Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is particularly problematic given the fact that often times these distributions are fitted to small samples. Furthermore, the distribution's parameters are generally not directly interpretable and not the key aim of the estimation. We present several orthogonal reparametrisations of the main extreme-value distributions, key in the modelling of rare events. In particular, we apply the theory developed in Cox and Reid (1987) to the Generalised Extreme-Value, Generalised Pareto, and Gumbel distributions. We illustrate the principal advantage of these reparametrisations in a simulation study.

Natural birth and death are fundamental mechanisms of population dynamics in ecosystems and have played pivotal roles in shaping population dynamics. Nevertheless, in studies of cyclic competition systems governed by the rock-paper-scissors (RPS) game, these mechanisms have often been ignored in analyses of biodiversity. On the other hand, given the prevalence and profound impact on biodiversity, understanding how higher-order interactions (HOIs) can affect biodiversity is one of the most challenging issues, and thus HOIs have been continuously studied for their effects on biodiversity in systems of cyclic competing populations, with a focus on neutral species. However, in real ecosystems, species can evolve and die naturally or be preyed upon by predators, whereas previous studies have considered only classic reaction rules among three species with a neutral, nonparticipant species. To identify how neutral species can affect the biodiversity of the RPS system when species' natural birth and death are assumed, we consider a model of neutral species in higher-order interactions within the spatial RPS system, assuming birth-and-death processes. Extensive simulations show that when neutral species interfere positively, they dominate the available space, thereby reducing the proportion of other species. Conversely, when the interference is harmful, the density of competing species increases. In addition, unlike traditional RPS dynamics, biodiversity can be effectively maintained even in high-mobility regimes. Our study reaffirms the critical role of neutral species in preserving biodiversity.

Entanglement is a central and subtle feature of quantum theory, whose structure and operational behavior can change dramatically when additional physical constraints, such as symmetries or superselection rules, are imposed. Such constraints can give rise to striking and counter-intuitive phenomena, including local broadcasting of entangled states and failures of entanglement monogamy. These effects naturally arise in tomographically nonlocal theories (like real quantum theory, twirled worlds, or fermionic quantum theory), where composite systems possess holistic degrees of freedom that are inaccessible to local measurements. In this work, we study entanglement in such theories within the framework of generalized probabilistic theories. We show that the failure of tomographic locality leads to two qualitatively distinct forms of entanglement, which we term $\textit{tomographically-local}$ entanglement and $\textit{tomographically-nonlocal}$ entanglement. We analyze the operational consequences of this distinction, proving that tomographically-nonlocal entanglement is useless for Bell nonlocality, steering, and teleportation, but sufficient for dense coding and perfectly secure data hiding. This framework clarifies the origin of several previously puzzling features of entanglement that arise when tomographic locality fails, as can happen even in quantum theory when one considers fermions or fundamental superselection rules.

Researchers often attribute social media's appeal to its ability to elicit flow experiences of deep absorption and effortless engagement. Yet prolonged use has also been linked to distraction, fatigue, and lower mood. This paradox remains poorly understood, in part because prior studies rely on habitual or one-shot reports that ask participants to directly attribute flow to social media. To address this gap, we conducted a five-day field study with 40 participants, combining objective smartphone app tracking with daily reconstructions of flow-inducing activities. Across 673 reported flow occurrences, participants rarely associated flow with social media (2 percent). Instead, heavier social media use predicted fewer daily flow occurrences. We further examine this relationship through the effects of social media use on fatigue, mood, and motivation. Altogether, our findings suggest that flow and social media may not align as closely as assumed - and might even compete - underscoring the need for further research.

We consider partition functions Z(g) = exp (-g(x))dx where g is a nonnegative polynomial action (a degree-2n form) vanishing only at the origin. Such integrals, known as integral discriminants, appear in statistical mechanics, quantum field theory, and the theory of exponential families. We show that the associated Boltzmann measure d$μ$ = exp(-g(x))dx satisfies a fixed-point property identity relating in a simple manner its degree-2n moments to the coefficients of g. This generalizes familiar identities for the exponential distribution (degree-1) on the positive orthant and the Gaussian measure (degree-2). We further show that g is characterized by three variational principles, including a maximum-entropy principle under scaled moments constraints, extending the Gaussian extremality principle to arbitrary even-degree homogeneous actions. Exploiting these identities in a truncatedmoment numerical scheme (known as the Moment-SOS hierarchy), strengthens the standard semidefinite relaxations, and results in a much faster convergence, thus allowing more efficient approximations of the partition function Z(g) as well as moments of $μ$.

We investigate a concept of passive, vibration-driven locomotion, in which a mechanical system achieves horizontal self-propulsion by resonantly harvesting energy from vertical environmental excitations (e.g. ambient vibrations of underwater pipelines), without a direct propulsive actuation. The system consists of a capsule containing an internal pendulum attached to its base mounted on a vertically vibrating substrate. The underlying locomotion mechanism relies on resonant energy transfer from the vertically vibrating substrate to the internal oscillatory element. Under appropriate forcing conditions and in the presence of asymmetric dissipative interactions, this internal oscillator induces a net unidirectional motion of the capsule. The analysis focuses on regimes of progressive motion arising in the vicinity of parametric resonances. Two asymptotic limits are considered: small-amplitude parametric excitation leading to a (2:1) resonant oscillatory motion of the pendulum, and large-amplitude excitation leading to a (1:1) resonant unidirectional rotational motion of the pendulum. Given the asymmetry of the dissipative force acting on the capsule, both resonant regimes result in a progressive motion of the capsule system. To identify optimal locomotion regimes in both cases, we employ tailored asymptotic approaches based on multi-scale expansions and direct averaging analysis. The resulting slow-flow and averaged-flow models reveal the full bifurcation structure of steady-state solutions associated with forward capsule motion for both low- and high- amplitude excitations. Analytical predictions are shown to be in good agreement with direct numerical simulations of the full capsule-pendulum system.

Many anisotropic layered materials, despite their strong in-plane birefringence, exhibit substantial visible absorption, which severely restricts cavity lengths and hinders the observation of purely birefringence-governed optical phenomena. Here, we realize a birefringence-driven anisotropic optical cavity using $α$-MoO3 flakes, capitalizing on their ultralow optical loss and pronounced in-plane birefringence. Using angle-resolved polarized Raman (ARPR) spectroscopy, we observe a mode-sensitive enhancement of anisotropy, dependent on both flake thickness and Raman shift. A unified model that incorporates the intrinsic Raman tensor, birefringence, and chromatic dispersion accurately reproduces the experimental data, elucidating how cavity resonances at both excitation and scattered wavelengths interact. Within this framework, the intrinsic phonon anisotropy is quantified, providing invaluable insights for accurately predicting ARPR responses and identifying crystallographic orientation. This work provides fundamental insights into birefringence-governed cavities and opens avenues for high-performance birefringent optics and cavity-enhanced anisotropic phenomena.

Symplectic integrators are the established standard for long-term simulations of nearly-integrable Hamiltonian systems due to their preservation of geometric structures. However, they suffer from an inherent limitation: secular phase-shift errors. While the qualitative ''shape'' of invariant tori is preserved, the numerical solution gradually drifts along the torus, leading to a phase-lag accumulation that degrades long-term positional accuracy. Inspired by the Craig-Wayne-Bourgain (CWB) scheme, originally developed as an analytical tool for infinite-dimensional systems, we introduce a numerical operator that incorporates frequency updates into a dimension-enlarged Newton iteration to compute quasi-periodic solutions. Unlike conventional time-stepping integrators, our alternating numerical procedure eliminates phase-lag accumulation by directly solving for instantaneous positions and phase angles. Theoretically, provided sufficient computational resources, the phase error can be reduced arbitrarily, remaining independent of the total integration time. Our algorithm translates the Nash-Moser iteration into a practical numerical framework, marking a significant departure from traditional Kolmogorov-Arnold-Moser (KAM) theory. While KAM provides rigorous existence proofs, its requirement for global Diophantine conditions and the total exclusion of resonant sets render it numerically inaccessible. By employing a ''step-by-step'' exclusion process and incrementally enlarging the dimension, our algorithm resolves irrationality conditions locally. This approach demonstrates that the ''numerical irrationality problem'' is not an intrinsic barrier to computation, offering a constructive, executable alternative to the non-executable nature of global KAM-based methods.

For a graph $G$, a vertex subset is called \emph{$1$-nearly independent} if the subgraph it induces contains exactly one edge. Let $σ_1(G)$ denote the number of such subsets in $G$. In this paper, we study Nordhaus-Gaddum type inequalities for $σ_1$, that is, bounds on the sum $σ_1(G)+σ_1(\overline{G})$, where $\overline{G}$ denotes the complement of $G$. We establish that, for any $n$-vertex graph $G$, we have $σ_1(G)+σ_1(\overline{G})\geq n(n-1)/2,$ with equality if and only if $G$ is either complete or edgeless. We further obtain that among all trees of order $n$, the star $K_{1,n-1}$ uniquely minimises $σ_1(T)+σ_1(\overline{T})$. Finally, we prove that for all graphs of order $n \ge 6$, \[ σ_1(G)+σ_1(\overline{G}) \le \frac{27}{64}\,2^{n} + \frac{1}{2}(n+2)(n-3), \] with equality if and only if $G$ or $\overline{G}$ is isomorphic to $3K_2 \cup \overline{K_{n-6}}$.

Hybrid received signal strength (RSS)-angle of arrival (AoA)-based positioning offers low-cost distance estimation and high-resolution angular measurements. Still, it comes at a cost of inherent nonlinearities, geometry-dependent noise, and suboptimal weighting in conventional linear estimators that might limit accuracy. In this paper, we propose a neural network-based approach using a multilayer perceptron (MLP) to directly map RSS-AoA measurements to 3D positions, capturing nonlinear relationships that are difficult to model with traditional methods. We evaluate the impact of input representation by comparing networks trained on raw measurements versus preprocessed features derived from a linearization method. Simulation results show that the learning-based approach consistently outperforms existing linear methods under RSS noise across all noise levels, and matches or surpasses state-of-the-art performance under increasing AoA noise. Furthermore, preprocessing measurements using the linearization method provides a clear advantage over raw data, demonstrating the benefit of geometry-aware feature extraction.

We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both $E_8\times E_8$ and Spin$(32)/Z_2$ heterotic strings, a pair of a binary code and a set of the corresponding metric, B field, and background gauge field, such that the lattice constructed from the binary code by Construction A coincides with the Narain lattice. We also construct heterotic Narain lattices using codes over $F_3$ and $F_5$ by Construction A${}_C$ and "Construction A${}_g$" with $g=SU(5)$, respectively. As a bi-product, we also clarify the relationship between codes that construct Euclidean even self-dual lattices and NSR-fermions, where the $Z_2$ inversion structure of the generator matrices plays a significant role.

Ring signatures are a powerful primitive that allows a member to sign on behalf of a group, without revealing their identity. Recently, ring signatures have received additional attention as an ingredient for post-quantum deniable authenticated key exchange, e.g., for a post-quantum version of the Signal protocol, employed by virtually all end-to-end-encrypted messenger services. While several ring signature constructions from post-quantum assumptions offer suitable security and efficiency for use in deniable key exchange, they are currently proven secure in the random oracle model (ROM) only, which is insufficient for post-quantum security. In this work, we provide four security reductions in the quantum-accessible random oracle model (QROM) for two generic ring signature constructions: two for the AOS framework and two for a construction paradigm based on ring trapdoors, whose generic backbone we formalize. The two security proofs for AOS ring signatures differ in their requirements on the underlying sigma protocol and their tightness. The two reductions for the ring-trapdoor-based ring signatures exhibit various differences in requirements and the security they provide. We employ the measure-and-reprogram technique, QROM straightline extraction tools based on the compressed oracle, history-free reductions and QROM reprogramming tools. To make use of Rényi divergence properties in the QROM, we study the behavior of quantum algorithms that interact with an oracle whose distribution is based on one of two different distributions over the set of outputs. We provide tight bounds for the statistical distance, show that the Rényi divergence can not be used to replace the entire oracle and provide a workaround.

The Lie theory of non-commutative integrability is used to reconstruct some integrable systems of ordinary differential equations in three dimensional Eucledian space. The Darboux-Brioschi-Halphen system is an example of the Lie integrable system associated with the simple Lie algebra sl(2,R). Other examples are related with solvable three dimensional real Lie algebras of Bianchi B class.

In this paper, we consider the existence, multiplicity and nonexistence of solutions for the following equation \begin{equation*} \begin{cases} \begin{aligned} &-Δu+ωu=μu^{p-1}+u^{q-1},~ u>0 \quad &&\text { in } Ω, \\ &u=0 &&\text { on } \partialΩ, \\ \end{aligned} \end{cases} \end{equation*} with prescribed $L^2$-norm $\|u\|_2^2=ρ$, where $N\ge 1$, $ρ>0$, $μ\in \mathbb{R}$, $1<p\le q$, and $Ω\subset\mathbb{R}^N$ is a bounded smooth domain. The parameter $ω\in\mathbb{R}$ arises as a Lagrange multiplier. Firstly, when $2<p\le q\le \frac{2N}{(N-2)^+}$ and $ρ$ is small, we establish the existence of a local minimizer of energy. Furthermore, when $μ\ge 0$ and $Ω$ is a star-shaped domain, using the monotonicity trick and the Pohozaev identity, we show that there exists a second solution which is of mountain pass type. Secondly, when $μ\ge 0$, $N\ge 3$, $1<p\le 2$, $q\ge \max\left\{\frac{2N}{N-2}, 3\right\}$ and $Ω$ is a convex domain, using the moving-plane method, we prove the nonexistence of normalized solutions for large $ρ$. Finally, when $μ=0$, $N\ge 3$, $q=\frac{2N}{N-2}$ and $Ω$ is a ball, we give a dichotomy result of normalized solutions for the Brézis-Nirenberg problem by continuation arguments.

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader-follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

We study nonparametric maximum likelihood estimation of probability densities under a total variation (TV) type penalty, sectional variation norm (also named as Hardy-Krause variation). TV regularization has a long history in regression and density estimation, including results on $L^2$ and KL divergence convergence rates. Here, we revisit this task using the Highly Adaptive Lasso (HAL) framework. We formulate a HAL-based maximum likelihood estimator (HAL-MLE) using the log-spline link function from \citet{kooperberg1992logspline}, and show that in the univariate setting the bounded sectional variation norm assumption underlying HAL coincides with the classical bounded TV assumption. This equivalence directly connects HAL-MLE to existing TV-penalized approaches such as local adaptive splines \citep{mammen1997locally}. We establish three new theoretical results: (i) the univariate HAL-MLE is asymptotically linear, (ii) it admits pointwise asymptotic normality, and (iii) it achieves uniform convergence at rate $n^{-(k+1)/(2k+3)}$ up to logarithmic factors for the smoothness order $k \geq 1$. These results extend existing results from \citet{van2017uniform}, which previously guaranteed only uniform consistency without rates when $k=0$. We will include the uniform convergence for general dimension $d$ in the follow-up work of this paper. The intention of this paper is to provide a unified framework for the TV-penalized density estimation methods, and to connect the HAL-MLE to the existing TV-penalized methods in the univariate case, despite that the general HAL-MLE is defined for multivariate cases.

In this paper, we investigate the existence and concentration of solutions to a $(p,N)$-Laplace equation in $\mathbb{R}^N$ involving a discontinuous nonlinearity and critical exponential growth. To establish the existence of solutions, we employ a penalization technique in the sense of Del Pino and Felmer adapted to a locally Lipschitz functional. Furthermore, by combining variational methods with Moser-type iteration techniques, we obtain the concentration behavior of the solutions. Our results contribute to the study of nonlinear elliptic problems with irregular nonlinearities and critical growth phenomena.

The melting of metallic nanoparticles is governed by surface pre-melting, a phenomenon traditionally modeled as the isotropic growth of a uniform liquid shell. Challenging this classical view, we report facet-dependent surface pre-melting in hexagonal close-packed Co nanoparticles, arising from the structural heterogeneity of the nanoparticle surface. Characterizing melting in molecular dynamics simulations (500 to 6000 atoms), we observe the onset of surface mobility, starting as low as $0.2\times T_{M,\infty}$ (the bulk melting point), driven by the early disordering of stepped $\{01\bar{1}1\}$ facets. We found that these facets consistently melt at temperatures nearly 200 Kelvin lower than flat $\{0001\}$ facets, regardless of particle size, and relate facets melting temperatures to the nanoparticle size via a 2D extension of the Gibbs-Thomson relation. We determine a critical liquid layer thickness that triggers the melting of the entire nanoparticle, which is found to be size-dependent. Our results confirm the recent experimental observation of the surface pre-melting effect, and extend it to anisotropic particles with different facet orientations.

We show that the generating series of the number of pairs of geodesics on a compact Shimura curve with given discriminants and intersection angle are coefficients of a non-holomorphic Siegel modular form, a theta lift of the constant function. This retrieves and generalizes counting results of Rickards via the Siegel-Weil formula. More generally, we study the genus two theta lift of Maass forms on this Shimura curve and prove a Fourier-Taylor expansion in terms of some generalized Whittaker functions. We also provide a geometric interpretation of all Fourier coefficients of these theta lifts in terms of averages of geodesic Taylor coefficients over special cycles.

Photonic devices depend critically on the dielectric materials from which they are made, with higher refractive indices and lower absorption losses enabling new functionalities and higher performance. However, these two material properties are intrinsically linked through the empirical Moss rule, which states that the refractive index of a dielectric decreases as its band gap energy increases. Materials that surpass this rule, termed super-Mossian dielectrics, combine large refractive indices with wide optical transparency and are therefore ideal candidates for advanced photonic applications. This Review surveys the expanding landscape of high-index dielectric and semiconductor materials, with a particular focus on those that surpass the Moss rule. We discuss how electronic band structures with a large joint density of states near the band edge give rise to super-Mossian behavior and how first-principles computational screening can accelerate their discovery. Finally, we establish how the refractive index sets the performance limits of nanoresonators, waveguides, and metasurfaces, highlighting super-Mossian dielectrics as a promising route toward the next performance leap in photonic technologies.

A pinching antennas (PAs)-aided integrated sensing and multicast communication framework is proposed. In this framework, the communication performance is measured by the multicast rate considering max-min fairness. Moreover, the sensing performance is quantified by the Bayesian Cramér-Rao bound (BCRB), where a Gauss-Hermite quadrature-based approach is proposed to compute the Bayesian Fisher information matrix. Based on these metrics, PA placement is optimized under three criteria: communications-centric (C-C), sensing-centric (S-C), and Pareto-optimal designs. These designs are investigated in two scenarios: the single-PA case and the multi-PA case. 1) For the single-PA case, a closed-form solution is derived for the location of the C-C transmit PA, while the S-C design yields optimal transmit and receive PA placements that are symmetric about the target location. Leveraging this geometric insight, the Pareto-optimal design is solved by enforcing this PA placement symmetry, thereby reducing the joint transmit and receive PA placement to the transmit PA optimization. 2) For the general multi-PA case, the PA placements constitute a highly non-convex optimization problem. To solve this, an element-wise alternating optimization-based method is proposed to sequentially optimize all PA placements for the S-C design, and is further incorporated into an augmented Lagrangian (AL) framework and a rate-profile formulation to solve the C-C and Pareto-optimal design problems, respectively. Numerical results show that: i) PASS substantially outperforms fixed-antenna baselines in both multicast rate and sensing accuracy; ii) the multicasting gain becomes more pronounced as the user density increases; and iii) the sensing accuracy improves with the number of deployed PAs.

Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality and matroid constraints, where greedy algorithms admit strong guarantees, the supermodular constraint regime remains poorly understood -- guarantees for greedy methods and other efficient algorithmic paradigms are largely open. We study this family of fundamental optimization problems under an upper-bound constraint on a supermodular cost function with curvature parameter $γ$. Our notion of supermodular curvature is less restrictive than prior definitions, substantially expanding the class of admissible cost functions. We show that our greedy algorithm that iteratively includes elements maximizing the ratio of the objective and constraint functions, achieves a $\left(1 - e^{-(1-γ)}\right)$-approximation before stopping. We prove that this approximation is indeed tight for this algorithm. Further, if the objective function has a submodular curvature $c$, then we show that the bound further improves to $\left(1 - (1- (1-c)(1-γ))^{1/(1-c)}\right)$, which can be further improved by continuing to violate the constraint. Finally, we show that the Greedy-Ratio-Marginal in conjunction with binary search leads to a bicriteria approximation for the dual problem -- minimizing a supermodular function under a lower bound constraint on a submodular function. We conduct a number of experiments on a simulation of LLM agents debating over multiple rounds -- the task is to select a subset of agents to maximize correctly answered questions. Our algorithm outperforms all other greedy heuristics, and on smaller problems, it achieves the same performance as the optimal set found by exhaustive search.

Accurate estimation of propagation characteristics of coronal mass ejections (CMEs) is crucial for predicting their geoeffectiveness. Stereoscopic techniques to study the kinematics of CMEs generally have been carried out using remote sensing observations from three viewpoints, i.e. STEREO-A, STEREO-B, and SOHO. Since the loss of STEREO-B in 2014, stereoscopic reconstruction of CMEs has been restricted to the observations from only two viewpoints, i.e., STEREO-A and SOHO. When the angle of separation between STEREO-A and SOHO is small, it leads to larger uncertainties in the CME kinematics derived using stereoscopic techniques. In this paper, we demonstrate how this limitation can be addressed and how uncertainties in the estimation of CME kinematics and propagation direction can be reduced. For this purpose, we selected the CME of April 21, 2023, which was observed by two spacecraft, i.e. STEREO-A and SOHO, separated by a small 10 degree angle. Using the Graduated Cylindrical Shell (GCS) model on the remote-sensing observations near the Sun and the Advanced Drag-Based Model (ADBM) in the heliosphere, we estimated the arrival time of the CME at different locations in the heliosphere and compared it with the actual arrival time obtained from the in-situ measurements taken by three spacecraft, BepiColombo, STEREO-A and Wind. Our analysis reveals a directional uncertainty of approx 20 degree from observations from two viewpoints. These uncertainties significantly affect the arrival-time prediction of the CME. We consider the actual chronology of CME arrival times at STEREO-A and Wind as critical parameters to constrain the direction of propagation, which serves as a key input in the ADBM. The chronology of arrival of the CME ejecta at STEREO-A, which is 4.5 hrs earlier than at Wind, proved essential for resolving directional ambiguities in the GCS reconstruction model

Mobile networks require safe optimization to adapt to changing conditions in traffic demand and signal transmission quality, in addition to improving service performance metrics. With the increasing complexity of emerging mobile networks, traditional parameter tuning methods become too conservative or complex to evaluate. For the first time, we apply safe Bayesian optimization to mobile networks. Moreover, we develop a new safe collaborative optimization algorithm called CoSBO, leveraging information from multiple optimization tasks in the network and considering multiple safety constraints. The resulting algorithm is capable of safely tuning the network parameter online with very few iterations. We demonstrate that the proposed method improves sample efficiency in the early stages of the optimization process by comparing it against the SafeOpt-MC algorithm in a mobile network scenario.

Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

Symmetry offers a useful approach to unfold the intertwined degrees of freedom. Thus it paves the way to resolve coexisting quantum orders into distinct symmetry sectors. Motivated by the recent observation of superconductivity in nano-flaked IrTe$_2$, we investigate the superconductivity in strain-stabilized two-dimensional (2D) limit of IrTe$_2$ by combining density-functional theory with mean-field solution of spin-fluctuation mediated pairing interaction on a symmetry-constrained ${\bf k}\cdot{\bf p}$ model. The spin-orbit coupled band structure shows $Γ$-centred Fermi sheets with coexistence of band-selective Rashba-like (in-plane) and Ising-like (out-of-plane) superconductivity. Remarkably, the superconducting gaps are odd in spin, orbital, and momentum channels despite the presence of global inversion symmetry. Fermi surface topologies and little-group symmetry enforce distinct irreducible representations to the Rashba and Ising channels, forbidding their mixing. Our findings open up a symmetry-based route to multichannel superconductivity in 2D transition-metal dichalcogenides with unique functionalities.

We report multiwavelength observations of the highly offset (~22.4 kpc) SN 2024abvb, the sixth Type Icn supernova to date. With a peak magnitude of Mr = -19.55 +/- 0.11 mag, it is among the most luminous in the existing sample and shows similar colours and decline rates to other SNe Icn. The early optical spectra show a blue continuum with narrow C II features (vFWHM ~ 2000 km s^-1), consistent with a typical wind velocity of a Wolf-Rayet star. The absence of C III lambda 5696 emission at the time of explosion is consistent with a Type Ibn supernova; however, the lack of narrow He lines in both the optical and near-infrared spectra supports a SNe Icn classification. Unlike the majority of SNe Icn, we do not detect broad features in the late-time (7-21 days relative to o-band peak) spectral phase of SN 2024abvb. Semi-analytical modelling of the light curves shows that it can be reproduced by ~2.6 Msun of SN ejecta interacting with ~0.3 Msun of circumstellar material (CSM), both larger than other SNe Icn but consistent with rapidly evolving SNe Ibn. The metallicity at the SN location is significantly lower than the global metallicity of its host galaxy, suggesting that line-driven mass loss required to strip the progenitor of its H and He envelopes was likely inefficient. We estimate the star-formation-rate history at the location of SN 2024abvb and find that it lies at the bottom ~5th percentile among SESNe hosts, inconsistent with a Wolf-Rayet progenitor. Based on its spectral features, local and host environment properties, and host-galaxy offset, we favour an 8-10 Msun star stripped by a compact companion as the progenitor, with a sufficient runaway velocity to reach the observed offset.

In this paper, we study $6$-dimensional GKM manifolds with $4$ fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex projective space $\mathbb{C} P^3$ with standard complex structure (P2) blow up of $S^6$ at a fixed point, diffeomorphic to $\mathbb{C} P^3$ (P3) $\mathbb{C} P^3$ as the homogeneous space $\mathrm{Sp}(2)/(\mathrm{U}(1) \times \mathrm{Sp}(1))$ with non-standard almost complex structure (Q1) complex quadric $Q_3$ with standard complex structure (Q2) blow up of $S^6$ along isotropy $2$-sphere, diffeomorphic to $Q_3$ (S) $S^2 \times S^4$, obtained as equivariant gluing along orbits of two $S^6$'s

We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=θ(t) X_tdt+ εdZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$ where $\{Z^{q,H}_t, t \geq 0\}$ is a Hermite process with known order $q$ and known self-similarity parameter $H \in (\frac{1}{2},1).$ We investigate the asymptotic behaviour of the estimator of the unknown function $θ(t)$ as $ε\rightarrow 0.$

We investigate space-time trade-offs for population protocols in sparse interaction graphs. In complete interaction graphs, optimal space-time trade-offs are known for the leader election and exact majority problems. However, it has remained open if other graph families exhibit similar space-time complexity trade-offs, as existing lower bound techniques do not extend beyond highly dense graphs. In this work, we show that -- unlike in complete graphs -- population protocols on bounded-degree trees do not exhibit significant asymptotic space-time trade-offs for leader election and exact majority. For these problems, we give constant-space protocols that have near-optimal worst-case expected stabilisation time. These new protocols achieve a linear speed-up compared to the state-of-the-art. Our results are based on two novel protocols, which we believe are of independent interest. First, we give a new fast self-stabilising 2-hop colouring protocol for general interaction graphs, whose stabilisation time we bound using a stochastic drift argument. Second, we give a self-stabilising tree orientation algorithm that builds a rooted tree in optimal time on any tree. As a consequence, we can use simple constant-state protocols designed for directed trees to solve leader election and exact majority fast. For example, we show that ``directed'' annihilation dynamics solve exact majority in $O(n^2 \log n)$ steps on directed trees.