Multi-objective re-ranking has become a critical component of modern multi-stage recommender systems, as it tasked to balance multiple conflicting objectives such as accuracy, diversity, and fairness. Existing multi-objective re-ranking methods typically optimize aggregate objectives at the item level using static or handcrafted preference weights. This design overlooks that users inherently exhibit Pareto-optimal preferences at the intent level, reflecting personalized trade-offs among objectives rather than fixed weight combinations. Moreover, most approaches treat re-ranking task for each user as an isolated problem, and repeatedly learn the preferences from scratch. Such a paradigm not only incurs high computational cost, but also ignores the fact that users often share similar preference trade-off structures across objectives. Inspired by the existence of homogeneous multi-objective optimization spaces where Pareto-optimal patterns are transferable, we propose PreferRec, a novel framework that explicitly models and transfers Pareto preferences across users. Specifically, PreferRec is built upon three tightly coupled components: Preference-Aware Pareto Learning aims to capture user intrinsic trade-offs among multiple conflicting objectives at the intent level. By learning Pareto preference representations from re-ranking populations, this component explicitly models how users prioritize different objectives under diverse contexts. Knowledge-Guided Transfer facilitates efficient cross-user knowledge transfer by distilling shared optimization patterns across homogeneous optimization spaces. The transferred knowledge is then used to guide solution selection and personalized re-ranking, biasing the optimization process toward high-quality regions of the Pareto front while preserving user-specific preference characteristics.

Understanding the infrared sensitivity of perturbative predictions in QCD is important for assessing the magnitude of possible non-perturbative power corrections to processes with large momentum transfer. In renormalon models, this sensitivity can be related to computable dependences of perturbative quantities on a small gluon mass. However, this procedure cannot be applied to collider processes with gluons at the Born level. To address this problem, we promote the gluon mass to a parameter of a consistent non-Abelian quantum field theory where the gauge symmetry is spontaneously broken through the Higgs mechanism. Working in the limit in which the gluon mass $m_\mathrm{g}$ is the smallest dimensionful parameter, we compute through two loops the $\mathcal{O}(m_\mathrm{g})$ contributions to the relation between the pole and $\overline{\rm MS}$ masses of a heavy quark and to the relation between corresponding field counterterms. We expect that the proposed framework will provide a useful laboratory for probing linear infrared sensitivity of collider observables in QCD.

While change point detection in time series data has been extensively studied, little attention has been given to its generalisation to data observed on spheres or other manifolds, where changes may occur within spatially complex regions with irregular boundaries, posing significant challenges. We propose a new class of estimators, namely, Change Region Identification and SeParation (CRISP), to locate changes in the mean function of a signal-plus-noise model defined on $d$-dimensional spheres. The CRISP estimator applies to scenarios with a single change region, and is extended to multiple change regions via a newly developed generic scheme. The convergence rate of the CRISP estimator is shown to depend on the VC dimension of the hypothesis class that characterises the change regions in general. We also carefully study the case where change regions have the geometry of spherical caps. Simulations confirm the promising finite-sample performance of this approach. The CRISP estimator's practical applicability is further demonstrated through two real data sets on global temperature and ozone hole.

In this article, we investigate the centered isoperimetric inequality on Cartan-Hadamard manifolds endowed with a warped product structure, namely, among all bounded measurable sets of finite perimeter and prescribed volume, the geodesic ball centered at the pole minimizes the perimeter. Exploiting the interplay between this inequality and the underlying warped product structure, we derive several necessary geometric conditions, some of which are closely related to and comparable with phenomena identified in the work of Simon Brendle [Publ. Math. Inst. Hautes Études Sci. 117 (2013)]. We also establish a sufficient condition ensuring the validity of the centered isoperimetric inequality in this setting. Furthermore, by introducing a suitable isoperimetric-type quotient, we obtain an improvement of the classical Cheeger inequality for a broad class of manifolds. Finally, we derive a quantitative lower bound for the first nonzero Dirichlet eigenvalue of geodesic balls centered at the pole, valid for a certain class of Riemannian manifolds.

Large optical coherent-state superpositions are essential to advance quantum sensing, quantum repeaters and error-correction codes. We propose a deterministic feedforward protocol employing qubit-mode dispersive coupling, currently available in cavity quantum electrodynamics (QED). We show this single-mode protocol to outperform the advanced three-mode Gaussian-photon-number-resolving detector scheme both in terms of average fidelity and quantum non-Gaussian phase-space properties, and propose sensitivity to weak displacements of interference fringes as a feasible and conclusive witness of quantum interference. This approach combining QED with electro-optical feedforward is extendable to tailored states for applications and other platforms.

We establish well posedness of the Poisson problem in weak local John domains, for linear second order elliptic equations with real coefficients, and with data in weighted Lebesgue spaces with a very broad range of acceptable parameters.

We comment on the recent work by Yamaguchi and Barré [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By performing extensive molecular dynamics simulations with $N=10^8$ particles, we demonstrate that the bifurcation analysis of the initial stationary distribution is insufficient to predict either the location or the nature of the phase transition to a quasi-stationary state (qSS). Specifically, we show that for bimodal momentum distributions, the instability threshold identified by the authors does not correspond to a ferromagnetic transition; instead, the system remains in a paramagnetic state characterized by magnetization oscillations with a zero time-average. We find that the true paramagnetic-ferromagnetic transition is discontinuous (first-order) and occurs at significantly larger coupling strengths, characterized by a clear coexistence of states. These results indicate that linear bifurcation and symmetry-breaking phase transitions are distinct phenomena in long-range interacting systems, and that the former lacks the predictive power to describe the long-time fate of the system.

The decoding problem is a ubiquitous algorithmic task in fault-tolerant quantum computing, and solving it efficiently is essential for scalable quantum computing. Here, we prove that minimum-weight decoding is NP-hard in three quintessential settings: (i) the color code with Pauli $Z$ errors, (ii) the surface code with Pauli $X$, $Y$ and $Z$ errors, and (iii) the surface code with a transversal CNOT gate, Pauli $Z$ and measurement bit-flip errors. Our results show that computational intractability already arises in basic and practically relevant decoding problems central to both quantum memories and logical circuit implementations, highlighting a sharp computational complexity separation between minimum-weight decoding and its approximate realizations.

A DAG compression of a (typically dense) graph is a simple data structure that stores how vertex clusters are connected, where the clusters are described indirectly as sets of reachable sinks in a directed acyclic graph (DAG). They generalize tree compressions, where the clusters form a tree-like hierarchy, and we give the first proof that DAG compressions can achieve better compressions than tree compressions. Our interest in DAG compression stems from the fact that several simple standard algorithms, like breadth-first search on graphs, can be implemented so that they work directly on the compressed rather than on the original graph and so that, crucially, the runtime is relative to the (typically small) size of the compressed graph. We add another entry to the list of algorithms where this is possible, by showing that Kruskal's algorithm for computing minimum spanning trees can be adapted to work directly on DAG compressions. On the negative side, we answer the central open problem from previous work, namely how hard it is to compute a minimum-size DAG compression for a given graph: This is NP-hard; and this is even the case for the dynamic setting, where we must update the DAG compression optimally when a single edge is added or deleted in the input graph.

Recent observations by the JIRAM instrument onboard NASA's Juno mission have confirmed that many of Io's volcanic hot spots are active lava lakes, characterized by a colder central crust surrounded by a hotter peripheral ring. In this study, we investigate the thermal properties of thirty such lava lakes, providing new constraints on their structure and energy budget. We find that most of the total power from Io's lava lakes comes from their low-temperature crusts rather than the hotter peripheral rings, suggesting previous estimates underestimated lava lake power by up to a factor of 10. Io's paterae undergo stochastic resurfacing on timescales of roughly a decade, with each lake possibly following its own characteristic cycle. We also explore the relationship between the average temperature of the crust and the evolutionary state of each lake, offering insights into the frequency of resurfacing processes. Finally, we propose an improved assessment of Io's global thermal output, emphasizing that only full-surface observation of Io with sufficient spatial and spectral resolution can yield realistic values for the moon's volcanic total heat flux.

Accreting neutron stars exhibit pulsed X-rays and complex temporal variability across multi-wavelengths and different timescales. This variability could be driven by various physical processes including instability or inhomogeneous motions within the accretion flow, thermonuclear bursts on the neutron star surface. In this review, we present a concise overview of the observational features for millihertz (mHz) quasi-periodic oscillations (QPOs) at a frequency range of $\sim 1- 1000$ mHz observed in light curves of X-ray pulsars for both low-mass X-ray binaries and high-mass X-ray binaries, based on recent X-ray missions, e.g., NICER, Insight-HXMT and NuSTAR. We further summarize current theoretical interpretations, discuss remaining challenges and propose potential directions for future studies to advance the understanding of the nature and physical origin of these QPOs.

This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic differential equations (BSDEs). First, we propose a theoretical model that endogenously derives the equilibrium risk premium. Agents with exponential preferences are heterogeneous in initial wealth, risk aversion, and unspanned stochastic terminal liability. We solve the optimal investment problem using the optimal martingale principle. The equilibrium is characterized by a mean field BSDE whose driver has quadratic growth in both the stochastic integrands and their conditional expectations. We prove the existence of solutions and show that the risk premium clears the market in the large population limit. Second, we extend the model to include consumption and habit formation, relaxing the time-separability assumption of utility functions. A similar mean field BSDE is derived, and its well-posedness and asymptotic behavior are examined. We also introduce an exponential quadratic Gaussian (EQG) reformulation to obtain equilibrium solutions in semi-analytic form. Finally, the model is extended to partially observable markets where agents must infer the risk premium from stock price observations to determine trading strategies. We provide semi-analytic expressions for the equilibrium via the EQG framework, and the equilibrium risk-premium process is constructed endogenously using Kalman-Bucy filtering theory. Numerical simulations are included to visualize the resulting market dynamics.

The theory of sharp geometric inequality in $\mathbb{R}^n$ and inside convex cone has been well-developed, much less known for sharp capillary geometric inequality outside convex domain. Recently, Fusco-Julin-Morini-Pratelli \cite{FJMP} obtained sharp capillary isoperimetric inequality and make it possible to obtain the sharp capillary geometric inequality outside convex domain. In this paper, we establish the sharp capillary Sobolev inequality and Moser-Trudinger inequality outside convex domain, which can be seen as geometric inequality on the Finsler manifold to some extent. Our method is based on constructing capillary Pálya-Szegö rearrangement inequality outside convex domain. Finally, we also consider the capillary Talenti-Comparison principle and Bossel-Daners inequality.

We study experimentally the nonlinear propagation of short pulses of forward volume spin waves in nanometer-thick YIG films. We show that nonlinearity of the spin system can efficiently counteract dispersion broadening of the pulses, leading to the formation of envelope solitons. We demonstrate that in microscopic YIG systems, microwave powers of the order of one milliwatt are sufficient to reach the soliton formation threshold. At powers slightly above this threshold, we achieve transmission of 3-ns spin-wave pulses over distances of up to 50 micrometers without increase in their temporal width. Our results demonstrate a promising way towards high-rate transmission of information in microscopic spin-wave circuits unaffected by detrimental dispersion effects.

Let G be a finitely generated group, let $π\colon G \to {\rm GL}(E)$ be a uniformly bounded $c_0$-representation on a superreflexive Banach space $E$, and let $b \colon G \to E$ be a $1$-cocycle for $π$. Then $b$ has sublinear growth with respect to the word length. As a corollary we obtain the corresponding Hilbert space statement for strongly mixing unitary representations.

The evolution of pulsed discharge behavior inside a preformed air bubble in water from the first to subsequent pulses was experimentally investigated using a synchronized needle to bubble system. A positive nanosecond high-voltage pulsed power supply, together with a pulse valve and ICCD imaging, was employed to generate reproducible preformed bubbles and to record the corresponding discharge development with good temporal synchronization. The results show that, although the preformed bubbles exhibit good repeatability in size and morphology under identical conditions, the first-pulse discharge inside the bubble remains highly stochastic. The first discharge is predominantly corona-like and is not significantly affected by bubble size once the electrode is covered by the bubble. By varying the pulse width, the discharge inside the bubble was observed to evolve progressively from corona-like emission to streamer discharge, accompanied by increasing instability of the bubble interface. At sufficiently large pulse width and pulse number, bubble wrinkling and even rupture were induced. The effect of solution conductivity was also examined. Increasing conductivity significantly enhanced discharge intensity, enlarged the luminous region, and promoted streamer propagation along the inner bubble surface. At sufficiently high conductivity, the first pulse already produced strong discharge and rapid bubble rupture. In addition, the current amplitude and the energy dissipated per pulse increased with conductivity and pulse number. These results demonstrate that the discharge evolution inside a preformed bubble is jointly governed by pulse history, pulse width, and solution conductivity, and that residual effects from previous pulses play an important role in the transition from the first pulse to subsequent discharges.

We study QCD with three degenerate flavors of dynamical quarks using first-principles lattice simulations. For a specific choice of imaginary isospin chemical potential, this theory possesses an exact center symmetry, just like pure gauge theory. This exact symmetry is expected to be intact at low temperatures and spontaneously broken in the high-temperature regime. By analyzing the finite-size scaling of the Polyakov loop distribution, obtained with a dedicated multi-histogram approach, we demonstrate that there is a first-order deconfinement phase transition in between. Our results are obtained employing stout-smeared rooted staggered quarks at one lattice spacing. Using simulations at different quark masses we sketch the behavior of QCD in the mass-isospin chemical potential plane, shedding new light on this corner of the fundamental phase diagram of the strong interactions and the relationship between chiral symmetry breaking and deconfinement.

There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary conditions and imaginary potentials, we compute the predicted distribution for an experimental setup involving a single non-relativistic quantum particle with spin 0 or 1/2 in a wave guide along the $z$ axis with the detector waiting downstream. We find that the distribution shows signs of partial reflection of the wave function off of the detector; for a spin-1/2 wave function, it is independent of the initial spin orientation but does depend, for boundary conditions coupling to the spin, on the width of the wave guide. We also compare our predictions with the competing ones of Das and Dürr [arXiv:1802.07141].

A relation modification problem gets a logical structure and a natural number k as input and asks whether k modifications of the structure suffice to make it satisfy a predefined property. We provide a complete classification of the classical and parameterized complexity of relation modification problems - the latter w. r. t. the modification budget k - based on the descriptive complexity of the respective target property. We consider different types of logical structures on which modifications are performed: Whereas monadic structures and undirected graphs without self-loops each yield their own complexity landscapes, we find that modifying undirected graphs with self-loops, directed graphs, or arbitrary logical structures is equally hard w. r. t. quantifier patterns. Moreover, we observe that all classes of problems considered in this paper are subject to a strong dichotomy in the sense that they are either very easy to solve (that is, they lie in paraAC^{0\uparrow} or TC^0) or intractable (that is, they contain W[2]-hard or NP-hard problems).

Landau theory usually treats free-energy coefficients as intrinsic parameters fixed by thermodynamic variables. We show that externally written microscale fields can survive coarse graining and enter the free-energy functional as spatially prescribed coefficient fields. This defines a nonintrinsic sector of Landau theory. The key condition is a hierarchy of correlation, writing, and frustration lengths. We identify ion-patterned FeRh as a plausible realization.

Satellite observations play a critical role in numerical weather prediction where they are assimilated through an observation operator that maps model states to radiances. In the traditional Ensemble Kalman Filter, these observations are used to update the state by weighting their associated errors against model uncertainties to produce an optimal estimate. This process requires radiative transfer simulations for passive, downward-viewing satellite radiometers operating in the visible, infrared, and microwave spectra. Typically, such simulations rely on numerically integrating physical laws via models like RTTOV. In this paper, we introduce two machine learning surrogate observation operators inspired by modern computer-vision architectures: First, a fully data-driven emulator of radiative transfer, and second, a hybrid incremental correction model that learns only the residual relative to RTTOV, thereby retaining established physics while enabling data-driven refinement in complex conditions such as cloud-affected situations. The residual formulation improves radiance accuracy (lower Root Mean Squared Error (RMSE) than the fully data-driven emulator and RTTOV) and adds only moderate computational costs to the assimilation step. Both models combine 3D convolutions for vertical profile encoding with a 2D U-Net operating on latitude-longitude grids, allowing joint learning of vertical structure, spatial correlations, and inter-channel dependencies. We further provide a theoretical justification for deploying the hybrid surrogate as an observation operator in data assimilation.

Nanoscale control of optical dispersion is essential for applications ranging from miniaturized spectrometers to color printing, all of which demand broadband spectral tunability. However, the Kramers-Kronig relations impose a fundamental trade-off between dispersion and loss, strictly limiting the design ability of single-material devices across the deep ultraviolet (DUV) to near-infrared (NIR) regimes. Consequently, the fabrication of miniaturized dispersion devices heavily relies on costly nanofabrication or heterogeneous integration. Here we overcome these limitations by shifting the light-matter interaction from solid structure into air-filled voids. We introduce a fabrication strategy termed "Mie-lithography", in which laser printed seed nanocavities excite Mie resonances in air and the resulting localized field enhancement drives the self-assembly of three-dimensionally tunable void-type optical resonators. Because the resonant modes are primarily confined within air voids, this architecture effectively circumvents material-imposed dispersion-loss constraints, allowing on-demand customization of the broadband spectral response. This approach enables single-step, high-throughput (>= 10^6 pixels/s) printing of dispersion units with a resolution of 63,500 DPI. As a proof of concept, we demonstrate a DUV-NIR nano spectrometer integrated in a single material covering an unprecedented range from 200 nm to 800 nm. Our approach can be extended into a platform for ultra-broadband nano devices fabrication and design, opening avenues for high-pixel-density displays and miniaturized spectrometers.

We prove a conjecture of Migdail and Wehrli regarding the odd Khovanov cobordism maps associated to knotted spheres. Our key tool is Daemi's plane Floer homology, which we use in place of a Lee deformation. Continuing the analogy with Lee homology, we see this work as a potential first step toward a genuinely functorial model for odd Khovanov homology.

Erlang's dynamic typing discipline can lead to runtime errors that persist even after process restarts. Some of these runtime errors could be prevented through static type checking. While Erlang provides a type specification language, the compiler does not enforce these types, thereby limiting their role to documentation purposes. Type checking Erlang code is challenging due to language features such as dynamic type tests, subtyping, equi-recursive types, polymorphism, intersection types in signatures, and untagged union types. This work presents a set-theoretic type system for Erlang which captures the core features of Erlang's existing type language. The formal type system guarantees type soundness, and ensures that type checking remains decidable. Additionally, an implementation of a type checker is provided, supporting all features of the Erlang type language and most term-level language constructs. A case study with modules from Erlang's standard library, an external project, and the type checker itself demonstrates its effectiveness in verifying real-world Erlang code.

The Drinfeld center fusion category $\mathcal{Z}(\mathrm{Vec}_G)$ famously models anyons in certain lattice models. Here we demonstrate how its fusion rules may also describe topological order in fractional topological insulator materials, in the vicinity of point defects in the Brillouin zone. Concretely, we prove that $\mathcal{Z}(\mathrm{Vec}_G)$ reflects, locally over a punctured disk in the Brillouin zone, the monodromy (topological order) of gapped quantum states over the parameter space of Bloch Hamiltonians whose classifying space has fundamental group $G$.

Photon superbunching, distinguished by second-order coherence values far exceeding the Gaussian thermal limit, represents a highly desirable resource for quantum optics and correlation-based imaging technologies. However, existing approaches typically rely on fragile experimental platforms, inefficient nonlinear conversion processes, or mechanically complex optical architectures. Here, we demonstrate a fully fiber-integrated superbunched random fiber laser (SRFL) in which intrinsic Rayleigh scattering cooperatively interacts with cascaded stimulated Brillouin scattering and quasi-phase-matched four-wave mixing to tailor extreme photon statistics. The SRFL generates a multi-wavelength comb, in which individual spectral components exhibit widely tunable photon bunching, with the second-order coherence g(2)(0) continuously controlled from ~1 to ~26 by tuning the pump power, spectral order and diffusion length. Moreover, we establish a direct correlation between photonic phase transitions (quantified by the Parisi overlap order parameter) and the emergence of superbunching, thereby bridging macroscopic disorder physics and microscopic photon statistics. Finally, we employ the superbunched emission for temporal ghost imaging, realizing high-fidelity temporal object reconstruction with a substantial reduction in required ensemble averaging. These findings validate random fiber lasers as a robust, scalable, and integrated platform for generating extreme photon statistics and unlock new avenues for correlation-enhanced photonic sensing and quantum optics investigations in complex photonic systems.

Causal effect estimation often succeeds cost-constrained sequential data collection. This work considers multivariate linear front-door models with arbitrary unobserved confounding on treatment and response. We optimize the experimental design by balancing the statistical efficiency and measurement costs through partial data. The full-data efficient influence function for the causal effect is derived, together with the geometry of all observed-data influence functions. This characterization yields a closed-form optimal sampling policy and an estimator to minimize the asymptotic variance of regular asymptotically linear (RAL) estimators within a class of augmented full-data influence functions. The resulting design also covers back-door estimation. In simulations and applications to biological, medical, and industrial datasets, the optimized designs achieve substantial efficiency gains ($5.3\%$ to $31.9\%$) over naive full-sampling strategies.

This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate the equilibrium value function essential for resolving cases where the present state affecting the target functional triggers the inconsistency. Additionally, the paper offers an application exemplifying this theory through the time-inconsistent linear--quadratic regulator.

We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the $Zα$-expansion and the all-order formalism (Furry picture) optimized for the medium-mass range $(3 \leq Z \lesssim 30)$ and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear charge radii, with unprecedented precision.

We demonstrate violation of objective realism in quantum world using unconstrained weak measurements. Instead of limited Leggett-Garg approach with artificial bounds on the observed values, we assume two identical and indepenent weak detectors and final conditioning. The experimental verification has been performed on public quantum computers, IBM and IonQ. Thanks to sufficiently large statistics, the violation is observed at the level of 10 standard deviations. The tests confirmed also high quality of parametric two-qubit gates offered by main quantum hardware providers.