Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through pathwise adjoint differentiation to reduce pricing and hedging errors. However, for options with discontinuous payoffs, such as digital or barrier options, the pathwise sensitivities are biased, and incorporating them into the loss function can magnify errors. We consider alternative methods for estimating sensitivities and find that they can substantially reduce test errors in prices and in their sensitivities. Using differential labels calculated through the likelihood ratio method expands the scope of Differential ML to discontinuous payoffs. A hybrid method incorporates gamma estimates as well as delta estimates, providing further regularization.

We study the set of normalized multi-lengths for representations of closed surface groups and free groups into $(\mathrm{PSL}_2\mathbf{R})^d$ whose projections to $\mathrm{PSL}_2\mathbf{R}$ are all convex cocompact. These multi-lengths define a convex cone in $\mathbf{R}^d_{\geq 0}$, called the limit cone. When $d=3$, we show the coexistence of different regimes: for some representations the limit cone has only a finite number of sides, which we can force to grow like the genus (or free rank); for other representations, extremal rays are dense in the boundary of the limit cone. We also give examples where the limit cone varies discontinuously with the representation.

PrecisionSM is an annotated database that compiles the available data on low-energy cross sections of electron-positron collisions into hadronic channels. This database organizes and collects data samples from $e^+e^-$ experiments, which are used as input for the data-driven theoretical evaluation of the muon anomalous magnetic moment, $a_μ$, serving as a precise test of the Standard Model when compared to the experimental measurements of $a_μ$. The database is accessible through a custom website (https://precision-sm.github.io) which contains details about the data samples, such as the treatment of radiative corrections, as well as links to papers on INSPIRE-HEP and to tables on HEPData. The PrecisionSM database was developed within a Joint Research Initiative in the group application of the European hadron physics community, STRONG2020, and is now incorporated into the RadioMonteCarLow2 Working Group (RMCL2 WG) activities, which have the more general goal of improving the theoretical description of scattering processes at $e^+e^-$ colliders. The results of Phase I of the new RMCL2 WG have been published in Aliberti et al, arXiv:hep-ph/2410.22882. In this proceeding, we will report on the status of the PrecisionSM database, which currently contains a list of the dominant $2π$ channel as well as $3π$ and $π^0γ$, and on the ongoing work for the other channels and for responsive plots.

Prompt cusps (PCs) form from the direct collapse of overdensities in the early Universe, reside at the center of every dark matter halo, and have density profiles steeper than $r^{-1}$ NFW cusps. Using a suite of high-resolution N-body simulations, we study the evolution of isolated halos in self-interacting dark matter (SIDM) with massive PCs embedded at their centers, a scenario that could be realized in certain SIDM models with light mediators that predict a small-scale suppression of the linear matter power spectrum. We track the evolution of three equally concentrated $10^7\,{\rm{M}}_\odot$ halos, hosting PCs of various total masses, and quantify how the presence of a PC affects the processes of core formation and collapse. Early in the core-formation phase, halos with more prominent PCs exhibit a delayed evolution by a factor of $\sim 2$ due to smaller velocity dispersion gradients in the inner region. During most of the core-collapse phase, the halo evolution becomes closely aligned in physical time, with appropriate rescaling of densities, radii, and velocity dispersions. The scale densities and radii preserve the virial mass of the original halos, but with increased concentration. Deviations occur at the late phase of core-collapse at the level of $\sim 5\%$ relative to the reference collapse track of an NFW halo. These deviations depend non-trivially on both the increased concentration incurred by the PCs, as well as the velocity dispersion (temperature) of the outer halo regions, which can inhibit or enhance the heat transfer process. Our simulations illustrate the complex interplay between the inner and outer halo profiles in determining the onset of core collapse and motivate future studies in the full cosmological context.

Let $f_n$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_n$ cluster uniformly around the unit circle as $n$ grows large. We give a simple and self-contained proof of local universality for the correlation functions of the roots at the microscopic scale $1/n$ around a fixed point on the circle. While previous proofs of local universality were focused on studying the logarithmic potential of $f_n$, we instead directly compare the scaled random polynomial to a limiting Gaussian analytic function, and establish convergence of correlations via a soft argument, using only basic complex analysis and an anti-concentration bound of Esseen.

In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial isotropy by incorporating a deformation-based mechanism, allowing the covariance structure to capture directional effects and nonstationary spatial dependence. Temporal dynamics are modeled through dynamic linear models, enabling coherent uncertainty propagation within a state-space formulation. Missing observations are handled via a data augmentation strategy that preserves the joint structure of the multivariate responses. The proposed methodology is evaluated through simulation studies and an application to air quality data. Results indicate that accounting for spatial deformation leads to substantial gains in predictive performance in anisotropic settings, while cross-variable dependence plays a secondary role in improving overall fit. The framework is computationally tractable for moderate numbers of spatial locations and responses, and provides a flexible basis for modeling multivariate spatiotemporal processes under incomplete data.

We prove some Liouville-type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary, thereby confirming some cases of Wang's conjecture (J. Geom. Anal. 31, 2021). We further investigate Wang's conjecture on warped product manifolds and provide a partial verification of this conjecture, which also yields an alternative proof of Gu-Li's resolution of the conjecture in the $\mathbb{B}^n$ case (Math. Ann. 391, 2025). Our approach is based on a general principle of employing the P-function method to such Liouville-type results, with particular emphasis on the role of a closed conformal vector field inherent to such manifolds.

Wigner's Friend-type paradoxes challenge the assumption that events are absolute -- that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer-independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely the Local Friendliness Theorem, we introduce the Causal Friendliness Paradox, a time-ordered analogue of it. In this framework, we replace the usual locality assumption with Axiological Time Symmetry (ATS), and show that, when combined with the assumptions of Absoluteness of Observed Events (AOE), No Retrocausality (NRC), and Screening via Pseudo Events (SPE), we obtain a causal inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.

We introduce a model of dynamic matching with transferable utility, extending the static model of Shapley and Shubik (1971). Forward-looking agents have individual states that evolve with current matches. Each period, a matching market with market-clearing prices takes place. We prove the existence of an equilibrium with time-varying distributions of agent types and show it is the solution to a social planner's problem. We also prove that a stationary equilibrium exists. We introduce econometric shocks to account for unobserved heterogeneity in match formation. We propose two algorithms to compute a stationary equilibrium. We adapt both algorithms for estimation. We estimate a model of accumulation of job-specific human capital using data on Swedish engineers.

Let $\mathcal{L}$ be a centric linking system associated to a saturated fusion system on a finite $p$-group $S$. An automorphism of $\mathcal{L}$ is said to be rigid if it restricts to the identity on the fusion system. An inner rigid automorphism is conjugation by some element of the center of $S$. If $\mathcal{L}$ is the centric linking system of a finite group $G$, then rigid automorphisms of $\mathcal{L}$ are closely related to automorphisms of $G$ that centralize $S$. For odd primes, all rigid automorphisms are known to be inner, but this fails for the prime 2. We determine which known quasisimple linking systems at the prime 2 have a noninner rigid automorphism. Based on previous results, this reduces to handling the case of the linking systems at the prime 2 of finite simple groups of Lie type in odd characteristic. These have no noninner rigid automorphisms with two families of exceptions: the 2-dimensional projective special linear groups and even-dimensional orthogonal groups for quadratic forms of nonsquare discriminant.

We establish a new connection between the iHowe duality of type AIII established by Luo-Xu and the iSchur duality established by Bao-Wang. We show that iweight $\overlineρ$ space in the iHowe duality is naturally isomorphic to the tensor space in the iSchur duality. Under this isomorphism, we show that the relative braid group action on this iweight space coincides with the action of the type B Hecke algebra in the iSchur duality. As a consequence, we derive from multiplicity-free decompositions that the iweight $\overlineρ$ spaces of irreducible modules over iquantum groups are irreducible modules over the type B Hecke algebra. Meanwhile, in the iHowe duality, we identify the relative braid group action from one side with the action of $K$-matrices and $R$-matrices from the other side.

This paper investigates a flexible intelligent metasurface (FIM)-enabled wireless communication system that integrates simultaneously transmitting and reflecting beyond diagonal reconfigurable intelligent surfaces (STAR-BD-RIS) with non-orthogonal multiple access (NOMA). The considered system consists of a multi-antenna FIM-assisted base station (BS) supported by dual-sector BD-RIS. The FIM is composed of low-cost radiating elements capable of independent signal transmission and dynamic vertical reconfiguration (morphing). The objective is to maximize energy efficiency (EE) by jointly optimizing the BS beamforming, STAR-BD-RIS configuration, NOMA-related variables, and the FIM surface shape under practical power constraints. Due to the highly non-convex nature of the problem, an adaptive inverse-weighted Meta-Soft Actor-Critic (AIW-Meta-SAC) algorithm is proposed. Unlike conventional Meta-SAC approaches, the proposed method employs an adaptive weighting mechanism to effectively incorporate system constraints into the reward function, thereby improving learning efficiency and convergence behavior. Simulation results demonstrate that the proposed AIW-Meta-SAC significantly outperforms the Meta-DDPG baseline. Furthermore, the FIM-assisted STAR-BD-RIS architecture achieves notable energy efficiency gains compared to conventional benchmark schemes.

As a branch of quantum machine learning, quantum reinforcement learning (QRL) aims to solve complex sequential decision-making problems more efficiently and effectively than its classical counterpart by exploiting quantum resources. However, in the noisy intermediate-scale quantum (NISQ) era, its realization is challenged by the ubiquitous noise-induced decoherence. Here, we propose a noise-resilient QRL scheme for a quantum eigensolver with a two-level system as an agent. By investigating the non-Markovian decoherence effect on the QRL for solving the eigenstates of the agent-environment interaction Hamiltonian, we find that the formation of a bound state in the energy spectrum of the total agent-noise system restores the QRL performance to that in the noiseless case. Providing a universal physical mechanism to suppress the decoherence effect on quantum machine learning, our result lays the foundation for designing NISQ algorithms and offers a guideline for their practical implementation.

In this work, focusing on a critical case for shear flows of nematic liquid crystals, we investigate multiplicity and stability of stationary solutions via the parabolic Ericksen-Leslie system. We establish a one-to-one correspondence between the set of the stationary solutions with the set of the solutions of an algebraic equation for a cusp case. This one-to-one correspondence is established essentially based on the treatment in the work of Jiao, et. al. [{\em J. Diff. Dyn. Syst. {\bf 34} (2022), 239-269}] for a different case, and the relation gives directly parameter ranges for existence of multiple stationary solutions; in particular, multiple stationary solutions are created through countably many saddle-node bifurcations for the algebraic equation at critical shear speeds. The main result of the paper is on the stability of stationary solutions associated to the bifurcations; more precisely, (i) for each critical shear speed, there is a unique stationary solution and, for smaller shear speed, the stationary solution disappears but, for larger shear speed, two stationary solutions nearby bifurcate; (ii) more importantly, under a generic condition, there is a simple zero eigenvalue for the linearization of the shear flow at the critical stationary solution and, for larger shear speed, the zero eigenvalue bifurcates to a negative eigenvalue for one of the two stationary solutions and to a positive eigenvalue for the other stationary solution.

Performance prediction is essential for energy-efficient computing in heterogeneous computing systems that integrate CPUs and GPUs. However, traditional performance modeling methods often rely on exhaustive offline profiling, which becomes impractical due to the large setting space and the high cost of profiling large-scale applications. In this paper, we present OPEN, a framework consists of offline and online phases. The offline phase involves building a performance predictor and constructing an initial dense matrix. In the online phase, OPEN performs lightweight online profiling, and leverages the performance predictor with collaborative filtering to make performance prediction. We evaluate OPEN on multiple heterogeneous systems, including those equipped with A100 and A30 GPUs. Results show that OPEN achieves prediction accuracy up to 98.29\%. This demonstrates that OPEN effectively reduces profiling cost while maintaining high accuracy, making it practical for power-aware performance modeling in modern HPC environments. Overall, OPEN provides a lightweight solution for performance prediction under power constraints, enabling better runtime decisions in power-aware computing environments.

A flux of ultra-high-energy (UHE) neutrinos, produced by astrophysical sources at cosmological distances, is anticipated to exist and reach Earth. In this paper, we investigate the impact on the total flux, energy spectrum, and arrival directions of UHE neutrinos of neutrino-dark matter (DM) scatterings. We study scatterings both in the intergalactic medium and in the Milky Way. We emphasize the complementarity among neutrino detectors at different latitudes, that can probe anisotropies induced by neutrinos scattering with the Milky Way DM halo. We also discuss that, with mild astrophysical assumptions, limits on the DM-$ν$ scattering cross section can be placed even if the neutrino sources are unknown. Finally, we explore all this phenomenology with the recent UHE neutrino event KM3230213A, and place the corresponding limits on the DM-$ν$ scattering cross section.

The individual component spins of binary black holes (BBHs) are difficult to resolve using gravitational-wave observations but carry key signatures of the processes shaping their formation and evolution. Recent analyses have found conflicting evidence for a sub-population of black holes with negligible spin, but the Default spin magnitude population model used in LIGO-Virgo-KAGRA analyses cannot formally accommodate an excess of systems with zero spin. In this work, we analyze several different simulated BBH populations to demonstrate that even in the face of this mismodeling, spinning and nonspinning populations can be reliably distinguished using the Default spin magnitude population model coupled with spin sorting. While typical analyses sort the binary components by their masses, sorting the components by their spin magnitudes instead offers a complementary view of the properties of individual systems consistent with equal mass and of population-level properties, given binary evolution processes like tidal-spin up that predict asymmetric spin magnitudes among the binary components. We conclude that current observations of the BBH population are inconsistent with a fully nonspinning population, but could be explained by a population with only one spinning black hole per binary or a population with up to 80% nonspinning sources.

A search for Higgs boson pair production in the $b \bar{b} γγ$ final state is performed. The proton-proton collision dataset corresponds to an integrated luminosity of 308 fb$^{-1}$, consisting of two samples, 140 fb$^{-1}$ at a centre-of-mass energy of $\sqrt{s} = 13$ TeV and 168 fb$^{-1}$ at $\sqrt{s} =13.6$ TeV, recorded between 2015 and 2024 by the ATLAS detector at the CERN Large Hadron Collider. In addition to a larger dataset, this analysis improves upon the previous search in the same final state through several methodological and technical developments. The Higgs boson pair production cross section divided by the Standard Model prediction is found to be $μ_{HH} = 0.9^{+1.4}_{-1.1}$ ($μ_{HH} = 1^{+1.3}_{-1.0}$ expected), which translates into a 95% confidence-level upper limit of $μ_{HH}<3.7$. At the same confidence level the Higgs self-coupling modifier is constrained to be in the range $-1.6 < κ_λ< 6.6$ ($-1.8 < κ_λ< 6.9$ expected).

Sharing health and behavioral data raises significant privacy concerns, as conventional de-identification methods are susceptible to privacy attacks. Differential Privacy (DP) provides formal guarantees against re-identification risks, but practical implementation necessitates balancing privacy protection and the utility of data. We demonstrate the use of DP to protect individuals in a real behavioral health study, while making the data publicly available and retaining high utility for downstream users of the data. We use the Adaptive Iterative Mechanism (AIM) to generate DP synthetic data for Phase 1 of the Lived Experiences Measured Using Rings Study (LEMURS). The LEMURS dataset comprises physiological measurements from wearable devices (Oura rings) and self-reported survey data from first-year college students. We evaluate the synthetic datasets across a range of privacy budgets, epsilon = 1 to 100, focusing on the trade-off between privacy and utility. We evaluate the utility of the synthetic data using a framework informed by actual uses of the LEMURS dataset. Our evaluation identifies the trade-off between privacy and utility across synthetic datasets generated with different privacy budgets. We find that synthetic data sets with epsilon = 5 preserve adequate predictive utility while significantly mitigating privacy risks. Our methodology establishes a reproducible framework for evaluating the practical impacts of epsilon on generating private synthetic datasets with numerous attributes and records, contributing to informed decision-making in data sharing practices.

In this paper, we describe some interesting properties of a non-Hermitian Jaynes-Cummings model. For this particular model, it is known that the Hilbert space can be described by infinitely-many two-dimensional invariant (closed) subspaces, together with the global ground state. We expose the appearance of exceptional points on such two-dimensional subspaces, together with quantum phase transitions marking the transition from real to complex eigenvalues. We also compute the spin-oscillator entanglement entropy on each invariant subspace to show that the two phases can be distinguished by their distinct entanglement-entropy profiles.

Although time-reversal and inversion symmetry constrain the angular momentum of each phonon mode to vanish, we show that the vacuum state of crystals with such symmetries can nevertheless exhibit finite angular momentum fluctuations, which persist at finite temperature. These fluctuations arise from quantum coherence between nondegenerate modes with noncollinear polarizations and are encoded in the off-diagonal components of the angular momentum operator. Their origin lies in the noncommutativity between the phonon Hamiltonian and angular momentum, which enables time-dependent rotational dynamics even in symmetric vacua. Using a minimal model, we provide an intuitive picture of this phenomenon in terms of beating between linearly polarized modes, which generates a finite instantaneous angular momentum while remaining symmetry-forbidden in the mean. We further show that these vacuum fluctuations give rise to distinct finite-frequency spectral signatures and outline a concrete route for their detection using time-resolved spectroscopic probes sensitive to lattice polarization and symmetry. Our results identify a previously unexplored regime of lattice dynamics, revealing that even the symmetric phonon vacuum can harbor structured, dynamical angular-momentum correlations.

Stellar streams are sensitive laboratories for understanding the small-scale structure in our Galaxy's gravitational field. Here, we analyze the morphology of the $300S$ stellar stream, which has an eccentric, retrograde orbit and thus could be an especially powerful probe of both baryonic and dark substructures within the Milky Way. Due to extensive background contamination from the Sagittarius stream (Sgr), we perform an analysis combining Dark Energy Camera Legacy Survey photometry, $\textit{Gaia}$ DR3 proper motions, and spectroscopy from the Southern Stellar Stream Spectroscopic Survey ($\textit{S}^5$). We redetermine the stream coordinate system and distance gradient, then apply two approaches to describe $300S$'s morphology. In the first, we analyze stars from $\textit{Gaia}$ using proper motions to remove Sgr. In the second, we generate a simultaneous model of $300S$ and Sgr based purely on photometric information. Both approaches agree within their respective domains and describe the stream over a region spanning $33^\circ$. Overall, $300S$ has three well-defined density peaks and smooth variations in stream width. Furthermore, $300S$ has a possible gap of $\sim 4.7^\circ$ and a kink. Dynamical modeling of the kink implies that $300S$ was dramatically influenced by the Large Magellanic Cloud. This is the first model of $300S$'s morphology across its entire known footprint, opening the door for deeper analysis to constrain the structures of the Milky Way.

We theoretically investigate the role of spatial dimension and driving frequency in a non-equilibrium phase transition of a driven-dissipative interacting bosonic system. In this setting, spatial dimension is dictated by the shape of the external driving field. We consider both homogeneous driving configurations, which correspond to standard integer-dimensional systems, and fractal driving patterns, which give rise to a non-integer Hausdorff dimension for the spatial density. The onset of criticality is characterized by critical slowing down in the excited density dynamics as the system asymptotically approaches the steady state. By analyzing the system-size dependence of the asymptotic decay rate using numerical simulations of the full multi-mode dynamics, complemented by an analytical statistical mean-field treatment, we determine the lower critical dimension of the non-equilibrium phase transition. We show that this dimension can be non-integer and fractal in nature, and that it can be tuned continuously via the frequency detuning of the driving field.

We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique strong solution to the associated Fokker-Planck equation. Our proof is based on tools from PDE analysis, stochastic analysis, functional inequalities, and also we use the dissipation of entropy which provides some bound on the Fisher information of the particle system. The approach applies to repulsive and attractive kernels.

Horizon Brightened Acceleration Radiation (HBAR) signifies a unique radiation process and provides a promising framework in exploring acceleration radiation in flat/ curved spacetime. Its construction primarily relies on the transition probability of an atom falling through a high-Q cavity while interacting with a quantum field. The HBAR effect has typically been explored in the context of minimal coupling between the atom and the field amplitude. However, the minimally coupled models are affected by the infrared (IR) divergences that arise in the massless limit of the quantum fields in (1+1) dimensions. Thus, in the present manuscript, we examine the HBAR process using both the point-like and finite size detectors coupled with the momentum of the field, which plays a crucial role in naturally resolving IR divergences. Our results suggest that the transition probability for the point-like detector is independent of its frequency. This can be interpreted as the influence of the local gravitational field which modifies the sensitivity of the detector to its frequency and broadens its effective frequency range. Through a comparative study based on the length of the detector, we find that for a detector with a smaller length, the steady state solution for the density matrix of the field vanishes. This may indicate the existence of a non equilibrium thermodynamic state under the condition of finite size detector-field interaction. These distinctive features are exclusive to the derivative coupling between the atom and the field, highlighting them as a compelling subject for future investigation.

The first transmission spectrum of the habitable-zone sub-Neptune K2-18 b with JWST has opened a new avenue for atmospheric characterisation of temperate low-mass exoplanets. The observations led to inferences of methane and carbon dioxide, as well as of dimethyl sulfide (DMS) and/or dimethyl disulfide (DMDS), both potential biosignatures. In the present work we conduct a broad and agnostic search for other chemical species in the atmosphere of K2-18 b. Our exploration includes 661 molecules, spanning a wide range of trace gases, including biotic, abiotic, and anthropogenic gases on Earth. We investigate possible preference for any of these gases, compared to a model only including the previously-detected CH$_4$ and CO$_2$, using three metrics: (a) preference in the JWST mid-infrared (MIR) spectrum, (b) preference in the JWST near-infrared spectrum, for species preferred in MIR and (c) plausible sources of production. We find that only DMS consistently results in Bayes factors $\ln B \geq 2.0$ across the datasets considered independently, though in the near-infrared this depends on detector offsets, as previously reported. The threshold of $\ln B \geq 2.0$ is motivated by the conventional threshold of $\ln B \geq 2.5$ for moderate preference, allowing for an empirical uncertainty of 0.5. A few other gases also provide comparable fits to a subset of the data or only with some of the retrieval codes used, but with limited known plausible sources. Our study highlights the need for further observations to distinguish between possible trace gases in the atmosphere of K2-18 b and theoretical work to establish their plausible sources.

Flat bands exhibit high degeneracy and intrinsic localization, offering a promising platform for enhanced light-matter interactions. Here, we investigate the resonant interaction between a two-level emitter and a chiral flat band hosted by a photonic lattice. In the weak coupling regime, the emitter undergoes Rabi oscillations with a lifted photonic mode whose spatial structure reflects the nature of compact localized states and the onset of Anderson localization. We show that weak hopping disorder induces a delocalization of the lifted mode whereas the effective emitter-field coupling strength, and the associated mode volume experienced by the emitter, remains protected against structural fluctuations. We illustrate our approach using selected flat band lattices. Our findings provide a route to flat band state preparation via quench dynamics and robust cavity-QED control.

A function $φ:\{0,1\}^n \to \{0,1\}^N$ is called an isometric embedding of the $n$-dimensional Hamming metric space to the $N$-dimensional edit metric space if, for all $x,y\in\{0,1\}^n$, the Hamming distance between $x$ and $y$ is equal to the edit distance between $φ(x)$ and $φ(y)$. The rate of such an embedding is defined as the ratio $n/N$. It is well known in the literature how to construct isometric embeddings with rate $Ω(1/\log n)$. However, achieving even near-isometric embeddings with positive constant rate has remained elusive until now. In this paper, we present an isometric embedding with rate $1/8$ by discovering connections to synchronization strings, which were studied in the context of insertion-deletion codes (Haeupler-Shahrasbi [JACM'21]). At a technical level, we introduce a framework for obtaining high-rate isometric embeddings using a novel object called misaligners. As an immediate consequence of our constant-rate isometric embedding, we improve known conditional lower bounds for various optimization problems in the edit metric, now with optimal dependence on the dimension. We complement our results by showing that no isometric embedding $φ:\{0,1\}^n \to \{0,1\}^N$ can have rate greater than $15/32$ for all positive integers $n$. En route to proving this upper bound, we uncover fundamental structural properties necessary for every Hamming-to-edit isometric embedding. We also prove similar upper and lower bounds for embeddings over larger alphabets. Finally, we consider embeddings $φ:Σ_{\mathrm{in}}^n \to Σ_{\mathrm{out}}^N$ between different input and output alphabets, where the rate is given by $\frac{n\log|Σ_{\mathrm{in}}|}{N\log|Σ_{\mathrm{out}}|}$. In this setting, we show that the rate can be made arbitrarily close to $1$.

Markovian open quantum systems are described by the Lindblad master equation $\partial_tρ=\mathcal{L}(ρ)$, where $ρ$ denotes the system's density operator and $\mathcal{L}$ the Liouville super-operator, which is also known as the Liouvillian. For systems with a finite-dimensional Hilbert space, it is a fundamental property of the Liouvillian that the real parts of all its eigenvalues are non-positive. Analogously, for infinite-dimensional Hilbert spaces, the Liouvillian as a map on trace-class operators only has spectral values with non-positive real parts. The usual arguments for these properties are indirect, using that $\mathcal{L}$ generates a quantum channel and that quantum channels are contractive. We provide a direct algebraic proof based on the Lindblad form of Liouvillians.

A slightly tilted permanent magnet rotating at high speed can induce a magnetic field capable of trapping another permanent magnet in a gravity independent levitated bound state, bypassing Earnshaw's theorem. During levitation, the floater magnet is locked in a conical orbit at the same frequency as the rotor. This rotation allows the sides of the same polarity of each magnet to face each other, which is responsible for the dynamic equilibrium of the floater magnet. Here, we theoretically explain the motion of the floater in-axis and off-axis and highlight levitation stability conditions and their dependence on the size of the floater and the speed of the rotor. We also experimentally studied the levitation conditions with respect to the rotational speed of the rotor for various floater's sizes and shapes. We observed and analyzed the lower and upper limits of levitation. Finally, we explained the off-axis motion of the center of mass of the floater from its equilibrium position by an extension of the dipole moment model.