Grothendieck's anabelian conjectures predict that certain classes of varieties over number fields are largely determined by their {é}tale fundamental groups. A theorem of Mochizuki shows that for hyperbolic curves over number fields or $p$-adic fields, dominant morphisms bijectively correspond to open homomorphisms between their {é}tale fundamental groups. Motivated by non-abelian Hodge theory, we formulate a Hodge-theoretic version of the anabelian conjecture in which the Galois action is replaced by the natural $\mathbb{C}^\times$-action on the pro-algebraic completion of the fundamental group arising from non-abelian Hodge theory. In particular, we prove a Hodge-theoretic analog of Mochizuki's theorem for smooth projective hyperbolic curves over $\mathbb{C}$. We also obtain a higher-dimensional analogue for complex hyperbolic manifolds of ball quotient type and discuss possible extensions to non-$K(π,1)$ spaces replacing fundamental groups by homotopy types.

We present a point source catalogue of the Large Magellanic Cloud (LMC) using observations from the MeerKAT radio telescope across a broad frequency band centred at 1295 MHz (L-band) with 12 sub-bands and an angular resolution of 8 arcsec x 8 arcsec. We investigate the source flux density distribution and spectral indices and compare these results with previous radio catalogues, such as surveys conducted with the Australian Square Kilometre Array Pathfinder (ASKAP) at 888 MHz. This new MeerKAT survey reaches a lower average noise level of 11 microJy beam^-1, compared with the previous ASKAP level of 58 microJy beam^-1. The higher sensitivity and resolution enable the detection of a significantly larger number of faint sources. The catalogue contains 339,128 point sources, representing a substantial increase compared with the 54,612 sources detected in the ASKAP survey. This catalogue provides improved insight into the source population distribution, spectral properties, positional accuracy, and the overall improvement in source recovery and survey depth in the LMC region.

In this study, we present a transformer-based multi-task model for Fast Radio Burst (FRB) detection, signal segmentation, and parameter estimation directly from time-frequency data, without requiring computationally expensive de-dispersion preprocessing. To overcome the scarcity of labeled observational data, we develop an FRB simulator and a rule-based automatic annotation pipeline, enabling training exclusively on simulated data. Evaluations on the FAST-FREX dataset show that our model achieves an F1 score of 97.8%, recall of 95.7%, and precision of 100%, outperforming both conventional tools (e.g., PRESTO, Heimdall) and recent AI-based baselines (e.g., RaSPDAM, DRAFTS) in both accuracy and inference speed. The model supports pixel-level signal segmentation and yields reliable estimates for dispersion measure (DM) and time of arrival (ToA). Large-scale blind searches on CRAFTS data further demonstrate robustness, with an average false positive rate of 0.28% and minimal human verification required. This search has already led to the identification of two pulsar candidates, both confirmed as known pulsars. Processing benchmarks indicate that the model enables real-time searches on a single consumer-grade GPU, making petabyte-scale blind searches feasible. The code is publicly available on GitHub, and the model can be easily integrated with existing tools to automate and streamline radio data analysis beyond FRB or pulsar searches.

We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the \emph{balanced constraint}). While this constraint is common in real-world scenarios such as team drafts or asset division, it significantly complicates the search for allocations that are both fair and efficient. Envy-freeness up to one good (EF1) is a well-established fairness notion for indivisible goods. Pareto optimality (PO) and its stronger variant, fractional Pareto optimality (fPO), are widely accepted efficiency criteria. Our main contribution establishes both the existence and polynomial-time computability of allocations that are simultaneously EF1 and fPO under balanced constraints in two fundamental cases: (1) when each agent has a personalized bivalued valuation, and (2) when agents have at most two distinct valuation types,. Our algorithms leverage novel applications of maximum-weight matching in bipartite graphs and duality theory, providing the first polynomial-time solutions for these cases and offering new insights for constrained fair division problems.

We propose a new classification of magnetic textures from the viewpoint of differential geometry. Magnetic textures are conventionally classified into collinear, coplanar, and noncoplanar magnets. These classes are typically characterized by the vector spin chirality (VSC) and the scalar spin chirality (SSC), which indicate noncollinearity and noncoplanarity, respectively. However, this conventional classification is incomplete: in particular, noncoplanar textures cannot be fully characterized by the SSC alone, as exemplified by conical magnets. To refine this classification, we analyze the curves and surfaces traced by spins in real space using differential geometry and introduce two novel scalar spin chiralities that properly characterize noncoplanarity: the geodesic scalar spin chirality and the torsional scalar spin chirality. These quantities are directly connected to differential geometry: the former reflects the geodesic curvature while the latter is related to the torsion. Based on these chiralities, we identify three distinct classes of noncoplanar magnetic textures. Furthermore, analogous to the roles of the VSC and the conventional SSC in emergent electrodynamics, the geodesic SSC gives rise to novel emergent phenomena. By constructing a semiclassical theory including nonadiabatic effects and higher-order spatial gradients of magnetic textures, we demonstrate that the geodesic SSC induces an emergent band asymmetry, leading to nonreciprocal responses as a quantum geometric effect. This mechanism is a purely orbital effect, requiring no spin-orbit coupling, and the resulting discussion runs in parallel with the conventional picture of the topological Hall effect driven by the SSC. The geometric viewpoint developed here will provide broad new insights into classification, quantum geometry, emergent electrodynamics, and a wider variety of emergent phenomena.

The Friedrichs model~\cite{Friedrichs} is revisited to obtain precise results about the asymptotic behaviour (the so-called Breit-Wigner formula~\cite{Breit}) of a resonance near an embedded eigenvalue and the ``spectral concentration" results as a corollary. Some of the abstract results involved can also be used to address similar questions about a rank-one perturbation of the Laplacian. Exact asymptotic properties are also obtained for the sojourn time, the scattering amplitude and time delay.

Separable extensions of noncommutative rings have already been studied extensively. Recently, N. Hamaguchi and A. Nakajima introduced the notions of weakly separable extensions and weakly quasi-separable extensions. They studied weakly separable polynomials and weakly quasi-separable polynomials in the case that the coefficient ring is commutative. The purpose of this paper is to give some improvements and generalizations of Hamaguchi and Nakajima's results. We shall characterize a weakly separable polynomial f(X) over a commutative ring by using its derivative f'(X) and its discriminant δ(f(X)). Further, we shall try to give necessary and sufficient conditions for weakly separable polynomials in skew polynomial rings in the case that the coefficient ring is noncommutative.

This paper investigates the behavior of two fundamental types of multipartite entangled states, namely GHZ(3) and W(3) states under Gaussian-distributed amplitude perturbations and White noise model. The Uhlmann-Jozsa fidelity is taken to be the quantitative measure to show the overall degradation of the quantum states, and is implemented via TQIX : a tool specifically designed for quantum state measurement and related applications. While fidelity analysis captures the progressive decay of quantum states under noise, it offers only limited understanding regarding the state decay and doesn't provide a detailed analysis of how entanglement structures respond to noise models. To reveal the phase-space characteristics and nonclassical signatures of three-qubit entangled states, we employ the spin Wigner function using equal-angle projection. This approach reveals a continuous fading of quantum coherence with increasing noise strength, ultimately providing a clear picture of transition toward classical-like behavior in phase space. This combined qualitative-quantitative framework provides deeper understanding of how different entanglement structures respond to noise, offering practical applications for designing and implementing noise resilient protocols in quantum computing, and quantum information processing.

We investigate nonlinear magnetoelastic wave dynamics and electrically tunable soliton excitations in hexagonal multiferroic media. By varying the magnetoelastic coupling strength and using a coupled magnetoelastic-ferroelectric continuum model, we found that the system evolves from weakly nonlinear quasiperiodic oscillations to strongly anharmonic yet phase-coherent multimode dynamics. Our results suggest that the dynamics remain bounded and approach distorted limit-cycle behavior rather than chaotic motion despite the enhanced nonlinearity. The excitation spectra and the band dispersion relations reveal that this nonlinear evolution originates from strong magnon-phonon hybridization and coupling-induced renormalization of collective excitation branches, leading to coherent energy exchange among magnetic, elastic, and polarization subsystems. In addition, the coupled dynamics can be reduced to an effective magnetoelastic nonlinear Schrödinger equation and support localized excitations such as bright and dark solitons and Kuznetsov-Ma type breathers. Furthermore, it is found that an external electric field modifies both the effective nonlinear coefficient and the dispersion curvature, enabling continuous control of soliton amplitude, width, and stability. The field also induces a saddle-node bifurcation in the magnetization phase space, defining a critical threshold separating multistable and monostable regimes. Our results establish a theoretical framework for electrically tunable nonlinear spin-lattice excitations and soliton engineering in multiferroic systems.

We investigate the Lamb shift of centripetally accelerated atoms coupled to electromagnetic vacuum fluctuations. Focusing on a very small orbital radius (so that the tangential speed remains nonrelativistic and the proper centripetal acceleration can be extremely small), we show that the resulting level shift is intrinsically anisotropic and depends sensitively on the atomic polarization direction. For atoms polarizable along the rotation axis, the leading noninertial contribution enters only at second order in the orbital radius and can slightly decrease or increase the energy-level spacing, depending on the angular-velocity regime. In contrast, for atoms polarizable perpendicular to the rotation axis, the noninertial contribution appears already at the leading order in the radius and always increases the energy-level spacing. Remarkably, when the angular velocity greatly exceeds the transition frequency, the rotation-induced correction can become comparable in magnitude to the inertial Lamb shift, indicating that circular motion can significantly modify the Lamb shift even in the regime of very small centripetal accelerations.

The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.

It seems that Morita invariance is a useful criterion for judging the importance of the classes of ring extensions concerned. Y. Miyashita introduced the notion of Morita equivalence in ring extensions, and he showed that the classes of $G$-Galois extensions and Frobenius extensions are Morita invariant. After that, S. Ikehata showed that the classes of separable extensions, Hirata separable extensions, symmetric extensions, and QF-extensions are Morita invariant. In this paper, we shall prove that the classes of several extensions are Morita invariant. Further, we will give an example of the class of ring extensions which is not Morita invariant.

Animal acoustic communication often exhibits temporal dependence, with calls triggering or suppressing subsequent calls within and across call types, individuals, or species. While Hawkes processes provide a natural framework for modeling excitation, incorporating inhibition in multivariate settings can raise identifiability issues and complicate parameter interpretation. We propose a flexible class of multivariate Hawkes processes that combines additive excitation with multiplicative inhibition. This formulation preserves the branching process interpretation of excitation while reducing confounding between excitation and inhibition, and allows direct quantification of background and excitation contributions to the event rate. Bayesian inference is conducted via Markov chain Monte Carlo, and model adequacy is assessed using the random time change theorem. The proposed methodology is evaluated through simulation and applied to two acoustic communication datasets: group-living meerkats, for which we analyze three selected call types with distinct behavioral roles, and a two-species baleen whale dataset involving humpback and North Atlantic right whales. The meerkat analysis reveals significant within- and cross-type excitation with cross-type inhibition, whereas the whale data show evidence primarily of within-species excitation.

Extremely Metal-Poor Galaxies (XMPGs), defined as having metallicities below 10\% of the solar value, are considered possible local analogs to primordial systems and offer a unique window into early galaxy evolution. This study presents a large-scale search for XMPGs using data from the Dark Energy Spectroscopic Instrument DR1, systematically evaluating their resemblance to high-redshift galaxies. From a parent sample of over 14 million galaxies, we identify 656 (551 new) confirmed XMPGs and 767 (670 new) high-quality candidates via the direct $T_{\mathrm{e}}$ method. Results reveal that XMPGs follow a distinct star-forming main sequence (SFMS) that is elevated and shallower than that of the comparing star-forming galaxies. Notably, at higher stellar masses ($M_{\star} > 10^{7.5} M_{\odot}$), the XMPG SFMS converges with the sequence observed in high-redshift galaxies by James Webb Space Telescope (JWST), indicating that mature XMPGs sustain star formation rates comparable to their primordial counterparts. Furthermore, XMPGs consistently deviate below the local fundamental metallicity relation, mirroring high-redshift galaxy behavior. These findings demonstrate that XMPGs not only exhibit low metallicities but also preserve scaling relations characteristic of the early Universe, confirming their potential value as local laboratories for studying early galaxy formation processes.

This paper studies an extremely large-scale reconfigurable intelligent surface (XL-RIS)-aided near-field physical layer security (PLS) communication system, aiming to maximize the secrecy rate by jointly optimizing precoding vector at the BS and the reflection coefficient matrix at the XL-RIS. Artifi-cial jamming was introduced to further enhance communication security. To solve the non-convex secrecy rate problem, an alternate optimization-based algorithm is adopted to decompose it into two sub-problems. Specifically, when optimizing the transmit beamformer at the BS, the non-convex prob-lem is transformed into a convex one through the weighted minimum mean-square error and the successive convex approximation-based algorithms. For the optimization problem of the XL-RIS phase-shifting matrix, a low-complexity alternating direction method of multipliers-based algorithm is employed to enhance the flexibility of the design. The proposed algorithm is capable of accommodating discrete phase optimization for the XL-RIS, thus better aligning with practical system requirements. Simulation results demonstrate that when the eavesdropper reside in the same direction as the legitimate user and is located closer to the XL-RIS, the proposed scheme in this paper can still ensure the secure communication.

We study the classical simulability of a polynomial-size quantum circuit $C_n$ on $n$ qubits followed by sparse classical post-processing (SCP) on $m$ bits, where $m \leq n \leq {\rm poly}(m)$. The SCP is described by a non-zero Boolean function $f_m$ that is classically computable in polynomial time and is sparse, i.e., has a peaked Fourier spectrum. First, we provide a necessary and sufficient condition on $C_n$ such that, for any SCP $f_m$, $C_n$ followed by $f_m$ is classically simulable. This characterization extends the result of Van den Nest and implies that various quantum circuits followed by SCP are classically simulable. Examples include IQP circuits, Clifford Magic circuits, and the quantum part of Simon's algorithm, even though these circuits alone are hard to simulate classically. Then, we consider the case where $C_n$ has constant depth $d$. While it is unlikely that, for any SCP $f_m$, $C_n$ followed by $f_m$ is classically simulable, we show that it is simulable by a polynomial-time probabilistic algorithm with access to commuting quantum circuits on $n+1$ qubits. Each such circuit consists of at most deg($f_m$) commuting gates and each commuting gate acts on at most $2^d+1$ qubits, where deg($f_m$) is the Fourier degree of $f_m$. This provides a better understanding of the hardness of simulating constant-depth quantum circuits followed by SCP.

CAPTCHAs remain a critical defense against automated abuse, yet modern systems suffer from well-known limitations in usability, accessibility, and resistance to increasingly capable bots and low-cost CAPTCHA farms. Behavioral and puzzle-based mechanisms often impose cognitive burdens, collect extensive interaction data, or permit outsourcing to human solvers. In this paper, we present ThermoCAPTCHA, a novel privacy-preserving human verification system that uses real-time thermal imaging to detect live human presence without requiring users to solve challenges. A lightweight YOLOv4-tiny model identifies human heat signatures from a single thermal capture, while cryptographically bound traceable tokens prevent forwarding attacks by CAPTCHA farm workers. Our prototype achieves 96.70% detection accuracy with a 73.60 ms verification latency on a low-powered server. Comprehensive security evaluation, including MITM manipulation, spoofing attempts, adversarial perturbations, and misuse scenarios, shows that ThermoCAPTCHA withstands threats that commonly defeat behavioral CAPTCHAs. A user study with 50 participants, including visually challenged users, demonstrates improved accuracy, faster completion times, and higher perceived usability compared to reCAPTCHA v2.

We present a Ginzburg-Landau theory on statics and dynamics of BaTiO$_3$-type ferroelectrics in the paraelectric phase with the cubic structure, where the order parameter is the polarization $\bi p$. Unique effects are caused by the electrostrictive (ES) coupling between ${\bi p}$ and the elastic displacement $\bi u$. We show that the ES coupling gives rise to a central peak in the Fourier-Laplace transform of the displacement time-correlation function at small wave numbers. It emerges and grows with a narrow width as the transition is approached. Such central peaks have long been observed in a number of scattering experiments in various ferroelectrics, but their origin has not been well understood. From the acoustic part of the displacement dynamic correlation we obtain the frequency-dependent elastic moduli $C_{11}^*(ω)$, $C_{12}^*(ω)$, and $C_{44}^*(ω)$, whose singular parts arise from the ES coupling, We then calculate the singular sound velocity and attenuation. In the central peak and the elastic moduli, the frequency $ω$ appears in the scaled form $ωτ_D$, where $τ_D$ is the Debye relaxation time in the frequency-dependent dielectric constant. {Keywords}: ferroelectric transition, central peak, acoustic anomaly, electrostrictive coupling

Rydberg-atom quantum receivers (RAQRs) enable electric-field sensing with quantum-noise-limited performance, yet their optical readout provides only magnitude measurements whose fluctuations follow Rician statistics governed by atomic projection noise, optical shot noise, reference-field injection, and short coherence times. These non-Gaussian, phase-blind measurements invalidate classical single-shot RF detectors and necessitate multi-shot quantum sensing strategies. This work develops a physically consistent multi-shot statistical model for RAQRs and derives both the optimal genie-aided likelihood-ratio test (LRT) and a practical phase-averaged LRT that removes dependence on the unknown RF-field phase. Closed-form test statistics and thresholds are obtained for both detectors, and the limits imposed by finite quantum shots-due to atomic dephasing and measurement backaction-are explicitly quantified. A fully non-coherent energy detector is also analysed, with exact detection probability derived using noncentral chi-square models. Monte Carlo results show that only 5-10 quantum shots yield major gains: the phase-averaged LRT closely approaches the genie bound and RAQR detection markedly outperforms classical RF energy detection under comparable received power. The proposed framework provides the first unified statistical basis for multi-shot Rydberg-based weak-field detection and underscores the potential of RAQRs for quantum-enhanced signal detection.

Our understanding of the physical mechanisms and environments conducive to the escape of Lyman-continuum (LyC) radiation within the first 2 Gyr of cosmic history remains limited. Here we present a detailed analysis of JWST/NIRSpec medium-resolution IFU observations of two LyC-leaker candidates, LACES-94460 and LACES-104037 at z = 3.1, selected from deep HST/WFC3 F336W imaging and supported by ground-based spectroscopy. We first rule out LACES-94460 as a genuine LyC leaker, demonstrating that its apparent F336W signal originates from a nearby low-redshift interloper at z = 1.6, unambiguously identified through IFU spectroscopy. In contrast, for LACES-104037 we spectroscopically confirm bona fide LyC emission arising from a tidal-tail structure during the early stage of a galaxy merger, dubbed LACES104037-LyC. LACES104037-LyC exhibits extremely low rest-frame optical emission-line equivalent widths together with an exceptionally strong LyC flux. Within a picket-fence model framework, we reproduce its observed spectral and photometric properties with a young stellar population of age $\sim5$ Myr and a LyC escape fraction of $f_{\mathrm{esc}} \sim 99\%$. Our identification and detailed modeling of LACES104037-LyC provide one of the first compelling observational demonstrations for merger-driven LyC escape, indicating that galaxy mergers may represent an important and previously underappreciated contributor to the ionizing photon budget relevant for cosmic reionization. Furthermore, our analysis highlights the critical role of sub-kiloparsec resolution spectroscopy in securely identifying LyC leakers, removing contamination from closely projected low-redshift interlopers, and pinpointing the physical regions responsible for LyC leakage.

As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schrödinger systems with attractive interactions in $\mathbb{R}^3$, which are trapped in ring-shaped potentials. For any given $N\in\mathbb{N}^+$, we prove that ground states exist if $0<a<a_N^*$, where $a$ denotes the strength of attractive interactions in the system, and $a_N^*$ is the best constant of a finite-rank Lieb-Thirring inequality. Moreover, for some $N\in\mathbb{N}^+$, we also prove the nonexistence of minimizers for the system as soon as $a\geq a_N^*$. Applying the energy estimates and the blow-up analysis, we further analyze the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$.

Quantum anomalous Hall insulator-superconductor heterostructures are predicted to host chiral Majorana fermions as edge modes, which is essential for topological quantum computing applications. Although the edge states have been extensively studied at zero chemical potential $μ= 0$, the practically relevant regime with a shifted chemical potential ($μ\neq 0$) remains less explored. Here, we present an analytical treatment of the edge states for $μ\neq 0$, deriving an approximate but highly accurate solution applicable to realistic experimental parameters. Surprisingly, we find that the energy dispersion of the edge band exhibits nonlinearity and transforms into a twisted, braid-like structure within specific parameter ranges. This unique braid-like band leads to non-chirality of the edge modes, allowing propagation in both directions.

We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that properties of its domain determine our minimax rates. Those exhibit a variety of regimes, including classical rates, governed by the better of source-only and target-only rates, as well as regimes in which the convergence rates exhibit multiplicative interactions between the sample sizes and are faster than the best-of-two benchmark. The rates are shown to be achieved up to logarithmic factors by a design-adaptive estimator. Compared with existing theory, our results cover the case in which covariates have unbounded support.

During the last 40-50 years, the TeV blazar Ton 599 has systematically experienced major outbursts detected in a wide wavelength range from radio to $γ$-rays. In this work, we present an analysis of Ton 599 quasi-periodic variability across multiple wavelengths using an observing baseline from 1983 to 2025. The $γ$-ray, optical, and radio emissions are found to be highly correlated with time lags $\sim0$-$360$ days, which indicates that they are triggered by the same population of particles. Using the Lomb-Scargle periodogram and the Weighted Wavelet Z-transform, we revealed several periodic components with characteristic periods of 1.4, 1.7, 2.3, 6.5, and 7.5 yrs. The result is consistent with the detection of periodic components in the 1997-2011 light curves, which means that we observe the same mechanism causing long-term periodic variability. A model of a binary supermassive black hole (SMBH) with a precessing jet, applied to the radio light curves of Ton 599, yields frequency-dependent best-fitting parameters with orbital periods ranging from $\sim$1.2 to 1.7 yrs and precession periods from $\sim$5.8 to 7.7 yrs. This result implies the existence of an SMBH system modulating emission through both the orbiting and jet precession effects, with differing observed periods possibly reflecting frequency-dependent emission regions along a structured, stratified jet. Nonetheless, the short-term periodicity and exceptionally strong flares likely arise from internal jet shocks, which aligns with typical blazar behavior. We suggest that the multiband quasi-periodicity of Ton 599 is reasonably described by a combination of geometric effects (orbital motion and precession) and stochastic processes.

Mixed reality (MR) notification systems currently display all messages in fixed central locations regardless of urgency, leading to unnecessary interruptions and cognitive overload. Drawing from previous MR/Virtual Reality (VR) notification design work and calm technology principles, we developed an adaptive notification system that adjusts spatial placement based on urgency levels: non-urgent notifications appear as peripheral icons accessible via head movement, moderately urgent messages anchor to the user's hand, and very urgent notifications transition progressively from peripheral to central view. Through a within-subjects study (N=18), we evaluated our adaptive system against the default centralised approach. Results demonstrate that the adaptive system significantly reduces mental workload (p=0.041), temporal workload (p=0.008), and frustration (p=0.004) while maintaining comparable notification awareness. Logistic regression analysis reveals that users prefer the adaptive system even with classification errors, provided the combined misclassification rate (disruptiveness + omission errors) remains below a determinable threshold. Our findings establish the first empirical evidence that urgency-based spatial notification distribution effectively addresses core MR usability challenges, offering practical design guidelines for immersive notification systems that balance user attention management with information accessibility.

Stacked intelligent metasurfaces (SIMs) facilitate computation by cascaded programmable layers so that part of the signal processing can be performed in the wave domain during signal propagation, rather than solely after reception. This approach expands the controllable degrees of freedom and supports the joint design of communication, sensing, and computation with the potential for reduced energy usage, shorter end-to-end latency, and improved task execution. Despite these advances, research on the SIM concept is still at an early stage, with challenges in scalability, controllability, nonlinearity, and robustness. This article reviews the state-of-the-art of SIM research, including applications, functions, and characteristics. We also demonstrate their potential through case studies on neural-like analog inference and communication enhancement. Finally, the paper outlines open challenges and future directions toward establishing SIMs as a new signal processing paradigm for in-wave computation in next-generation (NG) networks.

Differences in data distributions between demographic groups, known as the problem of infra-marginality, complicate how people evaluate fairness in machine learning models. We present a user study with 85 participants in a hypothetical medical decision-making scenario to examine two treatments: group-specific model performance and training data availability. Our results show that participants did not equate fairness with simple statistical parity. When group-specific performances were equal or unavailable, participants preferred models that produced equal outcomes; when performances differed, especially in ways consistent with data imbalances, they judged models that preserved those differences as more fair. These findings highlight that fairness judgments are shaped not only by outcomes, but also by beliefs about the causes of disparities. We discuss implications for popular group fairness definitions and system design, arguing that accounting for distributional context is critical to aligning algorithmic fairness metrics with human expectations in real-world applications.

Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from data. Classical stochastic and robust optimization offer two influential paradigms for handling such uncertainty, but they typically treat the underlying uncertainty description as given and do not directly integrate priors and updated to posteriors guarantees. This paper develops a Bayesian framework for linear programming in which uncertain quantities are modeled probabilistically, updated through observed data, and propagated into optimization through posterior feasibility requirements. We present two complementary computational strategies: a credible-region robustification that converts posterior uncertainty into deterministic protection, and a posterior-scenario approach that uses sampled posterior realizations to construct tractable optimization problems with finite-sample interpretability. We also propose a Monte Carlo certification procedure that provides conservative, data-conditioned assessments of residual infeasibility. Simulation experiments show that the proposed framework substantially improves safety relative to naive plug-in decisions, while a real-data study on single-cell transcriptomic data demonstrates that the approach can produce scientifically interpretable decisions together with explicit uncertainty-aware feasibility diagnostics. The proposed methodology offers a unified bridge between Bayesian learning, optimization under uncertainty, and practical decision certification.

We present a lattice QCD spectroscopy study of the conjectured H dibaryon for 5 different channels at nine different temperatures. The H dibaryon operator is constructed with five different channels which are flavor singlet, flavor 27-plet, $ΛΛ$, $N Ξ$ and $ΣΣ$. The nine different temperatures range from $T/T_c =0.24$ to $T/T_c = 1.90$. The simulations are performed on anisotropic lattice with $N_f=2+1$ flavours of clover fermion at quark mass which corresponds to $m_π=384(4) {\rm MeV} $. The thermal ensembles were provided by the FASTSUM collaboration and the zero temperature ensembles by the Hadspec collaboration. The simulations show that the mass of H-dibaryon for 27-plet channel is the largest at different temperatures, while the mass for $ΣΣ$ channel is the lightest. We also calculate the spectral function of the correlation function of H dibaryon for five channels. The spectral density distributions exhibit similar behavior for the five channels. The mass differences $Δm = m_H - 2\,m_Λ $ of H-dibaryon and $Λ$ pair at $T/T_c =0.24 $ for five channels are also estimated. The results show that $Δm = m_H - 2\,m_Λ $ for channels of 27-plet and $ΛΛ$ is positive, while $Δm = m_H - 2\,m_Λ $ for channels of singlet, $N Ξ$ and $ΣΣ$ is negative.

Gurau (2020) proposed a generalization of the trace of the matrix resolvent to tensors of higher order, and recent work has explored analogs of the Wigner semicircle and Marchenko-Pastur distributions from random matrix theory as well as aspects of free probability theory from this perspective. In particular, when evaluated with appropriate large random tensors, the limiting expectations of the coefficients of a series expansion of Gurau's resolvent trace give the moment sequences of probability measures analogous to the above distributions. We construct, on the other hand, individual deterministic tensors such that the same coefficients evaluated on those tensors do not give the moment sequence of any probability measure. Thus, the "spectral density" associated to Gurau's resolvent trace, while in a sense defined on average for certain random tensor ensembles, is not defined pointwise (unless perhaps as a signed measure) for all individual tensors.