Digital reminder systems are widely used in dementia care to support everyday tasks, but they are typically designed for one-way prompting rather than helping caregivers interpret engagement over time. We present Remindful, a caregiver-informed reminder platform that extends task prompting with caregiver-facing alerts, summaries, and review features to support awareness in home-based dementia care. Drawing on formative caregiver interviews, lived-experience advisor input, and in-home deployments with two caregiver-PLwD dyads, we examine how reminder-based caregiver awareness functions in practice. Our findings show that reminder systems can support caregiver reassurance, household coordination, and awareness of routines over time, but that reminder interaction data is highly context-dependent. Household participation, prompt attribution, routine mismatch, accessibility barriers, and technical failures all shaped what reminder logs could reasonably mean. We argue that reminder systems should not be treated as neutral behavioral sensors, but designed as assistive infrastructures for caregiver interpretation that preserve uncertainty and support contextual sensemaking in real homes.

This study presents a fast nonlinear programming algorithm for low-thrust multi-asteroid rendezvous missions. The core contribution is the derivation of analytical formulations for both first- and second-order gradients of low-thrust rendezvous $Δv$ through an iterative Lambert-based $Δv$ estimator and their application to derive the Hessian matrix or nonlinear programming of the multi-rendezvous trajectory optimization problem. Numerical simulations demonstrate the method's accuracy, with mean relative errors of $Δv$ approximation below 0.8\% for main-belt asteroid transfers, with the analytical gradients matching those computed via the central difference method. The nonlinear programming algorithm's effectiveness is validated through a 9-asteroid rendezvous sequence under both fuel-optimal and time-optimal configurations. Additional validation on three top-ranking sequences from the 12th Global Trajectory Optimization Competition (GTOC12) shows consistent improvement over the original solutions. The proposed approach is well-suited for integration into global trajectory optimization algorithms for multi-spacecraft multi-target missions, offering high computational efficiency while maintaining precise objective function evaluation capabilities.

We analyze information transmission in a recently proposed coarse-grained model of polymer replication by framing it as a communication channel between templates and copies. By calculating the mutual information in the steady-state limit of long chains, we recover the accurate-random phase diagram and establish that the information per-monomer depends solely on template specificity within the accurate regime. Crucially, even in the accurate region, small error fractions lead to substantial information loss due to the nonlinear relationship between errors and mutual information. Examining the information-to-energy cost ratio reveals non-monotonic behavior as a function of monomer alphabet size, with an optimum determined primarily by the per-monomer assembly free energy. For DNA's four-base alphabet, we find that the observed effective assembly energy (at least $14\,k_B T$) places the system far from the information-transmission optimum, suggesting that biological replication may prioritize the suppression of spontaneous random assembly over information-to-energy efficiency. We also characterize achievable rate-fidelity trade-offs using Shannon bounds, providing a theoretical framework for evaluating future proofreading mechanisms in ensemble models.

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they inadequately leverage reasoning capabilities of modern LLMs in high-level planning and self-critique. We argue that proof agents should not merely generate tactics but also reason strategically about proof plans and critically evaluate their own proposals. This paper introduces ReCent-Prover, a reasoning-centric LLM-based proof agent for Rocq that addresses two critical limitations in current systems. First, we present validation with reflection, enabling LLMs to scrutinize their generated tactics and synthesize failure summaries when reflection identifies potential errors, filtering out potentially misapplied tactics earlier. Second, we propose retrieval with planning, which conditions retrieval on LLM-generated proof plans rather than subgoal similarity, retrieving lemmas and proofs that align with the anticipated proof strategy. Both techniques increase the number of invocations of LLMs. However, when evaluated on the CoqStoq benchmark, even under the same budget of LLM invocations, ReCent-Prover achieves a 22.58% relative improvement in the number of proved theorems over the previous state-of-the-art, demonstrating that our reasoning-centric design significantly enhances automated theorem proving capabilities.

Supernovae are one of the most promising gravitational wave sources. But, since the system of the supernovae is nearly spherically symmetric, the expected gravitational waves from them are relatively weak, compared to the case of the compact binary mergers. Thus, at least using the current gravitational wave detectors, only the gravitational waves from a supernova that occurred in our galaxy could be detected. To reliably extract information from gravitational waves originating from such a low event rate, thorough preparation is essential. However, because supernova gravitational waves strongly depend on model parameters, such as progenitor mass and the equation of state for dense matter, it may be difficult to extract physical properties even if the gravitational waves are detected. The universal relations between gravitational-wave signals and physical properties, independent of model parameters, are important for solving this difficulty. To discuss such a universal relation, in this article, we systematically examine the protoneutron-star oscillation frequencies with the linear analysis, the so-called asteroseismology, and compare them with the gravitational wave signals in the simulations.

We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous stability and approximation results using computationally efficient quasi-interpolation operators. The primary contribution is the analysis of weakly admissible hierarchical meshes. Our framework relies on strictly nested cell sets that locally reproduce the full tensor-product spline space at each level. Theoretical and numerical results demonstrate that this intuitive approach is mathematically elegant and outperforms existing adaptive refinement strategies in various practical scenarios.

The goal of this article is to give a proof of a result seemingly absent from the literature characterizing global sections of standard $\mathcal{D}$-modules on the flag variety. This characterization yields a mixture of the Langlands Classification of admissible representations with the Knapp-Zuckerman classification of tempered representations of a real reductive group. We use this result to compute the Cousin-Zuckerman resolution of the trivial representation in terms of standard $(\mathfrak{g},K)$-modules. Further, in the case of $GL(n,\mathbb{H})$ we use this to prove the Lusztig-Vogan bijection for $n=2,3$ and compute the lowest $K$-type map for the zero and principal orbits for general $n$ as well as the image of the trivial representation for even orbits.

Motivated by recent experimental observations of the flavour-exotic $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, we present the first lattice QCD study of coupled-channel scattering of a charm meson with a light meson in the flavour-exotic sectors at the $SU(3)_f$ flavour symmetric point. Utilising five volumes with $m_π\approx 700$ MeV and employing large bases of meson-meson operators, finite-volume spectra are extracted and used to constrain infinite-volume scattering amplitudes with $J^P = \{0, 1, 2, 3, 4\}^+$ via the Lüscher formalism. In the flavour $\mathbf{6}$ sector, each $S$-wave channel considered is found to be attractive with the scattering amplitudes having an associated pole singularity on an unphysical sheet below threshold, giving six flavour-exotic poles in the energy region constrained. In $J^P = 0^+$ there is a virtual bound state and a resonance. The latter is identified with the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, appearing as one state in the $SU(3)_f$ flavour symmetric limit, and suggests the existence of an isospin-$\frac{1}{2}$ partner. In $J^P =1^+$ there are three poles, one of which is identified as a $J^P =1^+$ partner of the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, and $J^P =2^+$ contains one pole which is identified as their $J^P =2^+$ partner. Only mild interactions and no poles are seen in the $J^P = \{3, 4\}^+$ scattering amplitudes. In the flavour $\overline{\mathbf{15}}$ sector, weak interactions are observed in $J^P = \{0, 1, 2, 3, 4\}^+$ with no well-determined poles in the energy region constrained.

Biological microswimmers alter their motility in complex corner geometries, facilitating their survival. However, the dynamical features of low-Reynolds-number swimming at corners remain undefined. Here, we use active droplet microswimmers near a confined meniscus in a microchannel as a model system to study how microswimmer-corner interactions determine swimming patterns. Combining experiments, theory and simulations, we show that pusher-type micrsowimmers are attracted towards a meniscus corner, followed by transient trapping and eventual escape. We demonstrate that hydrodynamic interactions with the wall-interface corner intimately dictate the attraction and trapping or escape of the microswimmer on the basis of its strength. We show that the swimming trajectory at the meniscus corner can be tuned depending on the type of the microswimmer, the corner geometry and the viscosity ratio for the liquid interface. Our study provides a simple way to manipulate microswimmers by exploiting their hydrodynamic interactions near corner geometries.

Scaling Transformer-based click-through rate (CTR) models by stacking more parameters brings growing computational and storage overhead, creating a widening gap between scaling ambitions and the stringent industrial deployment constraints. We propose LoopCTR, which introduces a loop scaling paradigm that increases training-time computation through recursive reuse of shared model layers, decoupling computation from parameter growth. LoopCTR adopts a sandwich architecture enhanced with Hyper-Connected Residuals and Mixture-of-Experts, and employs process supervision at every loop depth to encode multi-loop benefits into the shared parameters. This enables a train-multi-loop, infer-zero-loop strategy where a single forward pass without any loop already outperforms all baselines. Experiments on three public benchmarks and one industrial dataset demonstrate state-of-the-art performance. Oracle analysis further reveals 0.02--0.04 AUC of untapped headroom, with models trained with fewer loops exhibiting higher oracle ceilings, pointing to a promising frontier for adaptive inference.

The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner fluctuations of a vacuum Dirac operator are calculated, using the standard technique of Connes' one-forms. This results in the non-commutative analogue of a gauge field, as expected, and also fluctuations of the spacetime geometry. In addition, the fluctuations include a derivative operator that depends on the particle charge. The integral over the fermions in the model is calculated, leading to some novel induced bosonic terms.

In this work, we investigate the viability of some cosmological models derived from generalized horizon entropies, using Big Bang Nucleosynthesis (BBN) constraints. By analyzing the deviations in the expansion rate, we derive bounds on the model parameters from freeze-out temperature, helium, and deuterium abundances. Our results show that the freeze-out condition provides the most stringent constraint, while helium and deuterium bounds remain consistent across all models. Although lithium constraints are not satisfied, this discrepancy is attributed to the well-known cosmological lithium problem. Furthermore, the parameter values required for late-time cosmic acceleration are found to lie well within the BBN bounds, demonstrating consistency between early- and late-Universe behavior. These results establish the viability of the considered models within the framework of BBN.

Observations of highly rotationally supported gas discs in high redshift ($z$ > 3) star-forming galaxies challenge our understanding of galaxy formation, as the prevailing view holds that galaxies in the early universe are dynamically hot due to frequent mergers, gas accretion, and strong stellar feedback. We examined the kinematic properties of massive ($M_{\star} \geq 10^{10}\,M_{\odot}$) star-forming galaxies in the TNG50 cosmological hydrodynamical simulation in the redshift range $3\leq z \leq 5$. Mock emission line datacubes were constructed and analysed using the same methodology as for [CII] observations with ALMA. We measured the ratio of the gas rotation velocity ($V$) to velocity dispersion ($σ$) finding that most galaxies have $V/σ\sim$ $2-3$, lower than observed. However, a few simulated galaxies show $V/σ$ > 5. Such "cold" discs, selected at $z=4$, remain dynamically colder than most of the TNG population across $z=3-5$. A galaxy with $V/σ\gtrsim10$ appears in a transient phase that lasts $\leq200$ Myr. Dynamically cold disc formation in TNG50 is promoted by gas accretion with angular momentum aligned with the pre-existing disc, while most galaxies undergo misaligned accretion. Dynamically cold discs also show lower mass accretion rates and better aligned stellar and dark-matter angular momentum vectors. By tracing their evolution to $z = 0$, we find that one-third become massive disc galaxies and two-thirds become ETGs.

We study solutions to the self-dual Abelian Yang--Mills--Higgs (YMH) equations in the singular limit $\e \to 0 $, where the associated self-dual Ginzburg--Landau type energy \begin{align*} E_\e\begin{pmatrix}u\\ A\end{pmatrix} = \int_M \left( |\nabla^A u|^2 + \e^2 |F_A|^2 + \frac{(1 - |u|^2)^2}{4\e^2} \right) \mathrm{dvol}_g \end{align*} exhibits concentration along codimension-two sets. Using techniques inspired by Allard's regularity theory, we construct approximate solutions concentrating near a minimal submanifold and analyse their perturbations via a linearised operator projected orthogonally to gauge and translational zero modes. By working in Fermi coordinates and enforcing Coulomb gauge conditions, we derive uniform Lipschitz and curvature estimates for the solutions and obtain Hölder regularity for the scalar and connection components. These results establish a geometric framework for understanding vortex sheet formation and provide a regularity theory for the limiting defect set in the context of Abelian gauge theories.

Desktop interaction streams provide a continuous, privacy-sensitive record of interleaved user tasks. Transforming these streams into task-organized personal logs on-device faces two main challenges: exhaustive Vision-Language Model (VLM) processing strains local resources, and global stream processing causes cross-task context pollution. We present FOCAL (Filtered On-device Continuous Activity Logging), a privacy-first multi-agent system utilizing a unified filter-plan-log architecture. It cascades a lightweight Filter Agent for noise suppression, a text-only Brain Agent for task attribution, a Record Agent for selective visual reasoning, and a task-isolated Memory Agent for context-coherent summarization. Experiments on DesktopBench (comprising 2,572 screenshots across 420 complex sessions) show FOCAL reduces total token consumption by 60.4% and VLM call count by 72.3% versus a baseline, while boosting Key Information Recall (KIR) from 0.38 to 0.61. Crucially, under $A{\to}B{\to}A$ task interruptions, FOCAL maintains Task Acc 0.81 and KIR 0.80, whereas the baseline collapses to Task Acc 0.03. FOCAL pioneers the efficient, on-device summarization of instruction-free desktop streams into multi-perspective personal logs.

We consider the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling (SOC) on $\mathbb{R}^2$, which is also called the Gross--Pitaevskii equation with SOC. The system describes SO-coupled spinor BEC in physics. In the literature of physics, the existence of small semi-vortex solutions and small ground state is known. In the present paper, we give their mathematical proofs by finding minimizers of the energy under small mass constraint.

NICER observations of millisecond pulsars (MSPs) suggest that non-dipolar magnetic fields are required to explain their surface X-ray hotspots. C. Kalapotharakos et al. (2021) modeled the NICER light curve of MSP J0030+0451 (J0030) using a static vacuum offset dipole-plus-quadrupole field and corresponding force-free (FF) solutions to jointly reproduce the X-ray and Fermi-LAT $γ$-ray emission. We substitute their static vacuum field model with a more realistic swept-back configuration that accounts for rotational effects. This field more closely resembles the corresponding FF solutions, making it a more physically motivated choice for future multiwavelength modeling. We adopt a centered swept-back vacuum multipolar magnetic field (SVM2F; J. Pétri 2015), expressed as a complete expansion in vector spherical harmonics, enabling flexible descriptions of arbitrary magnetic field geometries. We introduce a metric to quantify the complexity among different field prescriptions, illustrated for the static offset vacuum field. To efficiently explore parameter space, we train a neural network surrogate (G. Olmschenk et al. 2025) on SVM2F light curves including components up to the octupole, accelerating Markov chain Monte Carlo sampling by $\sim 10^3$ compared to direct physical model evaluations. Applying this framework to J0030, we constrain the field parameter space and find that a centered swept-back multipolar field including terms up to the octupole adequately reproduces the bolometric thermal X-ray light curve. Our study highlights the importance and inherent complexity of prescribing different multipolar magnetic field models for rotating stars, and can be extended to other MSPs to ultimately constrain the masses and radii of neutron stars, and hence their equation of state.

Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which each entry is binary, indicating whether the corresponding node belongs to the corresponding hyperedge. Although the incidence matrix has become a foundational tool for hypergraph analysis and mining, we argue that its binary nature is insufficient to accurately capture the complexity of node-hyperedge relationships arising from the fact that different hyperedges can contain vastly different numbers of nodes. Accordingly, based on the resource allocation process on hypergraphs, we propose a continuous-valued matrix to quantify the proximity between nodes and hyperedges. To verify the effectiveness of the proposed proximity matrix, we investigate three important tasks in hypergraph mining: link prediction, vital nodes identification, and community detection. Experimental results on numerous real-world hypergraphs show that simply designed algorithms centered on the proximity matrix significantly outperform benchmark algorithms across these three tasks.

The [CII] 158 $μ$m line is widely used to trace star formation and the gas contents of high-redshift galaxies. However, it remains unclear under which physical conditions it reliably traces the molecular reservoir, and whether a unique conversion factor $α_{\rm [CII]}$ can be applied across cosmic time. We investigate the evolution of the relation between the [CII] luminosity and molecular gas mass from $z\simeq10$ to $z\simeq0.2$ using the Vintergatan simulation, a high-resolution cosmological zoom-in of a Milky Way-like galaxy. We post-process the snapshots with the Skirt radiative transfer code to generate synthetic [CII] data cubes. We measure global and spatially resolved (100 pc) relations between [CII] luminosity ($L_{\rm [CII]}$), star formation rate (SFR), and molecular gas mass ($M_{\rm mol}$). We follow the redshift evolution of the [CII]-to-molecular gas conversion factor $α_{\rm [CII]}$, and link these trends to the evolution of the interstellar medium (ISM) phases. The global $L_{\rm [CII]}$-$M_{\rm mol}$ and $L_{\rm [CII]}$-SFR relations evolve from a steep, [CII]-deficient regime at very low metallicity to an almost linear behaviour, similar to calibrations at $z\approx2$, once the ISM reaches $Z \gtrsim 0.05$-$0.1\,Z_\odot$ at $z\lesssim5$. Over this evolution, $α_{\rm [CII]}$ spans nearly three orders of magnitude, from $\gtrsim 10^4$ down to $\approx10 \,\rm{M_\odot\,L_\odot^{-1}}$, even though the [CII] emission remains spatially correlated with the molecular gas. A unique, redshift-independent $α_{\rm [CII]}$ therefore cannot recover molecular gas masses across the regimes we explore. [CII] remains a viable tracer of molecular gas at very high redshifts, but only when used with conversion factors that explicitly account for metallicity, ISM phase mix, and merger events.

Activation processes govern noise-induced switching between long-lived states. In an equilibrium double well, the thermally activated switching rate exhibits a prefactor with a nonmonotonic dependence on environmental coupling, a foundational crossover known as Kramers turnover. Here, we demonstrate a Kramers turnover analogue in a Kerr parametric oscillator, a driven-dissipative nonlinear system featuring two stable phase states. First, we analytically establish turnover physics in this out-of-equilibrium setting. There, the strong physical correlation between the activation barrier and intrinsic damping fundamentally obscures the underlying turnover physics. To overcome this limitation, we rescale the rotating-frame dynamics and introduce a tunable effective friction controlled entirely by the parametric drive. This rescaling comes at the cost of a concurrent rescaling of the effective temperature. Exploiting this simultaneous scaling, we leverage the effective temperature to extract the turnover directly from temperature-dependent observations. Subsequently, measuring noise-induced phase slips in a micro-electromechanical device, we observe a distinct crossover in the prefactor's temperature dependence. Our results unambiguously isolate the out-of-equilibrium turnover regime and highlight that the competition between dissipation and fluctuations profoundly shapes activation dynamics also beyond equilibrium.

The superconducting diode effect (SDE) enables nonreciprocal supercurrent flow, holding immense potential for ultra-low-power quantum electronics. Intrinsic SDE typically requires materials with inherent symmetry breakings. Here, we report the discovery of SDE in chemical vapor deposition-grown molybdenum carbide ($\mathrm{Mo}_2\mathrm{C}$) nanoflakes, a material traditionally considered centrosymmetric. Strikingly, this system uniquely hosts both field-odd and field-free SDEs. Transport measurements reveal a field-odd SDE with tunable efficiency exceeding 40% at 4 K under a perpendicular in-plane magnetic field. In a separate sample, a robust field-free SDE persists under zero-field and field-coolings. Out-of-plane field sweeps confirm the intrinsic nature of these phenomena. We propose that domain-boundary supercurrents or charge density wave-like orders drive this unexpected combination of symmetry breakings. Our findings establish air-stable $\mathrm{Mo}_2\mathrm{C}$ as an ideal platform for nonreciprocal superconducting electronics operating at liquid-helium temperatures, expanding the search for SDE into nominally centrosymmetric superconductors.

We develop a compact theory of time-reversed Young (TRY) interference beyond the symmetric two-slit geometry by considering equally spaced three-slit, finite $N$-slit, and infinite periodic slit arrays. In the TRY configuration, a point emitter illuminates the aperture, a position-fixed detector records the signal, and the response is reconstructed in source space by correlating the detector record with the source-coordinate label. We show that the three-slit case already reveals the essential new physics beyond two slits: a quadratic Fresnel phase survives, modifies the reconstructed interference law, and lifts the nominal dark fringes in the generic case. For a general equally spaced $N$-slit array, we identify the exact reconstructed response and show that the familiar textbook grating factor is recovered only when the quadratic phase is negligible, compensated, or reduced to a common phase across the array. In that ideal limit, the reconstructed peaks are source-space analogues of classical grating orders rather than outgoing diffraction beams. For an infinite periodic TRY array, we further show that the same discrete quadratic phase generates full and fractional Talbot-like revivals in source space, governed by a reciprocal-distance condition rather than the conventional Talbot propagation law. These results show that the symmetric two-slit TRY geometry is exceptional, while multi-slit TRY systems naturally combine source-space discrimination with sensitivity to aperture-wide phase structure and periodic-array revival physics.

The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and regularity theory, its numerical approximation remains challenging: discretisation of the nonlocal term leads to dense operators, and the singularity of the kernel requires special treatment in collocation-based schemes. In this work, we develop an efficient and error-controlled numerical framework for the nonlocal Cahn-Hilliard system with constant mobility, logarithmic potential, Newtonian interaction kernel, and no-flux boundary conditions. Our approach is based on a pseudospectral multishape method that accurately approximates the action of singular convolution operators. We present high-resolution numerical solutions for this nonlocal system of equations that can be achieved with limited computational resources.

This study reports on advancements in operando characterization of volume changes in lithium-ion battery (LIB) electrode materials during electrochemical cycling. Volume changes are crucial for LIB operation because they are related to the amount of stored energy as well as LIB integrity, performance, and safety. The study introduces a method based on isotope multilayers as active material to track the intrinsic modification of electrode volume in real time under operating conditions with operando neutron reflectometry. A natGe-73Ge multilayer film is used as a model system to measure the volume change of amorphous germanium electrodes during charging and discharging. Isotope modulation produces a Bragg peak in the neutron reflectivity pattern, sensitive only to the modification of volume within the active material of the electrode. Battery side reactions, such as the growth and reduction of the solid-electrolyte interphase is excluded. Using this method, the volume modification as a function of Li content x in LixGe can easily be derived from the scattering vector position of the Bragg peak without fitting numerous complex reflectivity patterns. The experiments show a reversible volume change of amorphous germanium of up to 250 percent for x = 3, which appears to be largely independent of current density, cycle number, and the thickness of the individual Ge layers. Also, there are tentative indications that the crystallization and re-amorphization of LixGe are not influencing the volume change.

In the FDR-controlling literature, mirror statistics offer a flexible alternative to $p$-value based procedures. When prior information is available, however, it is unclear how to incorporate mirror statistics in a principled way, and the standard equal split used by data-splitting methods can be inefficient. In this paper, we characterize a broader class of mirror statistics for any fixed splitting scheme and establish asymptotic FDR control under mild weak-dependence conditions using a two-stage procedure inspired by \cite{li2021whiteout}. Within this class, we derive a Bayes-optimal mirror statistic. Theoretically, we demonstrate its power advantage through analyses in the Rare/Weak signal model. Building upon this Bayes-optimal mirror statistic, we propose \textsc{PRADAS} (PRior-Assisted DAta Splitting) that treats split ratio as a stopping time and recasts the data-splitting as an optional stopping over a natural filtration; the optimal stopping rule is characterized by the Snell envelope and computed efficiently via a Longstaff--Schwartz regression approximation. Both simulations and real data examples demonstrate the effectiveness of our proposed framework.

Perception-aware lossy source coding has attracted significant recent interest. It augments the classical distortion criterion with an explicit perception constraint, thereby enabling more refined control over fidelity and perceptual quality. Despite rapid progress, the diversity of rate-distortion-perception formulations and their underlying assumptions remains poorly understood by many practitioners. In particular, there is often a tendency to rely heavily on the expressive power of deep neural networks and generative models without clear theoretical guidance, using fundamental limits merely as performance benchmarks rather than as sources of design insight. This tutorial paper aims to bridge this gap by surveying information-theoretic principles that can be leveraged to develop constructive approaches to perception-aware lossy source coding. We distill practical guidelines implied by rate-distortion-perception theory and demonstrate how they inform the design of implementable coding schemes. A simple unit-circle example is used as a pedagogical tool to illustrate key ideas, architectural principles, and tradeoffs in an intuitive and unified manner. Both one-shot and asymptotic settings are examined to highlight conceptual similarities and operational differences. We also clarify the role of common randomness and the notion of universal representation, and elucidate the connections between perception-aware and conventional lossy source coding. Overall, this tutorial provides a principled foundation for developing perception-aware compression systems that go beyond black-box model design.

Exciton-polariton lasers are coherent light sources which do not require the population inversion (transparency) condition to be fulfilled. They have been conceptualized at the end of the XXth century but until now they operate almost exclusively under optical injection, which severely limits the widespread integration of the polariton-based devices implemented so far. Here we tackle this issue by reporting an electrically-pumped exciton-polariton laser based on GaN and operating at room temperature in a mode-locked regime. The laser architecture is close to the geometry of commercial ridge-waveguide GaN lasers, but based on a bulk GaN active region instead of quantum wells. Unique features of polariton lasers are demonstrated, in particular the breakdown of the transparency condition, which enables our polariton lasers to operate even when only a small fraction (20\%) of the cavity length is injected. Moreover, the large polaritonic gain allows for the operation of a short cavity length (60$μm$) compared to commercial lasers. From the very same sample, we also achieve polariton lasing under optical injection, confirming that the doped layers necessary for electrical injection do not prevent strong-coupling nor polariton lasing. Our results open a new perspective for polariton-based devices.

We define the Verma vector system for each finite dimensional irreducible representation of the orthosymplectic Lie superalgebra $\mathfrak{spo}(4|1)$ with the highest weight $λ,$ via the conditions that making a tableau with shape $λ$ to be a Kashiwara-Nakashima tableau. We then show the linearly independence of this vector system. It turns out to be a basis of the finite dimensional irreducible representation $L(λ)$ of the orthosymplectic Lie superalgebra $\mathfrak{spo}(4|1)$ with the highest weight $λ,$ which analogs to the Verma basis of representations of $\mathfrak{sp}_4,$ called the Verma basis of the finite dimensional irreducible representation of $\mathfrak{spo}(4|1)$.

We investigate the Cauchy problem for the focusing nonlinear Schrödinger (NLS) equation \begin{equation} iq_t(x,t)+q_{xx}(x,t)+2|q(x,t)|^2q(x,t)=0,\quad x\in\mathbb{R},\quad t\ge0,\nonumber \end{equation} subject to initial data $ q(x,0)$ satisfying the asymptotic boundary conditions \begin{equation}\label{eq:boundary} q(x,0) \sim q^{alg}(x,0) \quad \text{as} \quad x \to \pm\infty,\nonumber \end{equation} where $q^{alg}(x,t)$ denote finite-genus algebro-geometric quasi-periodic solutions of the focusing NLS equation. Employing the Riemann--Hilbert (RH) approach combined with the Deift--Zhou nonlinear steepest descent method, we analyze the long-time asymptotic behavior of solutions to this Cauchy problem. Our analysis distinguishes between two cases based on the genus $n$ of the underlying hyperelliptic Riemann surface: (i) Odd genus backgrounds: When the background solutions $q^{alg}(x,0)$ correspond to hyperelliptic curves of odd genus $n = 2s+1$ $(s \in \mathbb{N}_0)$, we identify distinct asymptotic regions in the $(x,t)$-plane characterized by the variable $ξ= x/t$, within which the leading-order asymptotics is expressed in terms of the second Painlevé transcendent. (ii)Even genus backgrounds: When the background solutions $q^{alg}(x,0)$ correspond to hyperelliptic curves of even genus $n = 2s$ $(s \in \mathbb{N})$, the asymptotic behavior in regions selected by $ξ$ is described in terms of parabolic cylinder functions. Specifically, we derive the leading-order asymptotics and establish explicit error bounds for the solution $q(x,t)$ as $t \to +\infty$, uniformly for $x \in \mathbb{R}$.

Cyclic equalizability is a notion introduced by Shinagawa and Nuida in 2025, in the study of card-based cryptography. Informally, a collection of words is cyclically equalizable if, by inserting the same letters at the same positions in all words, they can be transformed into words that are cyclic shifts of one another. Shinagawa and Nuida showed that two binary words of equal length are cyclically equalizable if and only if they have the same Hamming weight. They also posed the problem of characterizing cyclic equalizability over larger alphabets. In this paper, we completely characterize cyclic equalizability for two words over an arbitrary finite alphabet by proving that two words are cyclically equalizable if and only if they have the same Parikh vector.