Large Language Models for code often entail significant computational complexity, which grows significantly with the length of the input code sequence. We propose LeanCode for code simplification to reduce training and prediction time, leveraging code contexts in utilizing attention scores to represent the tokens' importance. We advocate for the selective removal of tokens based on the average context-aware attention scores rather than average scores across all inputs. LeanCode uses the attention scores of `CLS' tokens within the encoder for classification tasks, such as code search. It also employs the encoder-decoder attention scores to determine token significance for sequence-to-sequence tasks like code summarization. Our evaluation shows LeanCode's superiority over the SOTAs DietCode and Slimcode, with improvements of 60% and 16% for code search, and 29% and 27% for code summarization, respectively.

Synthesizing knowledge from large document collections is a critical yet increasingly complex aspect of qualitative research and knowledge work. While AI offers automation potential, effectively integrating it into human-centric sensemaking workflows remains challenging. We present ScholarMate, an interactive system designed to augment qualitative analysis by unifying AI assistance with human oversight. ScholarMate enables researchers to dynamically arrange and interact with text snippets on a non-linear canvas, leveraging AI for theme suggestions, multi-level summarization, and evidence-based theme naming, while ensuring transparency through traceability to source documents. Initial pilot studies indicated that users value this mixed-initiative approach, finding the balance between AI suggestions and direct manipulation crucial for maintaining interpretability and trust. We further demonstrate the system's capability through a case study analyzing 24 papers. By balancing automation with human control, ScholarMate enhances efficiency and supports interpretability, offering a valuable approach for productive human-AI collaboration in demanding sensemaking tasks common in knowledge work.

We examined the mechanisms underlying productivity and performance gains from AI agents using a large-scale experiment on Pairit, a platform we developed to study human-AI collaboration. We randomly assigned 2,234 participants to human-human and human-AI teams that produced 11,024 ads for a think tank. We evaluated the ads using independent human ratings and a field experiment on X which garnered ~5M impressions. We found human-AI teams produced 50% more ads per worker and higher text quality, while human-human teams produced higher image quality, suggesting a jagged frontier of AI agent capability. Human-AI teams also produced more homogeneous, or self-similar, outputs. The field experiment revealed higher text quality improved click-through rates and view-through duration, while higher image quality improved cost-per-click rates. We found three mechanisms explained these effects. First, human-AI collaboration was more task-oriented, with 25% more task-oriented messages and 18% fewer interpersonal messages. Second, human-AI collaboration displayed more delegation, as participants delegated 17% more work to AI agents than to human partners and performed 62% fewer direct text edits when working with AI. Third, recognition that the collaborator was an AI moderated these effects as participants who correctly identified they were working with AI were more task-oriented and more likely to delegate work. These mechanisms then explained performance as task-oriented communication improved ad quality, specifically when working with AI, while interpersonal communication reduced ad quality; delegation improved text quality but had no effect on image quality and was positively associated with diversity collapse, creating homogeneous outputs of higher average quality. The results suggest AI agents drive changes in productivity, performance, and output diversity by reshaping teamwork.

The electrochemical reduction of atmospheric CO$_2$ into high-energy molecules with renewable energy is a promising avenue for energy storage that can take advantage of existing infrastructure especially in areas where sustainable alternatives to fossil fuels do not exist. Automated laboratories are currently being developed and used to optimize the composition and operating conditions of gas diffusion electrodes (GDEs), the device in which this reaction takes place. Improving the efficiency of GDEs is crucial for this technology to become viable. Here we present a modeling framework to efficiently explore the high-dimensional parameter space of GDE designs in an active learning context. At the core of the framework is an uncertainty-aware physics model calibrated with experimental data. The model has the flexibility to capture various input parameter spaces and any carbon products which can be modeled with Tafel kinetics. It is interpretable, and a Gaussian process layer can capture deviations of real data from the function space of the physical model itself. We deploy the model in a simulated active learning setup with real electrochemical data gathered by the AdaCarbon automated laboratory and show that it can be used to efficiently traverse the multi-dimensional parameter space.

Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its support is low-dimensional), or strong smoothness assumptions on $F$, or a special structure $F$. Among the latter, compositional models $F=f\circ g$ with $g$ mapping to $\mathbb{R}^r$ with $r\ll d$ include classical single- and multi-index models, as well as neural networks. While the case where $g$ is linear is well-understood, less is known when $g$ is nonlinear, and in particular for which $g$'s the curse of dimensionality in estimating $F$, or both $f$ and $g$, may be circumvented. Here we consider a model $F(X):=f(Π_γX)$ where $Π_γ:\mathbb{R}^d\to[0,\textrm{len}_γ]$ is the closest-point projection onto the parameter of a regular curve $γ:[0, \textrm{len}_γ]\to\mathbb{R}^d$, and $f:[0,\textrm{len}_γ]\to \mathbb{R}^1$. The input data $X$ is not low-dimensional: it can be as far from $γ$ as the condition that $Π_γ(X)$ is well-defined allows. The distribution $X$, the curve $γ$ and the function $f$ are all unknown. This model is a natural nonlinear generalization of the single-index model, corresponding to $γ$ being a line. We propose a nonparametric estimator, based on conditional regression, that under suitable assumptions, the strongest of which being that $f$ is coarsely monotone, achieves, up to log factors, the $\textit{one-dimensional}$ optimal min-max rate for non-parametric regression, up to the level of noise in the observations, and be constructed in time $\mathcal{O}(d^2 n\log n)$. All the constants in the learning bounds, in the minimal number of samples required for our bounds to hold, and in the computational complexity are at most low-order polynomials in $d$.

We propose GE2E-KWS -- a generalized end-to-end training and evaluation framework for customized keyword spotting. Specifically, enrollment utterances are separated and grouped by keywords from the training batch and their embedding centroids are compared to all other test utterance embeddings to compute the loss. This simulates runtime enrollment and verification stages, and improves convergence stability and training speed by optimizing matrix operations compared to SOTA triplet loss approaches. To benchmark different models reliably, we propose an evaluation process that mimics the production environment and compute metrics that directly measure keyword matching accuracy. Trained with GE2E loss, our 419KB quantized conformer model beats a 7.5GB ASR encoder by 23.6% relative AUC, and beats a same size triplet loss model by 60.7% AUC. Our KWS models are natively streamable with low memory footprints, and designed to continuously run on-device with no retraining needed for new keywords (zero-shot).

One of the challenges in developing a high quality custom keyword spotting (KWS) model is the lengthy and expensive process of collecting training data covering a wide range of languages, phrases and speaking styles. We introduce Synth4Kws - a framework to leverage Text to Speech (TTS) synthesized data for custom KWS in different resource settings. With no real data, we found increasing TTS phrase diversity and utterance sampling monotonically improves model performance, as evaluated by EER and AUC metrics over 11k utterances of the speech command dataset. In low resource settings, with 50k real utterances as a baseline, we found using optimal amounts of TTS data can improve EER by 30.1% and AUC by 46.7%. Furthermore, we mix TTS data with varying amounts of real data and interpolate the real data needed to achieve various quality targets. Our experiments are based on English and single word utterances but the findings generalize to i18n languages and other keyword types.

The goal of Root Cause Analysis (RCA) is to explain why an anomaly occurred by identifying where the fault originated. Several recent works model the anomalous event as resulting from a change in the causal mechanism at the root cause, i.e., as a soft intervention. RCA is then the task of identifying which causal mechanism changed. In real-world applications, one often has either few or only a single sample from the post-intervention distribution: a severe limitation for most methods, which assume one knows or can estimate the distribution. However, even those that do not are statistically ill-posed due to the need to probe regression models in regions of low probability density. In this paper, we propose simple, efficient methods to overcome both difficulties in the case where there is a single root cause and the causal graph is a polytree. When one knows the causal graph, we give guarantees for a traversal algorithm that requires only marginal anomaly scores and does not depend on specifying an arbitrary anomaly score cut-off. When one does not know the causal graph, we show that the heuristic of identifying root causes as the variables with the highest marginal anomaly scores is causally justified. To this end, we prove that anomalies with small scores are unlikely to cause those with larger scores in polytrees and give upper bounds for the likelihood of causal pathways with non-monotonic anomaly scores.

This paper describes the PASH participation in TREC 2021 Deep Learning Track. In the recall stage, we adopt a scheme combining sparse and dense retrieval method. In the multi-stage ranking phase, point-wise and pair-wise ranking strategies are used one after another based on model continual pre-trained on general knowledge and document-level data. Compared to TREC 2020 Deep Learning Track, we have additionally introduced the generative model T5 to further enhance the performance.

Safety filtering is an effective method for enforcing constraints in safety-critical systems, but existing methods typically assume perfect state information. This limitation is especially problematic for systems that rely on neural network (NN)-based state estimators, which can be highly sensitive to noise and adversarial input perturbations. We address these problems by introducing GUARDIAN: Guaranteed Uncertainty-Aware Reachability Defense against Adversarial INterference, a safety filtering framework that provides formal safety guarantees for systems with NN-based state estimators. At runtime, GUARDIAN uses neural network verification tools to provide guaranteed bounds on the system's state estimate given possible perturbations to its observation. It then uses a modified Hamilton-Jacobi reachability formulation to construct a safety filter that adjusts the nominal control input based on the verified state bounds and safety constraints. The result is an uncertainty-aware filter that ensures safety despite the system's reliance on an NN estimator with noisy, possibly adversarial, input observations. Theoretical analysis and numerical experiments demonstrate that GUARDIAN effectively defends systems against adversarial attacks that would otherwise lead to a violation of safety constraints.

Little red dots (LRDs) are an abundant population of compact high-redshift sources with red rest-frame optical continua, discovered by the James Webb Space Telescope (JWST). Their red colors and power sources have been attributed either to dust reddening of standard hot accretion disks or to intrinsically cool thermal emission from dense hydrogen envelopes, in both cases surrounding accreting supermassive black holes. These scenarios predict order-of-magnitude differences in emission temperature but have lacked decisive temperature diagnostics. Here we report a prominent absorption feature at rest-frame $\sim 1.4 \, μ\mathrm{m}$ in two out of four LRDs at $z \sim 2$ with high signal-to-noise JWST spectra, among the coolest from a large LRD sample. The feature matches the shape and wavelength of the water absorption band seen in cool stars. Atmosphere models require $T \lesssim 3000\, \mathrm{K}$ to reproduce it, confirming unambiguously the presence of a cool, dense gas component contributing $20-30\%$ to the emergent continuum. A composite model reproduces both the absorption and the rest-frame optical-to-infrared continuum shape and suggests a temperature range ($\sim2000\, \mathrm{K} - 4000 \, \mathrm{K}$) rather than a single blackbody predicted by some gas envelope models. Molecular absorption demonstrates that the red continua of some LRDs are intrinsic rather than dust-reddened, implying order-of-magnitude lower bolometric luminosities and black-hole masses, and providing a new diagnostic of the emitting gas.

This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between the cancer and the population of cells is modeled by a chemotaxis model inspired by Keller-Segel-type equations, which is solved by a Hybridized Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the governing equations and to assess the uncertainty on the predictions of the dynamics due to the residual uncertainty on the parameters remaining after the tuning procedure. To this end, we apply techniques from uncertainty quantification for parametric differential models. We first perform a global sensitivity analysis using both Sobol and Morris indices to assess how parameter uncertainty impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining model parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the updated (residual) parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by using surrogate models, based on sparse-grids, to approximate the mapping of the uncertain parameters to the quantities of interest.

While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler characteristic-like structure. However, there are certain settings where the convexity property itself is important to consider. For example, this includes (preservation of) positivity properties of divisors on toric varieties under blowdowns. In the case of (restrictions of) conormal bundles, this can be interpreted in terms of interactions between local convexity data stored in rational equivalence relations. We consider generalizations to realizations of simplicial pseudomanifolds and replace rational equivalence with effects of PL homeomorphisms. Decomposing the PL homeomorphisms into edge subdivisions and contractions, we characterize the space of suitable contraction points compatible with local convexity properties in terms of convex unions and completions. This gives rise to certain external edge subdivisions that make this ``contraction space'' of the starting edge empty, which is unexpected given the expected ``increased convexity'' from edge subdivisions. We also obtain strong affine/linear restrictions on realizations of facets containing nearby edges preserving local convexity. This implies that contracting certain nearby edges results in a very large or very small contraction space of the starting edge. As for boundary behavior, there are parallels between effects of PL homeomorphisms on induced 4-cycles in the 1-skeleton. Finally, we find effects of PL homeomorphisms and suspensions on analogues of local convexity properties stored by linear systems of parameters. This indicates that simplicial spheres PL homeomorphic to the boundary of a cross polytope store record local convexity changes in the most natural way.

A transonic shear flow directed along magnetic field lines can linearly stabilize a steep pressure gradient in a confined magnetohydrodynamic (MHD) plasma. In Z-pinch geometry, we show that, like the edge pedestal in tokamak devices, this transport barrier -- which we call the ``MHD pedestal'' -- is metastable, i.e., unstable to finite-amplitude displacements of flux tubes. We simulate the slow formation of an MHD pedestal in a heated and sheared Z-pinch, which collapses on reaching a critical height, expelling an order-unity fraction of the confined thermal energy. The MHD pedestal then rebuilds and the process repeats, in a manner analogous to the ELM cycle seen in fusion experiments. We show that the available energy of the metastable equilibrium, and the most energetically favorable amount of ejected plasma, can be calculated from first principles via combinatorial optimization of flux-tube interchanges.

We prove vector-valued boundedness of (suitable) Calderon-Zygmund operators and of the (truncated) Hardy-Littlewood maximal function on a connected locally doubling metric measure space.

We test claims of large-scale anisotropy in the local expansion rate using cluster scaling relations as distance indicators. Using a Bayesian forward model, we jointly fit the X-ray luminosity--temperature (LT) and thermal Sunyaev-Zel'dovich--temperature (YT) relations, marginalising over the latent cluster distances and modelling selection effects as well as peculiar velocities. The latter are modelled using reconstructions of the local peculiar velocity field where we self-consistently account for possible anisotropic redshift--distance relations via an approximate scheme. This treatment proves crucial to the inferred anisotropy and breaks the degeneracy between anisotropy in scaling relation normalisations and underlying cosmological anisotropy. We apply our method to 312 clusters at $z \lesssim 0.2$, testing dipolar, quadrupolar and general (pixelised) anisotropy models. Bayesian model selection finds no more than weak evidence for any anisotropic model. For dipole models, we obtain upper limits of $δH_0 / H_0 < 3.2\%$ and bulk flow magnitude $< 1300\,\mathrm{km\,s^{-1}}$. Our results contrast with previous claims of statistically significant anisotropy from the same data, which we attribute to our principled forward modelling of both redshifts and scaling relation observables through latent distances and our treatment of the impact of anisotropic redshift--distance relations when modelling the local peculiar velocity field. Our work highlights the importance of accurately modelling peculiar velocities when testing isotropy with distance indicators, and motivates the further development of reconstructions that self-consistently treat large-scale deviations from the Hubble flow.

Fact-checking ecosystems on social media depend on the interplay between what users want checked and what contributors are willing to supply. Prior research has largely examined these forces in isolation, yet it remains unclear to what extent supply meets demand. We address this gap with an empirical analysis of a unique dataset of 1.1 million fact-checks and fact-checking requests from X's Community Notes platform between June 2024 and May 2025. We find that requests disproportionately target highly visible posts - those with more views and engagement and authored by influential accounts - whereas fact-checks are distributed more broadly across languages, sentiments, and topics. Using a quasi-experimental survival analysis, we further estimate the effect of displaying requests on subsequent note creation. Results show that requests significantly accelerate contributions from Top Writers. Altogether, our findings highlight a gap between the content that attracts requests for fact-checking and the content that ultimately receives fact-checks, while showing that user requests can steer contributors toward greater alignment. These insights carry important implications for platform governance and future research on online misinformation.

We introduce a novel combinatorial structure called pointed building sets, which can be viewed as families of lattices equipped with compatibility relations. To each pointed building set $\mathsf{B}$, we associate a complete lattice $\mathcal{O}(\mathsf{B})$, called the ornamentation lattice of $\mathsf{B}$. Special cases of this construction have already proven useful in understanding the structure of three families of posets: operahedron lattices, the affine Tamari lattice, and hypergraphic posets of subhypergraphs of the path hypergraph of an increasing tree. The goal of this paper is to establish the theory of these generalized ornamentations. We examine several natural classes of pointed building sets which recover classical lattices such as the Tamari lattice, the lattice of topologies ordered by coarsening, and the lattice of naturally labeled partial orders. Furthermore, several theoretical directions are explored, including inverse limits and group actions. Notably, this leads to a straightforward construction of inverse limits of Tamari lattices, yielding infinite analogs of the Tamari lattice.

Photonic quantum computing is a strong contender in the race to fault-tolerance. Recent proposals using qubits encoded in frequency modes promise a large reduction in hardware footprint, and have garnered much attention. In this encoding, linear optics, i.e., beam splitters and phase shifters, is necessarily not energy-conserving, and is costly to implement. In this work, we present designs of frequency-mode beam splitters based on modulated arrays of coupled resonators. We develop a methodology to construct their effective transfer matrices based on the SLH formalism for quantum input-output networks. Our methodology is flexible and highly composable, allowing us to define $N$-mode beam splitters either natively based on arrays of $N$-resonators of arbitrary connectivity or as networks of interconnected $l$-mode beam splitters, with $l<N$. We apply our methodology to analyze a two-resonator device, a frequency-domain phase shifter and a Mach-Zehnder interferometer obtained from composing these devices, a four-resonator device, and present a formal no-go theorem on the possibility of natively generating certain $N$-mode frequency-domain beam splitters with arrays of $N$-resonators.

Wide-field images made by radio interferometers are invariably affected by direction-dependent systematic effects such as the ionosphere or the beam pattern. Calibration along a set of discrete directions in the sky is the default technique to estimate and correct these systematic errors. However, additional processing such as smoothing and mosaicing are required to reconcile the step wise variation of the estimated systematic errors at the edges of the discrete directions (facets). We overcome the discrete nature of direction-dependent calibration by using image-domain gridding as the model for the calibration. Instead of discrete directions in the sky, calibration is performed using a basis that represents a set of sub-grids in the Fourier space. This automatically removes the need for extra operations to recover the wide-field systematics error model without any discontinuity. We provide results based on LOFAR data where we compare the traditional facet-based (discrete directional gains) calibration with the proposed approach. The comparison shows improved image quality, mainly because of the physical plausibility of the proposed approach as opposed to using a piecewise constant model for direction-dependent systematic errors.

We investigate the emergence of time quasicrystals (TQCs) in the open Dicke model, subjected to a quasi-periodic Fibonacci drive. TQCs are characterized by a robust sub-harmonic quasi-periodic response that is qualitatively distinct from the external drive. By directly analyzing the dynamics of the system in the thermodynamic limit, we establish the existence of TQC order in this system for a wide parameter regime. Remarkably, we demonstrate that this behavior persists even in the deep quantum regime with only two qubits. We systematically study the dependence of the TQC lifetime, $τ^{\ast}$, on the number of qubits and demonstrate that $τ^{\ast}$ increases monotonically with the system size. Our work demonstrates that quasi-periodically driven dissipative quantum systems can serve as a powerful platform for realizing novel non-equilibrium phases of matter.

We experimentally investigate the quantum noise mechanisms that limit continuously operating multiparameter quantum sensors. Using a hybrid rf-dc optically pumped magnetometer, we map the photon shot noise, spin projection noise, and measurement back-action noise over an order of magnitude in probe power and a factor of three in pump power while remaining quantum-noise-limited. We observe linear, quadratic, and cubic scaling of the respective total noise powers with probe photon flux, together with a quadratic dependence of back-action on pump photon flux, in quantitative agreement with a stochastic Bloch-equation model. At higher probe powers, additional probe-induced relaxation modifies the spin-noise spectrum while preserving the integrated noise scaling. Our results reveal fundamental, resource-dependent trade-offs unique to continuously monitored multiparameter sensors and establish experimentally the quantum limits governing their optimal operation.

We generalise to a group homomorphism $τ$ the $χ$-graded categories of Sözer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure theorem for semisimple $τ$-graded categories, and an alternative picture of $τ$-graded categories in terms of pseudofunctors into $\mathbf{Cat}$.

Studying the cross-correlation function between the soft and hard X-ray emission in Neutron Star Low Mass X-ray Binaries provides crucial insight into the structure and dynamics of the innermost accretion regions. In this work, we investigate the CCF of the Z-source GX 349+2 using an XMM-Newton observation. We noted that asymmetric CCFs with lags of a few hundred secondsbetween soft and hard band LCs in the horizontal branch, whereas CCFs remained symmetric in normal and flaring branches. We also performed a CCF study during the flux transition duration and observed lags of the order of a few tens to hundreds of seconds. Monte Carlo simulations were performed to assess the robustness of these CCFs, confirming their significance at a 95% confidence level. Spectral analysis during the flux transitions further suggests that the inner accretion disk extends close to the last stable orbit. We propose that the observed hard lags arise from the readjustment of the boundary layer/coronal region located near the inner edge of the accretion disk. From the measured lags, we estimate the characteristic size of the boundary layer. We show that the observed lags could also be associated with the depletion timescale of the boundary layer with low viscosity.

The emergence of Large Language Model (LLM) agents enables us to build agent-based intelligent systems that move beyond the role of a "tool" to become genuine collaborators with humans, thereby realizing a novel human-agent collaboration paradigm. Our vision is that LLM agents should resemble remote human collaborators, which allows HCI researchers to ground the future exploration in decades of research on trust, awareness, and common ground in remote human collaboration, while also revealing the unique opportunities and challenges that emerge when one or more partners are AI agents. This workshop establishes a foundational research agenda for the new era by posing the question: How can the rich understanding of remote human collaboration inspire and inform the design and study of human-agent collaboration? We will bring together an interdisciplinary group from HCI, CSCW, and AI to explore this critical transition. The 180-minute workshop will be highly interactive, featuring a keynote speaker, a series of invited lightning talks, and an exploratory group design session where participants will storyboard novel paradigms of human-agent partnership. Our goal is to enlighten the research community by cultivating a shared vocabulary and producing a research agenda that charts the future of collaborative agents.

The temperature range of the blue phases (BPs) formed in highly chiral mixtures based on cholesteryl oleyl carbonate (COC) and the nematic liquid crystal E7 was studied in the presence of various chemical structures. The $azo$ compounds used were of both chiral and achiral nature, and their molecular geometry was modified by substitution of modular "LEGO" molecular units of varying alkyl chain lengths and types of bridging groups, which could substantially affect the mesomorphic properties of the matrix mixture. It was shown that in many cases these dopants effectively broadened the BP temperature range. This effect depends on both the variation in the molecular geometry of the $azo$ compounds and the increase in the $cis$-isomer concentration under UV irradiation. The presence of the $cis$-isomers formed have a stronger impact on broadening the BP temperature range than the initial $trans$-isomers. These results demonstrate that the temperature range of BPs can be precisely controlled via a combination of molecular engineering and $trans$-$cis$ photo-isomerization.

Optical parametric amplifiers (OPAs) are promising to overcome the wavelength coverage and noise limitations in conventional optical amplifiers based on rare-earth doping and semiconductor gain. However, the high power requirement remains a major obstacle to the widespread use of OPAs. Integrated OPAs can in principle improve the pump efficiency with tight mode confinement; however, challenges associated with propagation loss, limited nonlinearity, and susceptibility to nanoscale fabrication imperfections prevent them from competing with conventional bulk and fiber-based OPAs. Here, we demonstrate a highly efficient integrated OPAs with continuous-wave net gain. The pump efficiency is improved by over one order of magnitude. Phase-sensitive gain of 23.5 dB is demonstrated, significantly exceeding previous integrated OPAs, using only 110 mW pump power and no cavity enhancement. This is achieved with parametric down-conversion in thin-film lithium niobate waveguides using the adapted poling technique to maintain the coherence of nonlinear interactions. Moreover, the high parametric gain exceeds fibre-chip-fibre losses, leading to appreciable net gain up to 10 dB. The 3 dB bandwidth is approximately 120 nm, covering telecommunication S-, C-, and Lbands. Quantum-limited noise performance is confirmed through the measurement of output field fluctuation below the classical limit. We further demonstrate that signalto-noise ratio in noisy optical communications can be increased by leveraging this efficient integrated OPA. Our work marks a significant step towards ideal optical amplifiers with strong amplification, high efficiency, quantum-limited noise, large bandwidth, and continuous-wave operation, unlocking new possibilities for next-generation photonic information processing systems.

We consider the inhomogeneous Landau equation with $γ\in (\sqrt{3},2]$ and construct smooth, strictly positive initial data that develop a finite time singularity. The $C^α$-norm of the distribution function blows up for every $α>0$, whereas its $L^{\infty}$-norm remains uniformly bounded. In self-similar variables, the solution becomes asymptotically hydrodynamic - the distribution function converges to a local Maxwellian, while the hydrodynamic fields develop an asymptotically self-similar implosion whose profile coincides with a smooth imploding profile of the compressible Euler equations. To our knowledge, this provides the first example of a collisional kinetic model which is globally well-posed in the homogeneous setting, but admits finite time singularities for inhomogeneous data.

The Rodeo Algorithm is a quantum computing method for computing the energy spectrum of a Hamiltonian and preparing its energy eigenstates. We discuss how to improve the performance of the rodeo algorithm for each of these two applications. In particular, we demonstrate that using a geometric series of time samples offers a near-optimal optimization space for a given total runtime by studying the Rodeo Algorithm performance on a model Hamiltonian representative of gapped many-body quantum systems. Analytics explain the performance of this time sampling and the conditions for it to maintain the established exponential performance of the Rodeo Algorithm. We finally demonstrate this sampling protocol on various physical Hamiltonians, showing its practical applicability. Our results suggest that geometric series of times provide a practical, near-optimal, and robust time-sampling strategy for quantum state preparation with the Rodeo Algorithm across varied Hamiltonians without requiring model-specific fine-tuning.

Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter problems have recently drawn a great deal of interest. These mixed sign problems have appeared in statistical inference setting as a way to generalize least squares regression to measure valued outputs and have appeared in numerical methods to improve the accuracy of Wasserstein gradient flow solvers. Unfortunately, the presence of negatively weighted distance terms destroys the Euclidean convexity of the unsigned problem, resulting in a much more challenging optimization task. The main focus of this work is to study properties of the signed barycenter problem for a general transport cost with a focus on establishing uniqueness of solutions. In particular, when there is only one positive weight, we extend the uniqueness result of Tornabene et al. (2025) to any cost satisfying a certain convexity property. In the case of arbitrary weights, we introduce the dual problem in terms of Kantorovich potentials and provide a sufficient condition for a stationary solution of the dual problem to induce an optimal signed barycenter.