ depends only on $d$, and that the exponent $d/(d-1)$ is best possible. As a corollary we obtain an isoperimetric inequality for downsets: every finite downset $D$ in $\mathbb{Z}^d_{\geq 0}$ satisfies $|D| \geq c_d |\max(D)|^{d/(d-1)}$, where $\max(D)$ is its set of maximal elements. By prime factorization the meet bound also yields a lower bound on greatest common divisors: a primitive set of $N$ integers supported on at most $d$ primes has at least $c_d N^{d/(d-1)}$ distinct pairwise gcds.

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 $η$-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 $ΔN_{\rm eff}$ 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.

We apply the mesoscopic coarse-graining framework of~\cite{OsanoMeso,OsanoExtensivity,OsanoPerturbation} to three problems in Cosmological Perturbation Theory and the backreaction debate. \textbf{(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. \textbf{(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 $k>\kNL$. \textbf{(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 $Λ$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).

We study the maximal number $m_{k,\ell,n}$ of empty convex $k$-gons ($k$-holes) determined by an $n$-point set in the plane in general position that contains no empty convex $\ell~$-gon, focusing on the first nontrivial case $\ell=k+1$. Our main result determines the exact value in the small-excess regime: for $n=k+a$ with $a\le k/2-1$, we prove $m_{k,k+1,k+a}=2^a.$ We also describe the extremal configurations attaining equality. Beyond this exact range, we provide upper and lower bounds in the proportional regime $n=αk$ and in the regime where $k$ is fixed and $n$ goes to infinity. In the last mentioned regime we prove that $m_{k,k+1,n}=Ω_k(n^{\lfloor\frac{k}{3}\rfloor})$ and $m_{k,k+1,n}=O_k(n^{\lceil\frac{k}{2}\rceil+1}).$

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 producing a hard logical decision, some decoders provide soft information that estimates the reliability of that decision. For minimum-weight perfect matching (MWPM), a common confidence measure is the complementary, or logical, gap. Here we test whether the logit of a graph neural network (GNN) decoder can act as a learned proxy for the logical gap. Using a pretrained GNN for the rotated surface code under uniform circuit-level noise [Physical Review Research, 7(2):023181, 2025], we compare its soft output with the MWPM complementary gap on the same sampled syndromes. We find that post-selection based on the GNN logit yields a lower logical error rate than one based on the MWPM gap. Shot-by-shot, the signed GNN confidence distribution resembles the signed MWPM gap at low and intermediate values, but assigns higher confidence to many correctly decoded shots. While both scores approximate the posterior log-likelihood ratio, the GNN confidence magnitude is closer to its ideal value. These results show that a neural-network decoder trained only on syndromes and logical labels learns both gap-like discrimination and a quantitative confidence scale, enabling confidence-based post-selection when MWPM gap estimates are unavailable, costly, or poorly matched to the noise model.

Altermagnets exhibit momentum-dependent spin splitting despite having zero net magnetization. Here, we show that rolling a two-dimensional (2D) $d$-wave altermagnet into a nanotube transforms this momentum-dependent spin splitting into chiral-angle-controlled one-dimensional (1D) spin splitting through dimensional projection. Using a minimal tight-binding model and first-principles calculations, we demonstrate that the nanotube spin splitting follows a characteristic $\cos(2θ)$ dependence, vanishing for nodal orientations and reaching extrema for antinodal orientations. The mechanism remains robust across a broad class of nanotubes derived from 2D altermagnets. Our results establish dimensional projection as a general route for transferring momentum-dependent altermagnetic spin splitting into 1D systems and provide a framework for engineering spin-split quantum states in low-dimensional magnetic materials.

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.

Let $f$ be a Hénon-Sibony map of $\mathbb{C}^k$ of algebraic degree $d_+\geq 2$, whose inverse $f^{-1}$ has algebraic degree $d_-$. The topological entropy of $f$ is equal to $\log d_+^{p} = \log d_-^{k-p}$. We show that every ergodic $f$-invariant measure $ν$ satisfying $h_ν(f)>\log \max\{ d_+^{p-1},d_-^{k-p-1}\}$ is supported on the Julia set $\mathcal{J}$ of $f$.

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 ($Γ\approx 1.6$--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$13 Hz. No other coherent pulsations or thermonuclear bursts are detected. Broadband spectral modeling favors a nonthermal power-law continuum with partial-covering absorption, and shows no significant thermal disk component. Optical imaging obtained with NOT/ALFOSC, LCO, and GaiaDR3 identifies two faint sources within the 2 arcsec Swift/XRT positional uncertainty. A MeerKAT observation at 1.28 GHz yielded no radio counterpart, with a 3$σ$ upper limit of 60 $μ$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.

This paper uses theoretical results previously established in the literature to design search algorithms to find new linear codes over $\mathbb{Z}_4$ from cyclic and negacyclic codes of even length. As a result of these searches, we have found 2500 new cyclic codes and 730 negacyclic codes. These new codes exhibit improved parameters compared to previously known codes. Additionally, we have obtained binary quantum codes with good parameters from such $\mathbb{Z}_4$ codes.

Deep learning (DL) methods are challenged to demonstrate robust performance across different segmentation datasets due to domain shifts, but active domain adaptation techniques enhance their generalization performance by querying a few samples from target domains for adaptation training. However in clinical practice, target domains often include private classes of new anatomical structures or pathologies that are not presented in the source data, and existing methods implement closed-set segmentation where source and target domains have the same segmentation classes. Additionally, source data are often inaccessible during adaptation due to strict data privacy regulations. To address these limitations, we propose an Active Source-free Open-set Domain Adaptation (ASFOSDA) method which is the first work to implement active learning for adapting DL models in open-set medical image segmentation without the access to source data. This method employs an active open-set query strategy to select the most informative target samples for training models based on Class-aware Decomposed Uncertainty (CDU) and Class-agnostic Prototype Discrepancy (CPD). CDU measures sample aleatoric uncertainty and model epistemic uncertainty by employing test time augmentation in stochastic processes. CPD measures cross-domain and self-domain discrepancy for selecting diverse samples. Subsequently, to boost the adaptation performance by enhancing training samples, a Target-refined Self-training strategy is proposed to generate high-quality pseudo labels for unselected samples, thus combining them with labeled samples for a semi-supervised training. We evaluated our method on cross-domain open-set volumetric medical image segmentation tasks, and it outperformed state-of-the-art adaptation methods.