We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

Let $X$ be a metric space and $BCl(X)$ the collection of nonempty bounded closed subsets of $X$. We show that Hausdorff distance $d_H$ belongs to a specific family of real-valued distances on $BCl(X)$, each of which can be expressed as the composition $μ\circ d_{sv}$ of a topology inducing set-valued function $d_{sv}:BCl(X)^2\rightarrow \mathcal{P}(Z)$ and a real-valued set-function $μ:Σ\subset\mathcal{P}(Z)\rightarrow\mathbb{R}$. With this observation, we construct several associated classes of inter-set distances, called set-valued metrics and generalized Hausdorff distances. Our constructions are both explicit and adaptable, and the resulting distance classes are expected to cover most practical applications involving distance between sets.

The basic observables in cosmology are known as in-in correlators. Recent calculations have revealed that in-in correlators in four dimensional de Sitter space exhibit hidden simplicity stemming from a close relation to scattering amplitudes in flat space. In this paper we explain how to make this property manifest by dressing flat space Feynman diagrams with certain auxiliary propagators. These dressing rules are derived for conformally coupled and massless scalar theories and we show that they reproduce the same infrared divergences predicted by the Schwinger-Keldysh formalism.

Current superconducting quantum computing platforms face significant scaling challenges, as individual signal lines are required for control of each qubit. This wiring overhead is a result of the low level of integration between control electronics at room temperature and qubits operating at millikelvin temperatures, which raise serious doubts among technologists about whether utility-scale quantum computers can be built. A promising alternative is to utilize cryogenic, superconducting digital control electronics that coexist with qubits. Here, we report the first multi-qubit system integrating this technology. The system utilizes digital demultiplexing, breaking the linear scaling of control lines to number of qubits. We also demonstrate single-qubit fidelities above 99%, and up to 99.9%. This work is a critical step forward in realizing highly scalable chip-based quantum computers.

For some discretely observed path of oscillating Brownian motion with level of self-organized criticality $ρ_0$, we prove in the infill asymptotics that the MLE is $n$-consistent, where $n$ denotes the sample size, and derive its limit distribution with respect to stable convergence. As the transition density of this homogeneous Markov process is not even continuous in $ρ_0$, the analysis is highly non-standard. Therefore, interesting and somewhat unexpected phenomena occur: The likelihood function splits into several components, each of them contributing very differently depending on how close the argument $ρ$ is to $ρ_0$. Correspondingly, the MLE is successively excluded to lay outside a compact set, a $1/\sqrt{n}$-neighborhood and finally a $1/n$-neighborhood of $ρ_0$ asymptotically. The crucial argument to derive the stable convergence is to exploit the semimartingale structure of the sequential suitably rescaled local log-likelihood function (as a process in time). Both sequentially and as a process in $ρ$, it exhibits a bivariate Poissonian behavior in the stable limit with its intensity being a multiple of the local time at $ρ_0$.

The site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while mitigating the geometric complexities of traditional bond-decorated models. The unconventional frustration and physics are clarified by exactly mapping the 1D site-decorated Ising model in a magnetic field onto a zero-field bond-decorated $J_1$-$J_2$ Ising model with conventional geometrical frustration. Furthermore, although higher-dimensional Ising models in an external field remain unsolved exactly, an exact solution for a spin-reversal transition -- driven by an exotic, hidden half-ice, half-fire state induced by site decoration -- is derived. This transition, triggered by a slight variation in temperature or magnetic field -- without changing its direction -- even in the weak-field limit, offers a promising route toward energy-efficient applications such as data storage and processing. The results suggest that site decoration offers an avenue for materials and device design, particularly in systems such as mixed $d$-$f$ compounds, optical lattices, and neural networks, calling for further studies with site-decorated Heisenberg models. In addition, the site-decorated model offers a rigorous test ground for artificial intelligence (AI) in science, as the analytic derivation of the present results was not only validated but also improved by a general-purpose large language model, inspiring the use of AI as scientific discoverer.

Open quantum systems are powerful effective descriptions of quantum systems interacting with their environments. Studying changes of Fock state probabilities can be intricate in this context since the prevailing description of open quantum dynamics is by master equations of the systems' reduced density matrices, which usually requires finding solutions for a set of complicated coupled differential equations. In this article, we show that such problems can be circumvented by employing a recently developed path integral-based method for directly computing reduced density matrices in scalar quantum field theory. For this purpose, we consider a real scalar field $ϕ$ as an open system interacting via a $λχ^2ϕ^2$-term with an environment comprising another real scalar field $χ$ that has a finite temperature. In particular, we investigate how the probabilities for observing the vacuum or two-particle states change over time if there were initial correlations of these Fock states. Subsequently, we apply our resulting expressions to a neutrino toy model. We show that, within our model, lighter neutrino masses would lead to a stronger distortion of the observable number of particles due to the interaction with the environment after the initial production process.

Matsuki and Oshima introduced the notion of clans, which are incomplete matchings with positive or negative signs on isolated vertices. They discovered that clans parametrise $K$-orbits in the flag varieties for classical linear groups, where $K$ is a fixed point subgroup of an involution in the same classical linear group. In this work we investigate the affine version of these orbits. For a field $\Bbbk$ with characteristic not equal to two, we construct an explicit bijection between the $\textsf{GL}_p(\Bbbk(\hspace{-0.5mm}(t)\hspace{-0.5mm})) \times \textsf{GL}_q(\Bbbk(\hspace{-0.5mm}(t)\hspace{-0.5mm}))$-orbits in the affine flag variety and certain objects called affine $(p,q)$-clans. These affine $(p,q)$-clans can be concretely interpreted as involutions in the affine permutation group with positive or negative signs on fixed points.

The modern Everett interpretation of quantum mechanics describes an emergent multiverse. The goal of this paper is to provide a perspicuous characterisation of how the multiverse emerges making use of a recent account of (weak) ontological emergence. This will be cashed out with a case study that identifies decoherence as the mechanism for emergence. The greater metaphysical clarity enables the rebuttal of critiques due to Baker (2007) and Dawid and Thébault (2015) that cast the emergent multiverse ontology as incoherent; responses are also offered to challenges to the Everettian approach from Maudlin (2010) and Monton (2013).

We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions, modeled by homogeneous external Dirichlet data. We provide a range of results on the existence and nonexistence of solutions tied to the spectral properties of the ambient space, corresponding to either survival or extinction of the population. We also discuss how the possible presence of nonlocal phenomena of concentration and diffusion affect the endurance or disappearance of the population. In particular, we give examples in which both classical and anomalous diffusion leads to the extinction of the species, while the presence of an arbitrarily small concentration pattern enables survival.

We study the speed of growth of iterates of outer automorphisms of virtually special groups, in the Haglund-Wise sense. We show that each automorphism grows either polynomially or exponentially, and that its stretch factor is an algebraic integer. For coarse-median preserving automorphisms, we show that there are only finitely many growth rates and we construct an analogue of the Nielsen-Thurston decomposition of surface homeomorphisms. These results are new already for right-angled Artin groups. However, even in this particular case, the proof requires studying automorphisms of arbitrary special groups in an essential way. As results of independent interest, we show that special groups are accessible over centralisers, and we construct a canonical JSJ decomposition over centralisers. We also prove that, for any virtually special group $G$, the outer automorphism group ${\rm Out}(G)$ is boundary amenable, satisfies the Tits alternative, and has finite virtual cohomological dimension.

Integrating 2D materials onto on-chip photonic devices holds significant potential for nonlinear frequency conversion across various applications. The lack of inversion symmetry in monolayers of transition metal dichalcogenides (TMDs), e.g., MoS$_2$, is particularly attractive for enabling nonlinear phenomena based on $χ^{(2)}$ in silicon-based photonic devices incorporated with these materials, which has been previously demonstrated. However, reports have largely overlooked the need to consider, in the nonlinear modal interaction, both the tensorial nature of the TMD's second-order susceptibility and the full vectorial nature of the electromagnetic fields. In this work, we investigate second-harmonic generation (SHG) in silicon nitride (SiN) waveguides integrated with a monolayer of MoS$_2$. We experimentally observed an enhancement in SHG in MoS$_2$-loaded waveguides compared to those without the monolayer. Notably, this enhancement occurred even when the dominant electric field component of the pump and/or signal mode was orthogonal to the TMD plane, highlighting co- and cross-polarized SHG interactions. This phenomenon cannot be predicted by the traditionally used scalar models. By taking into account the full vectorial and tensorial natures of the problem, we then designed a waveguide in which a TE pump mode is phase-matched to a TM second-harmonic mode. With a single 110-$μ$m-long MoS$_2$ flake, we experimentally achieved $14\times$ frequency conversion enhancement relative to the non-phase-matched case and $220\times$ enhancement relative to free-space (normal-incidence) excitation. Our work, thus, introduces fundamental guidelines for the design and optimization of nonlinear silicon-photonic devices based on 2D-material hybrid integration. These guidelines are material independent and may lead to significant further conversion efficiency enhancement.

We consider a sender-receiver game in which the receiver's action is binary and the sender's preferences are state-independent. The state is multidimensional. The receiver can select one dimension of the state to check (i.e., observe) before choosing his action. We identify a class of influential equilibria in which the sender's message reveals which components of the state are highest, and the receiver selects one of these components to check. The sender can benefit from communication if and only if she prefers one of these equilibria to the no-communication outcome. Similar equilibria exist when the receiver can check multiple dimensions.

A convenient way to represent quantum optical states is through the quadrature basis of single-modes of the field. This framework provides intuitive definitions for quasi-classical states, their phase-space representations, and enables the definition of a universal gate set. In this widely adopted representation of quantum optics, most pure states consist of coherent superpositions of photon-number states. However, this approach neglects the particle-number superselection rule - which prohibits coherence between states of differing photon numbers - and implicitly assumes a phase reference. We adopt a representation of quantum optical states that respects the superselection rule and revisit key tools and results in quantum optics and information encoding within quantum optics. This approach preserves the intuitive aspects of the traditional quadrature representation while unifying insights from quantum optics with those from symmetric spin-like and angular momentum systems. More than just an alternative representation, we show that a superselection rule-compliant framework provides a unified formalism for all bosonic encodings, from single-photon to continuous-variable encodings. This perspective allows for a precise characterization of the roles of Gaussian and non-Gaussian resources, as well as the interplay between modes and states in quantum universality and potential computational advantage.

Clinical trial design ensures that primary analysis outcomes have strong statistical properties. However, mainstream methodology for randomised study design does not establish a formal link between statistical and clinical significance. This paper contributes to bridging this gap by calibrating the operational characteristics of primary trial outcomes to establishing clinical equipoise imbalance. Common late phase designs are shown to provide at least 90% evidence of equipoise imbalance. Designs carrying 95% power at 5% false positive rate are shown to demonstrate 95% evidence of equipoise imbalance, providing an operational definition of a robustly powered study. Equipoise calibration is applied to design of clinical development plans comprising phase 2 and phase 3 studies using standard oncology endpoints. Commonly used power and false positive error rates are shown to provide strong equipoise imbalance when positive outcomes are observed in both phase 2 and phase 3. Establishing strong equipoise imbalance based on inconsistent outcomes of phase 2 and phase 3 studies is shown to require large sample sizes unlikely to be associated with clinically meaningful effect sizes.

Out-of-hospital cardiac arrest (OHCA) survival rates remain extremely low due to challenges in the timely accessibility of medical devices. Therefore, effective deployment of automated external defibrillators (AED) can significantly increase survival rates. Precise and interpretable predictions of OHCA occurrences provide a solid foundation for efficient and robust AED deployment optimization. This study develops a novel learn-then-optimize approach, integrating three key components: a machine learning prediction model, SHAP-based interpretable analytics, and a SHAP-guided integer programming (SIP) model. The machine learning model is trained utilizing only geographic data as inputs to overcome data availability obstacles, and its strong predictive performance validates the feasibility of interpretation. Furthermore, the SHAP model elaborates on the contribution of each geographic feature to the OHCA occurrences. Finally, an integer programming model is formulated for optimizing AED deployment, incorporating SHAP-weighted OHCA densities. Various numerical experiments are conducted across different settings. Based on comparative and sensitive analysis, the optimization effect of our approach is verified and valuable insights are derived to provide substantial support for theoretical extension and practical implementation.

Scintillation, the process of converting high-energy radiation to detectable visible light, is pivotal in advanced technologies spanning from medical diagnostics to fundamental scientific research. Despite significant advancements toward faster and more efficient scintillators, there remains a fundamental limit arising from the intrinsic properties of scintillating materials. The scintillation process culminates in spontaneous emission of visible light, which is restricted in rate by the oscillator strength of individual emission centers. Here, we observe a novel collective emission phenomenon under X-ray excitation, breaking this limit and accelerating the emission. Our observation reveals that strong interactions between simultaneously excited coupled perovskite quantum dots can create collective radioluminescence. This effect is characterized by a spectral shift and an enhanced rate of emission, with an average lifetime of 230 ps, 14 times faster than their room temperature spontaneous emission. It has been established that such quantum dots exhibit superfluorescence under UV excitation. However, X-ray superfluorescence is inherently different, as each high-energy photon creates multiple synchronized excitation events, triggered by a photoelectron and resulting in even faster emission rates, a larger spectral shift, and a broader spectrum. This observation is consistent with a quantum-optical analysis explaining both the UV-driven and X-ray-driven effects. We use a Hanbury-Brown-Twiss g^(2) (τ) setup to analyze the temperature-dependent temporal response of these scintillators. Collective radioluminescence breaks the limit of scintillation lifetime based on spontaneous emission and could dramatically improve time-of-flight detector performance, introducing quantum enhancements to scintillation science.

We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical results characterising the set of non-falsified parameters consistent with energy-bounded disturbances. We derive a semidefinite program which computes an exploration strategy that guarantees a desired accuracy of the parameter estimate. This design is based on sufficient conditions on the spectral content of the exploration data that robustly account for initial parametric uncertainty. Finally, we highlight the applicability of the exploration strategy through a numerical example involving a nonlinear system.

Near a gravitating compact object, massive particles traveling along timelike geodesics are gravitationally deflected similarly to light. In this paper, we study the deflection angles of these particles in the strong deflection limit. This analytical approximation applies when particles in unbound orbits approach the compact object very closely, circle around it at a radius close to that of the unstable circular orbit, and eventually escape. While previous studies have provided results for particular metrics, we offer a general solution applicable to any static, spherically symmetric and asymptotically flat spacetime. After briefly reviewing the exact expression for the deflection angle of massive particles, we present a strong deflection limit analysis for this general case. The developed formulas are then applied to three particular metrics: Schwarzschild, Reissner-Nordström and Janis-Newman-Winicour.

Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization, and growth of entanglement. The phenomenology of dynamical freezing, whereby a translationally invariant many-body system exhibits emergent conservation laws and a slow growth of entanglement entropy at certain fixed ratios of a drive amplitude and frequency, presents a novel paradigm for retaining memory of an initial state upto late times. Previous studies of dynamical freezing have largely been restricted to a high-frequency Floquet-Magnus expansion, and numerical exact diagonalization, which are unable to capture the slow approach to thermalization (or lack thereof) in a systematic fashion. By employing Floquet flow-renormalization, where the time-dependent part of the Hamiltonian is gradually decoupled from the effective Hamiltonian using a sequence of unitary transformations, we unveil the universal approach to dynamical freezing and beyond, at asymptotically late times. We analyze the fixed-point behavior associated with the flow-renormalization at and near freezing using both exact-diagonalization and tensor-network based methods, and contrast the results with conventional prethermal phenomenon. For a generic non-integrable spin Hamiltonian with a periodic cosine wave drive, the flow approaches an unstable fixed point with an approximate emergent symmetry. We observe that at freezing the thermalization timescales are delayed compared to away from freezing, and the flow trajectory undergoes a series of instanton events. Our numerical results are supported by analytical solutions to the flow equations.

In this paper, we study the past asymptotics of $(2+1)$-dimensional solutions to the Einstein scalar-field Vlasov system which are close to Friedman-Lemaître-Robertson-Walker spacetimes on an initial hypersurface diffeomorphic to a closed orientable surface $M$ of arbitrary genus. We prove that such solutions are past causally geodesically incomplete, form a curvature singularity and exhibit stable Kretschmann scalar blow-up in the contracting direction. In particular, the spacetime is $C^2$-inextendible towards the past where causal geodesics become incomplete. Moreover, we show that geometry and matter are asymptotically velocity term dominated toward the past, remaining close to their background counterparts. When viewed on the co-mass shell, the Vlasov distribution in particular converges to a limiting distribution on the Big Bang hypersurface, while asymptotics of the spatial metric lead to slight degeneracies when trying to control the components of the Vlasov energy-momentum tensor. These also manifest when viewing the distribution function on the mass shell, where velocities generally approach a smooth one-dimensional subbundle of the tangent bundle, leading the distribution to become highly anisotropic, when viewed in terms of the geometry induced by the constant curvature spatial reference metric. Compared to previous results in higher dimensions, in particular [FU25b], inhomogeneous terms in the wave and Vlasov equations factor in more strongly in our setting, which a priori creates additional hurdles at high orders while largely keeping the quiescent system intact. As a corollary, our main result shows that the Strong Cosmic Censorship conjecture holds for certain polarized $U(1)$-symmetric solutions to the Einstein vacuum equations that emanate from a spatial hypersurface diffeomorphic to $M\times\mathbb{S}^1$.

As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to non-graph algorithms, numerous graph-based methodologies benefited from the strong power of graphs for representing high-dimensional and non-Euclidean data. In the field of Graph Signal Processing (GSP), analogies of classical signal processing concepts, such as shifting, convolution, filtering, and transformations are developed. However, many GSP techniques usually postulate the graph is static in both signal and typology. This assumption hinders the effectiveness of GSP methodologies as the assumption ignores the time-varying properties in numerous real-world systems. For example, in the traffic network, the signal on each node varies over time and contains underlying temporal correlation and patterns worthy of analysis. To tackle this challenge, more and more work are being done recently to investigate the processing of time-varying graph signals. They cope with time-varying challenges from three main directions: 1) graph time-spectral filtering, 2) multi-variate time-series forecasting, and 3) spatiotemporal graph data mining by neural networks, where non-negligible progress has been achieved. Despite the success of signal processing and learning over time-varying graphs, there is no survey to compare and conclude the current methodology for GSP and graph learning. To compensate for this, in this paper, we aim to review the development and recent progress on signal processing and learning over time-varying graphs, and compare their advantages and disadvantages from both the methodological and experimental side, to outline the challenges and potential research directions for future research.

It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations of quantum physics and quantum computing. A variety of symmetry postulates was introduced and studied in this framework, including the transitivity of the automorphism group (1) on the pure states, (2) on the pairs of orthogonal pure states [these pairs are called 2-frames] and (3) on any frames of the same size. The second postulate is Müller and Ududec's bit symmetry, which they motivate by quantum computational needs. Here we explore these three postulates in the transition probability framework, which is more specific than the GPTs since the existence of the transition probabilities for the quantum logical atoms is presupposed either directly or indirectly via a certain geometric property of the state space. This property for compact convex sets was introduced by the author in a recent paper. We show that bit symmetry implicates the symmetry of the transition probabilities between the atoms. Using a result by Barnum and Hilgert, we can then conclude that the third rather strong symmetry postulate rules out all models but the classical cases and the simple Euclidean Jordan algebras.

We provide a proof of the BRST Noether 1.5th theorem, conjectured in [JHEP 10 (2024) 055], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any BRST invariant gauge fixed Lagrangian decomposes on-shell into a sum of a BRST-exact term and a corner term that defines Noether charges. This extends the holographic consequences of Noether's second theorem to gauge fixed theories and, in particular, offers a universal gauge independent Lagrangian derivation of the invariance of the S-matrix under asymptotic symmetries. Furthermore, we show that these corner Noether charges are inherently non-integrable. To address this non-integrability, we introduce a novel charge bracket that accounts for potential symplectic flux and anomalies, providing an honest canonical representation of the asymptotic symmetry algebra. We also highlight a general origin of a BRST cocycle associated with asymptotic symmetries.

Phase selection design for reconfigurable intelligent surfaces (RISs) is a significant research challenge, as a closed-form optimal solution for a multi-user (MU) system is believed to be intractable. While existing methods achieve strong near-optimal performance, they typically entail high computational complexity. In this work, we take a different approach and propose a practical method that achieves competitive performance while substantially reducing computational complexity. To do so, we consider a RIS divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) for the proposed subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over SD, which increases as the number of RIS elements increases. The SD is significantly simpler than the lowest complexity MU method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.

Backdoor watermarking has emerged as the predominant approach for protecting public datasets, enabling dataset ownership verification (DOV) through embedded triggers that induce predefined model behaviors. While existing works assume that DOV results can serve as reliable evidence for copyright infringement claims, we argue that this assumption is fundamentally flawed. In this paper, we expose critical vulnerabilities in current backdoor watermarking schemes by demonstrating that attackers can forge watermarks that are statistically indistinguishable from the original ones, thereby evading infringement allegations. Specifically, we propose a Forged Watermark Generator (FW-Gen), a lightweight variational autoencoder-based framework that generates forged watermarks preserving the statistical properties of original watermarks while exhibiting distinct visual patterns. Our attack operates under a realistic threat model where an accused attacker, upon receiving an infringement claim, extracts watermark information from the protected dataset and produces counterfeit evidence to refute the allegation. Extensive experiments across six backdoor watermarking methods, two benchmark datasets, and two model architectures demonstrate that forged watermarks achieve equivalent or superior statistical significance in hypothesis testing compared to original watermarks. These findings reveal that current DOV mechanisms are insufficient as standalone evidence for copyright disputes and call for more robust dataset protection schemes.

Silicon Photonics-based AI Accelerators (SPAAs) have been considered as promising AI accelerators achieving high energy efficiency and low latency. While many researchers focus on improving SPAAs' energy efficiency and latency, their physical security has only recently received attention. While it is essential to deliver strong optical neural network inferencing approaches, their success and adoption are predicated on their ability to deliver a secure execution environment. Towards this end, this paper proposes PrometheusFree, an optical neural network framework that is capable of concurrent detection of laser fault injection attacks. This paper first presents an illustrative threat of laser fault injection attacks on SPAAs, capable of subjecting the optical neural network to misclassifications. The threat then is addressed in this paper by developing techniques for concurrent detection of the laser fault injection attacks. Furthermore, this paper introduces a novel application of Wavelength Division Perturbation (WDP) technique where wavelength-dependent Vector Matrix Multiplication (VMM) results are utilized to boost fault attack detection accuracy. Simulation results show that PrometheusFree achieves over 96% attack-caused misprediction recall as the use of the WDP technique squashes the attack success rate by 38.6% on average. Compared with prior art, PrometheusFree limits the average attack success ratio to 0.019, yielding a 95.3% reduction. The experimental results confirm the superiority of the concurrent detection and the boost in attack detection abilities imparted by the WDP approaches.

We investigate the existence of Wilton ripple solutions of the Kawahara equation. Without loss of generality, these are $2π$-periodic, traveling-wave solutions whose profiles at zero amplitude have a codimension-1 bifurcation from a linear combination of $\cos(x)$ and $\cos(Kx)$ for $K \in \mathbb{N} \setminus \{1\}$. Using a Lyapunov-Schmidt reduction, we prove the existence of these solutions for all $K$, in contrast to previous work demonstrating existence only for $K = 2$. Although the proof holds only for the Kawahara equation, many ideas introduced in the proof can be applied to more general contexts, including Wilton ripples of the gravity-capillary water wave equations.

In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general polygonal meshes. Our contribution includes a rigorous a priori error estimate that holds for general polynomial order. On the numerical side, we present (i) an initial convergence test that reflects our theoretical findings, (ii) a second test analyzing the role of the stabilization term in the Virtual Element Method (VEM) formulation and its influence on the approximation error, and (iii) a third test case based on a more application-oriented experiment. The stabilization-free approach is proposed as an alternative strategy to circumvent issues related to the choice of the stabilization parameter in standard VEM formulations.

We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the former. We show that this is equivalent to ordinary garbling conditional on a payoff-irrelevant event. We also characterize the order in terms of induced posterior belief distributions, showing that it depends only on their support. Our main results provide two decision-theoretic characterizations of this order. First, in static decision problems, one experiment dominates another if and only if its value of information is at least a fixed fraction of the other's across all problems. Second, in a class of stopping time problems with a hidden Markov process and repeated experimentation, one experiment dominates another if and only if it yields weakly higher expected payoffs for every problem with a regular prior.