This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly on the group structure using a minimal Lie algebra parametrization, avoiding redundant matrix representations and eliminating explicit dependence on Riemannian metrics. A primal-dual formulation is developed in which the Newton system is constructed through sensitivity and curvature matrices. Also, multiplicative updates are performed via the exponential map, ensuring intrinsic feasibility with respect to the group structure while maintaining strict positivity of slack and dual variables through a barrier strategy. A local analysis establishes quadratic convergence under standard regularity assumptions and characterizes the behavior under inexact Newton steps. Statistical comparisons against Riemannian Interior-Point Methods, specifically for optimization problems defined over the Special Orthogonal Group SO(n) and Special Linear Group SL(n), demonstrate that the proposed approach achieves higher success rates, fewer iterations, and superior numerical accuracy. Furthermore, its robustness under perturbations suggests that this method serves as a consistent and reliable alternative for structured manifold optimization.

The kSZ effect has recently emerged as a powerful probe for precision cosmology through its ability to reconstruct the large-scale velocity field. In particular, the kSZ-reconstructed velocity-galaxy cross-correlation is sensitive to signatures of primordial non-Gaussianity through its imprint on the galaxy bias. The kSZ velocity reconstruction is performed using small-scale information from CMB temperature and galaxy overdensities. As the sensitivity of these measurements improves, systematic effects such as extragalactic foreground contamination present in CMB maps become increasingly important. We present a study of foreground biases to the kSZ-reconstructed velocity-galaxy cross-correlation. We derive the relevant foreground contributions from the thermal Sunyaev-Zel'dovich effect and the cosmic infrared background, modeling them using a halo model description of the dominant one- and two-halo terms. We compare our analytic predictions to measurements obtained using ACT DR6 temperature maps and DESI Legacy Imaging Survey galaxies, finding qualitative agreement. We introduce a parity-odd estimator constructed from antisymmetric combinations of tomographic velocity-galaxy correlations and show analytically that, under the Limber approximation, this estimator entirely cancels the foreground contamination while preserving the full cosmological signal without loss of signal-to-noise. Finally, we apply this parity-odd estimator to the data combination mentioned above and show that the fit to the velocity-galaxy correlation is dramatically improved compared to the analysis without mitigation; our estimator detects the signal at 11$σ$, with an amplitude consistent with recent studies.

We construct the first weakly special surfaces that are not Campana-special, including the complement of the plane curve $x^2y^3 = 1$ in $\mathbb{A}^2$. We prove that the set of $\mathcal{O}_{K,S}$-integral points on this surface is non-dense for every number field $K$ and finite set $S$ of finite places of $K$ if and only if Campana's Orbifold Mordell conjecture holds for $(\mathbb{G}_m, \tfrac{1}{2}[1])$. This basic example carries a natural $\mathbb{G}_m$-action, and the quotient stack is an Artin stack parametrizing points on a C-pair. This leads to the introduction of ``Campana stacks'', which encode morphisms of C-pairs in a manner analogous to the role of root stacks for integral points satisfying prescribed divisibility conditions.

The directed flow ($v_1$) of identified hadrons ($π^{\pm}, K^{\pm}, p, \bar{p}, ϕ, Λ$, and $\barΛ$) is studied in symmetric nuclear collisions (O+O, Cu+Cu, Ru+Ru, Au+Au, and U+U) at $\sqrt{s_{NN}} = 200$ GeV using the string-melting version of a multiphase transport model with improved quark coalescence. The mid-rapidity $v_1$-slope ($dv_1/dy$) and its charge-dependent splitting ($Δdv_1/dy$) between particles and anti-particles are investigated as a function of nuclear mass number ($A$) and collision centrality in both low-$p_\mathrm{T}$ (0.2$-$2.0 GeV/$c$) and high-$p_\mathrm{T}$ (2.0$-$5.0 GeV/$c$) regions. At low-$p_\mathrm{T}$, the $v_1$-slope shows weak system-size dependence, while at high-$p_\mathrm{T}$ strong system-size dependence is found and it becomes negative with nuclear mass number, reflecting the hard-soft asymmetry in particle production. The charge-dependent splitting $Δdv_1/dy$ reveals a striking baryon-meson dichotomy: baryon pairs ($p-\bar{p}$ and $Λ-\barΛ$) exhibit significant splitting that grows with system size, whereas meson pairs ($π^+-π^-$ and $K^+-K^-$) show minimal splitting. The effect of final state hadronic interactions on the $v_1$-slope is found to be negligible confirming that it is primarily generated during the partonic phase and coalescence process. A comparison of the AMPT results with measurements from the STAR experiment at RHIC in Au+Au collisions establish the transported quark contribution as a baseline for the observed charge-dependent $v_1$ splitting, on top of which electromagnetic field effects must be considered.

We present SNID-SAGE (SuperNova IDentification-Spectral Analysis and Guided Exploration), a framework for supernova spectral classification with both a fully interactive graphical interface and a scriptable command-line pipeline for large-scale processing. The pipeline combines deterministic spectral preprocessing, FFT-based cross-correlation against a curated template library, ranking of candidate matches using a composite quality metric, and consolidation of redshift and classification solutions into a single result with associated quality and confidence estimates. SNID-SAGE includes an upgradeable template library (about 6000 spectra), interactive line identification with velocity measurements, and optional natural-language summaries of classification results. We evaluate SNID-SAGE using two complementary tests: (i) leave-one-out cross-validation, in which each template spectrum is matched against the remainder of the library; and (ii) large-scale application to WISeREP spectra with valid coverage across the 4000-7000 A interval, irrespective of spectral type, comprising approximately 46 000 spectra, with redshift validation against known host-galaxy measurements where available. The full validation results and the SNID-SAGE framework are publicly available, supporting integration into spectroscopic survey workflows.

We prove a general upper bound on the $k$-th adjacency eigenvalue of a graph. For $k\ge 2$, we show that \[ λ_k(G)\le \frac{(k-2)\sqrt{k+1}+2}{2k(k-1)}\,n-1 \] for every graph $G$ on $n$ vertices. We build on a recent approach that addresses the case $k=3$ and generalize the upper bound for all $k \geq 3$ by using the positivity of Gegenbauer polynomials. The upper bound is tight for $k \in \{2,3,4,8,24\}$. We also highlight the close relation of $λ_k(G)$ to questions about equiangular lines.

This paper introduces a methodology to calibrate Radio-Frequency Digital Twins (RF-DTs) for Integrated Sensing and Communication (ISAC) in dynamic wireless environments. The approach leverages high-resolution ray tracing in combination with wideband channel sounding to ensure consistency between simulated and measured propagation. The methodology is validated in urban scenarios featuring both mono-static and bi-static configurations, as well as moving user platforms and vehicles. Results show that the calibrated RF-DT reproduces key propagation effects, including multipath evolution, dynamic scatterers, and Doppler-induced signatures, with close agreement to measurements. These findings confirm that accurate geometry, material modeling, antenna patterns, and diffuse scattering are essential for realistic high-frequency ISAC simulation. By bridging the gap between simulation and measurement, the proposed calibration framework provides a scalable tool for developing and evaluating ISAC algorithms in complex, time-varying environments envisioned for 6G.

Multicomponent gel systems have garnered much interest due to their compelling mechanical properties in the past decade. Yet, some mechanisms associated with multicomponent gels, such as sequential gelation, have been explored primarily in the context of chemical nonreversible polymeric and protein gels than in physical reversible colloidal ones. In this study, we use mesoscale simulation techniques to model the sequential gelation of two-component colloidal systems whose components' interspecies and intraspecies electrostatic interactions can be modified independently. We show that by simply leveraging temporal control and interspecies interactions, we can construct markedly different networks; from double networks to mixed and core-shell composite structures of varying coarseness and heterogeneity natures. These findings present a compelling case for further exploration of multicomponent colloidal systems.

The advent of quantum computing poses significant threats to classical public-key cryptographic primitives such as RSA and elliptic-curve cryptography. As many critical network and security protocols depend on these primitives for key exchange and authentication, there is an urgent need to understand their quantum vulnerability and assess the progress made towards integrating post-quantum cryptography (PQC). This survey provides a detailed examination of nine widely deployed protocols - TLS, IPsec, BGP, DNSSEC, SSH, QUIC, OpenID Connect, OpenVPN, and Signal Protocol - analysing their cryptographic foundations, quantum risks, and the current state of PQC migration. We find that TLS and Signal lead the transition with hybrid post-quantum key exchange already deployed at scale, while IPsec and SSH have standardised mechanisms but lack widespread production adoption. DNSSEC and BGP face the most significant structural barriers, as post-quantum signature sizes conflict with fundamental protocol constraints. Across all protocols, key exchange proves consistently easier to migrate than authentication, and protocol-level limitations such as message size and fragmentation often dominate over raw algorithm performance. We also discuss experimental deployments and emerging standards that are shaping the path towards a quantum-resistant communication infrastructure.

Today's internet concentrates identity, payments, communication, and content hosting under a small number of corporate intermediaries, creating single points of failure, enabling censorship, and extracting economic rent from participants. We present BitSov, an architectural framework for sovereign internet infrastructure that composes existing decentralized technologies (Bitcoin, Lightning Network, decentralized storage, federated messaging, and mesh connectivity) into a unified, eight-layer protocol stack anchored to Bitcoin's base layer. The framework introduces three architectural patterns: (1) payment-gated messaging, where every transmitted message requires cryptographic proof of a Bitcoin payment, deterring spam through economic incentives rather than moderation; (2) timechain-locked contracts, which anchor subscriptions and licenses to Bitcoin block height (the timechain) rather than calendar dates; and (3) a self-sustaining economic flywheel that converts service revenue into infrastructure growth. A dual settlement model supports both on-chain transactions for permanence and auditability and Lightning micropayments for high-frequency messaging. As a position paper, we analyze the quality attributes, discuss open challenges, and propose a research agenda for empirical validation.

Floquet engineering provides a powerful pathway for creating non-equilibrium phases of matter with tailored electronic structures and properties through time-periodic driving. As the original theoretical prototype, graphene established the framework in which the Floquet topological insulator with light-induced anomalous Hall effect was proposed. However, the defining spectroscopic signature of Floquet engineering in graphene--light-induced hybridization (avoided-crossing) gap at Floquet band crossings, has remained experimentally elusive. Here, we report direct observation of Floquet-induced hybridization gap in monolayer graphene under resonant driving by a strong light field. Time- and angle-resolved photoemission spectroscopy reveals gap opening at Floquet band crossings, accompanied by coherent Floquet sidebands. The gap exhibits pronounced momentum anisotropy, featuring two Dirac nodes protected by the spatiotemporal symmetry and tunable by light polarization. These results provide long-sought experimental demonstration of Floquet band engineering in graphene, opening up opportunities for light-field engineered quantum phases in graphene and related materials.

Articulatory-to-acoustic inversion strongly depends on the type of data used. While most previous studies rely on EMA, which is limited by the number of sensors and restricted to accessible articulators, we propose an approach aiming at a complete inversion of the vocal tract, from the glottis to the lips. To this end, we used approximately 3.5 hours of RT-MRI data from a single speaker. The innovation of our approach lies in the use of articulator contours automatically extracted from MRI images, rather than relying on the raw images themselves. By focusing on these contours, the model prioritizes the essential geometric dynamics of the vocal tract while discarding redundant pixel-level information. These contours, alongside denoised audio, were then processed using a Bi-LSTM architecture. Two experiments were conducted: (1) the analysis of the impact of the audio embedding, for which three types of embeddings were evaluated as input to the model (MFCCs, LCCs, and HuBERT), and (2) the study of the influence of the dataset size, which we varied from 10 minutes to 3.5 hours. Evaluation was performed on the test data using RMSE, median error, as well as Tract Variables, to which we added an additional measurement: the larynx height. The average RMSE obtained is 1.48\,mm, compared with the pixel size (1.62\,mm). These results confirm the feasibility of a complete vocal-tract inversion using RT-MRI data.

We study the number entropy and quasiparticle width in one-dimensional quasiperiodic many-body localized (MBL) systems and observe slow dynamics that have previously been investigated in detail only in random systems. In contrast, quasiperiodic systems exhibit more structured growth of both observables. We identify the modulation of the Rabi oscillation amplitude of single-particle hoppings as the mechanism underlying the slow growth even deep in the MBL regime. This quantum amplitude modulation and associated beats arise from the interaction between single-particle hopping processes at different positions in the chain. Interestingly, this mechanism is not weakened by increasing the distance between particles and is generic to many-body quantum systems. We develop an analytical model based on the aforementioned mechanism that explains the observed dynamics at all accessible timescales and provides a microscopic picture of the slow dynamics in the MBL regime. Our results are consistent with the stability of the MBL phase in the thermodynamic limit.

Sleep is vital for maintaining cognitive function, facilitating metabolic waste removal, and supporting memory consolidation. However, modern societal demands, particularly shift work, often disrupt natural sleep patterns. This can induce excessive sleepiness among shift workers in critical sectors such as healthcare and transportation and increase the risk of accidents. The primary contributors to this issue are misalignments of circadian rhythms and enforced sleep-wake schedules. Regulating circadian rhythms that are tied to alertness can be regarded as a control problem with control inputs in the form of light and sleep schedules. In this paper, we address the problem of optimizing alertness by optimizing light and sleep schedules to improve the cognitive performance of shift workers. A key tool in our approach is a mathematical model that relates the control input variables (sleep and lighting schedules) to the dynamics of the circadian clock and sleep. In the sleep and circadian modeling literature, the newer physiology-based model shows better accuracy in predicting the alertness of shift workers than the phenomenology-based model, but the dynamics of physiological-based model have differential equations with different time scales, which pose challenges in optimization. To overcome the challenge, we propose a hybrid version of the PR model by applying singular perturbation techniques to reduce the system to a non-stiff, differentiable hybrid system. This reformulation facilitates the application of the calculus of variation and the gradient descent method to find the optimal light and sleep schedules that maximize the subjective alertness of shift worker. Our approach is validated through numerical simulations, and the simulation results demonstrate improved alertness compared to other existing schedules.

We study dispersive decay for non-autonomous Hamiltonian systems. While the general theory for dispersion in such non-autonomous systems is largely open, it was shown \cite{kraisler2025time} that there exists a time-periodically forced one-dimensional Dirac equation with unusually slow dispersive decay rate of $t^{-1/5}$. It is to be expected that such behavior is not generic and requires a very particular forcing term; we provide a more general ansatz and systematic procedure to construct such an equation with a dispersive decay rate no faster than $t^{-1/10}$. Our limitations are purely algebraic and it stands to reason that arbitrarily slow decay, $t^{-\varepsilon}$ for every $\varepsilon > 0$, should be achievable.

Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining coherence via a set of orthogonal projectors. Within this framework, we investigates the construction and comparison of block coherence measures. First, we propose two universal methods for constructing coherence measures and introduce a two-parameter family of measures based on the $α$-$z$ Rényi relative entropy and a family of measures based on the Tsallis relative operator entropy. Second, through theoretical proofs and numerical counterexamples, we compares the ordering relations and numerical magnitudes among different block coherence measures and establishes a series of universal numerical inequalities to constrain their values. Besides, we also use $C_{α,1}$ to show the role of coherence in complex dynamic evolution of the Kominis master equation that includes recombination reactions.

The human heart is a sophisticated system composed of four cardiac chambers with distinct shapes, which function in a coordinated manner. Existing shape models of the heart mainly focus on the ventricular chambers and they are derived from relatively small datasets. Here, we present a spatio-temporal (3D+t) statistical shape model of all four cardiac chambers, learnt from a large population of nearly 100,000 participants from the UK Biobank. A deep learning-based pipeline is developed to reconstruct 3D+t four-chamber meshes from the cardiac magnetic resonance images of the UK Biobank imaging population. Based on the reconstructed meshes, a 3D+t statistical shape model is learnt to characterise the shape variations and motion patterns of the four cardiac chambers. We reveal the associations of the four-chamber shape model with demographics, anthropometrics, cardiovascular risk factors, and cardiac diseases. Compared to conventional image-derived phenotypes, we validate that the four-chamber shape-derived phenotypes significantly enhance the performance in downstream tasks, including cardiovascular disease classification and heart age prediction. Furthermore, we demonstrate the effectiveness of shape-derived phenotypes in novel applications such as heart shape retrieval and heart re-identification from longitudinal data. To facilitate future research, we will release the learning-based mesh reconstruction pipeline, the four-chamber cardiac shape model, and return all derived four-chamber meshes to the UK Biobank.

The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at extreme scales. To address these challenges, asynchronous computing approaches that relax communication and synchronization at a mathematical level have been proposed. In particular, the asynchronous discontinuous Galerkin (ADG) method with asynchrony-tolerant (AT) fluxes has recently been shown to recover high-order accuracy under relaxed communication, supported by detailed analyses of its accuracy and stability. However, the scalability of this approach in modern large-scale parallel DG solvers has not yet been systematically investigated. In this paper, we address this gap by implementing the ADG method coupled with AT fluxes in the open-source finite element library deal.II. We employ a communication-avoiding algorithm (CAA) that reduces the frequency of inter-process communication while accommodating controlled delays in ghost value exchanges. We first demonstrate that applying standard numerical fluxes in this asynchronous setting degrades the solution to first-order accuracy, irrespective of the polynomial degree. By incorporating AT fluxes that utilize data from multiple previous time levels, we successfully recover the formal high-order accuracy of the DG discretization. The accuracy of the proposed method is rigorously verified using benchmark problems for the compressible Euler equations. Furthermore, we evaluate the performance of the method through extensive strong-scaling studies for both two- and three-dimensional test cases. Our results indicate that CAA substantially suppresses synchronization overheads, yielding speedups of up to 1.9x in two dimensions and 1.6x in three dimensions compared to a baseline synchronous DG solver.

This paper presents the design and physical implementation of UET-RVMCU, a lightweight RISC-V microcontroller derived from the UETRV-PCore. Aimed at creating an accessible and flexible open-source RISC-V-based microcontroller, UET-RVMCU simplifies the application-class UETRV-PCore by reducing pipeline stages, removing MMU functionality, and integrating GPIO peripherals. The final GDSII layout was generated using an open-source RTL-to-GDS flow (OpenLane). This project demonstrates the feasibility of transforming an application-class SoC into a feature-rich microcontroller suitable for embedded systems, emphasizing low area, design simplicity, and open-source development.

Fully implicit tensor-product space-time discretizations of time-dependent $(p,δ)$-Navier-Stokes models yield, on each time step, large nonlinear monolithic saddle-point systems. In the shear-thinning regime $1<p<2$, especially as $p\downarrow 1$ and $δ\downarrow 0$, the decisive difficulty is the constitutive tangent: its ill-conditioning impairs Newton globalization and the preconditioning of the arising linear systems. We therefore develop a scalable monolithic modified Newton framework for tensor-product space-time finite elements in which the exact constitutive tangent in the Jacobian action is replaced by a better-conditioned surrogate. Picard and exact Newton serve as reference linearizations within the same algebraic framework. Scalability is achieved through matrix-free operator evaluation, a monolithic multigrid V-cycle preconditioner, order-preserving reduced Gauss-Radau time quadrature, and an inexact space-time Vanka smoother with single-time-point coefficient freezing in local patch matrices. We prove coercivity of the linearized viscous-Nitsche term in the uniformly elliptic regime $ν_\infty>0$ and consistency of the reduced time quadrature. Numerical tests demonstrate robustness with respect to model parameters, nonlinear and linear iteration counts, and scalable parallel performance.

Recent work by Vavrek et al. (2025) showed that machine learning methods can be used to exploit spatial patterns of performance variations within the highly-segmented H3D M400 gamma spectrometer to improve an overall spectroscopic performance metric. That work also introduced the spectre-ml software, which tests various greedy, heuristic, random, and machine learning clustering algorithms to find the best performing mask for excluding detector regions to improve a user-defined performance metric by training on a given dataset. In this work, we build off of Vavrek et al. (2025) and seek to determine to what extent an optimized binary voxel mask trained on a given dataset can generalize to other datasets. In particular, this paper evaluates the transferability of masks trained on one M400 dataset to another M400 detector, in order to determine whether the total effort required in designing masks for different detectors and applications can be substantially reduced by using a single common mask. It also examines testing and training on different subsets of the same dataset to determine the natural level of variability in optimization results. In the inter-detector analysis, as expected, the best performing model on each detector is often one trained on that dataset, with an average performance enhancement of $16\%$ when considering the relative uncertainty in a Doniach fit to the $186$ keV peak. In comparison, the best transferred masks, with the best on average performance metric across all six detectors, show only a slightly smaller improvement of $13\%$ on average. These results suggest that high-performing, well-transferable masks can be shared among detectors, reducing or even eliminating the laborious processes of collecting a training dataset and performing the optimization for each detector, ultimately improving safeguards efficiency.

In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erdös-Rényi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a configuration, is typically of order $n^{3/4}$ and when multiplied by $n^{-3/4}$ converges in distribution to a non-trivial random variable, whose density we describe. In the regular graph case, the Small Subgraph Conditioning Method applies, and the limiting density is of the form $\frac1{Z}\exp(-C_d z^4)$. Surprisingly, in the Erdös-Rényi case, while the ratio of the second moment and first moment squared is bounded, the short cycle count is not enough to explain the fluctuations of the partition function restricted to a particular magnetization. We identify the additional source of randomness as path counts of slowly diverging length. This quantity is motivated by the heuristic that correlations between distant vertices are proportional to their local branching rate. Augmenting the Small Subgraph Conditioning Method with these path counts allows us to prove convergence of the magnetization to a non-deterministic limiting distribution. To our knowledge, the need to condition on graph observables beyond the cycle counts is a new phenomenon for spin systems. As further corollaries, we derive a polynomial lower bound on the mixing time of the stochastic Ising model on sparse random graphs at the critical temperature complementing recent upper bounds. Moreover, we establish the fluctuations of the free energy in the Erdös-Rényi case, answering a recent question of Coja-Oghlan et. al.

SNR G106.3+2.7 is a complex TeV emitting source whose emission is still poorly understood. It has especially been at the center of numerous discussions on its potential for being a supernova remnant (SNR) PeVatron, since its gamma-ray spectra seems not to exhibit any significant suppression in the multi--TeV range, up to $\sim 600$ TeV, thereby indicating the presence of $\sim$ PeV particles. We study the hypothesis in which a SNR evolving in a clumpy or cloudy environment is powering the TeV gamma-ray emission, detected mainly from two regions, the "head" and the "tail". We discuss the implications of such an hypothesis. We rely on a simple physically motivated analytical modeling of the shock dynamics and of the content of accelerated particles and confront it to available gamma-ray observations. We find that the current observed TeV gamma-ray emission in the head and tail regions can be accounted for by an active single SNR, with a natural hardening of the spectrum due to the expansion in a clumpy medium or escaping to a dense region in the tail. However, in all scenarios, the broadband gamma-ray emission from the GeV range to the $\gtrsim 100$ TeV range is difficult to reconcile with a standard SNR - whether originating from a thermonuclear or a core-collapse supernova - and instead points toward an association with the pulsar.

The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the terminals, such that the sum of weights of the edges connecting vertices in different parts of the partition is minimized. The problem is APX-hard for $k\ge3$. The currently best known approximation algorithm for the problem for arbitrary $k$, obtained by Sharma and Vondrák [STOC 2014] more than a decade ago, has an approximation ratio of 1.2965. We present an algorithm with an improved approximation ratio of 1.2787. Also, for small values of $k \ge 4$ we obtain the first improvements in 25 years over the currently best approximation ratios obtained by Karger et al. [STOC 1999]. (For $k=3$ an optimal approximation algorithm is known.) Our main technical contributions are new insights on rounding the LP relaxation of Călinescu, Karloff, and Rabani [STOC 1998], whose integrality ratio matches Multiway Cut's approximability ratio, assuming the Unique Games Conjecture [Manokaran et al., STOC 2008]. First, we introduce a generalized form of a rounding scheme suggested by Kleinberg and Tardos [FOCS 1999] and use it to replace the Exponential Clocks rounding scheme used by Buchbinder et al. [STOC 2013] and by Sharma and Vondrák. Second, while previous algorithms use a mixture of two, three, or four basic rounding schemes, each from a different family of rounding schemes, our algorithm uses a computationally-discovered mixture of hundreds of basic rounding schemes, each parametrized by a random variable with a distinct probability distribution, including in particular many different rounding schemes from the same family. We give a completely rigorous analysis of our improved algorithms using a combination of analytical techniques and interval arithmetic.

We study Gaussian wave packet solutions for Maxwell's equations in an isotropic, inhomogeneous medium and derive a system of ordinary differential equations that captures the leading-order correction to geodesic motion. The dynamical quantities in this system are the energy centroid, the linear and angular momentum, and the quadrupole moment. Furthermore, the system is closed to first order in the inverse frequency. As an immediate consequence, the energy centroids of Gaussian wave packets with opposite circular polarisations generally propagate in different directions, thereby providing a mathematical proof of the spin Hall effect of light in an inhomogeneous medium.

Jets are collimated clusters of particles formed by the hadronization of partons following a hard interaction. In proton-proton ($pp$) collisions at the Relativistic Heavy Ion Collider (RHIC), jet production is dominated by $gg$ and $qg$ partonic processes, allowing us to directly probe the gluon parton distribution function (PDF) in the proton in a way complementary to deep inelastic scattering. In this paper, we report the double-differential inclusive-jet cross sections as a function of jet transverse momentum, $p_{\rm T}$, and pseudorapidity, $η$, at center-of-mass energies $\sqrt{s} = 200$ and $510$~GeV, from $pp$ collisions studied with the STAR detector. The jet $p_{\rm T}$ is corrected for underlying event contributions by applying an off-axis cone method. At mid-pseudorapidity, $|η| < 0.9$, the kinematic coverage of our data extends to $0.07 < x_{\rm T} \text{ (}= 2p_{\rm T}{} / \sqrt{s} \text{)} < 0.5$ and $0.03 < x_{\rm T} < 0.31$ at $\sqrt{s} = 200$~and 510 GeV, respectively, where the gluon PDF is poorly constrained by the TeV-scale $pp$~($p\bar{p}$) colliders. The inclusive jet cross sections are compared to the next-to-next-to-leading order perturbative quantum chromodynamics calculations using several recent PDF sets as inputs. These results will further constrain the gluon PDF, help tune Monte Carlo generators, and provide critical reference data needed to study the quark-gluon plasma.

In this paper we develop a theory for Patterson--Sullivan measures for non-Borel Anosov groups on the Furstenberg boundary. Previously, such a theory has been successfully developed for measures supported on the partial flag manifold associated to the Anosov condition, which coincides with the Furstenberg boundary only under the strongest Anosov condition, Borel Anosov. We establish existence, uniqueness, and ergodicity results for the measures on the Furstenberg boundary under arbitrary Anosov conditions; we show ergodicity of Bowen--Margulis--Sullivan measures on the homogeneous space; and we establish strict convexity results for the critical exponent associated to functionals on the entire Cartan subspace. Using this strict convexity, we establish an entropy rigidity result for Anosov groups with Lipschitz limit set. A key tool we develop is a new sufficient condition for the existence of a measurable boundary map associated to a Zariski dense representation. This result not only applies to Anosov groups, but also to transverse groups, mapping class groups, and discrete subgroups of the isometry groups of Gromov hyperbolic spaces.

In higher rank, there is a well-studied theory of Patterson--Sullivan measures supported on partial flag manifolds. However, establishing the existence and uniqueness of such measures is a difficult question. In this paper, we develop a theory for Patterson--Sullivan measures supported on certain vector-valued horofunction boundaries of the associated symmetric space, where existence is straightforward. We also introduce a notion of shadows for this compactification and establish a shadow lemma. For transverse groups, we prove uniqueness and ergodicity results.

Quantum optomechanical STIRAP (Stimulated Raman Adiabatic Passage) is investigated for a system of two mechanical modes coupled to an optical mode. We show analytically that in a system without loss, fractional STIRAP can generate a mechanical Bell state from a single phonon Fock state of one of the mechanical modes with the other mechanical mode in the vacuum state, and a product state from a coherent state. Relative phases between Fock basis components in the final state of STIRAP are determined by the phonon-number parity of the initial state. Furthermore, the system is numerically studied to determine the effects of dissipation, and it is concluded that high-fidelity entanglement can be achieved via fractional STIRAP using state-of-the-art cryogenic cooling and mechanical devices. Finally, an interferometric protocol using time-reversed fractional STIRAP is proposed to quantify entanglement between two mechanical modes.

We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend along localisations, which we accomplish by analysing mapping spaces of localisations. Along the way we introduce a directed version of the join construction, giving a sequential colimit description of the full image of any functor.