We prove that if two very general cubic fourfolds are L-equivalent then they are isomorphic, and we observe that there exist special cubic fourfolds which are L-equivalent but not isomorphic. When the cubic fourfolds are very general in certain Hassett divisors, we prove that if they are L-equivalent then they are also Fourier-Mukai partners. We also provide further examples in support of the fact that L-equivalent hyper-Kähler manifolds should be D-equivalent, as conjectured by Meinsma.

This paper presents a framework for target detection and downlink data transmission in a repeater-assisted bi-static integrated sensing and communication system. A repeater is an active scatterer that retransmits incoming signals with a complex gain almost instantaneously, thereby enhancing sensing performance by amplifying the echoes reflected by the targets. The same mechanism can also improve downlink communication by mitigating coverage holes. However, the repeater introduces noise and increases interference at the sensing receiver, while also amplifying the interference from target detection signals at the downlink users. The proposed framework accounts for these sensing-communication trade-offs and demonstrates the potential benefits achievable through a carefully designed precoder at the transmitting base station. In particular, our finding is that a higher value of probability of detection can be attained with considerably lower target radar-cross-section variance by deploying repeaters in the target hot-spot areas.

We study the extended Hubbard model (EHM) with both onsite Hubbard interaction and the intersite density-density interaction between nearest-neighbors using the standard Hartree mean-field approximation (MFA) on the Bethe lattice. We found that, at the ground state, the system can be in a charge-ordered insulating (COI), a charge-order metallic (COM) or a non-charge-ordered (NO) state. Moreover, the finite-temperature phase diagrams are presented. Several observables like a charge-order parameter, a spectral function, and particularly at finite temperatures, a charge carrier concentration (to visualize the degree of metallicity) are analyzed. The results show that increasing onsite repulsion suppresses charge order and change the properties of the system from insulating to metallic. Worth noting, that a number of phenomena can be found within the MFA, where their analysis is much simpler than in more advanced approaches. The method used for the EHM on the Bethe lattice also allows for a series of analytical derivations and simplification to see general geometry-independent features and analytical results, avoiding the numerical inaccuracies and other issues that appear with a purely numerical solution.

The active stabilization of polarization channels is a task of growing importance as quantum networks move to deployed demonstrations over existing fiber infrastructure. However, the uniquely strict requirements for high-fidelity qubit transmission complicate the extent to which classical solutions may apply to future quantum networks, particularly in terms of recognizing noise sources present in low-flux, nonunitary channels. Here we introduce a novel in situ benchmarking approach that augments a classical polarization tracking system, limited to unitary correction, with simultaneously transmitted quantum light for ancilla-assisted process tomography of the full quantum map. Implemented in a local-area quantum network, our method uses the reconstructed map both to validate the classical compensation and to expose noise sources it fails to capture. A sliding measurement window that continuously updates the estimated quantum process further increases sensitivity to rapid channel fluctuations. Our results should unlock new opportunities for in situ channel characterization in quantum-classical coexistence networks.

We present a new formalism to separate large- and small-scale contributions to cosmic shear through \textit{lensing counterterms} (LCT) inspired by effective field theory (EFT). Marginalizing over these LCTs isolates the large-scale cosmological signal in weak lensing power spectra while simultaneously constraining the impact of baryonic feedback or new physics (e.g. axion dark matter) at small scales. Our formalism removes the need for hard scale cuts in standard analyses, even when theoretical predictions are limited to below a physical cutoff $Λ$, resulting in significant improvements in constraining power -- up to $5\times$ smaller in the case of a LSST-Y10-like analysis without marginalizing over baryons when the analysis cutoff is set to $Λ= 1.0h$ Mpc$^{-1}$. We conduct a proof-of-principle analysis on the publicly available DES Y3 data, finding $S_8= 0.783\pm 0.029$ and $S_8 = 0.798\pm 0.026$ for analyses with cutoffs of $Λ= 0.5h$ Mpc$^{-1}$ and $1.0 h$ Mpc$^{-1}$, respectively, with no detection of modifications to small-scale clustering at $k > Λ$ beyond the predictions of collisionless dark matter in a $Λ$CDM universe. We make our \texttt{JAX}-based pipeline, \texttt{gholax}, integrated with intrinsic alignment predictions from the EFT of large-scale structure at 1-loop, publicly available.

In this paper, we address the stabilization problem for force-controlled nonholonomic mobile robots under safety-critical constraints. We propose a continuous, time-invariant control law based on the gamma m-quadratic programming (gamma m-QP) framework, which unifies control Lyapunov functions (CLFs) and control barrier functions (CBFs) to enforce both stability and safety in the closed-loop system. For the first time, we construct a global, time-invariant, strict Lyapunov function for the closed-loop nonholonomic mobile robot full-dynamic system with a nominal stabilization controller in polar coordinates; this strict Lyapunov function then serves as the CLF in the QP design. Next, by exploiting the inherent cascaded structure of the vehicle dynamics, we develop a CBF for the mobile robot via an integrator backstepping procedure. Our main results guarantee both asymptotic stability and safety for the closed-loop system. Both the simulation and experimental results are presented to illustrate the effectiveness and performance of our approach.

We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve are the electroneutral Navier--Stokes--Onsager--Stefan--Maxwell (NSOSM) equations, which model momentum transport, multicomponent diffusion and electrical effects within the electrolyte. Our algorithms can be applied in the steady and transient settings, in two and three spatial dimensions, and under a variety of boundary conditions. Moreover, we allow for the material parameters (e.g. viscosity, diffusivities, thermodynamic factors and density) to be dependent on the local state of the mixture and thermodynamically non-ideal. The flexibility of our approach requires us to address subtleties that arise in the governing equations due to the interplay between boundary conditions and the equation of state. We demonstrate the algorithms in various physical configurations, including (i) electrolyte flow around a microfluidic rotating disk electrode and (ii) the flow in a Hull cell of a cosolvent electrolyte mixture used in lithium-ion batteries.

We study the dynamics of a mean-field Ising model whose coupling depends on the magnetization via a linear feedback function. A key feature of this linear feedback Ising model (FIM) is the possibility of temperature-induced bistability, where a temperature increase can favor bistability between two phases. We show that the linear FIM provides a minimal model for a transcritical bifurcation as the temperature varies. Moreover, there can be two or three critical temperatures when the external magnetic field is non-negative. In the bistable region, we identify a Maxwell temperature where the two phases are equally probable, and we find that increasing the temperature favors the lower phase. We show that the probability distribution becomes non-Gaussian on certain time intervals when the magnetization converges algebraically at either zero temperature or critical temperatures. Near critical points in the parameter space, we derive a Fokker-Planck equation, construct the families of equilibrium distributions, and formulate scaling laws for transition rates between two stable equilibria. The linear FIM offers considerable flexibility in controlling steady-state bifurcations and their associated equilibrium distributions, which can be desirable for modeling feedback systems across various disciplines.

This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schrödinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics. While 1D solitons are generally stable, their 2D and 3D counterparts are prone to collapse. Several mechanisms have been proposed to mitigate this, including optical lattices, modulation of the nonlinearity via Feshbach resonance management, and Rabi coupling between hyperfine states. Other approaches involve competing nonlinearities and quantum corrections, such as Lee-Huang-Yang effects. Emphasis is placed on conditions enabling long-lived or fully stable solitons. Despite experimental feasibility, achieving robust stabilization remains challenging due to the intricate interplay of nonlinearities and external controls. The paper surveys collapse dynamics, stabilization strategies, and soliton existence based on key theoretical contributions.

Classical rupture is attributed to molecular (van der Waals) forces acting at nanometric thicknesses. Nonetheless, micron-thick liquid sheets routinely perforate far above the scale where these molecular forces act, yet the mechanism that selects opening versus healing has remained unclear. Using direct numerical simulations of a draining sheet with an entrained air bubble (cavity), we show that irreversible rupture occurs only when a deterministic double-threshold is crossed: (i) the outward driving (from airflow or inertia) is strong enough and (ii) the cavity is distorted enough. If either condition falls short, surface tension heals the cavity and the sheet reseals. The time for this process is set by the balance between inertia and viscosity -- fast for inertia-dominated sheets and slower for viscous ones. This double-threshold mechanism explains why micrometer-thick films perforate and offers practical control options -- driving strength and defect geometry -- for predicting and controlling breakup in spray formation processes, wave breaking, and respiratory films.

Boundaries such as walls, windows, and doors are ubiquitous in the physical world, yet their potential in mixed reality (MR) remains underexplored. We present Unbounded, a Research through Design inquiry into object--boundary interaction (OBI). Building on prior work, we articulate a design space aimed at providing a shared language for OBI. To demonstrate its potential, we design and implement eight examples across productivity and art exploration scenarios, showcasing how OBIs can enrich and reframe everyday interactions. We further engage with six MR experts in one-on-one feedback sessions, using the design space and examples as design probes. Their reflections broaden the conceptual scope of OBI, reveal new possibilities for how the framework may be applied, and highlight implications for future MR interaction design. https://www.zhuoyuelyu.com/unbounded

Accurate and efficient prediction of multicomponent adsorption equilibria across pressures, temperatures, and compositions remain a central challenge for designing energy-efficient adsorption-based separation processes. Traditional approaches, including model fitting and ideal adsorbed solution theory (IAST), often fail to balance accuracy, computational efficiency, and transferability under process-relevant conditions. Here, we introduce a material-to-process modeling framework that integrates macrostate probability distributions (MPDs) from flat-histogram Monte Carlo simulations with rigorous cyclic process optimization. MPDs directly capture the joint occupancy distributions of adsorbates, producing reweightable landscape that enables high-fidelity mixture adsorption equilibria without repeated simulations or model assumptions. We show that coupling this statistical mechanical foundation with process modeling delivers accurate and computationally efficient evaluations for binary and ternary gas mixture separations. This integration establishes MPD-based modeling as a generalized method for predictive multicomponent adsorption equilibria, accelerating the discovery and design of adsorbent materials for carbon capture and other separation challenges.

Optical tomograms can be envisaged as patterns. The Wasserstein generative adversarial network (WGAN) algorithm provides a platform to train the machine to compare patterns corresponding to input and generated tomograms. Using a deep-learning framework with two convolutional neural networks and WGAN, we have trained the machine to generate tomograms of Fock states, coherent states (CS) and the single photon added CS ($1$-PACS). The training process was continued until the Wasserstein distance between the input and output tomographic patterns levelled off at a low value. The mean photon number, variances and higher moments were extracted directly from the generated tomograms, to distinguish between different Fock states and also between the CS and the $1$-PACS, without using an additional classifier neural network. The robustness of our results has been verified using two error models and also with different colormaps that define the tomographic patterns. We have examined if the training program successfully reflected some of the findings in a recent experiment in which state reconstruction was carried out to establish that the fidelities between an amplified CS, an optimal CS and a $1$-PACS were close to unity, over a range of parameter values. By training the machine to reproduce tomograms corresponding to these specific states, and comparing the mean photon numbers of these states obtained directly from the tomograms, we have established that the variations in these observables reflect the experimental trends. State reconstruction from tomograms could be challenging, in general, since the Hilbert space associated with quantized light is large. The tomographic approach provides a viable alternative to detailed state reconstruction. Our work demonstrates the use of machine learning to generate optical tomograms from which the states can be directly characterized.

Cyclic swing adsorption processes, such as pressure/vacuum swing adsorption (PVSA), are a promising technology for upgrading biogas by separating carbon dioxide (CO2) from methane (CH4). The rational design of adsorbent materials with tailored properties is important for the deployment of high-performance PVSA technology. Metal-organic frameworks (MOFs), particularly the CALF-20 isoreticular series, have attracted interest due to their high CO2 selectivity, thermal, and water stability. In this study, we report a multiscale assessment of CALF-20 and its isoreticular five derivatives by integrating molecular simulations with PVSA process optimization and techno-economic analysis. Structural and adsorption characteristics were calculated and employed to assess how each material performs in terms of energy efficiency and cost. The analysis reveals distinct differences in cost performance among the CALF-20 series, with CALF-20 showing the most favorable economics with \gt97\% purity CH4 production cost at \$4.31 per kg of CH4 and energy consumption of 9.35 kWh per kg of CH4. This study demonstrates that the integrated molecular-process optimization framework can effectively guide the search for adsorbent materials for biogas upgrading.

City council meetings are vital sites for civic participation where the public can speak directly to their local government. By addressing city officials and calling on them to take action, public commenters can potentially influence policy decisions spanning a broad range of concerns, from housing, to sustainability, to social justice. Yet studies of these meetings have often been limited by the availability of large-scale, geographically-diverse data. Relying on local governments' increasing use of YouTube and other technologies to archive their public meetings, we propose a framework that characterizes comments along two dimensions: the local concerns where concerns are situated (e.g., housing, election administration), and the societal concerns raised (e.g., functional democracy, anti-racism). Based on a large record of public comments we collect from 15 cities in Michigan, we produce data-driven taxonomies of the local concerns and societal concerns that these comments cover, and employ machine learning methods to scalably apply our taxonomies across the entire dataset. We then demonstrate how our framework allows us to examine the salient local concerns and societal concerns that arise in our data, as well as how these aspects interact.

We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain $D\subset\mathbb R^2$. We compute the small time asymptotics of the AH's exponential trace up to order $O(\log t)$, and of the PAM's mass up to order $O(t\log t)$. Our proof is probabilistic, and relies on the asymptotics of intersection local times of Brownian motions and bridges in $\mathbb R^2$. Applications of our main result include the following: (i) If the boundary $\partial D$ is sufficiently regular, then $D$'s area and $\partial D$'s length can both be recovered almost surely from a single observation of the AH's eigenvalues. This extends Mouzard's Weyl law in the special case of bounded domains (Ann. Inst. H. Poincaré Probab. Statist. 58(3): 1385-1425). (ii) If $D$ is simply connected and $\partial D$ is fractal, then $\partial D$'s Minkowski dimension (if it exists) can be recovered almost surely from the PAM's small time asymptotics. (iii) The variance of the white noise can be recovered almost surely from a single observation of the AH's eigenvalues.

The Local Structure Theorem (LST) for Graph Minors roughly states that for every $H$-minor-free graph $G$ that contains a sufficiently large wall $W$, there is a small vertex subset $A,$ whose removal yields a graph that admits an "almost embedding" $δ$ on a surface $Σ$ on which $H$ does not embed. By almost embedding, we mean that there exists a hypergraph $\mathcal{H}$ whose vertex set is a subset of the vertex set of $G - A$ and an embedding of $\mathcal{H}$ on $Σ$ such that the drawing of each hyperedge of $\mathcal{H}$ corresponds to a cell of $δ,$ the boundary of each cell intersects only the vertices of the corresponding hyperedge, and all remaining vertices and edges of $G - A$ are drawn in the interior of cells. The cells corresponding to hyperedges of arity at least $4$, called vortices, are few in number and have small "depth", while "most" of the wall $W$ is disjoint from the vortices and is "grounded" in the embedding $δ$. Suppose that the subgraphs drawn inside each of the non-vortex cells are equipped with some finite index, i.e., each such cell is assigned a color from a finite set. We prove a version of the LST in which the set $C$ of colors assigned to the non-vortex cells exhibits "large" bidimensionality: $G - A$ contains a minor model of a large grid $Γ$ such that, for every color $α\in C$, the model of each vertex of $Γ$ contains the subgraph drawn within an $α$-colored cell. Moreover, $Γ$ can be chosen in a way that is "well-connected" to the original wall $W$.

Warped AdS$_3$ backgrounds provide set-ups to study holography beyond AdS and, in particular, holography for near-extremal Kerr black holes. A certain $U(1)$ charged warped BTZ background supported by pure NS-NS flux was constructed in string theory in arXiv:2111.02243. While older works found, in absence of $U(1)$ charges, that the warped black holes' thermal entropy obeys a Cardy formula, the addition of $U(1)$ charges in arXiv:2111.02243 leads to the universal entropy formula in a $J\bar{T}$-deformed CFT and not to the charged Cardy formula. In this article, we explore further the implications of this result for warped AdS$_3$ holography. We compute the asymptotic symmetries of the warped BTZ background of arXiv:2111.02243 and obtain an infinite-dimensional non-linear Poisson algebra that can be linearized, after a non-linear redefinition of generators, to two commuting copies of the $(Virasoro\times U(1)Kac-Moody)$ algebra. The algebra matches the symmetry algebra of a symmetric product orbifold of $J\bar{T}$-deformed CFTs. We contrast the results with those for a similar warped BTZ background supported by both NS-NS and RR flux.

This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join equidistribution result between a 5-tuple of statistics on rooted trees and a corresponding 5-tuple of statistics on parking functions. Some enumerative questions are also considered.

Spreadsheet collaboration provides valuable opportunities for learning and expertise sharing between colleagues. Sharing expertise is essential for the retention of important technical skillsets within organisations, but previous studies suggest that spreadsheet experts often fail to disseminate their knowledge to others. We suggest that social norms and beliefs surrounding the value of spreadsheet use significantly influence user engagement in sharing behaviours. To explore this, we conducted 31 semi-structured interviews with professional spreadsheet users from two separate samples. We found that spreadsheet providers face challenges in adapting highly personalised strategies to often subjective standards and evaluating the appropriate social timing of sharing. In addition, conflicted self-evaluations of one's spreadsheet expertise, dismissive normative beliefs about the value of this knowledge, and concerns about the potential disruptions associated with collaboration can further deter sharing. We suggest these observations reflect the challenges of long-term learning in feature-rich software designed primarily with initial learnability in mind. We therefore provide implications for design to navigate this tension. Overall, our findings demonstrate how the complex interaction between technology design and social dynamics can shape collaborative learning behaviours in the context of feature-rich software.

A quantitative word automaton (QWA) defines a function from infinite words to values. For example, every infinite run of a limit-average QWA A obtains a mean payoff, and every word w is assigned the maximal mean payoff obtained by nondeterministic runs of A over w. We introduce quantitative language automata (QLAs) that define functions from language generators (i.e., implementations) to values, where a language generator can be nonprobabilistic, defining a set of infinite words, or probabilistic, defining a probability measure over infinite words. A QLA consists of a QWA and a language aggregator. For example, given a QWA A, the infimum aggregator maps each language L to the greatest lower bound assigned by A to any word in L. For boolean value sets, QWAs capture trace properties, and QLAs capture hyperproperties. For more general value sets, QLAs serve as a specification language for a generalization of hyperproperties, called quantitative hyperproperties. A nonprobabilistic (resp. probabilistic) quantitative hyperproperty assigns a value to each set (resp. distribution) G of traces, e.g., the minimal (resp. expected) average response time exhibited by the traces in G (resp. by traces sampled according to G). We give several examples of quantitative hyperproperties and investigate three paradigmatic problems for QLAs: evaluation, nonemptiness, and universality. In the evaluation problem, given a QLA AA and an implementation G, we ask for the value that AA assigns to G. In the nonemptiness (resp. universality) problem, given a QLA AA, a threshold k, and a comparison in {>, >=} we ask whether AA assigns a value meeting the threshold to some (resp. every) language. We provide a comprehensive picture of decidability and complexity for these problems for QLAs with common aggregators as well as their restrictions to omega-regular languages and distributions generated by finite Markov chains.

In neutrino-dense astrophysical environments, these particles exchange flavor through a coherent weak field, forming a collisionless neutrino plasma with collective flavor dynamics. Instabilities, which grow and affect the environment, may arise from neutrino-neutrino refraction alone (fast limit), vacuum energy splittings caused by masses (slow limit), or neutrino-matter scattering (collisional limit). We present a comprehensive analytical description of the dispersion relation governing these unstable modes. Treating vacuum energy splittings and collision rates as small perturbations, we construct a unified framework for fast, slow, and collisional instabilities. We classify modes into gapped, where collective excitations are already present in the fast limit but rendered unstable by slow or collisional effects, and gapless, which are purely generated by these effects. For each class, we derive approximate dispersion relations for generic energy and angle distributions, which reveal the order of magnitude of the growth rates and the nature of the instabilities without solving directly the dispersion relation. This approach confirms that slow and collisionally unstable waves generally grow much more slowly than they oscillate. Consequently, the common fast-mode approximation of local evolution within small boxes is unjustified. Even for fast modes, neglecting large-distance propagation of growing waves, as usually done, may be a poor approximation. Our unified framework provides an intuitive understanding of the linear phase of flavor evolution across all regimes and paves the way for a quasi-linear treatment of the instability's nonlinear development.

We consider coherent states of weakly interacting bosons under the conditions of external resonant excitation, with a focus on a two-dimensional polariton fluid driven by a plane electromagnetic wave near the ground state. The coherent driving breaks the U(1) symmetry explicitly, which prevents the occurrence of quantum vortices in a uniform scalar condensate. Surprisingly, a spinor (two-component) system of the same kind admits topological excitations, such as domain walls of relative phase or confined half-vortex molecules, typical of a freely evolving spinor Bose system. Opposite-phase domains arise from the spontaneous breakdown of the spin symmetry $(\mathbb{Z}_2)$. Domain walls form with time even when the initial state of the system is uniform or completely disordered; they fall into different topological types distinguished by the total phase variation in the transverse direction. One type of domain walls is similar to ``magnetic'' solitons in Bose-Einstein condensates and exhibits nonzero spin polarization whose sign depends on the direction of motion. Domain walls of the second type, by contrast, behave like monopoles with broken spatiotemporal symmetry and tend to move in certain preferred directions. The interaction of vortices and domain walls results in a long-range ordering of the system.

Adsorption breakthrough modeling often requires complex software environments and scripting, limiting accessibility for many practitioners. We present AIM, a MATLAB-based graphical user interface (GUI) application that streamlines fixed-bed adsorption modeling and analysis through an integrated workflow, which includes isotherm fitting, estimation of the enthalpy of adsorption, prediction of mixture behavior, and multicomponent breakthrough simulations. AIM supports 13 isotherm models for isotherm fitting and includes the implementation of Ideal Adsorbed Solution Theory (IAST) (FastIAS) and extended Langmuir models for predicting mixture isotherms. Moreover, the isotherm models can be used to run non-isothermal breakthrough simulations along with isosteric enthalpies of adsorption from the Clausius-Clapeyron and Virial equations. Users can export detailed column and outlet profiles (e.g., composition, temperature) in multiple formats, enhancing reproducibility and data sharing among practitioners. We compared the breakthrough simulation results from the AIM workflow and compared that with the experimental data in the literature for a ternary gas mixture (CO2/H2/N2) and found excellent agreement for outlet compositions and temperature profiles.

Buoyant plumes are encountered in both natural and artificial scenarios, ranging from volcanic ash clouds and wildfires to smoke from chimneys and industrial pollutant discharge to rivers and lakes. These plumes are driven by the buoyancy forces arising from the density differences between the plume and the ambient fluids. Measurements of three dimensional density field is limited in literature and not available for buoyant plumes. Such data can lead to better understanding of the pollutant dispersion as well as fundamental nature of concentration dispersion in three-dimensional and turbulent flow. We present the three-dimensional density field measurement in buoyant plumes, particularly for forced and lazy plumes, using an in-house developed experimental rig and associated processing software. The density field reconstruction has been obtained using the tomographic background-oriented Schlieren (TBOS) technique. The experimental rig consists of eight cameras, facing random dot backgrounds placed diametrically opposite, mounted circumferentially around the buoyant plume. For the dot displacement calculation, we use a cross-correlation method. A finite difference-based Poisson solver is employed to calculate projected integrated density. The reconstruction has been performed using the Simultaneous Algebraic Reconstruction Technique (SART). The three-dimensional density field data, thus obtained is validated using existing theoretical models in the literature. We demonstrate that the 3D density field can serve as valuable data for validating and improving theoretical models of plume dynamics e.g. for the lazy plumes the measured density field is effectively used to show the puffing phenomenon.

Everyday object-based interactions (EOIs) and mid-air gesture interactions (MAIs) have been widely explored, yet prior work on their integration often targets narrow use cases or specific technologies, leaving designers and developers with limited guidance that generalizes across diverse EOIs and MAIs. We introduce Objestures ("Obj" + "Gestures") -- five interaction types spanning EOIs and MAIs, forming a design space for expressive uni- and bimanual interaction. To evaluate the usefulness of Objestures, we conducted an exploratory user study (N=12) on basic 3D tasks (rotation and scaling), which showed performance comparable to the headset's native freehand manipulation. To understand the user experience, we conducted case studies with the same participants across three applications (Sound, Draw, and Shadow), where participants found the interactions intuitive, engaging, and expressive, and indicated interest in everyday use. We further demonstrate the potential of Objestures across diverse contexts through 30 examples, and discuss limitations and implications. https://www.zhuoyuelyu.com/objestures

The stochastic Airy and sine operators, which are respectively a random Sturm-Liouville operator and a random Dirac operator, characterize the soft edge and bulk scaling limits of $β$-ensembles. Dirac and Sturm-Liouville operators are distinct operator classes which can both be represented as canonical systems, which gives a unified framework for defining important properties, such as their spectral data. Seeing both as canonical systems, we prove that in a suitable high-energy scaling limit, the Airy operator converges to the sine operator. We prove this convergence in the vague topology of canonical systems' coefficient matrices, and deduce the convergence of the associated Weyl-Titchmarsh functions and spectral measures. Our proof relies on a coupling between the Brownian paths that drive the two operators, under which the convergence holds in probability. This extends the corresponding result at the level of the eigenvalue point processes, proven by Valkó and Virág (2009) by comparison to the Gaussian $β$-ensemble.

In this paper, we study the null and approximate controllability of a class of fully nonlocal coupled stochastic reaction--convection--diffusion systems. The system consists of two forward stochastic parabolic equations driven by general second-order differential operators and incorporates four nonlocal zero-order integral terms. The nonlocality arises from integral kernel terms present in both equations, defined over a bounded domain $G \subset \mathbb{R}^N$ ($N \geq 1$). Since the coefficients depend on time, space, and random variables, we introduce three controls: a spatially localized control acting on the drift term of the first equation, and two additional controls acting on the diffusion terms of both equations. These additional controls are necessary to overcome difficulties due to the stochastic nature of the associated adjoint backward system. Using a standard duality argument, the controllability problem for the forward system is reduced to an observability problem for the corresponding adjoint nonlocal backward system. To establish this observability, we derive a new global Carleman estimate for the adjoint system, in which the drift terms belong to a negative Sobolev space and the equations include nonlocal integral terms. Our results are obtained under suitable cascade structure conditions on the coupling zero-order, nonlocal, and first-order terms of the system.

We study a generalization of the manifold-valued Rudin-Osher-Fatemi (ROF) model, which involves an initial datum $f$ mapping from a curved compact surface with smooth boundary to a complete, connected and smooth $n$-dimensional Riemannian manifold. We prove the existence and uniqueness of minimizers under curvature restrictions on the target and topological ones on the range of $f$. We obtain a series of regularity results on the associated PDE system of a relaxed functional with Neumann boundary condition. We apply these results to the ROF model to obtain Lipschitz regularity of minimizers without further requirements on the convexity of the boundary. Additionally, we provide variants of the regularity statement of independent interest: for 1-dimensional domains (related to signal denoising), local Lipschitz regularity (meaningful for image processing) and Lipschitz regularity for a version of the Mosolov problem coming from fluid mechanics.

The study of non-classicality is essential to understand the quantum-to-classical transition in physical systems. Recently, a witness of non-classicality has been proposed, linking the ability of a system (``the mediator") to create quantum correlations between two quantum probes with its non-classicality, intended as the existence of at least two non-commuting variables. Here, we propose a new inequality that quantitatively links the increase in quantum correlations between the probes to a function of the non-commutativity of the mediator's observables. We test the inequality for various degrees of non-classicality of the mediator, from fully quantum to fully classical. This quantum-to-classical transition is simulated via a phase-flip channel applied to the mediator, inducing an effective reduction of the non-commutativity of its variables. Our results provide a general framework for witnessing non-classicality, assessing the non-classicality of a system via its intrinsic properties, independently of the specific chosen interaction dynamics.