We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords from a geometric point of view, interpreting them in terms of the combinatorial structure of the associated simplicial complex. This approach allows us to describe the minimum distance of the codes in terms of certain geometric features of the complex. Subsequently, we analyse how various topological operations on simplicial complexes affect the classical parameters of the codes. This study leads to the formulation of geometric criteria that make it possible to explicitly control and manipulate these parameters. Finally, as an application of the obtained results, we construct several families of optimal linear codes over F2 using these geometric methods. Thanks to the previously established geometric properties, we can precisely determine the parameters of these families.

A simple numerical method for loading of a relativistic Maxwellian-type distribution is proposed based on inverse transform sampling. The relativistic Maxwellian energy distribution is introduced as an alternative to the Maxwell-Jüttner distribution. The cumulative distribution of the shifted-Maxwellian energy distribution is approximated by an invertible function. Random variates of energy is transformed from uniformly distributed random variables. Then, the energy variates are converted to momentum vector variates. Numerical tests are presented to show that the present method successfully reproduce the relativistic Maxwellian energy distribution.

A well-established insight in mortality forecasting is that combining predictions from a set of models improves accuracy compared to relying on a single best model. This paper proposes a novel ensemble approach based on Shapley values, a game-theoretic measure of each model's marginal contribution to the forecast. We further compute these SHapley Additive exPlanations (SHAP)-based weights age-by-age, thereby capturing the specific contribution of each model at each age. In addition, we introduce a threshold mechanism that excludes models with negligible contributions, effectively reducing the forecast variance. Using data from 24 OECD countries, we demonstrate that our SHAP ensemble enhances out-of-sample forecasting performance, especially at longer horizons. By leveraging the complementary strengths of different mortality models and filtering out those that add little predictive power, our approach offers a robust and interpretable solution for improving mortality forecasts.

We consider a class of two-stage nonconvex nonsmooth stochastic conic program, where the objective functions in both stages can contain nonsmooth terms that are functions with easily computed proximal mappings, further composed with affine mappings. This kind of problem is capable of modeling various applications. Solving these problems, however, can be challenging due to the two-stage structure with possibly large number of scenarios, the nonconvex, nonsmooth and even non-Lipschitz discontinuous terms, as well as the conic constraints. In this paper, we define a KKT point of the problem, show that it is a necessary optimality condition under mild conditions, and transform it to an equivalent nonmonotone nonsmooth two-stage stochastic variational inequality (SVI). We then propose a successive difference-of-convex (SDC) method by making use of Moreau envelope to solve it, the subproblems of which are approximately solved by the progressive hedging method for solving maximal monotone two-stage SVI. We show the rigorous convergence of our method under suitable assumptions. An extension of Markowitz's mean-variance model is provided as an application and numerical results on it demonstrate the effectiveness of the model and the SDC method.

In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact metric space, wherein the concept of measure-theoretic entropy of the map and its utility in defining the pressure of a function are well-studied, we define the measure-theoretic entropy of a holomorphic correspondence and use the same to define the pressure of continuous functions. These ideas naturally lead to the formulation of a variational principle in the context of the dynamics of a holomorphic correspondence.

We investigate the principles of quantum field theory using a stiff de Sitter space. We demonstrate that a non-unitary Lagrangian on a Euclidean AdS geometry can produce the perturbative expansion of late-time correlation functions to all orders. This discovery greatly simplifies perturbative computations while also allowing us to prove fundamental features of these correlators, which are part of a Euclidean CFT. This allows us to construct an OPE expansion, limit the operator spectrum, and deduce the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function. In general, the standard CFT concept of unitarity does not apply to dimensions and OPE coefficients. Rather, the positivity of the spectral density represents the unitarity of the de Sitter theory. This assertion is non-perturbative and does not depend on the use of Euclidean AdS Lagrangians. In a scalar theory, we compute tree-level and entire one-loop-resummed exchange diagrams to demonstrate and verify these characteristics. In the spectrum density, an exchanged particle shows up as a resonant characteristic that may be helpful in experimental searches.

In this paper, we introduced some notions on the n-Normed Spaces. Those are bounded k-linear (or multilinear) functionals and k-continuous (or multicontinuous) functions with k \in \mathbb{N}. We defined k-linear functionals under several types of boundedness, and constructed the corresponding dual spaces based on each type of boundedness. We then proved that these types of boundedness are actually equivalent. This means the boundedness of a multilinear functional can be verified using any of the equivalent notions of boundedness that we defined earlier. The equivalent also implies that all of the resulting dual spaces are identical as a set. We also defined two norms on the dual spaces and showed that both norms are equivalent. Moreover, we gave some examples of bounded k-linear functionals on an n-normed space and calculated their norms with respect to the types of boundedness. We also defined a new notion of k-continuous function in n-normed spaces. Then we gave a relation between the bounded k-linear functional and k-continuous function in n-normed spaces.

Since its discovery, the study of magnetic skyrmions has been on the rise. In this paper, we discuss our investigations on the light-induced mechanisms for skyrmion generation in a centrosymmetric triangular magnetic lattice with competing $J_1$-$J_3$ interactions, and easy-axis anisotropy. We solve the stochastic Landau-Lifshitz-Gilbert equation for the lattice spin dynamics under Laguerre-Gaussian beam irradiation. Numerical results show that skyrmions are nucleated in two thermodynamic regions, each favoring different phases: the ferromagnetic phase and the skyrmion-lattice phase. In the ferromagnetic region, isolated skyrmions are generated mainly through stochastic thermal nucleation. In this regime, higher temperatures and larger beam widths are required to overcome the nucleation barrier. In contrast, in the skyrmion-lattice region, skyrmion nucleation occurs via thermal annealing, where the system relaxes toward its true ground state. These findings establish a comprehensive theoretical framework for optimizing optical control to generating light-induced skyrmionic textures in frustrated magnets.

Clouds are the largest source of uncertainty in climate simulations. For exoplanets, cloud simulation is particularly challenging because of the lack of observational data to tune parameterized cloud models. Here we apply Community Aerosol and Radiation Model for Atmospheres (CARMA), a size-resolved bin cloud microphysics model, to the atmospheric global climate model Community Atmosphere Model (CAM6) and simulate exoplanets with a range of planetary rotation rates. CARMA produces fewer liquid clouds than the native CAM6 parameterized cloud microphysics scheme (Morrison-Gettelman two-moment microphysics, MG), more ice clouds, and a significantly different ice cloud size distribution. Overall, this leads to a decrease in the magnitude of the net CRE by 4-10 $W/m^2$, which is unlikely to change the determination of habitability from a climate perspective in most cases. The difference in ice cloud size distribution is likely to strongly affect transmission spectral retrievals. Our work confirms that the MG parameterized cloud microphysics scheme can produce reasonable climate simulation when extrapolated to some exoplanet contexts and highlights the value of resolved cloud microphysics for evaluating parameterized schemes and for interpreting observations.

Let $Y_{1|1}$ be the Yangian associated to the general linear Lie superalgebra $\mathfrak{gl}_{1|1}$, defined over an algebraically closed field $\mathbbm{k}$ of characteristic $p>2$. In this paper, we classify the finite dimensional irreducible representations of the restricted super Yangian $Y_{1|1}^{[p]}$ and the restricted truncated shifted super Yangian $Y_{1|1,\ell}^{[p]}(σ)$.

We investigate the $T_{cc}$ tetraquark, treating it as a bound state of a heavy diquark and a light antidiquark. Using the Silvestre-Brac potential and solving the Schrödinger equation via the Gaussian Expansion Method, we find that the excitation energy between the heavy diquark and light antidiquark is unexpectedly larger than that between the two light anti-quarks within the anti-diquark -- contrary to the naive expectation where the former is smaller than the latter. We trace this inversion of the mass hierarchy to the centrifugal force acting on the light degree of freedom. Applying the same framework to other systems ($T_{bb}, Λ_b, Λ_c$) yields qualitatively identical behavior, demonstrating the robustness of the mechanism. These results provide new insights into diquark dynamics and the mass structure of exotic hadrons.

The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This study investigates asymptotic properties of the kernel conditional density estimator and the regression estimator with large bandwidth matrix elements for cases of multi-index model. It is clarified that the optimal convergence rate of the estimators depends on not the number of the variables but the effective dimension without eliminating the irrelevant variables. Thus, the kernel conditional density estimator and regression estimator are demonstrated to equip the reduction of the curse of dimensionality by nature. Finite sample performances are investigated by a numerical study, and the bandwidth selection is discussed. Finally a case study on the Boston housing data is provided.

Masur and Minsky showed that the curve graph is quasi-isometric to the Teichmüller space electrified along its thin part, and hence the Teichmüller space is weakly relatively hyperbolic with respect to the thin part. In this paper, we extend this result to the $k$-multicurve graph by electrifying the Teichmüller space along the thin part where the extremal length of $k$ curves is sufficiently small. A key ingredient is a bound on the $k$-multicurve graph distance in terms of the intersection number, which is obtained by adapting the upper bound for the pants graph due to Lackenby and Yazdi.

The inverse design of nonlocal metasurfaces requires the precise optimization of lattice geometry to engineer spatial dispersion and high-Q resonances. However, gradient-based optimization is frequently bottle-necked by the evaluation of the periodic Dyadic Green's Function (DGF), where traditional Finite Difference (FD) methods suffer from an inherent trade-off between truncation error and numerical instability near spectral singularities. In this work, we present an end-to-end Analytic Gradient Engine for 2D Bravais lattices. By mapping the spectral lattice sums of the Coupled Dipole Approximation (CDA) to the theory of Quasi-Modular Forms (QMF), we derive exact, closed-form expressions for the gradients of the interaction matrix with respect to the modular lattice parameter $τ$. Our framework explicitly handles conditionally convergent terms via regularization and addresses the non-holomorphic outlier $σ_4^{(2)}$ via a hybrid numerical strategy. We further introduce a robust evaluation scheme combining $SL(2, \mathbb{Z})$ domain reduction with automatic error certificates. Experimental validation demonstrates that our engine achieves machine-precision derivatives ($10^{-15}$) and a 6.5$\times$ speedup in optimization convergence compared to finite-difference baselines, enabling the robust design of giant anisotropy in regimes where traditional methods fail.

The present study investigates influence of compressibility on separation induced transition in a low pressure turbine cascade using high fidelity direct numerical simulations of the T106A blade. Simulations are performed for inlet Mach numbers, Ms ranging from 0.15 to 0.35 at a fixed Reynolds number and high incidence, representative of off design LPT operation. A dispersion relation preserving numerical framework is employed to accurately capture instability waves, separation bubbles, and separation induced transition to turbulence. A comprehensive analysis is carried out using surface pressure and skin friction distributions, boundary layer integral parameters, spectral analyses, and budgets of compressible enstrophy. Increasing Ms systematically reduces streamwise extent of both leading edge and trailing edge separation bubbles and promotes earlier transition and reattachment, consistent with trends observed under increased free stream disturbances. Despite shorter separation regions, suction side momentum thickness at trailing edge increases from Ms = 0.15 to 0.35, indicating higher profile losses at elevated Ms. Spectral analyses demonstrate a redistribution of turbulent spatial and temporal scales, with energy injection occurring at progressively larger scales as Ms increases. Flow field visualizations reveal a transition pathway that shifts from two dimensional spanwise rolls and intermittent turbulent spots at low Ms to streak dominated, bypass like transition at higher Ms.

We investigate the accretion dynamics of the black hole X-ray binary Swift J1727.8-1613 during its $2023-2024$ discovery outburst that lasted for $\sim10$ months. Insight-HXMT monitored the rising phase of the outburst of Swift J1727.8-1613 roughly continuously from 2023 Aug 25 to 2023 Oct 05. Strong signatures of type-C Quasi-Periodic Oscillations (QPOs) are observed during this phase of the outburst. In our recent paper, nature of the QPOs are studied with the propagating oscillatory shock (POS) model. In this paper, we report on the observation of both positive (or hard) and negative (or soft) time-lags in the $4-10$ keV (LE), $10-30$ keV (ME), and $30 -150$ keV (HE) bands, computed with respect to the $2-4$ keV reference band. We detect a clear transition from hard to soft lags as the outburst evolves. We show the evolution of QPOs and associated time-lags between different X-ray energy bands, correlated with changes in the QPO frequency, spectral state, and the size of the Comptonizing region. Our analysis reveals strong anti-correlations between the time-lags and both QPO frequency and photon index, and a strong positive correlation with the shock location. These evolving lag characteristics and their correlations provide crucial insights into the changing accretion geometry and the interplay of radiative processes, further supporting dynamic models like the POS in explaining the coupled spectro-temporal evolution in black hole X-ray binaries.

We characterize matrix polynomials $P,Q$ such that the inequality $$ \left\Vert Q(D)u\right\Vert _{L^{2}}\leq C\left\Vert P(D)u\right\Vert _{L^{2}}\quad\text{for all }u\in C_c^\infty(Ω), $$ holds on bounded open sets $Ω$. We also characterize the operators $P,Q$ for which the linear continuous embedding above is compact, i.e., if $u_n\in C_c^\infty(Ω)$ are such that $(P(D)u_n)_{n\geq 1}$ is bounded in $L^2$, then $(Q(D)u_n)_{n\geq 1}$ is strongly compact in $L^2$.

Hybrid Automatic Repeat Request (HARQ) schemes typically allocate all available resources to retransmit failed packets to ensure reliability. However, under stringent delay constraints, these schemes often exhibit low spectral efficiency and increased transmission latency. To address these challenges, this paper proposes an efficient Non-Orthogonal HARQ with Chase Combining (N-HARQ-CC) transmission strategy. Specifically, the proposed approach allocates a larger portion of retransmission resources to new data packets, reserving only a small fraction for retransmitting previously erroneous packets. This is based on the observation that only a small number of information bits are typically incorrect, enabling surplus communication resources to be utilized for transmitting new messages. The N-HARQ-CC scheme retransmits the same redundant version of a failed packet and employs Maximum Ratio Combining (MRC) for decoding. To minimize complex packet scheduling and decoding complexity, the proposed scheme limits superposition to at most two messages per transmission round. At the receiver, Successive Interference Cancellation (SIC) is used to decouple the superimposed messages. The proposed N-HARQ-CC system was implemented using GNU Radio and USRP platforms for validation. Compared to conventional Type-I HARQ and HARQ-CC schemes, the proposed scheme achieves a significant improvement in spectral efficiency of approximately 0.5 bps/Hz, aligning with the low-latency requirements of 6G networks.

This is the second of five papers comprising The Semantic Arrow of Time. Part I established that computing's arrow of time is semantic rather than thermodynamic, and that the Forward-In-Time-Only (FITO) assumption constitutes a category mistake. This paper develops the constructive alternative. We present the semantics of Open Atomic Ethernet (OAE) links as a concrete realization of a non-FITO protocol architecture. The key insight is that causal order is not assumed a priori but created through transaction structure: the link state machine progresses through TENTATIVE to REFLECTING to COMMITTED, with the option to abort at any point before commitment. Delivery does not imply commitment; commitment requires reflective acknowledgment -- proof that information has round-tripped and been semantically validated by both endpoints. We formalize this through three frameworks. First, the OAE link state machine, a six-state finite automaton whose normative invariants guarantee that semantic corruption cannot occur at the link level. Second, Indefinite Logical Timestamps (ILT), a four-valued causal structure that admits a genuinely indefinite relation between concurrent events, resolving only after symmetric link-level exchange. Third, the Slowdown Theorem applied to links, which establishes that round-trip measurement is the minimum interaction required to establish causal order. We show that ILT is strictly more expressive than Definite Causal Order systems for reversible link protocols. We connect these results to the Knowledge Balance Principle from quantum information theory. The paper concludes with a comparative analysis showing that OAE achieves infinite consensus number while RDMA, NVLink, and UALink remain limited to finite consensus numbers due to their FITO semantics.

As the convergence of cloud computing and advanced networking continues to reshape modern software development, edge-cloud-native paradigms have become essential for enabling scalable, resilient, and agile digital services that depend on high-performance, low-latency, and reliable communication. This study investigates the practical challenges of developing, deploying, and maintaining edge-cloud-native applications through in-depth interviews with professionals from diverse domains, including IT, finance, healthcare, education, and industry. Despite significant advancements in cloud technologies, practitioners, particularly those from non-technical backgrounds-continue to encounter substantial complexity stemming from fragmented toolchains, steep learning curves, and operational overhead of managing distributed networking and computing, ensuring consistent performance across hybrid environments, and navigating steep learning curves at the cloud-network boundary. Across sectors, participants consistently prioritized productivity, Quality of Service, and usability over conventional concerns such as cost or migration. These findings highlight the need for operationally simplified, SLA-aware, and developer-friendly platforms that streamline the full application lifecycle. This study contributes a practice-informed perspective to support the alignment of edge-cloud-native systems with the realities and needs of modern enterprises, offering critical insights for the advancement of seamless cloud-network convergence.

Parylene C thin films have significant applications in advanced packaging of microelectronics. Their thermal properties are critical for thermal management of electronic devices. However, a unified understanding of the tunable structure and the corresponding thermal conductivity is still missing. This study investigated parylene C thin films of varying thickness and post-annealing temperatures grown via thermal chemical vapor deposition. The ultralow thermal conductivity of as-deposited parylene C measured by time domain thermoreflectance (TDTR) is 0.10 W/m-K. The thermal conductivity can be tuned by post-annealing. Significant increase in thermal conductivity is observed in the annealed samples (0.18 W/m-K) which induces melting and recrystallization. The results of XRD and polarized Raman spectroscopy show that the enhanced thermal conductivity is due to improved crystalline quality and the change in chain orientations. The measured thermal conductivities of the as-deposited and annealed films are much lower than the values predicted by the Cahill minimum thermal conductivity model, which can be explained by the diffuson-mediated minimum thermal conductivity model. Parylene C is found to possess the lowest thermal conductivity among dense low-k materials. Our work provides guidance for the structural design of ultra-low thermal conductivity polymers and corresponding thermal design of electronics.

Every link disconnection or flap in a datacenter corrupts the network's self-knowledge -- its graph. We call this corruption a ghost: a node that appears reachable but is not, a link that reports "up" but silently drops traffic, or an IP address that resolves to a partitioned machine. Ghosts arise at every scale -- chiplet-to-chiplet (PCIe, UCIe), GPU-to-GPU (NVLink, NVSwitch), node-to-node (Ethernet, Thunderbolt), and cluster-to-cluster (IP, BGP) -- because all these protocols inherit Shannon's forward-in-time-only (FITO) channel model and use Timeout And Retry (TAR) as their failure detector. TAR cannot distinguish "slow" from "dead," which is precisely the ambiguity that Fischer--Lynch--Paterson proved unresolvable in asynchronous systems. We survey the problem using production data from Meta (419 interruptions in 54 days of LLaMA 3 training), ByteDance (38,236 explicit and 5,948 implicit failures in three months), Google (TPUv4 optical circuit switching), and Alibaba (0.057% NIC--ToR link failures per month). At 2025 cluster scale (${\sim}3$ million GPUs, ${>}10$ million optical links), a link flap occurs every 48 seconds. We show that every existing mitigation -- Phi Accrual failure detectors, SWIM, BFD, OSPF/ISIS fast convergence, SmartNIC offload, lossless Ethernet (RoCE/PFC), and Kubernetes pod eviction -- still creates ghosts because each is fundamentally timeout-based. We connect ghosts to gray failures (Huang et al., HotOS 2017) and metastable failures (Bronson et al., HotOS 2021; validated across 22 failures at 11 organizations, OSDI 2022). We argue that Open Atomic Ethernet eliminates ghosts at the link layer through a Reliable Link Failure Detector, Perfect Information Feedback, triangle failover, and atomic token transfer -- making topology knowledge transactional.

A machine-learning-based method is developed to identify objects with unusual stellar spectra. The method employs an autoencoder, a neural network trained to compress spectral data into a low-dimensional representation and subsequently reconstruct it. Spectra that deviate significantly from the dominant patterns in the training dataset are identified using the reconstruction error as an anomaly score. The models are applied to selected datasets from the MaNGA Stellar Library, an empirical library of stellar spectra. Several spectra are flagged as anomalous: an object with likely instrumental and/or reduction issues, two carbon stars, and an oxygen-rich thermally pulsating asymptotic giant branch star. The sources of the large reconstruction errors are examined, and the effectiveness and limitations of autoencoder-based approaches for detecting anomalous stellar spectra are discussed.

Determining precise stellar ages and masses for evolved giants is crucial for Galactic archaeology but challenged by spectral degeneracies. Gaia's low-resolution XP spectra offer a unique opportunity to infer these parameters on a massive scale using data-driven methods. We extend a transformer-based astronomical foundation model to evolved stars, establishing a unified framework to simultaneously predict atmospheric parameters ($T_{\mathrm{eff}}$, $\log g$, $[\mathrm{M}/\mathrm{H}]$) and evolutionary labels (mass, age) with physical consistency. Treating spectra as token sequences, we integrated mass and age into the model's vocabulary. The model is trained on Gaia XP spectra cross-matched with the APOGEE DR17 DistMass catalog. Our generative approach enables flexible input handling, including spectral inpainting and parameter-to-spectrum generation. On an independent test set, the model achieves a prediction scatter of $σ\approx 0.114 \, M_{\odot}$ for mass and $σ\approx 1.334$ Gyr for age. Beyond numerical accuracy, it successfully reproduces the giant branch's mass-luminosity relation and autonomously disentangles interstellar extinction from intrinsic temperature variations without explicit physical priors. It also robustly recovers missing spectral data and estimates reliable uncertainties. Validating that foundation models can internalize stellar physics from data, this physically-aware, probabilistic framework offers a powerful tool for unraveling Milky Way history using large-scale spectroscopic surveys.

The emergence of large-scale, sparse, multimodal, and agentic AI models has coincided with a shift in hardware toward supernode architectures that integrate hundreds to thousands of accelerators with ultra-low-latency interconnects and unified memory pools. However, existing AI frameworks are not designed to exploit these architectures efficiently, leading to high programming complexity, load imbalance, and poor memory utilization. In this paper, we propose a supernode-affinity AI framework that treats the supernode as a single logical computer and embeds hardware-aware orchestration into the framework. Implemented in MindSpore, our HyperParallel architecture comprises HyperOffload for automated hierarchical memory management, HyperMPMD for fine-grained MPMD parallelism across heterogeneous workloads, and HyperShard for declarative parallel strategy specification. Together, these techniques significantly improve training and inference efficiency while reducing parallel programming and system tuning overhead, demonstrating the necessity of supernode affinity for next-generation AI frameworks.

The spatial extent of the proton is a key factor in nuclear physics. Different measurement techniques probe different aspects of the proton, yielding different radii. The mass and charge radii depend on the parton and quark distributions respectively, while the mechanical radius depends on the mass/energy distribution. Here, we probe the spatial distribution of a new proton characteristic, studying the distribution of baryon number within the proton. We investigate the baryon number distribution by studying four exclusive meson production channels arising from photon-proton collisions ($γp \rightarrow p ρ^0$, $γp \rightarrow p ω$, $γp \rightarrow n π^+$, and $γp \rightarrow p π^0$). The two-dimensional transverse sizes of the interacting systems are extracted by analyzing the transverse momentum, $p_T$, dependence of the meson production cross section, using Fourier-Bessel transformations. We find that baryon number is confined to a transverse radius of $0.33 - 0.53$~fm. In comparison, the transverse radius of the proton charge and mass distributions are considerably larger, at least 0.67~fm. The baryon number is concentrated in the center of the proton.

The rapid deployment of large-scale low Earth orbit (LEO) satellite constellations has positioned direct-to-handset (D2H) communications as a key enabler of future non-terrestrial networks. However, the limited link budget of handheld devices makes broadband service delivery challenging, and multi-satellite cooperative transmission is often required to provide sufficient power gain. In practice, such cooperation is severely hindered by asynchronous reception across satellites. This paper analyzes the received-signal model under the 3rd Generation Partnership Project (3GPP) transmitter structure and shows that satellite-dependent propagation delays prevent simultaneous timing alignment for multiple user terminals (UTs). This timing mismatch induces severe inter-carrier interference (ICI) and inter-symbol interference (ISI), even from the intended signals, which fundamentally constrains the achievable cooperative gain. To address this issue, we propose a timing-aware satellite association strategy that enables cooperation only with satellites expected to satisfy a UT-side timing tolerance, thereby avoiding dominant asynchronous interference by design. Simulation results demonstrate that the proposed strategy improves throughput performance compared to single-satellite transmission and fully connected multi-satellite baselines.

In this contribution, we present a recently introduced approach [BorkLeeOnishchenko2025] to the calculation of slightly off-shell dual conformal integrals based on the method of regions with regularization preserving dual conformal invariance (DCI). Unlike conventional dimensional regularization, which breaks DCI, our approach uses a combination of dimensional and analytic regularizations specifically designed to retain DCI throughout the calculation. Our approach drastically simplifies the computation of slightly off-shell dual conformal integrals. For the two-loop five-point DCI integrals we find that with DCI-preserving regularization, the contributions of all regions can be expressed in terms of $Γ$-functions, resulting in a remarkably compact final expression in terms of logarithms of cross-ratios only. This is in sharp contrast to conventional approach which yields complex polylogarithmic expressions [Belitsky&Smirnov2025]. We argue that a similar approach might be useful also for non-DCI integrals.

Recently, an exact rotating black hole solution in a parity-violating theory of gravity was obtained via a conformal transformation of the Kerr solution in general relativity, with parity-violating effects encoded in the conformal factor. We study the quasinormal modes (QNMs) of a test scalar field minimally coupled to gravity on this conformal Kerr background, treating the parity-violating effects perturbatively while allowing for arbitrary black hole spin, from the non-rotating case to the near-extremal regime. For low spin, we derive a perturbative formula for the QNM frequencies that includes the leading-order parity-violating correction. For high spin, particularly in the near-extremal regime, we find sizable deviations from the Kerr QNM frequencies. Our results point to a new avenue for probing parity-violating physics in the strong-gravity regime through black hole QNMs.

We study the set of isomorphism classes of polarized superspecial abelian varieties $(A,λ)$ of a fixed dimension over $\mathbb{F}_p$ with Frobenius endomorphism $π_A=\sqrt{-p}$ and $\ker λ=\ker π_A$. This set plays an important role in the geometry of the supersingular locus, and the generalizations of Deuring's $2T-H$ Theorem by Ibukiyama and Katsura. We determine when this set is nonempty and classify its genera. Our method reduces the problems of superspecial abelian varieties to those of certain hermitian lattices by the lattice description established by Jordan et. al and Ibukiyama--Karemaker--Yu, and we treat these problems on the lattices concerned by arithmetic methods.