We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an environmental qubit via an X-X coupling, with a "cooling" bath acting on the environment qubit. This model is known to exhibit abrupt transitions between Markovian and non-Markovian behavior. The second non-Markovian model uses the post-Markovian master equation (PMME), which represents the bath correlation through a memory kernel; we consider an exponentially decaying kernel and both underdamped and overdamped dynamics. We systematically compare these non-Markovian error models against the Markovian case and against each other, for a variety of different codes. We start with a single qubit, which can be solved analytically. We then consider the three-qubit repetition code and the five-qubit "perfect" code. In all cases, we find that the fidelity decays more rapidly in the Markovian case than in either non-Markovian model, suggesting that continuous quantum error correction has enhanced performance against non-Markovian noise. We attribute this difference to the presence of a quantum Zeno regime in both non-Markovian models.

We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.

This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes with a special focus on the stability of the discrete approximations when they undergo arithmetic operations. The main results are a simple upper bound of the approximation error in terms of the Wasserstein-1 distance that is valid for all continuous distributions with finite mean. In many use-cases, the studied method achieve optimal rate of convergence, and numerical experiments show that the algorithm is more stable than pre-existing approximation schemes in the context of arithmetic operations.

Rigorous performance evaluation is essential for developing robust algorithms for high-throughput computational chemistry. Traditional benchmarking, however, often struggles to account for system-specific variability, making it difficult to form actionable conclusions. We present a Bayesian hierarchical modeling framework that rigorously quantifies performance metrics and their uncertainty, enabling a nuanced comparison of algorithmic strategies. We apply this framework to analyze the Dimer method, comparing Conjugate Gradient (CG) and L-BFGS rotation optimizers, with and without the removal of external rotations, across a benchmark of 500 molecular systems. Our analysis confirms that CG offers higher overall robustness than L-BFGS in this context. While the theoretically-motivated removal of external rotations led to higher computational cost (>40% more energy and force calls) for most systems in this set, our models also reveal a subtle interplay, hinting that this feature may improve the reliability of the L-BFGS optimizer. Rather than identifying a single superior method, our findings support the design of adaptive "chain of methods" workflows. This work showcases how a robust statistical paradigm can move beyond simple performance rankings to inform the intelligent, context-dependent application of computational chemistry methods.

We present the first large-scale, high-resolution simulations of dusty, star formation feedback-driven galactic outflows. Using the Cholla hydrodynamics code, we investigate dust sputtering in these environments for grains ranging in size from $1-0.001~{μ\mathrm{m}}$. We compare results for two feedback models: one representative of low-redshift nuclear starburst galaxies and one similar to high-redshift main sequence galaxies. In general, our simulations show that multi-phase outflows are capable of safely transporting a vast majority of their dust to large distances ($\sim10~\textrm{kpc}$) from the disk. This work also shows that environmental shielding in cool gas clouds boosts dust survival rates significantly. The evolutionary path of dust depends strongly on grain size. Large grains ($a\geq0.1~{μ\mathrm{m}}$) can be transported efficiently in all phases. Smaller grains, however, experience significant destruction in the hotter phases. $0.001~{μ\mathrm{m}}$ grains in particular are quickly sputtered in all but the coolest gas, resulting in these grains strongly tracing the cool phase in outflows. These results may also indicate the importance of in-situ formation mechanisms, such as shattering, for the small dust grains and PAHs observed in emission throughout outflows in nearby galaxies. Surprisingly, we find that the hot phase dominates the transport of dust that survives to populate the circumgalactic medium.

In this text, we illustrate the use of local methods in the theory of (irregular) holonomic D-modules. I. (The Euler characteristic of the de~Rham complex) We show the invariance of the global or local Euler characteristic of the de~Rham complex after localization and dual localization of a holonomic D-module along a hypersurface, as well as after tensoring with a rank one meromorphic connection with regular singularities. II. (Local generic vanishing theorems for holonomic D-modules) We prove that the natural morphism from the proper pushforward to the total pushforward of an algebraic holonomic D-module by an open inclusion is an isomorphism if we first twist the D-module structure by suitable closed algebraic differential forms. III. (Laplace transform of a Stokes-filtered constructible sheaf of exponential type) Motivated by the construction in [YZ24], we~propose a slightly different construction of the Laplace transform of a Stokes-perverse sheaf on the projective line and show directly that it corresponds to the Laplace transform of the corresponding holonomic D-module via the Riemann-Hilbert-Birkhoff-Deligne-Malgrange correspondence. This completes the presentation given in [Sab13, Chap. 7]}, where only the other direction of the Laplace transformation is analyzed. We~also compare our approach with the construction made previously in [YZ24].

Cosmic ray muons enable non-invasive imaging of dense structures through multipleCoulomb scattering (MCS), with scattering angles dependent on atomic number (Z). Traditional algorithms like Point of Closest Approach (PoCA) assume single scattering, limiting accuracy. This work presents the $μ$TRec algorithm, which models muon paths using a Bayesian approach with Gaussian approximations, accounting for MCS and energy loss. $μ$TRec is applied to simulate muon imaging of dry storage casks (DSCs) used for spent nuclear fuel, with four loading configurations: fully loaded, one row missing, one assembly missing, and half assembly missing. The results demonstrate improved accuracy and resolution in identifying missing assemblies compared to conventional methods. It is observed that the $μ$TRec algorithm exhibits markedly superior performance over the classical PoCA method achieving respective improvements of 122% in signal-to-noise ratio (SNR), 35% in contrast-to-noise ratio (CNR), and 201% in detection power (DP) for the case of one missing fuel assembly with a muon flux of $10^6$ and a voxel size of 5 cm. Furthermore, μTRec supports high-resolution reconstruction with voxel sizes as small as 1 cm which enables the accurate localization of structural components such as the 2.5 cm thick steel canister. Notably, $μ$TRec is also capable of reliably detecting a single missing fuel assembly at a muon flux as low as $10^5$, a task that remains infeasible using PoCA under the same conditions.

This paper aims to investigate a three-dimensional fully magnetic effected piezoelectric beam model with strong sources and nonlinear interior dampings. By employing nonlinear semigroups and the theory of monotone operators, the existence of local weak solutions is established. By the potential well method, we obtain the global existence of potential well solutions. Decay rates of the total energy are obtained in terms of the behavior of the damping terms. The main advantage in this work is that the stabilization estimate does not generate lower-order terms, and in addition we remove some strong conditions in previous results to obtain a weaker energy decay. Finally, when the initial total energy is negative, positive but small, respectively, the blow-up results for weak solutions if the source terms are stronger than damping terms are obtained according to the differential inequality technique. Moreover, if interior dampings are linear, a blow-up result with arbitrarily high initial energy is established by the concavity method and an upper bound for the blow-up time is also derived. All results are independent of any relation among the model coefficients.

The Atlantic Meridional Overturning Circulation (AMOC), a crucial ocean current system, could transition to a weak state. Despite severe associated climate impacts, assessing the AMOC's response under global warming and its proximity to possible critical thresholds remains difficult. To understand future Earth system stability, a global dynamical view is needed beyond the local stability analysis underlying classical early-warning methods. Using an intermediate-complexity climate model, we explore the stability landscape of the AMOC for different atmospheric CO$_2$ concentrations. We explicitly compute the edge state (or Melancholia state), a chaotic saddle on the basin boundary separating the strong and weak AMOC attractors found in the model. While being unstable, the edge state can govern the transient climate for centuries, supporting centennial AMOC oscillations driven by atmosphere-ice-ocean interactions in the North Atlantic. At increased CO$_2$ levels projected for the near future, we reveal a boundary crisis where the current AMOC attractor disappears by colliding with the edge state. Under crisis overshoot, long chaotic transients due to "ghost states" lead to diverging ensemble trajectories under time-varying forcing. Rooted in dynamical systems theory, our results offer an explanation of large ensemble variance and apparent "stochastic bifurcations" observed in earth system models under intermediate forcing scenarios.

Artificial intelligence (AI) is transforming modern life, yet the growing scale of AI applications places mounting demands on computational resources, raising sustainability concerns. Photonic integrated circuits (PICs) offer a promising alternative, enabling massive parallelism, low latency, and reduced electrical overhead, particularly excelling in high-throughput linear operations. However, passive and fully optical nonlinear activation functions with equally superb performance remain rare, posing a critical bottleneck in realizing all-optical neural networks in PICs. Here, we demonstrate a compact and integrated all-optical nonlinear activation method, experimentally realized through strong second-order optical nonlinearities in periodically poled lithium niobate (PPLN) nanophotonic waveguides, achieving 80% absolute conversion efficiency. This activation exhibits a sigmoid-like, wavelength-selective response with femtosecond-scale dynamics and light-speed processing, operating passively without external control and auxiliary signals. We validate its feasibility for neural inference by cascading the PPLN-driven activations with a linear silicon PIC, demonstrating all-optical nonlinear neuron expressivity. Moreover, combining the measured nonlinearity with linear operations calculated by the PIC, we show that PPLN-activated multi-layer optical neural networks can achieve performance on par with digital implementations in real-world tasks, including airfoil regression and medical image classification. These results pave the way toward scalable, high-speed, and fully integrated all-optical neural networks for next-generation photonic AI hardware.

Scanning tunneling microscopy (STM) measurements have been extensively performed on the easily cleavable (011) surface of UTe$_2$, using both normal-metal and superconducting tips. Motivated by these experiments, we theoretically investigate the topological surface states on the (011) surface of UTe$_2$. We find that a two-dimensional nearly flat band emerges in the $B_{3u}$ state, giving rise to a pronounced zero-energy peak in the surface density of states. This flat band is supported by two key mechanisms: (i)~nontrivial Berry phases defined at multiple momenta give rise to low-energy in-gap states, and (ii)~weak spin conservation allows the gap function to acquire phase winding. Furthermore, to investigate the relation between the zero-bias peak observed in recent STM experiments with a superconducting tip and the topological surface states, we calculate the nonequilibrium dc tunneling current in a junction between an $s$-wave superconductor and the (011) surface of UTe$_2$. Our results provide crucial insights into the superconducting pairing symmetry realized in UTe$_2$.

We propose the Branched Hilbert Subspace Interpretation (BHSI) as an alternative perspective on quantum measurement. BHSI describes measurement as a unitary branching of the local Hilbert space into decoherent, independent, and unitarily evolving subspaces, while updating observer states (through their equipment) by causally engaging and disengaging operators. Unlike the Copenhagen Interpretation (CI), BHSI avoids wave function collapse while maintaining the Born rule through the branch weights associated with the initial system state. Unlike the Many-Worlds Interpretation (MWI), BHSI sidesteps parallel worlds by entangling branches with the local environment within a single world. We compare BHSI features with those of CI, MWI, and Bohmian Mechanics (BM). We investigate its implications for the double-slit experiment, Bell tests, Wigner and his friend, black hole radiation, and the delayed-choice quantum eraser. We examine quantum teleportation, demonstrating that locally controlled decoherence and recoherence processes (CDRP) can be observed. Specifically, we suggest experiments using modern Stern-Gerlach interferometers (SGI) to visualize the CDRP, measure branch weights that encode the Born rule, and predict the electromagnetic (EM) phase shift resulting from the independent unitary evolution of decoherent branches. BHSI thus provides a minimalist alternative to interpretations based on collapse or many-worlds.

In this paper, we study MRC fibrations of compact Kähler manifolds with partially semi-positive curvature. We first prove that a compact Kähler manifold is rationally connected if its tangent bundle is BC-$p$ positive for all $1\leq p\leq \dim X$. As applications, we confirm a conjecture that any compact Kähler manifold with positive orthogonal Ricci curvature must be rationally connected, and generalize a result of Heier-Wong and Yang to the conformally Kähler case. The second result concern structure theorems for two immediate curvature conditions. We prove that, a compact Kähler manifold with $k$-semi-positive Ricci curvature or semi-positive $k$-scalar curvature, either the rational dimension $\geq n-k+1$ or it admits a locally constant fibration $f: X\rightarrow Y$ such that the fibre is rationally connected and the image $Y$ is Ricci-flat.

Remarkable progress has been made in difference-in-differences (DID) approaches to causal inference that estimate the average effect of a treatment on the treated (ATT). Of these, the semiparametric DID (SDID) approach incorporates a propensity score analysis into the DID setup. Supposing that the ATT is a function of covariates, we estimate it by weighting the inverse of the propensity score. In this study, as one way to make the estimation robust to the propensity score modeling, we incorporate covariate balancing. Then, by attentively constructing the moment conditions used in the covariate balancing, we show that the proposed estimator is doubly robust. In addition to the estimation, we also address model selection. In practice, covariate selection is an essential task in statistical analysis, but even in the basic setting of the SDID approach, there are no reasonable information criteria. Here, we derive a model selection criterion as an asymptotically bias-corrected estimator of risk based on the loss function used in the SDID estimation. We show that a penalty term can be derived that is considerably different from almost twice the number of parameters that often appears in AIC-type information criteria. Numerical experiments show that the proposed method estimates the ATT more robustly compared with the method using propensity scores given by maximum likelihood estimation, and that the proposed criterion clearly reduces the risk targeted in the SDID approach in comparison with the intuitive generalization of the existing information criterion. In addition, real data analysis confirms that there is a large difference between the results of the proposed method and those of the existing method.

Recent advances in quantum error correction (QEC) across hardware platforms have demonstrated operation near and beyond the fault-tolerance threshold, yet achieving exponential suppression of logical errors through code scaling remains a critical challenge. Erasure qubits, which enable hardware-level detection of dominant error types, offer a promising path toward resource-efficient QEC by exploiting error bias. Single erasure qubits with dual-rail encoding in superconducting cavities and transmons have demonstrated high coherence and low single-qubit gate errors with mid-circuit erasure detection, but the generation of multi-qubit entanglement--a fundamental requirement for quantum computation and error correction--has remained an outstanding milestone. Here, we demonstrate a superconducting processor integrating four dual-rail erasure qubits that achieves the logical multi-qubit entanglement with error-biased protection. Each dual-rail qubit, encoded in pairs of tunable transmons, preserves millisecond-scale coherence times and single-qubit gate errors at the level of $10^{-5}$. By engineering tunable couplings between logical qubits, we generate high-fidelity entangled states resilient to physical qubit noise, including logical Bell states (98.8% fidelity) and a three-logical-qubit Greenberger-Horne-Zeilinger (GHZ) state (93.5% fidelity). A universal gate set is realized through a calibrated logical controlled-NOT (CNOT) gate with 96.2% process fidelity, enabled by coupler-activated $XX$ interactions in the protected logical subspace. This work advances dual-rail architectures beyond single-qubit demonstrations, providing a blueprint for concatenated quantum error correction with erasure qubits.

We investigate the emergence of locality in infrared (IR) physics, which indicates an asymmetric renormalization group (RG) flow from a $d$-dimensional ultraviolet (UV) conformal field theory (CFT) to a lower-dimensional IR effective theory. In the holographic setup, this phenomenon can be described by a $(d+1)$-dimensional AdS charged black hole. At zero temperature, in particular, it has a $(d+1)$-dimensional anti-de Sitter (AdS) in the asymptotic region and AdS$_2 \times R^{d-1}$ near the horizon, whose dual field theory is mapped to IR quantum field theory (QFT) defined in $R_t \times R^{d-1}$. We show that the IR QFT can be reduced to effective conformal quantum mechanics due to the rapid suppression of the correlation in $R^{d-1}$. In this case, the IR conformal dimension of an operator crucially relies on the details of the UV theory. We further investigate another asymmetric RG flow from a four-dimensional UV CFT to a two-dimensional IR CFT by turning on an external magnetic field, which leads to localization in the directions perpendicular to the magnetic field.

Entangled states that cannot be distilled to maximal entanglement are called bound entangled and they are often viewed as too weak to break the limitations of classical models. Here, we show a strongly contrasting result: that bound entangled states, when deployed as resources between two senders who communicate with a receiver, can generate correlation advantages of unlimited magnitude. The proof is based on using many copies of a bound entangled state to assist quantum communication. We show that in order to simulate the correlations predicted by bound entanglement, one requires in the many-copy limit either an entanglement visibility that tends to zero or a diverging amount of overhead communication. This capability of bound entanglement is unlocked by only using elementary single-qubit operations. The result shows that bound entanglement can be a scalable resource for breaking the limitations of physical models without access to entanglement.

The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically independent elements within the semimodule, this quantity has remained elusive due to the challenges of computing it in practice. We establish that the tropical rank is, in fact, precisely equal to the topological dimension of the semimodule, one more than the dimension of the associated linear system of divisors. This implies that the equality of divisorial and tropical ranks in the definition of tropical linear series is equivalent to the pure dimensionality of the corresponding linear system. We then address the question of computing the tropical rank. In particular, we show that checking whether a given family of tropical rational functions is tropically independent is equivalent to solving a turn-based stochastic mean-payoff game, whereas calculating the tropical rank of a finitely generated semimodule of tropical rational functions is NP-hard. We conclude with several complementary results and questions regarding combinatorial and topological properties of the tropical rank.

We consider a polynomial $P\in \mathbb{R}[x_{1},\cdots, x_{d}]$ of degree $ δ$ that depends non-trivially on each of $x_1,...,x_d$ with $d\geq 2$. For any integer $t$ with $2\leq t\leq d$, any natural number $n \in \mathbb{N}$, and any finite set $A \subset \mathbb{R}$ of size $n$, our first result shows that \[ |P(A, A, \dots, A)| \gg_δ n^{\frac{3}{2} - \frac{1}{2^{d-t+2}}}, \] unless \begin{align*} &P(x_1, x_2, \dots, x_d) = f\big( u_1(x_1) + u_2(x_2) + \cdots + u_d(x_d) \big) \quad \text{or } &P(x_1, x_2, \dots, x_d) = f\big( v_1(x_1) v_2(x_2) \cdots v_d(x_d) \big), \end{align*} where $f$, $u_i$, and $v_i$ are nonconstant univariate polynomials over $\mathbb{R}$, and there exists an index subset $I \subseteq [d]$ with $|I| = t$ such that for any $i, j \in I$, we have $u_i = λ_{ij} u_j$ (in the additive case) or $|v_i|= |v_j|^{κ_{ij}}$ (in the multiplicative case) for some constants $λ_{ij}\in \mathbb{R}^{\neq 0},κ_{ij}\in\mathbb{Q}^{+}$. This result generalizes the symmetric Elekes-Rónyai theorem proved by Jing, Roy, and Tran. Our second result is a generalized Erdős-Szemerédi theorem for two polynomials in higher dimensions, generalizing another theorem by Jing, Roy, and Tran. A key ingredient in our proofs is a variation of a theorem by Elekes, Nathanson, and Ruzsa.

Data availability is essential in the development of acoustic signal processing algorithms, especially when it comes to data-driven approaches that demand large and diverse training datasets. For this reason, an increasing number of databases have been published in recent years, including either room impulse responses (RIRs) or audio recordings during motion. In this paper we introduce the trajectoRIR database, an extensive, multi-array collection of both dynamic and stationary acoustic recordings along a controlled trajectory in a room. Specifically, the database contains moving-microphone recordings and stationary RIRs that spatially sample the room acoustics along an L-shaped trajectory. This combination makes trajectoRIR unique and applicable to a wide range of tasks, including sound source localization and tracking, spatially dynamic sound field reconstruction, auralization, and system identification. The recording room has a reverberation time of 0.5 s, and the three different microphone configurations employed include a dummy head, with additional reference microphones located next to the ears, 3 first-order Ambisonics microphones, two circular arrays of 16 and 4 channels, and a 12-channel linear array. The motion of the microphones was achieved using a robotic cart traversing a 4.62 m-long rail at three speeds: [0.2, 0.4, 0.8] m/s. Audio signals were reproduced using two stationary loudspeakers. The collected database features 8648 stationary RIRs, as well as perfect sweeps, speech, music, and stationary noise recorded during motion. Python functions are provided to access the recorded audio and retrieve the associated geometric information.

The nonreciprocal magnetoelectric effect in Tellegen materials enables exotic phenomena such as axion-modified electrodynamics and fosters the development of magnet-free nonreciprocal media. As the nonreciprocal counterpart to the well-known chiral electromagnetic response, it offers a parallel framework in which many concepts developed for chiral materials can be translated to Tellegen media, potentially unlocking new avenues for fundamental studies and applications. Although predicted over 75 years ago and observed in only a handful of natural materials with very low strength, the strong optical Tellegen effect has remained experimentally elusive. Here, we report the first experimental demonstration of a resonant optical diagonal Tellegen effect in a metasurface, showcasing a response that is 100 times greater than that of any known natural material. This optical metasurface, consisting of randomly distributed cobalt-silicon nanoscatterers with strong shape anisotropy, utilizes spontaneous magnetization to achieve a robust Tellegen effect without the need for an external magnetic field. In addition to the Tellegen response, the metasurface exhibits both gyroelectric and gyromagnetic effects, contributing to nonreciprocal cross-polarized light reflection. We introduce a technique to independently extract the amplitudes of these three effects using conventional magneto-optical single-side-illumination measurements. The observation of the resonant Tellegen effects in the optical frequency range may lead to the experimental observation of axionic electrodynamics and compact bias-free nonreciprocal optical devices.

Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum-selected passively via a beam splitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver, who similarly performs a random measurement in one of the two bases. In this implementation, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. To assess the scalability of this spatial-mode encoding scheme, we theoretically show that using a brighter entangled photon source along with next-generation single-photon cameras - featuring improved quantum efficiency, timing and spatial resolution - this approach could achieve 9 bits per photon at 2000 spatial modes, and a bit rate of over 700 Mb/s at 4400 modes while accounting for finite-key effects. These results quantify the opportunities and performance bounds of spatially encoded, entanglement-based QKD and provide a benchmark for future high-dimensional quantum communication systems.

The concept of compatibility originally emerged as a synonym for the commutativity of observables and later evolved into the notion of measurement compatibility. In any case, however, it has remained predominantly algebraic in nature, tied to the formalism of quantum mechanics. Recently, still within the quantum domain, the concept of context incompatibility has been proposed as a resource for detecting eavesdropping in quantum communication channels. Here, we propose a significant generalization of this concept by introducing the notion of theory-independent context compatibility, a concept that is trivially satisfied by classical statistical theory but is found in conflict with quantum mechanics. Moreover, we propose a figure of merit capable of quantifying the degree of violation of theory-independent context incompatibility, and we experimentally demonstrate, using a quantum optics platform, that quantum systems can exhibit pronounced degrees of violation. Besides yielding a concept that extends to generic probabilistic theories and retrieving the notion of measurement incompatibility in the quantum domain, our results offer a promising perspective on evaluating the role of incompatibility in the manifestation of non-local correlations.

We formulate p-adic versions of following three: (1) Grothendieck Inequality, (2) Johnson-Lindenstrauss Flattening Lemma, (3) Bourgain-Tzafriri Restricted Invertibility Theorem.

This paper presents a Virtual Inertia Skyhook (VISKY) controller for magnetorheological (MR) dampers in semi-active suspensions. The proposed law is derived from a continuous sky-ground damping baseline augmented with acceleration feedback on the sprung and unsprung masses. In the closed-loop equations, these acceleration terms appear as a mass-like virtual inertia matrix rather than as a change in physical hardware. This interpretation motivates the VISKY name while making the underlying sky-ground hybrid structure explicit. Numerical evaluations under half-sine bump, representative ISO 8608 random-road and while-acceleration metrics relative to conventional Skygroundhook, with the largest gains appearing near the wheel-hop mode. The controller retains low computational overhead because it requires only algebraic force computation and bounded MR inversion.

This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.

Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile $+1/2$ disclinations. We investigate how this tendency toward chaotic fluid stirring can, counterintuitively, produce certain ordered, periodic flows in confinement, characterized by stable periodic orbits of $+1/2$ disclinations. We computationally study two-dimensional active nematics in systems with boundary conditions requiring a prescribed number $n$ of excess $+1/2$ disclinations, using Beris-Edwards nematohydrodynamics simulations alongside an agent-based simulation approach. We find that when confinement is sufficiently strong to prevent defect pair-nucleation, but not strong enough to arrest all flow, then $n=3$ defects generically follow a "golden braid" orbit as observed recently in experiments, and we predict a "silver braid" orbit of $n=4$ defects. For these results and for greater numbers of defects, we show that the periodic or chaotic nature of the dynamics is determined by a balance between the number of defects and the number of vortices in the flow field, suggesting a new design criterion for ordered flows in active nematics.

Given the prevalence of superconducting platforms for uses in quantum computing and quantum sensing, the simulation of quantum superconducting circuits has become increasingly important for identifying system characteristics and modeling their relevant dynamics. Various numerical tools and software packages have been developed with this purpose in mind, typically utilizing the harmonic oscillator basis or the charge basis to represent a Hamiltonian. In this work, we instead consider the use of discrete variable representations (DVRs) to model superconducting circuits. In particular, we use `sinc DVRs' of both charge number and phase to approximate the eigenenergies of several prototypical examples, exploring their use and effectiveness in the numerical analysis of superconducting circuits. We find that not only are these DVRs capable of achieving decoherence-accurate simulation, i.e., accuracy at the resolution of experiments subject to decay, decoherence, and dephasing, they also demonstrate improvements in efficiency with smaller basis sizes and better convergence over standard approaches, showing that DVRs are an advantageous alternative for representing superconducting circuits.

Retrieval Augmented Generation (RAG) uses vector databases to expand the expertise of an LLM model without having to retrain it. The idea can be applied over data lakes, leading to the notion of embedding data lakes, i.e., a pool of vector databases ready to be used by RAGs. The key component in these systems is the indexes enabling Approximated Nearest Neighbor Search (ANNS). However, in data lakes, one cannot realistically expect to build indexes for every dataset. Thus, we propose an adaptive, partition-based index, CrackIVF, that performs much better than up-front index building. CrackIVF starts answering as a small index, and only expands to improve performance as it sees enough queries. It does so by progressively adapting the index to the query workload. That way, queries can be answered right away without having to build a full index first. After seeing enough queries, CrackIVF will produce an index comparable to those built with conventional techniques. CrackIVF can often answer more than 1 million queries before other approaches have even built the index, achieving 10-1000x faster initialization times. This makes it ideal for cold or infrequently used data and as a way to bootstrap access to unseen datasets.

Serverless computing has emerged as a compelling solution for cloud-based model inference. However, as modern large language models (LLMs) continue to grow in size, existing serverless platforms often face substantial model startup overhead. This poses a significant challenge in efficiently scaling model instances to accommodate dynamic, bursty workloads commonly observed in real-world inference services. In this paper, we introduce λScale, an efficient serverless inference system to achieve fast model scaling. The key idea behind λScale is to leverage high-speed RDMA networks between GPU nodes for fast model multicast, while enabling distributed inference execution during model transmission -- referred to as "execute-while-load". λScale proposes an efficient model scaling scheme, λPipe, which supports adaptive model multicast and dynamically constructs execution pipelines across receiving nodes for collaborative, distributed inference. Additionally, λScale supports efficient model management across GPU and host memory, allowing fast scaling for models across different storage tiers. Evaluation results show that λScale enables fast model scaling and effectively handles load spikes, achieving up to 5x tail-latency improvement and 31.3% cost reduction compared to state-of-the-art solutions on real-world LLM inference traces.