In this paper, we study the advective unstable Cahn--Hilliard equation on $\mathbb T^2$ with shear flow: \begin{equation*} \begin{cases} u_t+Av_1(y) \partial_x u+\varepsilon Δ^2 u= Δ(a u^3+ b u^2) \quad & \quad \textrm{on} \quad \mathbb T^2; \\ \\ u \ \textrm{periodic} \quad & \quad \textrm{on} \quad \partial \mathbb T^2, \end{cases} \end{equation*} where $u_0\in H_0^2(\mathbb T^2)$, $A,\varepsilon>0$, $a<0$, and $b\in\mathbb R$. The condition $a<0$ puts the model in an unstable phase-field regime: the nonlinear chemical potential may amplify, rather than restore, concentration fluctuations, as in spinodal decomposition. The shear term $Av_1(y)\partial_xu$ models imposed stirring along the shear direction; through mixing, it enhances dissipation and counteracts the growth driven by the unstable cubic term $Δ(au^3)$. Assuming that the shear profile has finitely many critical points and that linearly growing modes occur only in the shear direction, we prove that the $L^2$-energy converges exponentially to zero, provided $|a|$ and $\|\int_{\mathbb T} u_0(x,\cdot)\,dx\|_{L_y^2}$ are sufficiently small.

We investigate the ultraviolet completion of an $O(N)$ scalar field theory non-minimally coupled to gravity using the Wilsonian functional renormalization group in the proper-time formulation. Focusing on the spontaneously broken phase, we study the RG flow of the scalar potential and the non-minimal curvature coupling expanded around a running minimum. We identify two distinct classes of fixed-point solutions, one of which is ultraviolet attractive and characterized by a vanishing quartic coupling together with finite, interacting gravitational couplings. For a finite region of infrared initial conditions, the RG trajectories remain regular at all scales and approach this fixed point. This mechanism renders the theory asymptotically safe and leads to a flat scalar potential in the ultraviolet. We show that this mechanism is robust under changes of cutoff scheme and truncation, allowing the ultraviolet completion requirement to constrain the infrared values of the scalar couplings and the mass scale in the broken phase.

In this work, we exploit a dictionary that maps solutions of the Einstein--Scalar--Maxwell theory to those of gauged Skyrme--Maxwell--Einstein models in $(3+1)$ dimensions, allowing gravitating scalar-field configurations in external electromagnetic backgrounds to be interpreted in terms of baryonic quantities. Using the definition of Baryonic charge as the integral of a topological density, we derive novel mass formulas that relate the spacetime mass parameter to the Baryonic charge, the external magnetic field, and other solution parameters. As a result, the mass and Baryonic charge are not independent. These closed analytic expressions encode physical information that would otherwise be difficult to extract. In particular, for the class of solutions considered here, the relation between mass and Baryonic charge is linear at large mass, while significant nonlinear deviations appear at intermediate values. This framework provides a useful tool for both extracting new physical insights from known solutions and constructing new baryonic configurations using the solution-generating techniques available for Einstein--Scalar--Maxwell theory.

This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu representation for the azimuthal component of the vector potential in both air and conductive regions. The central contribution is a unified regularization framework for the two-dimensional (2D) singular integrals arising in Galerkin BEM. This framework handles both logarithmic and Cauchy singularities through a common set of integral transformations, eliminating the need for case-by-case analytical singularity extraction and enabling straightforward numerical quadrature. The regularization and quadrature stability are proved and verified numerically. The method is validated on several representative axisymmetric geometries, including cylindrical, conical, and spherical shells. Numerical experiments demonstrate consistently high accuracy and computational efficiency over the tested frequency interval and coil lift-off distances. The results confirm that the proposed axisymmetric Galerkin BEM, combined with the integral transformation technique, provides a robust and efficient framework for axisymmetric eddy-current nondestructive evaluation.

We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposition-based central-upwind (LCDCU), low-dissipation central-upwind (LDCU), and viscous finite volume (VFV) methods, whose higher-order extensions are obtained via the framework of the alternative weighted essentially non-oscillatory (A-WENO) schemes. These methods are applied to several benchmark problems, including several two-dimensional Riemann problems and a Kelvin-Helmholtz instability test. The numerical results demonstrate that for methods converging only weakly in space and time, the limiting solutions are generalized DW solutions, approximated in the sense of ${\cal K}$-convergence and dependent on the numerical scheme. For all of the studied methods, we compute the associated Young measures and compare the DW solutions using entropy production and energy defect criteria.

Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and stating that a non-persistent sequence can be permuted into a persistent one. We identify Petri net classes for which persistent permutability already suffices to imply overall persistence. These classes generalise free-choice nets and are related to Petri's concept of ``confusion'', while they are distinguished from each other by diverse restrictions on the choice structure of a net. We prove Ochmanski's conjecture to be correct for these classes.

Measurement non-invariance arises when the psychometric properties of a scale differ across subgroups, undermining the validity of group comparisons. At the item level, this manifests as differential item functioning (DIF), where item responses differ across groups after controlling for the latent trait. This paper develops a framework for detecting DIF in ordinal scales without requiring known group labels or anchor items. We formulate a proportional-odds latent-class item response model in which individuals are assigned probabilistically to latent classes. DIF is captured through class-specific intercept and slope shifts, allowing both uniform and non-uniform DIF. Identification is achieved through an \(\ell_1\)-penalised marginal likelihood under a sparsity assumption, with estimation implemented using a tailored EM algorithm. Because class-specific slopes leave both the location and scale of each latent class unidentified, sparsity anchors the latent metric while selecting DIF effects. Simulation studies demonstrate accurate recovery of item parameters and both types of DIF. An empirical application to a personality test reveals latent subgroups with distinct response patterns and identifies items displaying potential class-specific measurement non-invariance. The framework provides a flexible approach for assessing measurement invariance in ordinal scales when comparison groups are unobserved or poorly defined.

The field of definition of the Mordell-Weil group of an elliptic surface $E \rightarrow \mathbb{P}^1$ defined over $\mathbb{Q}$ is the smallest number field $k$ such that all of its $\Bar{\mathbb{Q}}(t)$-rational points are defined over $k(t)$. In this paper, we present an algorithm, implemented in \Magma{}, which can determine arithmetic information, including the field of definition, associated to any rational elliptic surface. As an application of this, we also demonstrate that the field of definition of Shioda's rank $68$ elliptic surface given by $y^2 = x^3 + t^{360} + 1$ is a number field of degree $829,440$.

We study embeddings of $L^p$-operator algebras arising from (twis\-ted) étale groupoids, with particular emphasis on rigidity phenomena for $p\neq 2$. Our methods rely on a detailed analysis of core normalizers and their functorial behavior under algebra homomorphisms. Using the notion of actors between groupoids, we show that under natural hypotheses, embeddings between reduced $L^p$-groupoid algebras can be described entirely in terms of morphisms of the underlying groupoids. We further show that embeddings of $L^p$-groupoid algebras induce embeddings of the associated topological full groups. Our results provide new tools for studying embeddability questions in the $L^p$-setting, and are particularly helpful when ruling out the existence of embeddings. As applications, we obtain strong embeddability results both for spatial AF $L^p$-operator algebras and for tensor products of $L^p$-Cuntz algebras. For $p\not \in \{1,2\}$, a reduced $L^p$-groupoid algebra associated with a principal étale groupoid embeds into a spatial AF $L^p$-operator algebra if and only if the underlying groupoid is AF. In particular, and in contrast with classical results of Pimsner-Voiculescu, irrational $L^p$-noncommutative tori do not embed into spatial AF $L^p$-operator algebras for $p\neq 2$. Furthermore, if $p\neq 2$, there is no unital contractive homomorphism from $\mathcal{O}_2^p \otimes_p \mathcal{O}_2^p$ into $\mathcal{O}_2^p$, showing that there is no $L^p$-analog of Kirchberg's $\mathcal{O}_2$-embedding theorem.

The COVID-19 pandemic triggered not only a global health crisis but also an infodemic, where exposure to heterogeneous information sources influenced public emotional responses. In this work, we investigate the determinants of self-reported fear of infection using data from the Delphi US CTIS survey. In particular, we analyze how demographic variables, epidemiological conditions, and exposure to different information sources shape fear levels. We introduce a Probabilistic Causal Model to estimate causal relationship strengths, identifying the variables that most strongly influence fear. Our results indicate that exposure to information sources accounts for a greater proportion of the variance in fear than demographic and epidemiological variables do. We further compute the Average Treatment Effect to quantify the impact of different information sources on fear. After causal adjustment, institutional and expert-driven sources are associated with increased fear levels, whereas politicians, religious leaders, and alternative information channels are associated with reduced fear. These findings highlight both the central role of the information ecosystem in shaping emotional responses during public health crises and the value of causal inference approaches for studying behavioral responses to pandemics.

We investigate the redshift 1.98 galaxy cluster XLSSC 122 using the Hubble Space Telescope (HST) from the core of the cluster out to 3 Mpc, a scale equivalent to 10 times the R500 = 295 kpc radius. We present an expanded photometric and spectroscopic catalogue of the cluster, bringing the total number of spectroscopically classified member galaxies to 74, with 35 new member galaxies added in the outer regions of the cluster. We compute the radial galaxy number density profile in the cluster, and observe no clear evidence of infalling groups or cosmic filaments. We observe a clear bimodal colour relation in member galaxies, with red fraction increasing towards the cluster centre. This rapid increase of red fraction upon infall is indicative of a fast quenching mechanism, such as ram pressure stripping, as galaxies enter the cluster centre. We fit a luminosity function to the cluster members, finding a similar low mass slope but fainter scale magnitude than z = 1 clusters of similar temperature, implying a similar galaxy evolution rate to clusters at lower redshift.

Dealers in foreign exchange markets provide bid and ask prices to their clients at which they are happy to buy and sell, respectively. To manage risk, dealers can skew their quotes and hedge in the interbank market. Hedging offers certainty but comes with transaction costs and market impact. Optimal market making with execution has previously been addressed within the Almgren-Chriss market impact model, which includes instantaneous and permanent components. However, there is overwhelming empirical evidence of the transient nature of market impact, with instantaneous and permanent impacts arising as the two limiting cases. In this note, we consider an intermediate scenario and study the interplay between risk management and impact resilience.

We prove that a homogeneous 0-dimensional complete intersection satisfies the Strong Lefschetz Property (SLP) in degree 1 if and only if its associated form has nonzero Hessian. This result is essentially known in the literature, but our proof differs from previous ones. We then investigate properties of the associated forms and show that they can always be reconstructed from their partial derivatives, in particular from their Jacobian ideals. As an application of our method, we prove that every smooth homogeneous polynomial which is not of Sebastiani-Thom type is uniquely determined by any nontrivial graded component of its Jacobian ideal.

We revisit the problem of rigorously and deterministically finding elements of large order in the multiplicative group of integers modulo a natural number $N$. Solving this problem is an essential step in several recent deterministic algorithms for factoring $N$, including the currently fastest ones. In 2018, the second author gave an algorithm that for a given target order $D \geq N^{2/5}$, finds either an element of order exceeding $D$, or a nontrivial divisor of $N$, or proves that $N$ is prime. The running time was \[ O\left(\frac{D^{1/2}}{(\log \log D)^{1/2}} \log^2 N \right) \] bit operations, asymptotically the same as the cost of computing the order of a single element using Sutherland's optimisation of the classical babystep-giantstep method. Subsequent work by several authors weakened the hypothesis $D \geq N^{2/5}$ to $D \geq N^{1/6}$. In this paper, we show that the hypothesis may be dropped altogether. Moreover, if $N$ is prime, we can guarantee returning an element of order exceeding $D$, rather than a proof that $N$ is prime.

We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to approximating the physical domain by a polygonal mesh. Unless boundary conditions can be accurately transferred from the true boundary to the computational one, such geometric approximation errors generally lead to suboptimal convergence. To overcome this limitation, a higher-order strategy based on polynomial reconstruction of boundary data was introduced for classical finite element methods in [31, 32] and in the finite volume context in [8, 14]. More recently, this approach was extended to discontinuous Galerkin methods in [35], leading to the DG-ROD method, which restores optimal convergence rates on polygonal approximations of domains with curved boundaries. In this work, we provide a rigorous theoretical analysis of the DG-ROD method, establishing existence and uniqueness of the discrete solution and deriving error estimates for a two-dimensional linear advection-diffusion-reaction problem with homogeneous Dirichlet boundary conditions on both convex and non-convex domains. Following and extending techniques from classical finite element methods [32], we prove that, under suitable regularity assumptions on the exact solution, the DG-ROD method achieves optimal convergence despite polygonal approximations. Finally, we illustrate and confirm the theoretical results with a numerical benchmark considering triangular meshes

Nanoscale transistors require aggressive reduction of all channel dimensions: length, width, and thickness. While monolayer two-dimensional semiconductors (2DS) offer ultimate thickness scaling, good performance has largely been achieved only in micrometer-wide channels. Here, we demonstrate both $\it{n}$- and $\it{p}$-type nanoribbon transistors based on monolayer 2DS, fabricated using a multi-patterning process, reaching channel widths and lengths down to 25-30 nm. 'Anchored' contacts improve device yield, while nanoscale imaging, including tip-enhanced photoluminescence, reveals minimal edge degradation. The devices reach on-state currents up to 560, 420, and 130 $μ$A $μ$m$^{-1}$ at 1 V drain-to-source voltage for $\it{n}$-type MoS$_{2}$, WS$_{2}$, and $\it{p}$-type WSe$_{2}$, respectively, integrated with thin high-$κ$ dielectrics. These results surpass prior reports for single-gated nanoribbons, the WS$_{2}$ by over 100 times, even in normally off (enhancement-mode) transistors. Taken together, these findings suggest that top down patterned 2DS nanoribbons are promising building blocks for future nanosheet transistors.

This paper studies online power control for battery-limited point-to-point energy harvesting communications over slow block-fading channels. A linear-policy-based approximation is developed for the relative-value function in the Bellman equation of the power control problem. This approximation leads to two fundamental parameterized clipped affine policies: an optimistic policy derived from a certainty-equivalence-type approximation and a robust policy derived from worst-case analysis. For independent and identically distributed energy arrivals and channel states, two families of power control schemes are developed based on the optimistic clipped affine (OCA) and robust clipped affine (RCA) policies, respectively. The proposed adaptive RCA policy based on reinforcement learning (RCA-RL) is further extended to address four scenarios with contextual information: one-step energy lookahead, one-step channel lookahead, one-step joint energy-channel lookahead, and Markov energy arrivals. Extensive simulation results show that the proposed schemes provide a favorable tradeoff between computational complexity and performance. The adaptive RCA policy based on the maximin optimal linear-policy-slope approximation (RCA-OLA-A) and the RCA-RL scheme achieve the best overall performance, while the RCA policy based on the maximin optimal linear policy (RCA-OL) is the best-performing closed-form policy. In particular, RCA-OLA-A, RCA-RL, and the aforementioned RCA-RL extensions achieve less than 2% performance loss relative to the optimal policy across a range of scenarios, consistently outperforming the considered benchmark approaches, including generic reinforcement learning baselines. The RCA-OL policy also performs well with less than 4% performance loss.

In many metals, thermal transport is often dominated by electrons, although the lattice contribution can remain appreciable depending on the material. Here, through rigorous first-principles calculations, we uncover a phonon-dominated thermal transport regime in the Weyl semimetals TaAs and TaP. Remarkably, despite its metallic character, TaP exhibits an exceptionally high phonon thermal conductivity ($κ_{\text{ph}}$) of 162 Wm$^{-1}$K$^{-1}$ at room temperature, surpassing its electronic counterpart by nearly an order of magnitude. This anomalously high $κ_{\text{ph}}$ is enabled by the unique electronic and phononic band structures, including the Weyl nodes near the Fermi level, acoustic phonon bunching, and a wide frequency gap in the phonon spectrum, which collectively suppress phonon-electron and three-phonon scattering processes. The linearly dispersing bands near the Fermi level give rise to a low electronic density of states, thereby limiting both electrical conductivity and electronic thermal transport in these Weyl semimetals. By further surveying a broad range of topological semimetals, we show that the prominence of phonon thermal transport is a universal characteristic of this material class. Our work provides deeper insight into thermal transport mechanisms in topological semimetals and broadens the scope for discovering metals with high thermal conductivity.

We study high-dimensional sparse regression under simultaneous heavy-tailed covariates and noise. Heavy-tailed data affect sparse optimization in two different ways: extreme covariates can destabilize the gradient field during global localization, while heavy-tailed noise limits the final statistical accuracy during local refinement. Motivated by this two-phase structure, we propose two-stage RIGHT, a robust sparse first-order method based on coordinate-wise median-of-means (MoM) gradient estimation and delayed sample splitting. The MoM gradient estimator is computationally simple, compatible with hard-thresholded updates, and admits phase-adaptive concentration bounds whose rates depend on the current localization radius. Delayed splitting reuses data during global localization and reserves fresh batches for the shorter refinement stage, reducing the sample-splitting cost. The theoretical results reveal a decoupled rate structure: the design-tail index controls gradient stability and sample complexity, whereas the noise-tail index controls the final statistical rate. We also provide phase-wise lower-bound benchmarks showing that the design-driven localization barrier is intrinsic. Extensive simulation experiments and real data analysis showcase the efficacy of the proposed method over existing competitors.

The paper is concerned with a nonlinear system of two coupled fractional Schrödinger equations with both attractive intraspecies and attractive interspecies interactions in $\mathbb{R}$. By analyzing an associated $L^2$-constrained minimization problem, the uniqueness of solutions to this system is proved via the implicit function theorem. Under a certain type of trapping potential, by establishing some delicate energy estimates, we present a detailed analysis on the concentration behavior of the solutions as the total strength of intraspecies and interspecies interactions tends to a critical value, where each component of the solutions blows up and concentrates at a flattest common minimum point of the associated trapping potentials. An optimal blow-up rate of solutions to the system is also given.

The persistence of ferroelectricity in ultrathin HfO$_2$ films challenges conventional theories, particularly given the paradoxical observation that the out-of-plane lattice spacing increases as the film thickness decreases, an anomalous size effect absent in perovskite ferroelectrics. Here, we resolve this puzzle by revealing that this lattice expansion is counterintuitively coupled to a suppressed out-of-plane polarization. First-principles calculations combined with analytical modeling identify two mechanisms behind this expansion: a negative longitudinal piezoelectric response to the residual depolarization field and a positive surface stress that becomes significant at reduced thickness. Their interplay quantitatively reproduces the experimentally observed lattice expansion. Furthermore, (111)-oriented HfO$_2$ films can support out-of-plane polarization even under open-circuit conditions, in contrast to (001) films that stabilize a nonpolar ground state. This behavior points to the emergence of orientation-induced hyperferroelectricity, an unrecognized mechanism that enables polarization persistence through orientation engineering without electrode screening. We further demonstrate that this principle generalizes to conventional perovskites such as PbTiO$_3$, offering a strategy to eliminate the critical thickness limit by choosing the appropriate film orientation. As a practical pathway to device integration, we also identify the two-dimensional electride Ca$_2$N as a near-ideal electrode that fully restores the ferroelectric properties of HfO$_2$ in ultrathin capacitors.

With the release of the Gravitational-Wave Transient Catalog GWTC-4.0 by the LIGO-Virgo-KAGRA (LVK) collaboration, 218 candidate detections of gravitational waves (GWs) from compact binary coalescences (CBCs) have been reported. This milestone represents a major advancement for GW cosmology, as many methods, particularly those employing the spectral siren approach, critically depend on the number of available sources. We investigate the impact of a novel parametric model describing the full population mass spectrum of CBCs on the estimation of the Hubble constant. This model is designed to test the impact of heavy black holes in GW cosmology. We perform a joint inference of cosmological and population parameters using 142 CBCs from GWTC-4.0 with a false alarm rate smaller than 0.25 per year, using both spectral and dark siren approaches. With spectral sirens, we estimate the Hubble constant to be $H_0 = 78.8^{+19.0}_{-15.3}\,{\rm km s^{-1} Mpc^{-1}}$ (68% CL), while the dark siren method yields $H_0 = 82.5^{+16.8}_{-14.3}\,{\rm km s^{-1} Mpc^{-1}}$ (68% CL). These results improve the uncertainty by approximately 30.4% and 36.2%, respectively. We show that this improvement is linked to the presence of a new mass scale in the binary black hole mass spectrum at $63.3^{+4.8}_{-4.8}\,M_{\odot}$, which provides additional constraints on the Hubble constant. Besides providing the tightest standard-siren constraints on $H_0$, this highlights the importance of a heavy-mass feature in the black hole spectrum.

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a Kähler metric $ω$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form $Ω$. We introduce the notions of $(ω,\,Ω)$-Hermite-Einstein holomorphic vector bundles and $(ω,\,Ω)$(-semi)-stable coherent sheaves on $X$ by generalising the classical definitions depending only on $ω$. We then prove that the $(ω,\,Ω)$-Hermite-Einstein condition implies the $(ω,\,Ω)$-semi-stability of a holomorphic vector bundle and its splitting into $(ω,\,Ω)$-stable subbundles. This extends a classical result by Kobayashi and Lübke to our generalised setting. In the appendix, we propose notions of both strongly and weakly (strictly) positive forms and currents and discuss their various properties.

Topological markers provide an efficient and powerful characterization of topological features of many systems, especially when the translation symmetry is broken. Recently, a universal topological marker applicable in different symmetry classes of topological systems is proposed. However, it suffers from irregular behaviors at the boundary and its connection to other topological indexes remains elusive. In this work, we construct regularized universal topological markers that apply to Dirac systems by utilizing position operators that are compatible with periodic boundary conditions. The regularized markers eliminate the obstructive boundary irregularities successfully and give rise to the desired global topological invariants, such as the Chern number, consistently when integrated over all the lattice sites. Furthermore, the regularized form allows us to establish an explicit connection between the markers and some other known topological indices in two dimensions. For instance, it turns out to be equivalent to the Bott index in classes A, D, and C and equivalent to the spin Chern number in classes DIII and AII. We further examine the utility and stability of this marker in disordered scenarios. We find that its variance shows peaks at the phase boundaries, which promotes it as a useful indicator for detecting disorder-induced topological phase transitions.

Let $\mathbb{S}^1$ denote the unit circle. We introduce and develop the analytic and bias theory of unimodular fake Möbius functions, i.e. multiplicative functions $\mathfrak{f}:\mathbb{N} \to \mathbb{S}^1 \cup \{0\}$ whose prime-power values are prescribed by a fixed sequence $\{\varepsilon_k\}_{k\ge1}$ via the rule $\mathfrak{f}(p^k)=\varepsilon_k$ for every prime $p$ and every $k\ge1$. A key feature of these functions is that their Dirichlet series admit a factorization into complex powers of the Riemann zeta function. Our main analytic result is an explicit formula for the smoothed summatory function $\sum_{n\ge1}\mathfrak{f}(n)e^{-n/x}$, consisting of a leading main term together with a sequence of lower-order terms. The formula may be viewed as an extension of the Selberg-Delange method and is expected to be of independent interest. As an application, we introduce a notion of bias at a natural scale and obtain an explicit criterion distinguishing persistent bias, apparent bias, and no bias for unimodular fake Möbius functions.

Let $F$ be a finite field, let $f$ be a function from $F$ to $F$, and let $a$ be a nonzero element of $F$. The discrete derivative of $f$ in direction $a$ is $Δ_a f \colon F \to F$ with $(Δ_a f)(x)=f(x+a)-f(x)$. The differential spectrum of $f$ is the multiset of cardinalities of all the fibers of all the derivatives $Δ_a f$ as $a$ runs through $F^*$. An almost perfect nonlinear (APN) function is one for which the largest cardinality in its differential spectrum is $2$. Almost perfect nonlinear functions are of interest as cryptographic primitives. If $d$ is a positive integer, then the power function over $F$ with exponent $d$ is the function $f \colon F \to F$ with $f(x)=x^d$ for every $x \in F$. There is a small number of known infinite families of APN power functions. In this paper, we re-express the exponents for one such family in a more convenient form. This enables us not only to obtain the differential spectrum of each power function $f$ with an exponent in our family, but also to determine the elements that lie in an arbitrary fiber of the discrete derivative of $f$. This differential analysis, which is far more detailed than previous results, is achieved by composing the discrete derivative of $f$ with some permutations and a double covering of its domain to obtain a function whose fibers can more readily be analyzed.

Semantic communications (SemCom), as one of the key technologies for 6G, is shifting networks from bit transmission to semantic information exchange. On this basis, introducing agentic artificial intelligence (AI) with perception, memory, reasoning, and action capabilities provides a practicable path to intelligent communications. This paper provides a systematic exposition of how agentic AI empowers SemCom from the perspectives of research foundations, system architecture, and application scenarios. We first provide a comprehensive review of existing studies by agent types, covering embedded agents, large language model (LLM)/large vision model (LVM) agents, and reinforcement learning (RL) agents. Additionally, we propose a unified agentic AI-enhanced SemCom framework covering the application layer, the semantic layer, and the cloud-edge collaboration layer, forming a closed loop from intent to encoding to transmission to decoding to action to evaluation. We also present several typical scenarios, including multi-vehicle collaborative perception, multi-robot cooperative rescue, and agentic operations for intellicise (intelligent and concise) networks. Furthermore, we introduce an agentic knowledge base (KB)-based joint source-channel coding case study, AKB-JSCC, where the source KB and channel KB are built by LLM/LVM agents and RL agents, respectively. Experimental results show that AKB-JSCC achieves higher information reconstruction quality under different channel conditions. Finally, we discuss future evolution and research directions, providing a reference for portable, verifiable, and controllable research and deployment of agentic SemCom.

Mountain huts are buildings located at high altitude, offering a place for hikers and providing shelter. Energy supply on mountain huts is still an open issue. Using renewable energies could be an appropriate solution. Jiujiu Cabins, a famous mountain hut in Shei-Pa National Park, Taiwan, has operated an off-grid solar energy storage system (ESS) with lead-acid batteries. In 2021, a serious system failure took place, leading to no electricity. After a detailed on-site survey, a reorganization and repair project implemented, the energy system came back to operate normally. Meanwhile, an eco-friendly lithium iron phosphate battery (LFP battery) ESS replaces part of the lead-acid battery ESS, forming a hybrid ESS, making a better and green off-grid solar ESS. In this case report, the energy architecture, detailed descriptions, and historical status of the system are provided. An on-site survey of the failed energy system, a system improvement project, and future plan are listed.

Flaky tests, tests that pass or fail nondeterministically without changes to code or environment, pose a serious threat to software reliability. While classical software engineering has developed a rich body of techniques to study flakiness, corresponding evidence for quantum software remains limited. Prior work relies mainly on static analysis or small sets of manually reported incidents, leaving open questions about their prevalence, characteristics, and detectability. This paper presents the first large-scale dynamic characterization of flaky tests in quantum software, focusing on the Qiskit Terra core library. We executed the Qiskit Terra test suite 10,000 times across 23 releases in controlled environments. For each release, we measured test-outcome variability, identified flaky tests, estimated empirical failure probabilities, analyzed recurrence across versions, used Wilson confidence intervals to quantify rerun budgets for reliable detection, and mapped flaky tests to Terra subcomponents. Across 27,026 fully qualified test identifiers, we identified 62 unique flaky tests. Although overall flakiness rates were low (0-0.17%), recurrence was substantial: 52 of 62 flaky tests (83.87%) reappeared in multiple releases, while only 10 tests (16.13%) were confined to a single release. Empirical failure probabilities spanned several orders of magnitude, with a median of $9 \times 10^{-4}$ and 34 tests (54.84%) at or below $10^{-3}$, implying that thousands to tens of thousands of executions may be required for confident detection. These results show that quantum test flakiness is rare but difficult to detect under typical continuous integration budgets. To support future research, we release a public dataset of per-test execution outcomes.

We study the implications for leptogenesis in a class of left-right symmetric model, where all fermion masses are induced through the Universal Seesaw mechanism. Unlike conventional analyses, we do not use the decays of the neutrino embedded in the right-chiral lepton doublet, but rather those of the gauge-singlet mediators required for neutrino mass generation in the canonical Type-I seesaw. This model features a generalized parity symmetry, which is motivated by the solution to the strong $CP$ problem. Since this discrete symmetry doubles the fermionic degrees of freedom in this model, we can generate the required $CP$ violation in the heavy fermion decays with only a single generation of mediators. One of the distinct features of our scenario is that the bounds from thermalization or washout via gauge interactions typically encountered in the canonical left-right symmetric models do not apply here. Moreover, the heavy mediators can decay to both the left and the right-chiral neutrinos, leading to a cancellation in the resulting baryon asymmetry for decays above the left-right symmetry breaking scale. We discuss ways to avoid this cancellation and show that low scale left-right symmetry breaking above the current collider limits $v_R > 18$ TeV is viable. The right chiral neutrinos also obtain their masses from the seesaw mechanism, and the lightest one turns out to have a sub-eV scale mass. We find that its abundance is consistent with standard cosmology, and it acts as potentially observable dark radiation.