We give a complete calculation of the cobordism ring of stably almost complex $C_p$-manifolds in terms of generators and relations. We also compare these generators with the geometrically-defined generators obtained by Kosniowski.

Let $\bar{a}_s(n)$ denote the number of partitions of $n$, wherein each odd part is multicolored (atmost $s\ge 1$ colors) and the first appearance of parts may be overlined. In this paper, we establish new families of congruences modulo powers of $2$ satisfied by $\bar{a}_s(n)$ for infinitely many $s$. Our approach builds upon generating function manipulations, Hecke eigenform theory and results of Newman.

Fanaroff-Riley type 0 (FR0) radio galaxies host anomalously compact jets whose disruption mechanism and high-energy emission remain poorly understood. We combine three-dimensional relativistic hydrodynamical (RHD) simulations with broadband spectral energy distribution (SED) modeling from radio to TeV energies, focusing on LEDA~55267 and LEDA~58287. Our simulations show that recollimation shocks trigger hydrodynamical instabilities that drive turbulence and rapid deceleration, preventing the jets from propagating beyond a few tens of parsecs and reproducing the observed compact radio morphology. Leptonic SED models adequately describe the observed emission up to GeV energies, but when simulated CTAO observations are included, statistical model comparison indicates strong evidence in favor of lepto-hadronic scenarios at TeV energies for both sources, a result that should be interpreted as a theoretical prediction to be tested by future observations. A leptonic analysis of the simulations reveals magnetized emitting regions with plasma beta parameters $β_{\rm p} \sim 10^{-5}$-$10^{-3}$, orders of magnitude below values reported for extended FRI jets, consistent with jets retaining the magnetization inherited from the launching region and providing a natural physical link between the compact jet dynamics and the lepto-hadronic emission.

Motor-imagery (MI) EEG can be classified using supervised machine learning techniques such as Linear Discriminant Analysis applied to features extracted by Common Spatial Patterns. Performance of these models varies widely, possibly due to MI studies commonly utilising differing post-cue time windows and frequency bands to one another. This study aims to assess how the simultaneous optimisation of both these parameters impact MI classification performance. This is done by iteratively training and testing a series of subject-specific models on different combinations of frequency bandwidth and time window options across 109 subjects. This is followed by a statistical analysis using repeated measures ANOVA to uncover significant differences between different bandwidths and time windows in terms of accuracy across the patient cohort. The resulting visualisations and statistical tests show that there are, indeed, significant differences between both specific time windows and specific bandwidths in terms of accuracy. While the comparison of classification accuracies across 23 frequency bandwidths during five different time windows demonstrates an optimal temporal and spectral scale combination of (0, 4) s at the range of (4, 12) Hz across all subjects, the subjects demonstrate similar accuracies for other parameter combinations. These findings highlight the efficacy of personalised models to detect optimal temporal and spectral parameter combinations to best classify MI EEG signals that inherently vary across subjects.

Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^β$ with $\hatβ\approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant distributional series, and develop three principled time-domain adaptations of the protocol. We find that (i) the distributional power law is rejected on UTXO balances and daily |returns|, with lognormal preferred decisively; (ii) the fitted time-domain exponent varies by nearly a factor of three across reasonable shifts of the time origin -- it is not specification-robust in the sense required for a shift-invariant structural reading; (iii) standard residual diagnostics and scale-invariance tests proposed in earlier work cannot distinguish a power law from a multi-component sigmoid stack fit to the same data; (iv) Bitcoin price stands apart in a cross-asset comparison spanning Bitcoin on-chain metrics and traditional asset classes: it is the only series in the nine-series in-sample test where no single-component growth curve improves on the power law, and the quarterly $K=3$ wave-stability bootstrap rejects the PL+AR(1) null on Bitcoin at $p = 0.015$ (strict 15% CV threshold) -- a clear cross-asset separation, although not a Bonferroni-robust rejection; and (v) walk-forward Diebold-Mariano evaluation against ten candidates -- including standard time-series baselines (RW with drift, auto-ARIMA, ETS, local-linear-trend) -- shows the in-sample winner (multi-sigmoid) is among the worst long-horizon forecasters, while the simple power law dominates 12-24 month horizons against every standard baseline at $p < 0.05$, precisely because it does not commit to specific wave shapes. The fit-prediction tradeoff is the practical counterpart of the descriptive findings.

Reconstruction of the individual energies and the opening angle between the electrons emitted in neutrinoless double-beta decay can probe the nature of the beyond-the-Standard-Model exchange mechanism that underlies the process. Although it is often stated that discrimination of the mechanism would require such measurements to be performed with high statistics, we show that this is not the case. If a single mechanism dominates the process, its discrimination at the 1$σ$ level is already achieved with just a few well-reconstructed events; only $\sim$10 such events are required to reach 3$σ$-level discovery sensitivity. In the presence of realistic reconstruction uncertainties, this requirement increases to $\sim$25 events, indicating that substantial discrimination power is retained as long as backgrounds remain small. We conclude that the pursuit of tracking detectors for exchange-mechanism discrimination remains valuable even for ``discovery-class'' experiments in which only a few signal counts are expected.

The double-logarithmic series of non-relativistic $B_c \to η_c$ form factors at large recoil is governed by a coupled set of integral equations, reflecting an intricate interplay between arbitrarily many soft-quark and soft-gluon exchanges. Whereas we previously derived these integral equations with diagrammatic resummation techniques, we analyze the form factors in the limit $m_b \gg m_c \gg Λ_{\rm QCD}$ with methods from Soft-Collinear Effective Theory (SCET) in this work. Although the resulting factorization theorem for the so-called soft-overlap contribution is known to be spoilt by endpoint divergences, it can still be used at the level of bare (regularized) quantities at any fixed order in perturbation theory. By calculating the required ingredients, we show that the SCET analysis confirms the predictions of the integral equations up to three-loop order. We also argue that the iterative structure and the intertwined soft-quark and soft-gluon effects can be derived from standard renormalization-group equations of the $B_c$-meson light-cone distribution amplitudes, provided their inverse moments are regularized with an appropriate cutoff.

Gravitational-wave astronomy has opened a direct observational window onto compact-object dynamics, strong-field gravity, and cosmology. Among the transient sources accessible through this window, core-collapse supernovae (CCSNe) are uniquely valuable because their signals can probe the engine of stellar collapse, proto-neutron-star dynamics, and explosion asymmetries, yet their weak, stochastic, and model-dependent waveforms remain difficult to detect. In this work, we develop a contrastive self-supervised convolutional autoencoder (CS-CAE) for CCSNe gravitational-wave signal detection. The method combines a convolutional autoencoder (CAE), a noise-centered latent regularizer, and a projection head trained with a contrastive objective. This design encourages independent noisy realizations of the same CCSNe signal to be mapped to nearby latent representations, thereby reducing the influence of random noise fluctuations. CS-CAE achieves performance comparable to a supervised convolutional neural network while clearly outperforming a conventional CAE baseline, and generalizes better to unseen numerical CCSNe waveform families. Under the Einstein Telescope (ET) detector configuration, the method achieves an effective sensitive distance of approximately 120 kpc and shows improved separation of CCSNe signals from stationary noise and transient glitches in the low-false-alarm regime. These results highlight the potential of CS-CAE as a robust and less template-dependent framework for CCSNe gravitational-wave searches.

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data set subject to missing values, proceeds by maximising a secondary variational lower bound on the model log marginal likelihood using gradient-based optimisation. Consequently, the theoretical development for a new family of tails-up spatio-temporal stream network models is introduced which rely on the sparse Gaussian process inducing variable framework, the Bayesian Gaussian process latent variable model, and local variational methods. These spatio-temporal models use stream distance instead of Euclidean distance and capture spatial and temporal dependencies using auto/cross-correlation and process convolution, respectively, which allows for the development of valid separable spatio-temporal stream network-based covariance functions. Results from the simulation-based case studies indicate that the proposed framework performs well when considering benchmark comparisons and several performance metrics.

We report the detection of a long-period companion to the nearby solar-type star HD\,38973 using precision radial-velocity measurements. The radial-velocity data reveal a coherent Keplerian signal with a period of $\sim$3000~days and moderate eccentricity, yielding a minimum mass in the sub-Jovian regime. We complement the radial-velocity analysis with astrometric constraints from the \emph{Hipparcos--Gaia} Catalog of Accelerations (HGCA). Although no significant proper-motion anomaly is detected for HD\,38973, the absence of an astrometric signal provides an informative upper limit on the companion mass. By combining the radial-velocity posterior with the HGCA likelihood, we rule out high-mass solutions at low inclinations and derive a robust upper bound on the true companion mass. We find the best-fitting true mass to be $0.240_{-0.040}^{+0.102}\,M_{\rm Jup}$, on an orbit with period $2733^{+210}_{-190}$ days, making HD\,38973b a likely cold Saturn. This study highlights the diagnostic power of astrometric non-detections when combined with precision radial velocities, demonstrating that meaningful constraints on companion masses can be obtained even in the absence of a detected astrometric signal.

We study topological analogues of Kalai's cascade conjecture. Given a continuous map from an $n$-simplex to $\mathbb R^d$, let $T_r(f)$ be the set of points contained in the images of $r$ pairwise disjoint faces. We prove that if $r$ is a prime power and $\dim T_r(f)\le k$, then there exists a point that remains an $r$-Tverberg point after any $t$ vertices are deleted, provided $n=(r-1)(d+1)+t(k+1)$. For $t=1$, this gives a topological analogue of a standard consequence of Kalai's cascade conjecture. We also confirm the cascade conjecture for finite point sets whose Radon set is $0$-dimensional.

In high-throughput biology, it is common to fit thousands of linear regressions -- one per gene, protein, or other unit -- with very few samples per unit. Limma-trend, one of the most widely used methods in this setting, improves power by shrinking variance estimates parametrically toward a fitted curve (the trend) relating variance to a unit-level summary (e.g., average intensity, peptide count), before computing p-values and applying the Benjamini-Hochberg procedure to control the false discovery rate (FDR). We study limma-trend through the lens of empirical partially Bayes inference, a paradigm in which a prior is posited and estimated for the nuisance parameters while parameters of interest remain fixed. From this perspective, limma-trend computes approximate partially Bayes p-values that condition on the residual sample variance and the unit-level summary. The same framework explains why MAnorm2, a popular variant for ChIP-seq, can sometimes fail to control FDR. We then derive a nonparametric generalization of limma-trend that estimates the residual variance prior using nonparametric maximum likelihood. Under dense signals, this procedure asymptotically controls the FDR -- even when the trend is misspecified or inconsistently estimated. To allow the full shape of the conditional variance distribution to depend on the unit-level summary, we develop a second procedure that learns it directly.

Day- and night-induced thermal cycling offers a promising route for harvesting ambient thermal energy to drive sustainable hydrogen production and pollutant degradation. Pyroelectric materials enable this process by converting temperature fluctuations into surface charges capable of promoting catalytic water splitting and advanced oxidation reactions. In this work, we demonstrate efficient pyrocatalytic hydrogen evolution and Rhodamine B (RhB) degradation using orthorhombic ferroelectric Potassium niobate (KNbO$_3$) nanoplatelets (KN-np). Under thermal cycling between 20 and 50 $^\circ$C, KN-np achieved a hydrogen yield of 680 $μ$mol g$^{-1}$ after 30 thermal cycles, corresponding to an average hydrogen production rate of 22.67 $μ$mol g$^{-1}$ per cycle. In addition, KN-np exhibited excellent pyrocatalytic activity toward RhB degradation, reaching 84% removal after only 16 thermal cycles with an apparent kinetic rate constant of 0.11 cycle$^{-1}$. The remarkable catalytic performance is attributed to the strong spontaneous polarization and excellent pyroelectric properties of the KNbO$_3$ nanoplatelets, which promote efficient charge generation and interfacial redox reactions. These findings highlight the potential of KNbO$_3$ nanostructures as efficient pyrocatalysts for clean hydrogen production and environmental remediation.

Single molecule probes are widely used to characterize dynamic heterogeneity in glass forming liquids, but interpreting probe dynamics remains challenging because the measured response depends on how the probe couples to its host environment. Using molecular dynamics simulations of dilute probe dimers embedded in a supercooled polymer melt, we show that the probe--host interaction strength determines which heterogeneous environment of the host matrix is reflected in the probe dynamics. Weakly interacting probes partially decouple from their local cages and remain able to access dynamically active environments, whereas strongly interacting probes are more constrained within less mobile, cage-like environments. This interaction-dependent response provides a microscopic basis for the variation in fragility inferred from the probe dynamics, even though the intrinsic host dynamics remains essentially unperturbed. By comparing probe rotational relaxation with the wavevector-dependent structural relaxation and dynamic susceptibility of the host, we establish a scale-dependent correspondence between probe dynamics and host dynamic heterogeneity. Our results show that molecular probes do not simply report the bulk host relaxation, but instead encode the spatial scale and heterogeneous environment associated with the probe--host interaction.

A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay between nonlinear diffusion and density saturation leads to a rich variety of behaviors across different parameter regimes. We establish the existence of global weak solutions, a weak-strong uniqueness result, the exponential convergence to the homogeneous steady state, pattern formation in one spatial dimension, as well as the parabolic-elliptic and vanishing diffusion limits. The analysis relies on a priori estimates derived from suitable entropy functionals. Pattern formation is demonstrated by reducing the system to a first-order equation and conducting a detailed analysis of the resulting nonlinearity. Numerical simulations from a one-dimensional finite-volume scheme illustrate the asymptotic regimes.

The observational determination of the lower limit of neutron star masses is crucial for the physics of core-collapse supernovae. In this light, SMC X-1 is an important object because of its estimated pulsar mass lying near or potentially below the theoretical lower limit. SMC X-1 exhibits a double peaked optical orbital light curve due to the tidal distortion of the donor star, and analysis of this allows us to constrain the binary parameters. In this study, we analyzed optical and X-ray light curves of SMC X-1 obtained by Transiting Exoplanet Survey Satellite and Monitor of All-sky X-ray Image. We found the systematic variations in the optical orbital light curves synchronized with the X-ray super-orbital modulation, regarding the following two aspects: the minimum at inferior conjunction and the double-peak asymmetry. To explain this behavior, we developed a modified ellipsoidal modulation model in which the precessing accretion disk changes the geometry of X-ray irradiation on the donor and that of optical irradiation on the disk. As a result, this model succeeded in reproducing the observed optical and X-ray light curves. Furthermore, we discovered that intense X-ray irradiation could cause the optical emission center to shift away from the gravitational center, potentially leading to an underestimation of the radial velocity of the donor by approximately 20%. Correcting for this effect yields an updated pulsar mass estimation of about $1.35\>M_\odot$.

Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a classical explanation can be ruled out if the devices perform certain measurements on an entangled quantum state, underpinning the security of cryptographic protocols that are device-independent (DI). For certain protocols, such as those performed in a tight space, it might be difficult to perfectly enforce the non-signaling assumption required in Bell's theorem. This prompts the question: is quantum nonlocality robust to such imperfections? We show that if a binary channel sends a noisy copy of one party's input to the other before any measurements take place, the answer is yes. We completely characterize the vertices and facets of the local polytope in this scenario, and identify Bell inequalities that certify non-signaling quantum correlations. This is possible even when a near perfect copy of the input is sent. We go on to show that the identified inequalities are more robust to depolarizing noise than the Clauser-Horne-Shimony-Holt inequality when certifying DI randomness in this scenario. In addition, we characterize the local polytope when both parties receive a noisy copy of each other's input and make similar conclusions, leaving many new potential Bell inequalities to be explored.

Neutral-current semileptonic $B$ decays are plagued by hadronic resonances across the dilepton invariant-mass squared spectrum, $q^2$. For light leptons, $\ell=e,μ$, these resonances can be avoided with suitable $q^2$ cuts. This strategy is less straightforward for $τ$ modes, where missing energy from the $τ$ decay makes $q^2$ difficult to reconstruct. In fact, while Belle II is able to discriminate between different regions in $q^2$ due to its clean environment, this is not directly possible in a hadronic one. Therefore, the interpretation of $b\to sτ^+τ^-$ measurements from e.g. LHCb, CMS requires the description of these resonant effects. In this article, we adopt a different strategy by including the resonant contributions (in particular from $ψ(2S)$) into our predictions for $B\to K^{(*)}τ^+τ^-$ decays, instead of avoiding them. We provide predictions for different initial kinematic points ($4m_τ^2, 14.18\,$GeV$^2$ and $15\,$GeV$^2$) that can be convenient for LHCb, CMS and Belle II. For this, we use a data-driven approach based on the LHCb measurements of $B\to K^{(*)}μ^+μ^-$ decays. Including the resonances and integrating over the full $q^2$ range substantially enhances the Standard Model predictions. However, for sufficiently large New Physics, motivated by the current tensions in $R(D^{(*)})$ and $B\to K^{(*)}νν$ decays, the short-distance contribution becomes comparable to or even exceeds the resonant one. This highlights two advantages of this strategy: it exploits the additional phase space associated with the resonant regions to probe large New Physics contributions, and it enables the use of hadron-collider data, where the resonances cannot be resolved. We further quantify how including or neglecting the resonances affects the total branching ratio as a function of New Physics contributions and, equivalently, of the experimental precision.

With 20 years of INTEGRAL/SPI observations, Yoneda et al. (2025) created the most detailed map of the positron annihilation line at 511keV. While central bulge and extended disk are readily recognised in this map, several hotspots at high latitude regions may either be imaging artefacts or true signals. We discuss the possibility of extragalactic positron annihilation signals from hotspots in this map. We also calculate a cosmological positron annihilation signal as a contribution to the Cosmic Gamma-ray Background (CGB). For this investigation, we compare 511 keV emission hotspots away from the Galactic plane with a high velocity cloud column density map as well as with the catalogue of Local Volume Galaxies (LVGs) up to 25 Mpc. We find that in particular the Magellanic Stream in the southern and Complex C in the northern sky matches the brightest hotspots, which may indicate a higher positron production rate inside the Milky Way than measured from the Galactic interstellar medium alone, of $10^{44}\,\mathrm{s^{-1}}$. In addition, we can explain other hotspots by the cumulative effect of LVGs in the selected regions. The CGB contribution from positron annihilation might be sub-dominant on the per-cent level. However, depending on the true intrinsic annihilation spectrum, in particular depending on the positron injection energy for in-flight annihilation and the star formation rate per galaxy, a much higher imprint beyond 10% is possible above several MeV. If these findings turn out to be true, next generation MeV telescopes will, for the first time, identify individual extragalactic 511 keV sources. In particular, several dwarf spheroidal galaxies with fluxes of up to $(1$-$2) \times 10^{-5}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$, the galaxies M31 and M33, as well as some of their satellites, with potentially several $10^{-6}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$, each, may be detected.

Magnetic topological insulators (TIs) provide a highly tunable platform for engineering quantum states that emerge from the interplay between topology and magnetism. In this review article, we summarize experimental progress over the past decade in designing magnetic TI multilayers by molecular beam epitaxy (MBE). By treating magnetically doped and undoped TI layers as topological Legos, we discuss how layer thickness, magnetic doping, heterostructure architecture, and stacking sequence can be used to control magnetic exchange gaps, interlayer coupling, and the Chern number C with atomic-layer precision. We first briefly review the realization of the C = 1 quantum anomalous Hall (QAH) effect in uniformly Cr-doped (Bi,Sb)2Te3 films in 2013 and uniformly V-doped (Bi,Sb)2Te3 films in 2015. We then discuss how Cr-doped and undoped (Bi,Sb)2Te3 layers can be combined to realize the C = 1 QAH effect in magnetically modulation-doped trilayers, including its extension into the three-dimensional (3D) regime. Next, we review the development of high-C QAH states, engineered plateau phase transitions, mesoscopic QAH devices, and electrical switching of chiral edge-current chirality. Finally, we discuss the realizations of axion insulator and C = 1/2 parity anomaly states in asymmetric magnetic TI trilayers. These advances establish magnetic TI multilayers as a versatile materials platform for creating new designer quantum states, including synthetic Weyl semimetal and QAH metal phases, and for probing the topological magnetoelectric effect in thick axion insulators and 3D QAH insulators.

Harnessing low ultrasonic vibration energy to drive piezocatalytic reactions has attracted increasing attention in response to current environmental and energy challenges. In this study, we investigate the effect of heterovalent bismuth doping on the piezocatalytic degradation of Rhodamine B (RhB) under low-power ultrasonic excitation. Bismuth ions (Bi$^{3+}$) were substituted into the lead-free ferroelectric BaTi${0.89}$Sn${0.11}$O$_3$, yielding BTSn11-xBi with x = 0, 0.02, and 0.04. The powders were synthesized by the sol-gel method as submicron cubes. The structural, morphological, optical, and piezocatalytic properties were strongly influenced by the Bi content. Compared with pristine BTSn11 and BTSn11-0.04Bi, the BTSn11-0.02Bi sample exhibited the lowest band gap (3.22 eV), the smallest particle size (283 nm), the highest piezoelectric current (approximately 8 microA cm$^{-2}$), and the lowest coercive field required to obtain piezoresponse force microscopy hysteresis loops. As a result, BTSn11-0.02Bi showed the highest RhB degradation efficiency and the largest apparent kinetic rate constant, confirming its superior piezocatalytic performance. Total organic carbon measurements revealed significant mineralization of RhB. In addition, BTSn11-0.02Bi demonstrated good reusability and stability, maintaining high degradation efficiency over three consecutive cycles. These results highlight the potential of Bi-doped BTSn11 ferroelectric materials, particularly BTSn11-0.02Bi, as efficient piezocatalysts for environmental remediation.

Altermagnets host spin-split electronic bands despite zero net magnetization, opening new routes for spintronics beyond conventional ferromagnets. Going beyond symmetry-based classifications, which specify allowed terms but not their hierarchy, here we use first-principles calculations and Wannier Hamiltonian engineering to uncover the microscopic bonding contributions of altermagnetic spin splitting in the $g$-wave altermagnet Co$_{1/4}$NbSe$_2$. We show that the splitting is captured by a short-range tight-binding model, establishing its local origin. By selectively controlling hopping channels, we demonstrate that the dominant contribution arises not from direct magnetic-ion hopping, but from ligand-mediated hybridization that transfers anisotropy to itinerant states. This identifies ligand-assisted coupling as the key mechanism of altermagnetic spin splitting and provides a microscopic bridge between minimal models and symmetry guided first-principles material searches, enabling real-space design of altermagnetic functionality.

We introduce a continuous-time Markov chain framework for estimating population size from multi-list data, which allows directional interactions to be modelled and can accommodate absorbing lists, such as death records, or more general data collection processes. The standard model of the continuous-time Markov chain framework and the log-linear model for multi-list data are equivalent when lists are independent and we show empirically that they give similar results in the presence of dependencies between lists. Through a simulation study, we highlight the need to account for an absorbing list by using the Markov model or the log-linear model with forced absorbing interactions, observing biased estimates of the population size otherwise. We motivate our approach with an epidemiological dataset concerning individuals suffering from a first ever stroke in North-West England, in which one of the lists is a death record. We illustrate a further use of our approach by considering a case of ordered lists on drug use data from the City of London.

Magnetic monopoles arise generically in unified theories and offer a natural explanation of charge quantization. Beyond collider searches and cosmic-ray experiments, their flux is constrained by Parker-type bounds requiring galactic magnetic fields to survive monopole energy extraction. We formulate a self-consistent Parker bound anchored in the lowest eigenmode of the galactic mean-field dynamo and convert the resulting limit to the present flux. Small-scale turbulent fields both seed this eigenmode and set the monopole velocity via stochastic acceleration before energy extraction from the coherent field. These unavoidable effects substantially modify the standard extended Parker bound at low and intermediate masses, yielding flux limits robust to primordial magnetic fields (PMFs); PMFs strong enough to alter them lie in regimes constrained by Ly$α$ data or testable by 21-cm and cosmological probes.

We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces, which allow composition operators to be realized as adjoints of linear operators. For spaces with the bounded approximation property, we characterize composition operators between spaces of holomorphic Lipschitz functions vanishing at the origin and describe when composition operators are onto isomorphisms. We further investigate compactness and weak compactness properties of composition operators. In the finite-dimensional setting, compactness and weak compactness are shown to coincide, and a complete characterization is obtained in terms of the symbol. Finally, we analyze the asymptotic behavior of the iterates of composition operators, proving convergence to zero whenever the supremum norm of the symbol is less than one, and we extend several results to the case not vanishing at 0.

We present deep Chandra observations of the pulsar wind nebula (PWN) powered by PSR J0007+7303 in the composite supernova remnant CTA 1. The merged ACIS image shows a $\sim20''$ jet extending south of the pulsar and bending toward the southwest, a faint counter-jet to the north, and a compact torus oriented approximately perpendicular to the jet axis. Using an archival observation from 2003 we perform relative astrometry over a $\sim20$ yr baseline and constrain the pulsar's transverse velocity to $\lesssim 200~\mathrm{km~s^{-1}}$ at the distance of 1.4 kpc at 95% confidence. Spatially resolved spectroscopy shows hard spectra for the jet and torus (photon indicies $Γ\approx 1.2-1.4$) and a softer spectrum for the extended nebula ($Γ= 1.85 \pm 0.11$), indicating minimal radiative cooling in the compact regions. Modeling of the torus, associated with the termination shock, as an inclined circle yields a viewing angle $ζ\approx 50^\circ$. The outer gap and two-pole caustic pulsar emission models then imply a moderate magnetic inclination ($α\sim 20^\circ$-$70^\circ$). Broadband spectral energy distribution (SED) modeling from radio to PeV $γ$-rays for a one-zone leptonic scenario yields a low magnetic field ($B \approx 1.4$-$3.2~μ\mathrm{G}$) and a high electron cutoff energy ($E_{\rm cut} \sim 0.2$-$0.3~\mathrm{PeV}$), indicating that the magnetic field decreases rapidly outside of the compact nebula. These results establish CTA 1 as a young, low X-ray efficiency PWN with a hard injection spectrum capable of accelerating particles to PeV energies.

The Hatsugai-Kohmoto (HK) model is an exactly solvable electronic lattice model where the interaction between electrons with opposite spin is diagonal in momentum space. We generalize the HK model by introducing momentum-mixing Landau interactions. Within a self-consistent mean-field analysis we find that the ground state of this model exhibits a partially flat energy band, in agreement with the fermion condensation scenario proposed by Khodel and Shaginyan [JETP Lett. 51, 553 (1990)]. Inspired by Andersons pseudospin formulation of BCS theory, we show that the HK model with Landau interactions can be mapped onto a generalized Ising model where each site of the reciprocal lattice hosts two Ising spins. In the pseudospin picture the emergence of a partially flat electronic band corresponds to the smoothing of a magnetic domain wall. Moreover, guided by the pseudospin picture, we propose an exactly solvable variant of the HK model which has a unique ground state for all densities.

We report on a performance comparison between physical and logical computations on a prototypical machine-learning application: solving differential equations using quantum kernel methods. The algorithm is implemented on an atom-based logical quantum processor, both at the physical and logical levels. We show that the kernel estimated from the logical implementation performs better than its physical counterpart on relevant metrics. We observe how such performance improvement can be traced back to specific noise-induced errors detected by the chosen encoding. We apply the computed quantum kernel to the task of solving differential equations, confirming how the superior performance of a logical quantum kernel is retained also at an end-to-end applicative level. Our findings show that experimental validation of end-to-end protocols can already highlight the positive impact of fault-tolerant implementations despite their higher quantum resource count, and guide application-informed architectural choices.

While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that reformulates cloning optimization as a search over completely positive trace-preserving maps using the Choi-Jamiolkowski isomorphism and Semidefinite Programming. The framework (i) numerically certifies global optimality through primal-dual strong duality and (ii) automatically extracts operational Kraus operators from the optimal Choi matrix via spectral decomposition. We systematically treat universal, phase-covariant, asymmetric, and entanglement cloning scenarios, providing -for the first time - a unified computational catalogue of explicit, implementable Kraus representations across all major cloning families, including higher-order processes and arbitrary input state distributions. As an application, we analyse optimal cloning attacks on BB84 under depolarizing noise, demonstrating how the extracted operators enable quantitative security analysis in realistic noisy quantum channels. An open-source implementation enables community validation and extension.

In the present work we consider the subject of dark fractional solitary waves in the realm of generalized (fractional) forms of the nonlinear Schrödinger (NLS) equation. While earlier studies have examined such states in the realm of real field theories, we showcase the existence and stability of individual dark solitary waves in such NLS settings and subsequently turn to two-soliton solutions. We find different branches of such two-soliton solution equilibria and contrary to the real field-theoretic setting all possible branches of two-soliton equilibria are found to be potentially unstable, although with different types of instabilities. Odd branches are potentially subject to oscillatory instabilities, while even branches are always exponentially unstable. The dynamics that results from the instabilities is also examined and is found to potentially feature breathing characteristics. This prompts us to seek and find associated periodic (breathing) orbits that are also unprecedented in this context, to the best of our knowledge. The effective particle-like dynamics of the solitary waves also prompts us to seek ordinary differential equation (ODE) descriptions to the dark soliton interaction dynamics. These are shown to hold promise toward providing us with effective reduced order models, indicating some potential directions for further investigation.