We introduce a novel method that we call Single-Shot Cross-Spectroscopy (SSCS), for extracting the auto- and cross-power spectral densities of dephasing noise of a qubit pair. The method uses straightforward input, namely single-shot readouts from single-qubit Ramsey-type experiments, and is resilient against errors in state preparation and measurement. We apply it to experimental data from a semiconductor spin-qubit device and obtain noise spectra over five orders of magnitude in frequency (5 mHz--500 Hz). Compared to other techniques, SSCS enables access to noise correlations in the previously inaccessible intermediate-frequency range (1--500 Hz) for spin qubits, and can be further extended with faster readout. More broadly, the frequency range accessible with SSCS is limited only by the experiment repetition rate, and scales accordingly on other platforms.

Every large galaxy has a black hole in its center. The interaction between the black hole and its host profoundly shapes galactic evolution and the Universe as a whole. The key features of this interaction are black hole jets -- or more generally, winds -- which every black hole must have. Despite the proximity and importance of our Galaxy's central black hole, Sagittarius A* (Sgr A*), the active wind from it has eluded scientists for over half a century. Here we report the discovery of a large active wind from Sgr A* using unprecedentedly deep (T$_b \sim30$ mK) and high angular resolution (<0.25") observations with the Atacama Large Millimeter/Submillimeter Array (ALMA). We detect a large conical clearing in the cold molecular gas surrounding Sgr A* that is at least 1~parsec long and has a ~45 degree opening angle. The morphology and energetics of this structure are consistent with active clearing of gas by a hot wind from Sgr A*.

This study provides a comprehensive empirical investigation of long-range dependence (LRD) in financial markets and evaluates the ability of deep generative models to reproduce such temporal structures. Using daily data from three representative sectors--equity (S&P 500, DAX, Nikkei 225), commodities (Wheat, Corn, Soybeans), and energy (UNG, USO, XLE)--we examine the presence of LRD through three complementary approaches: rescaled range (R/S) analysis, detrended fluctuation analysis (DFA), and an ARFIMA--FIGARCH model with Student's $t$-distributed innovations. The empirical evidence suggests that while mean returns exhibit limited persistence, pronounced long memory is consistently observed in conditional volatility across most assets. Building on these findings, we assess whether Quant Generative Adversarial Networks (Quant GANs) can learn and reproduce these stylized temporal dependencies. Although the generated series successfully mimic heavy-tailed return distributions and certain aspects of volatility clustering, they generally fail to capture the magnitude and consistency of LRD observed in real data, particularly in volatility dynamics. These results highlight an important limitation of current deep generative architectures in modeling slow-decaying dependence structures and underscore the need for incorporating explicit long-memory mechanisms when synthetic financial data are intended for risk management or long-horizon forecasting applications.

In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, the bound implies the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate, even in infinite-dimensional Hilbert spaces. Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, constant composition codes, and classical data compression with quantum side information via fixed-length or variable-length coding. Our technical ingredient is to establish an operator layer cake theorem - the directional derivative of an operator logarithm admits an integral representation of certain projections. This shows that a kind of pretty-good measurement is equivalent to a randomized Holevo-Helstrom measurement, which provides an operational explanation of why the pretty-good measurement is pretty good.

STACIE (STable AutoCorrelation Integral Estimator) is a novel algorithm and Python package that delivers robust, uncertainty-aware estimates of autocorrelation integrals from time-correlated data. While its primary application is deriving transport properties from equilibrium molecular dynamics simulations, STACIE is equally applicable to time-correlated data in other scientific fields. A key feature of STACIE is its ability to provide robust and accurate estimates without requiring manual adjustment of hyperparameters. Additionally, one can follow a simple protocol to prepare sufficient simulation data to achieve a desired relative error of the transport property. We demonstrate its application by estimating the ionic electrical conductivity of a NaCl-water electrolyte solution. We also present a massive synthetic benchmark dataset to rigorously validate STACIE, comprising 15360 sets of time-correlated inputs generated with diverse covariance kernels with known autocorrelation integrals. STACIE is open source and available on GitHub and PyPI, with comprehensive documentation and examples.

We show that multisoliton solutions to the Benjamin--Ono equation are uniformly orbitally stable in $H^s(\mathbb{R})$ for every $-\tfrac12<s\leq \frac12$. This improves the regularity required for stability up to the sharp well-posedness threshold; previous work (even on single solitons) had required $s\geq \frac12$. One key ingredient in our argument is a new variational characterization of multisolitons. A second ingredient is the extension to low-regularity slowly-decaying solutions of the Wu identity on eigenfunctions of the Lax operator. This extension also allows us to clarify the spectral type of the Lax operator for such potentials by precluding embedded eigenvalues.

We study cumulants of numbers of $q$-step walks on Erd\H os-Rényi random graphs with distance-dependent edge probability in the limit when the number of vertices $N$, concentration $c$, and interaction radius $R$ tend to infinity. These cumulants can be associated with a formal cumulant expansion of the free energy of matrix models of exponential random graphs widely known in mathematical and theoretical physics. We show that in three different asymptotic regimes, the limiting values of $k$-th cumulants ${\cal F}_k^{(q)}$ exist and can be associated with one or another family of tree-type diagrams, in dependence on the asymptotic behavior of parameters $cR/N$ for $q$-step non-closed walks and $c^2R/N^2$ for 3-step closed walks, respectively. In some cases, we obtain explicit expressions for ${\cal F}_k^{(q)}$ with the help of a modified Prüfer codification. These results allow us to prove Limit Theorems for the number of non-closed walks and for the number of triangles in corresponding ensembles of large random graphs. We indicate an asymptotic threshold that separates the normal probability distribution and the Poisson one for the number of triangles in random graphs. We show that in the random graph ensemble that we consider the average vertex degree can be bounded from above while the total number of triangles infinitely increases, thus rigorously solving a graph collapse problem known in applications.

Disordered (amorphous) materials, such as glasses, are emerging as promising candidates for applications within energy storage, nonlinear optics, and catalysis. Their lack of long-range order and complex short- and medium-range orderings, which depend on composition as well as thermal and pressure history, offer a vast materials design space. To this end, relying on machine learning methods instead of trial and error is promising, and among these, inverse design has emerged as a tool for generating materials with desired properties. Although inverse design methods based on diffusion models have shown success for crystalline materials and molecules, similar methods targeting amorphous materials remain less developed, mainly because of the limited availability of large-scale datasets and the requirement for larger simulation cells. In this work, we propose and validate an inverse design method for amorphous materials, introducing AMDEN (Amorphous Material DEnoising Network), a diffusion model-based framework that generates structures of amorphous materials. These low-energy configurations are typically obtained through a thermal motion-driven random search-like process that cannot be replicated by standard denoising procedures. We therefore introduce an energy-based AMDEN variant that implements Hamiltonian Monte Carlo refinement for generating these relaxed structures. We further introduce several amorphous material datasets with diverse properties and compositions to evaluate our framework and support future development.

We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is relatively form-bounded with respect to the real part of the magnetic Laplacian, we introduce the operator as an m-sectorial operator. In two dimensions, sufficient conditions are established to guarantee that the resolvent is compact. In the case of non-critical complex magnetic fields, a WKB approach is used to construct semiclassical pseudomodes, which do not exist when the magnetic field is real-valued.

High-level theories rooted in the Bayesian Brain Hypothesis often frame cognitive effort as the cost of resolving the conflict between habits and optimal policies. In parallel, evidence accumulator models (EAMs) provide a mechanistic account of how effort arises from competition between the subjective values of available options. Although EAMs have been combined with frameworks like Reinforcement Learning to bridge the gap between high-level theories and process-level mechanisms, relatively less attention has been paid to their implications for a unified notion of cognitive effort. Here, we combine Active Inference (AIF) with the Drift-Diffusion Model (DDM) to investigate whether the resulting AIF-DDM can simultaneously account for effort arising from both habit violation and value discriminability. To our knowledge, this is the first time AIF has been combined with an EAM. We tested the AIF-DDM on a behavioral dataset from the two-step task and compared its predictions to an information-theoretic definition of cognitive effort based on AIF. The model's predictions successfully accounted for second-stage reaction times but failed to capture the dynamics of the first stage. We argue the latter discrepancy likely stems from the experimental design rather than a fundamental flaw in the model's assumptions about cognitive effort. Accordingly, we propose several modifications of the two-step task to better measure and isolate cognitive effort. Finally, we found that integrating the DDM significantly improved parameter recovery, which could help future studies to obtain more reliable parameter estimates.

Modules for Experiments in Stellar Astrophysics (MESA) is a widely used open-source code for modeling stellar evolution. Many applications of the code rely on large computational grids containing thousands of models, which can be time-consuming to analyze. The mesalab package was developed to automate this post-processing. This Python-based, modular pipeline supports the analysis of large MESA grid outputs and can identify selected evolutionary features, such as the blue loop phase of the evolution of classical Cepheids. The pipeline can automatically prepare input files for and launch MESA-RSP and GYRE to investigate the pulsation properties associated with these evolutionary phases. The pipeline also includes tools for visualizing evolutionary tracks, including Hertzsprung-Russell diagrams and Gaia color-magnitude diagrams.

The epoch of reionization (EoR) marks the last phase transition of hydrogen in our Universe, as it evolves from cold and neutral to hot and ionized in the intergalactic medium (IGM). While its endpoint and duration can be estimated from current observations, albeit with large uncertainties, there is no known avenue to constrain its onset. We propose a novel method based on the Pearson cross-correlation coefficient between 21-cm brightness temperature maps and line-intensity maps tracing star-formation (e.g., [OIII], CO, [CII]). This real-space estimator evolves from negative to positive as X-ray heating progresses, and saturates prior to the EoR. We predict a sharp drop from saturation during the earliest EoR stages, when the IGM ionized fraction is $x_{\rm HII}\lesssim 10\%$. We show that in standard scenarios, where IGM heating precedes reionization, the drop is a clear, model-robust signature that the EoR is still in its early stages, even when $\bar{x}_{\rm HII}$ cannot be measured precisely. This information is not accessible through the detection of an anticorrelation alone, which only indicates that reionization is ongoing. To assess the detectability of this feature, we provide a preliminary estimate of its signal-to-noise ratio in our fiducial scenario, assuming SPHEREx-like and SKAO-like noise levels, indicating that it is within reach of next-generation surveys. The detection of the Pearson drop therefore will provide a unique anchor for the EoR onset, and an upper bound on $x_{\rm HII}$, complementing existing probes and tightening constraints on early galaxy formation models.

Enhancing heat transport within thermochemical heat storage (TCHS) materials is essential for improving their heat output. A common strategy is to combine salts with highly thermally conductive additives, such as carbon or metallic materials. However, such composites often exhibit interfacial instability and reduced gas permeability. In this work, we propose an alternative approach based on microstructural orientation control, aiming to create efficient heat-transport pathways without relying on conductive additives. $β$-La$_2$(SO$_4$)$_3$, which undergoes reversible hydration and dehydration below 250 $^\circ$C, was selected as a model TCHS material. Highly oriented rod-like La$_2$(SO$_4$)$_3\cdot$9H$_2$O crystals with centimeter-scale lengths were grown from solution, cut into plate-shaped specimens, and then dehydrated to $β$-La$_2$(SO$_4$)$_3$. Two types of specimens with different microstructural orientations, which form spontaneously during the dehydration of La$_2$(SO$_4$)$_3\cdot$9H$_2$O to $β$-La$_2$(SO$_4$)$_3$, were prepared. In the "cross-plane-gb" specimen, the aligned grain boundaries were predominantly oriented parallel to the through-thickness direction of the plate, whereas in the "in-plane-gb" specimen, they were predominantly oriented perpendicular to this direction. Laser flash analysis (LFA) of $β$-La$_2$(SO$_4$)$_3$ revealed a clear orientation dependence of heat transport: the apparent thermal diffusivity was approximately 0.24 mm$^2$/s for the cross-plane-gb specimens, in which the grain boundaries are aligned along the heat-flow direction during LFA, and it was approximately 0.15 mm$^2$/s for the in-plane-gb specimens. These findings demonstrate that controlling the microstructural orientation is a viable route for enhancing heat transport in TCHS materials, offering an additive-free design strategy.

We report the in-situ 3D reconstruction of through-going muons in the CUORE experiment, a cryogenic calorimeter array searching for neutrinoless double beta ($0νββ$) decay, leveraging the segmentation of the detector. Due to the slow time response of the detector, time-of-flight estimation is not feasible. Therefore, the track reconstruction is performed using a multi-objective optimization algorithm that relies on geometrical information from the detector as a whole. We measure the integral flux of cosmic-ray muons underground at the {\it Laboratori Nazionali del Gran Sasso}, and find our value to be in good agreement with other experiments that have performed a similar measurement. To our knowledge, this work represents the first demonstration of 3D particle tracking and reconstruction of through-going muons with per-event angular determination in a millikelvin cryogenic detector array. The analysis performed for this work will be critical for validating the muon-related background in CUPID, a next-generation $0νββ$ experiment, and for follow-up studies on detector response and on delayed products induced by cosmic-ray muons.

Wireless baseband processing (WBP) serves as an ideal scenario for utilizing vector processing, which excels in managing data-parallel operations due to its parallel structure. However, conventional vector architectures face certain constraints such as limited vector register sizes, reliance on power-of-two vector length multipliers, and vector permutation capabilities tied to specific architectures. To address these challenges, we have introduced an instruction set extension (ISE) based on RISC-V known as unlimited vector processing (UVP). This extension enhances both the flexibility and efficiency of vector computations. UVP employs a novel programming model that supports non-power-of-two register groupings and hardware strip-mining, thus enabling smooth handling of vectors of varying lengths while reducing the software strip-mining burden. Vector instructions are categorized into symmetric and asymmetric classes, complemented by specialized load/store strategies to optimize execution. Moreover, we present a hardware implementation of UVP featuring sophisticated hazard detection mechanisms, optimized pipelines for symmetric tasks such as fixed-point multiplication and division, and a robust permutation engine for effective asymmetric operations. Comprehensive evaluations demonstrate that UVP significantly enhances performance, achieving up to 3.0$\times$ and 2.1$\times$ speedups in matrix multiplication and fast Fourier transform (FFT) tasks, respectively, when measured against lane-based vector architectures. Our synthesized RTL for a 16-lane configuration using SMIC 40nm technology spans 0.94 mm$^2$ and achieves an area efficiency of 21.2 GOPS/mm$^2$.

We review how to use von Neumann's measurement procedure to estimate a phase, using an efficient Hamiltonian simulation subroutine acts on a block-encoded Hamiltonian. We show that the resulting algorithm can be used to solve quantum phase estimation (QPE) or quantum energy estimation (QEE) {with competitive complexity scaling.} We then use recent results for block-encoding implementations to derive the Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. With this result, we demonstrate an efficient algorithm for QEE beginning from any linear combinations of Pauli strings. In this way, we argue that a well-understood and long-standing idea retains practical legitimacy for fault-tolerant era algorithms, once the costs of Hamiltonian simulation are accounted for.

Collaboration among distributed agents is fundamental to many complex systems, particularly in communication networks where connectivity must be maintained under energy constraints. In this study, we utilize intelligent agents (nodes) trained through reinforcement learning techniques to establish connections with their neighbors, ultimately leading to the emergence of a large-scale communication cluster. Notably, there is no centralized administrator; instead, agents must adjust their connections based on information obtained from local observations. The connection strategy is formulated using a physical Hamiltonian, thereby categorizing this intelligent system under the paradigm of "Physics-Guided Machine Learning". Agents are trained via a Deep Q-Network using local observations to minimize changes in the Hamiltonian, enabling adaptive decision-making in dynamic environments. Simulation results demonstrate that the proposed collaborative strategy forms robust large-scale communication clusters while reducing transmission energy compared to baseline approaches. The network maintains high connectivity under agent mobility, density variations, node failures, and environmental obstacles, highlighting strong adaptability and resilience. These findings indicate that physics-guided reinforcement learning provides an effective mechanism for distributed topology optimization in emerging IoT and vehicular communication networks.

We investigate the role of quantum geometry in the Meissner response for odd-frequency superconducting pairs in multiband systems. Odd-frequency pairing is traditionally associated with a paramagnetic Meissner response, which raises questions about the stability of the superconducting phase, especially in multiband systems where odd-frequency pairing is ubiquitous. Using analytical calculations in a general two-band, we show that the quantum geometric contribution to the Meissner response from odd-frequency pairs is always diamagnetic for its interband processes, while intraband processes always yield a paramagnetic response. With odd-frequency pairing itself generated by interband pairing, an overall diamagnetic response may often be anticipated. We confirm these results with numerical calculations of models with both flat and dispersive bands. In flat band systems, where geometric effects dominate, the diamagnetic odd-frequency response can even exceed the even-frequency contribution, making odd-frequency pairs the primary source of the diamagnetic Meissner response. In a dispersive two-band system with finite quantum geometry, we similarly find a robust diamagnetic contribution from odd-frequency pairing, even when the total response turns paramagnetic due to even-frequency contributions. These results establish that quantum geometry stabilizes odd-frequency superconductivity and also identify flat-band materials as candidates for realizing odd-frequency superconductivity with a diamagnetic Meissner effect.

We numerically investigate the two-dimensional Bose-Hubbard model with local onsite disorder, where the competition between disorder and short-range interactions leads to the emergence of a Bose glass (BG) phase between the Mott insulator (MI) and superfluid (SF) phases. In order to analyze the inhomogeneous system we employ real-space bosonic dynamical mean-field theory (RBDMFT) and perform an ensemble average over disorder realizations. To distinguish the MI from the BG phase, we compare the Edwards-Anderson order parameter and the compressibility with the energy-gap condition. To identify the insulator to SF transition, we apply a percolation analysis to the condensate order parameter. In qualitative accordance with the theorem of inclusions we always find an intermediate BG phase between the SF and MI. However, the quantitative comparison indicates significant deviations between the MI to BG phase boundary expected in the thermodynamic limit and the one obtained for a finite system size. Additionally, RBMDFT is capable of reliably calculating spectral information throughout the phase diagram. Analyzing the spectral function reveals evidence for analytically predicted damped localized modes in the dispersion relation in the strong-coupling regime.

A wide range of methods currently exist for testing the presence of malaria, each with its own advantages and disadvantages. New technologies are urgently needed to develop more effective diagnosis tools to fight and eradicate malaria. Optical biosensors that employ surface plasmon resonance (SPR) techniques are a promising category of devices for detecting malaria biomarkers. One such biomarker is plasmodium lactate dehydrogenase (pLDH), a protein produced during the life cycle of the malaria parasite, which is a metabolic enzyme found in all plasmodium species, including the most widespread falciparum. This work reports on the design, probing, and experimental performance of an optical biosensor for detecting pLDH based on SPR and extraordinary optical transmission. The biosensor is composed of an aluminum metasurface made from an array of nanoholes. The sensor operates in the visible spectral region and achieves label-free sensing of plasmodium falciparum LDH (pfLDH) spiked in phosphate-buffered saline. The sensor has a spectral sensitivity of 360 nm/RIU and an LOD of 1.3 nM, equivalent to 45.6 ng/mL of pfLDH. This type of optical biosensor may offer a cost-effective and high sensitivity method for active infection diagnosis.

Superconducting fluxonium qubits show a highly tunable energy-level structure, with transition frequencies spanning from a few MHz to few GHz. This range is well-aligned to the operational frequencies of highly coherent micro- and nano-mechanical resonators, making fluxonium an attractive candidate for hybrid electromechanical systems. In this work, we theoretically investigate a flux-tunable electromechanical system consisting of a fluxonium qubit coupled to a suspended mechanical resonator. The coupling arises from the motion-induced modulation of magnetic flux through the fluxonium loop, enabling both transverse and longitudinal electromechanical interactions that are tunable via external magnetic fields. By optimizing the design parameters of the fluxonium qubit, we demonstrate the feasibility of achieving strong resonant single-photon coupling near the flux-frustration point. We analyze the system dynamics across different coupling regimes, identifying signatures of electromagnetically induced transparency (EIT) in the longitudinal regime and mode splitting in the transverse regime. Additionally, we show that ground-state preparation of both subsystems is possible through sideband cooling of the mechanical resonator. These results suggest that a fluxonium-based hybrid electromechanical device could be a promising platform for studying macroscopic quantum phenomena and for applications in quantum technology.

We are concerned with the dependence of the lowest eigenvalue of the magnetic Dirichlet Laplacian on the geometry of rectangles, subject to homogeneous fields. We conjecture that the square is a global minimiser both under the area or perimeter constraints. Contrary to the well-known magnetic-free analogue, the present spectral problem does not admit explicit solutions. By establishing lower and upper bound to the eigenvalue, we establish the conjecture for weak magnetic fields. Moreover, we relate the validity of the conjecture to the simplicity of the eigenvalue and symmetries of minimisers of a non-convex minimisation problem.

A novel approach to adding an additional parameter to a family of distributions for better adaptability has been put forth. This approach yields a versatile class of distributions supported on the positive real line. An important advantage of the proposed family is that the additional parameter admits a clear interpretation in terms of tail behavior, providing a simple mechanism for modulating tail heaviness. We proceed to analyze its mathematical characteristics, such as critical points, modality, stochastic representation, identifiability, quantiles, moments, and truncated moments. We present two new regression models for positive continuous data based on submodels of the newly proposed family of distributions, in which the distribution of the response variable is reparameterized in terms of the median. We use the maximum likelihood method to estimate the parameters, which was implemented through the gamlss package in R. The proposed regression models were applied to a real dataset, and their advantages over common alternative regression models were demonstrated through quantile residual analysis and information criteria.

Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to account for power loss due to this window in the likelihood function. We show that the inclusion of this factor leads to biased inference. The simplest solution to this, omitting the factor, leads to unbiased posteriors and Bayes factor estimates provided the window does not suppress the signal for signal-to-noise ratios $\lesssim O(100)$, but unreliable estimates of the absolute likelihood. Instead, we propose a multi-stage method that yields consistent estimates for the absolute likelihood in addition to unbiased posterior distributions and Bayes factors for signal-to-noise ratios $\lesssim O(1000)$. Additionally, we demonstrate that the commonly held wisdom that using rectangular windows necessarily leads to biased inference is incorrect.

Gutzwiller projections of non-interacting chiral topological phases are known to give rise to fractional, topologically ordered chiral phases. Here, we carry out a similar construction using two copies of non-interacting Euler insulators to produce a class of spinful interacting Euler models. To that end, we take advantage of the recently discovered exact representation of certain Euler insulators by a projected entangled pair state (PEPS) of bond dimension $D = 2$. The Gutzwiller projection can be implemented within the tensor network formalism, giving rise to a new PEPS of bond dimension $D = 4$. We, moreover, apply very recent state-of-the-art tensor network tools to evaluate these phases. In particular, we analyze its entanglement entropy scaling and find no topological correction to the area law, indicating that the state is not intrinsically topologically ordered. Its entanglement spectrum shows a clear cusp at momentum zero, similar to non-interacting Euler insulators, and the spectrum of the transfer operator indicates that the state is gapped, which could imply non-intrinsic topological features. Finally, the static structure factor displays Bragg peaks, indicating the simultaneous presence of local order.

Quantum kernel methods (QKMs) offer an appealing framework for machine learning on near-term quantum computers. However, QKMs generically suffer from exponential concentration, requiring an exponential number of measurements to resolve kernel values, with the exception of trivial (i.e., classically simulable) kernels. Here we propose a QKM that is free of exponential concentration, yet remains hard to simulate classically. Our QKM utilizes the weak ergodicity-breaking many-body dynamics in the Rydberg blockade of coherently driven neutral atom arrays. We demonstrate the fundamental properties of our QKM by analytically solving an approximate toy model of its underpinning quantum dynamics, as well as by extensive numerical simulations on randomly generated datasets. We further show that the proposed kernel exhibits effective learning on real data. The proposed QKM can be implemented in current neutral atom quantum computers. Along the way, we uncover novel physical insights into the thermalization of weak ergodicity-breaking systems through the non-stabilizerness of the underlying Rydberg-blockaded dynamics, which directly governs the classical simulability of the proposed kernel.

In clustering tasks, it is essential to structure the feature space into clear, well-separated distributions. However, because short text representations have limited expressiveness, conventional methods struggle to identify cluster centers that truly capture each category's underlying semantics, causing the representations to be optimized in suboptimal directions. To address this issue, we propose IOCC, a novel few-shot contrastive learning method that achieves alignment between the cluster centers and the semantic centers. IOCC consists of two key modules: Interaction-enhanced Optimal Transport (IEOT) and Center-aware Contrastive Learning (CACL). Specifically, IEOT incorporates semantic interactions between individual samples into the conventional optimal transport problem, and generate pseudo-labels. Based on these pseudo-labels, we aggregate high-confidence samples to construct pseudo-centers that approximate the semantic centers. Next, CACL optimizes text representations toward their corresponding pseudo-centers. As training progresses, the collaboration between the two modules gradually reduces the gap between cluster centers and semantic centers. Therefore, the model will learn a high-quality distribution, improving clustering performance. Extensive experiments on eight benchmark datasets show that IOCC outperforms previous methods, achieving up to 7.34\% improvement on challenging Biomedical dataset and also excelling in clustering stability and efficiency. The code is available at: https://anonymous.4open.science/r/IOCC-C438.

Most existing robust control barrier functions (CBFs) can only handle matched disturbances, restricting their applications in real-world scenarios. While some recent advances extend robust CBFs to unmatched disturbances, they heavily rely on differentiability property of disturbances, and fail to accommodate non-differentiable case for safety constraints with high relative degree.To address these limitations, this paper proposes a class of disturbance rejection CBFs (DRCBFs), including knowledge-based DRCBFs (kDRCBFs) and reciprocal-compensated DRCBFs (rDRCBFs).These two DRCBFs can strictly guarantee safety under general bounded disturbances, which includes both matched or unmatched, differentiable or non-differentiable disturbances as special cases. Moreover, no information of disturbance is needed in rDRCBFs. Simulation results illustrate that the proposed DRCBFs outperform existing robust CBFs.

This paper studies the problem of inferring a $k$-factor, specifically a spanning $k$-regular graph, planted within an Erdos-Renyi random graph $G(n,λ/n)$. We show that as the average degree $λ$ surpasses the critical threshold of $1/k$, the inference problem undergoes a transition from almost exact recovery to partial recovery. Moreover, as $λ$ tends to infinity, the accuracy of recovery diminishes to zero. In addition, we characterize the recovery accuracy of a linear-time iterative pruning algorithm and show that it achieves almost exact recovery when $λ< 1/k$. A key component of our analysis is a two-step cycle construction: we first build trees through local neighborhood exploration and then connect them by sprinkling using reserved edges. Interestingly, for proving impossibility of almost exact recovery, we construct $Θ(n)$ many small trees of size $Θ(1)$, whereas for establishing the algorithmic lower bound, a single large tree of size $Θ(\sqrt{n\log n})$ suffices.

The existence of galaxies with no heavy elements is a key prediction of cosmological models. So far no "zero-metallicity", or Population~III, galaxies have been identified. Here, we report the identification of an extremely metal-poor galaxy AMORE6 at redshift $z=5.7253$, multiply imaged by a foreground galaxy cluster. JWST spectra consistently detect ${\rm Hβ}$ at both positions, but [OIII]$_{λ\lambda4960,5008}$ remains undetected. This places a firm upper limit on its oxygen abundance, $<$0.19% of solar metallicity at 3$σ$, establishing itself as the most pristine galaxy by far. AMORE6 exhibits exceptional properties that indicate the presence of pristine massive star formation. Finding such an example at a relatively late cosmic time is surprising, but it also validates the basic ideas behind the Big Bang model.