In this work, we analyze 126 publicly available IAM climate scenarios modeled by six leading teams in climate science. We define a simple numerical metric that measures the decarbonization speed implied by each IAM scenario. With this metric, the narrative based, high-dimensional time series scenario datasets can be ranked and compared in a transparent way. We find that the ranking of IAM scenarios according to the decarbonization speed is consistent with their representative concentration pathway assumptions, showing that the decarbonization metric is a useful summary of a scenario's mitigation policy. We further construct an empirical distribution and a fitted parametric distribution of the decarbonization speed estimates. Key statistics such as mean, median and their confidence intervals by the bootstrap resample technique are also reported.

ROI (Region of Interest) video selective encryption based on H.265/HEVC is a technology that protects the sensitive regions of videos by perturbing the syntax elements associated with target areas. However, existing methods typically adopt Tile (with a relatively large size) as the minimum encryption unit, which suffers from problems such as inaccurate encryption regions and low encryption precision. This low-precision encryption makes them difficult to apply in sensitive fields such as medicine, military, and remote sensing. In order to address the aforementioned problem, this paper proposes a fine-grained ROI video selective encryption algorithm based on Coding Units (CUs) and prompt segmentation. First, to achieve a more precise ROI acquisition, we present a novel ROI mapping approach based on prompt segmentation. This approach enables precise mapping of ROIs to small $8\times8$ CU levels, significantly enhancing the precision of encrypted regions. Second, we propose a selective encryption scheme based on multiple syntax elements, which distorts syntax elements within high-precision ROI to effectively safeguard ROI security. Finally, we design a diffusion isolation based on Pulse Code Modulation (PCM) mode and MV restriction, applying PCM mode and MV restriction strategy to the affected CU to address encryption diffusion during prediction. The above three strategies break the inherent mechanism of using Tiles in existing ROI encryption and push the fine-grained level of ROI video encryption to the minimum $8\times8$ CU precision. The experimental results demonstrate that the proposed algorithm can accurately segment ROI regions, effectively perturb pixels within these regions, and eliminate the diffusion artifacts introduced by encryption. The method exhibits great potential for application in medical imaging, military surveillance, and remote areas.

Large language models (LLMs) exhibit memory-intensive behavior during decoding, making it a key bottleneck in LLM inference. To accelerate decoding execution, hybrid-bonding-based 3D-DRAM has been adopted in LLM accelerators. While this emerging technology provides strong performance gains over existing hardware, current 3D-DRAM accelerators (3D-Accelerators) rely on closed-source evaluation tools, limiting access to publicly available performance analysis methods. Moreover, existing designs are highly customized for specific scenarios, lacking a general and reusable full-stack modeling for 3D-Accelerators across diverse usecases. To bridge this fundamental gap, we present ATLAS, the first silicon-proven Architectural Three-dimesional-DRAM-based LLM Accelerator Simulation framework. Built on commercially deployed multi-layer 3D-DRAM technology, ATLAS introduces unified abstractions for both 3D-Accelerator system architecture and programming primitives to support arbitrary LLM inference scenarios. Validation against real silicon shows that ATLAS achieves $\le$8.57% simulation error and 97.26-99.96\% correlation with measured performance. Through design space exploration with ATLAS, we demonstrate its ability to guide architecture design and distill key takeaways for both 3D-DRAM memory system and 3D-Accelerator microarchitecture across scenarios. ATLAS will be open-sourced upon publication, enabling further research on 3D-Accelerators.

Optical spectroscopy provides a powerful, contact-free probe of topological quantum states, yet exact constraints on antisymmetric Hall absorption remain much less well developed than their longitudinal counterparts. Motivated by earlier Hall-conductivity sum rules, we formulate the corresponding first-frequency-moment constraint for the antisymmetric optical conductivity, whose imaginary part governs chirality-dependent absorption. We then demonstrate this sum rule in two classes of time-reversal-breaking topological systems. For a zero-field moiré continuum model hosting topological bands, the moment vanishes exactly, implying that any low-frequency anomalous Hall absorption must be compensated by higher-frequency spectral weight of the opposite sign. For a Hofstadter model under a uniform magnetic field, the same moment takes a universal value fixed by the magnetic flux density, independent of microscopic model details. By linking low- and high-frequency spectral contributions, this optical Hall absorption sum rule provides a rigorous framework for quantifying circular dichroism constraints and diagnosing Landau-level mixing. Our results show how a known Hall spectral constraint acquires new and experimentally relevant content in modern interacting topological materials.

This paper studies global solvability of the Cauchy problem for a generalized time-fractional Kuramoto-Sivashinsky equation in the Shwartz space, which is a complete topological space generated by a family of semi-norms. The main approach is based on separating the linear and nonlinear parts of the equation and applying appropriate analytical methods to each of them. The linear part of the equation is analyzed using the Fourier transform. The nonlinear equation is treated by the method of successive approximations, and uniform estimates for the constructed sequence are derived. Furthermore, taking into account the topological structure of the Schwartz space, the convergence of the sequence in the sense of semi-norms is rigorously established. The results provide a rigorous analytical framework for fractional Kuramoto-Sivashinsky type equations in topological function spaces.

The number of subgroups and the number of cyclic subgroups are natural combinatorial invariants of a finite group. We investigate how restrictions on these quantities, together with the number of distinct prime divisors of $|G|$, enforce nilpotency, supersolvability, and solvability of $G$. These criteria improve earlier results that relied solely on the total number of subgroups, and they are sharp in the sense that for each bound there exist non-nilpotent (respectively non-supersolvable, non-solvable) groups attaining the bound.

We report direct experimental observations of self-organized rotating flames of premixed CH4 and air in an open circular Hele-Shaw burner equipped with an annulus cavity flame holder. These flames formed spontaneously at sufficiently low flow rates, where flame flashback was counteracted by thermal quenching, resulting in a dynamic balance between the local flame speed and flow velocity. Unlike flames propagating in closed micro-channels, these flames exhibited stable traveling-wave patterns with heads gliding along the leading edge of the cavity, where rapid expansion created a low-speed zone that facilitated flame stabilization. At low flow rates, the rotating flames were single-headed, with their rotation frequencies roughly proportional to the laminar flame speeds, suggesting that the flame fronts traveled in a nearly constant-shape fashion. As the flow rate increased, the rotating flames split into multiple heads at approximately equal spacing, and the number of heads and rotation frequency increased with the flow rate, until these rotating flames transitioned into steady ring-shaped flames anchored at the cavity leading edge. Blow-off or extinction occurred at sufficiently high flow rates, where the flame front was pushed out of the rear side of the cavity. Parametric measurements were conducted over a wide range of equivalence ratios and flow rates, from which a regime diagram of different flame modes and their transition boundaries was obtained. Additional experiments were conducted on C3H8 and DME. It was found that the critical total mass flow rate at the rotating-steady flame transition boundary is insensitive to equivalence ratio, gap distance, and fuel type. These results should be useful not only for the fundamental understanding of flame dynamics in micro-channels but also for the practical design of micro-combustors and the application of micro-combustion technologies.

Integrated photonics is a powerful platform for exploring Hermitian and non-Hermitian physics. Beyond device geometry, controlling how resonators are driven is crucial to access and tailor their modes. Coherent excitation via multiple input ports (interferometric excitation) enables such control, but its accurate description requires extending standard temporal coupled-mode theory to include interference between excitation pathways. Experimental realizations have so far been limited by phase-unstable, off-chip interferometers. Here we implement a fully integrated, phase-stable interferometric excitation scheme for an infinity-loop-microresonator, an established structure operating on an exceptional surface, and use it to test the extended theory. Phase-resolved measurements in the linear and thermo-optic nonlinear regimes show that the relative phase between inputs governs the intracavity energy distribution, enabling up to a twofold increase of the circulating power compared to single-port excitation. This integrated platform enables reproducible studies of phase-dependent effects and coherent-control schemes in non-Hermitian photonic devices.

Recent deep learning (DL) methods for log anomaly detection increasingly rely on semantic log representation methods that convert the textual content of log events into vector embeddings as input to DL models. However, these DL methods are typically evaluated as end-to-end pipelines, while the impact of different semantic representation methods is not well understood. In this paper, we benchmark widely used semantic log representation methods, including static word embedding methods (Word2Vec, GloVe, and FastText) and the BERT-based contextual embedding method, across diverse DL models for log-event level anomaly detection on three publicly available log datasets: BGL, Thunderbird, and Spirit. We identify an effectiveness--efficiency trade off under CPU deployment settings: the BERT-based method is more effective, but incurs substantially longer log embedding generation time, limiting its practicality; static word embedding methods are efficient but are generally less effective and may yield insufficient detection performance. Motivated by this finding, we propose QTyBERT, a novel semantic log representation method that better balances this trade-off. QTyBERT uses SysBE, a lightweight BERT variant with system-specific quantization, to efficiently encode log events into vector embeddings on CPUs, and leverages CroSysEh to enhance the semantic expressiveness of these log embeddings. CroSysEh is trained unsupervisedly using unlabeled logs from multiple systems to capture the underlying semantic structure of the BERT model's embedding space. We evaluate QTyBERT against existing semantic log representation methods. Our results show that, for the DL models, using QTyBERT-generated log embeddings achieves detection effectiveness comparable to or better than BERT-generated log embeddings, while bringing log embedding generation time closer to that of static word embedding methods.

We give extensive characterizations for an open subset of an affine space of arbitrary dimension, resp. of an inverse limit of prime spectra to be quasi-compact. Among other things weak stability, retro-compactness, and cylinder sets provide equivalent criteria in both settings. We also exhibit an example of a non-quasi-compact affine space.

Flow through porous media can reshape the medium through erosion and deposition, producing preferential flow channels across a wide range of natural and industrial systems. Yet the mechanisms by which spatial disorder triggers channelization remain unclear. Here we derive a continuum description for the coupled evolution of flow and porosity by coarse-graining pore-scale dynamics and validating the resulting model with pore-scale simulations. Using this framework, we show that different sources of disorder lead to qualitatively distinct behaviors. Disorder in erosion resistance produces a discontinuous transition to localized flow, with permanent channels appearing only above a finite disorder strength. In contrast, even extremely weak fluctuations in the initial porosity destabilize homogeneous flow and trigger persistent channelization. These results reveal an unexpected sensitivity of evolving porous media to structural heterogeneity, suggesting that channelization can arise generically even in nearly uniform materials.

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental decoherence can lead to improved semi-classical theories that are exact descriptions of the original quantum dynamics. In doing so, we show how consistent models of classical-quantum dynamics can arise as effective descriptions of open quantum systems.

The dark-state effect, caused by destructive interference, not only is an important fundamental research topic in atomic physics and quantum optics, but also has wide potential application in quantum physics and quantum information science. Using the arrowhead-matrix method, here we study the dark-state effect in a coupled cavity-Rydberg-atom system, in which $N$ Rydberg atoms with the dipole-dipole interactions are coupled to a single-mode cavity field. We obtain the numbers and form of the dark states in certain excitation-number subspaces for the two-, three-, and four-atom cases, as well as in the single-excitation subspace for a general $N$-atom case. We also suggest to characterize the dark states by inspecting the populations of some specific quantum states, which can be detected in experiments. Furthermore, we analyze the dark-state effect in a realistic case, where both the atomic dipole-dipole interaction strengths and the atom-cavity-field coupling strengths depend on the position of the atoms. Our findings pave the way for studying dark-state physics and applications in the cavity-Rydberg-atom platform.

Double perovskite halides are emerging as promising materials for a wide range of applications, particularly in renewable energy technologies such as solar cell devices, thereby contributing to addressing global energy demands. In this work, the structural, electronic, optical, dielectric, thermoelectric, and photocatalytic properties of Li2InBiX6 (X = Cl, Br, I) halides are systematically investigated using density functional theory. The calculated formation energies confirm the thermodynamic stability of these compounds in the cubic phase. The studied materials exhibit semiconducting behavior with direct bandgaps of 1.7 eV, 1.3 eV, and 1.1 eV for Li2InBiCl6, Li2InBiBr6, and Li2InBiI6, respectively. The complex dielectric function is analyzed to explore their optical response, revealing strong absorption in the infrared and visible regions, indicating suitability for optoelectronic applications. Thermoelectric properties, including the Seebeck coefficient, electrical conductivity, and figure of merit (ZT), are evaluated over a temperature range of 30 to 800 K. The relatively small bandgaps contribute to enhanced thermoelectric performance, reflected in improved power factors. Furthermore, photocatalytic analysis indicates that Li2InBiX6 compounds are suitable candidates for water oxidation reactions within the pH range of 0 to 7. Overall, the combined thermoelectric and optical performance highlights these double perovskite halides as promising materials for future energy conversion applications.

Database research and the development of learned query optimisers rely heavily on realistic SQL workloads. Acquiring real-world queries is increasingly difficult, however, due to strict privacy regulations, and publicly released anonymised traces typically strip out executable query text to preserve confidentiality. Existing synthesis tools fail to bridge this training data gap: traditional benchmarks offer too few fixed templates for statistical generalisation, while Large Language Model (LLM) approaches suffer from schema hallucination fabricating non-existent columns and topological collapse systematically defaulting to simplistic join patterns that fail to stress-test query optimisers. We propose SynQL, a deterministic workload synthesis framework that generates structurally diverse, execution-ready SQL workloads. As a foundational step toward bridging the training-data gap, SynQL targets the core SQL fragment -- multi-table joins with projections, aggregations, and range predicates -- which dominates analytical workloads. SynQL abandons probabilistic text generation in favour of traversing the live database's foreign-key graph to populate an Abstract Syntax Tree (AST), guaranteeing schema and syntactic validity by construction. A configuration vector $Θ$ provides explicit, parametric control over join topology (Star, Chain, Fork), analytical intensity, and predicate selectivity. Experiments on TPC-H and IMDb show that SynQL produces near-maximally diverse workloads (Topological Entropy $H = 1.53$ bits) and that tree-based cost models trained on the synthetic corpus achieve $R^2 \ge 0.79$ on held-out synthetic test sets with sub-millisecond inference latency, establishing SynQL as an effective foundation for generating training data when production logs are inaccessible.

Humanitarian organizations help to ensure people's livelihoods in crisis situations. Typically, multiple organizations operate in the same region. To ensure that the limited budget of these organizations can help as many people as possible, organizations perform cross-organizational deduplication to detect duplicate registrations and ensure recipients receive aid from at most one organization. Current deduplication approaches risk privacy harm to vulnerable aid recipients by sharing their data with other organizations. We analyzed the needs of humanitarian organizations to identify the requirements for privacy-friendly cross-organizational deduplication fit for real-life humanitarian missions. We present xDup, a new practical deduplication system that meets the requirements of humanitarian organizations and is two orders of magnitude faster than current solutions. xDup builds on Fuzzy PSI, and we present otFPSI, a concretely efficient Fuzzy PSI protocol for Hamming Space without input assumptions. We show that it is more efficient than existing Fuzzy PSI protocols.

In this paper, we consider data-driven reconstruction of unknown inputs to linear time-invariant (LTI) multiple-input multiple-output (MIMO) systems. We propose a novel autoregressive estimator based on a constrained least-squares formulation over Hankel matrices, splitting the problem into an output-consistency constraint and an input-history-matching objective. Our method relies on previously recorded input-output data to represent the system, but does not require knowledge of the true input to initialize the algorithm. We show that the proposed estimator is strictly stable if and only if all the invariant zeros of the trajectory-generating system lie strictly inside the unit circle, which can be verified purely from input and output data. This mirrors existing results from model-based input reconstruction and closes the gap between model-based and data-driven settings. Lastly, we provide numerical examples to demonstrate the theoretical results.

We construct left, right and bilateral fundamental solutions for generalized steady Stokes' operators $S$ with smooth coefficients coefficients, associated with the de Rham complex of differentials on differential forms over a domain $X$ in ${\mathbb R}^n$. The investigated operators are Douglis-Nirenberg elliptic under reasonable assumptions. As an immediate corollary we produce a homotopy formula for regular solutions to this operator.

Folsom, Males, Rolen, and Storzer recently proved Andrews' Conjecture~4 for the coefficients of \[ v_1(q)=\sum_{n\ge 0}\frac{q^{n(n+1)/2}}{(-q^2;q^2)_n}=\sum_{n\ge 0}V_1(n)q^n. \] They also proved a refined density-one version of Andrews' Conjecture~3. In this paper we prove Andrews' Conjectures~5 and~6. Our proof relies on an investigation of the simple zeros of the trigonometric factor in the Folsom--Males--Rolen--Storzer asymptotic and showing that the relevant quadratic sequence stays a positive distance from the integers infinitely often. The argument is unconditional.

We give an explicit algorithm to Legendrian realize a homologically nontrivial simple closed curve on a ribbon surface of a Legendrian graph in the standard contact structure $(\mathbb{R}^3,ξ_{\rm st})$. As an application, we obtain an algorithm that converts an abstract open book whose monodromy is written as a product of Dehn twists along homologically nontrivial curves into a contact surgery diagram for the supported contact manifold. Along the way, we also record a uniqueness statement which is implicit in earlier work but, to our knowledge, was never written in the form needed here: any two Legendrian realizations of the same curve on a ribbon surface are Legendrian isotopic, and likewise for Legendrian knots lying on pages of open books and representing the same isotopy class on the page.

REST APIs enable collaboration among microservices. A single fault in a REST API can bring down the entire microservice system and cause significant financial losses, underscoring the importance of REST API testing. Effectively testing REST APIs requires thoroughly exercising the functionalities behind them. To this end, existing techniques leverage REST specifications (e.g., Swagger or OpenAPI) to generate test cases. Using the resource constraints extracted from specifications, these techniques work well for testing simple, business-insensitive functionalities, such as resource creation, retrieval, update, and deletion. However, for complex, business-sensitive functionalities, these specification-based techniques often fall short, since exercising such functionalities requires additional business constraints that are typically absent from REST specifications. In this paper, we present LoBREST, a log-based, business-aware REST API testing technique that leverages historical request logs (HRLogs) to effectively exercise the business-sensitive functionalities behind REST APIs. To obtain compact operation sequences that preserve clean and complete business constraints, LoBREST first employs a locality-slicing strategy to partition HRLogs into smaller slices. Then, to ensure the effectiveness of the obtained slices, LoBREST enhances them in two steps: (1) adding slices for operations missing from HRLogs, and (2) completing missing resources within the slices. Finally, to improve test adequacy, LoBREST uses these enhanced slices as initial seeds to perform business-aware fuzzing. LoBREST outperformed eight tools (including Arat-rl, Morest, and Deeprest) across 17 real-world services. It achieved top operation coverage on 16 services and line coverage on 15, averaging 2.1x and 1.2x improvements over the runner-up. LoBREST detected 108 5XX bugs, including 38 found by no other tool.

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic stability in the strong sense: convergence of the densities of the stationary measures to the density of the physical measure of the unperturbed map in the $L^1$-norm. This improves the main result in \cite{Me}.

We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for the pseudo-true factor order under misspecification, provided that all globally optimal models share a common pseudo-true covariance set, the population Gaussian criterion has a local quadratic margin away from that set, and the BIC complexity counts are order-separating at the pseudo-true order. The candidate models may have an unknown mean vector, exact-zero restrictions in the loading matrix, and either diagonal or spherical error covariance structures, and the selection target is the smallest candidate factor order that yields the best Gaussian approximation, in Kullback--Leibler divergence, to the data-generating covariance structure. The proof works directly in covariance space, so it does not require a regular loading parametrization and accommodates the familiar singularities caused by rotations and redundant factors. Under correct specification, the assumptions reduce to familiar properties of the true covariance matrix. More generally, the same argument applies to other information criteria whose penalties satisfy the same gap conditions, including several BIC-type modifications.

Decoding Bivariate Bicycle (BB) quantum error correction codes typically requires Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) post-processing when BP fails to converge. Whether BP will converge on a given syndrome is currently determined only after running BP to completion. We show that convergence can be predicted in advance by a single modulo operation: if the syndrome defect count is divisible by the code's column weight w, BP converges with high probability (100% at p <= 0.001, degrading to 87% at p = 0.01); otherwise, BP fails with probability >= 90%. The mechanism is structural: each physical data error activates exactly w stabilizers, so a defect count not divisible by w implies the presence of measurement errors outside BP's model space. Validated on five BB codes with column weights w = 2, 3, and 4, mod-w achieves AUC = 0.995 as a convergence classifier at p = 0.001 under phenomenological noise, dominating all other syndrome features (next best: AUC = 0.52). The false positive rate scales empirically as O(p^2.05) (R^2 = 0.98), confirming the analytical bound from Proposition 2. Among BP failures on mod-w = 0 syndromes, 82% contain weight-2 data error clusters, directly confirming the dominant failure mechanism. The prediction is invariant under BP scheduling strategy and decoder variant, including Relay-BP - the strongest known BP enhancement for quantum LDPC codes. These results apply directly to IBM's Gross code [[144, 12, 12]] and Two-Gross code [[288, 12, 18]], targeted for deployment in 2026-2028.

Cross-Domain Sequential Recommendation (CDSR) aims to en-hance recommendation quality by transferring knowledge across domains, offering effective solutions to data sparsity and cold-start issues. However, existing methods face three major limitations: (1) they overlook varying contexts in user interaction sequences, resulting in spurious correlations that obscure the true causal relationships driving user preferences; (2) the learning of domain- shared and domain-specific preferences is hindered by gradient conflicts between domains, leading to a seesaw effect where performance in one domain improves at the expense of the other; (3) most methods rely on the unrealistic assumption of substantial user overlap across domains. To address these issues, we propose CoDiS, a context-aware disentanglement framework grounded in a causal view to accurately disentangle domain-shared and domain-specific preferences. Specifically, Our approach includes a variational context adjustment method to reduce confounding effects of contexts, expert isolation and selection strategies to resolve gradient conflict, and a variational adversarial disentangling module for the thorough disentanglement of domain-shared and domain-specific representations. Extensive experiments on three real-world datasets demonstrate that CoDiS consistently outperforms state-of-the-art CDSR baselines with statistical significance. Code is available at:https://anonymous.4open.science/r/CoDiS-6FA0.

Motion tracking has been an important technique for imitating human-like movement from large-scale datasets in physics-based motion synthesis. However, existing approaches focus on tracking either single character or a particular type of interaction, limiting their ability to handle contact-rich interactions. Extending single-character tracking approaches suffers from the instability due to the challenge of forces transferred through contacts. Contact-rich interactions requires levels of control, which places much greater demands on model capacity. To this end, we propose a robust tracking method based on progressive neural network (PNN) where multiple experts are specialized in learning skills of various difficulties. Our method learns to assign training samples to experts automatically without requiring manually scheduling. Both qualitative and quantitative results show that our method delivers more stable motion tracking in densely interactive movements while enabling more efficient model training.

We present the discovery of SN 2025mkn, a gravitationally lensed Type II supernova. First detected as a blue transient in ZTF, 0.83$^{\prime\prime}$ from a $z=0.42$ elliptical galaxy, follow-up SNIFS/UH2.2m and LRIS/Keck spectra revealed absorption lines at $z=1.371$. Later JWST NIRCam imaging shows that the bright transient is a close pair of point sources separated by $\sim 0.07^{\prime\prime}$, and a 30 times fainter counterimage opposite the lens, for which NIRSpec reveals strong H$α$ emission also at $z=1.371$. The light curves and spectra are consistent with the Type II supernova source being magnified $\gtrsim 100$ times, with $\sim 250$ required to reconcile its luminosity with that of nearby events such as SN 2023ixf. Lens models are consistent with such high magnifications, and always show that the faint image arrived first (undetected in earlier ZTF imaging), consistent with the later spectral phase of this fainter image. A fourth image is also predicted and possibly detected in the NIRSpec data. Light-curve-based time-delay measurements are not possible due to the first image being the faintest; however, the resolved NIRSpec spectra offer a future opportunity for time-delay cosmography through supernova phase measurements.

We study the heavy quark dynamics in the presence of memory within the framework of a generalized Langevin equation. Time correlated thermal noise with power-law decay is generated by a fractional differential equation, formulated using the Caputo fractional derivative with order parameter $ν$. The effect of memory is calculated through the momentum correlation, the time evolution of the average squared momentum, the average squared displacement, and the average kinetic energy. The effect of memory is further studied for the higher normalised central moments of the heavy quark transverse-momentum distribution. The results indicate that time correlated thermal noise substantially influences heavy quark dynamics in the quark gluon plasma.

In a smoothly bounded domain $Ω\subset \mathbb{R}^N$ $(N\in \mathbb{N})$, a no-flux initial-boundary value problem for the degenerate chemotaxis system with volume-filling effects, \begin{align*} u_t = \nabla \cdot (D(u,v) \nabla u - h(u,v) \nabla v), \quad v_t = Δv + g(u,v), \quad x\in Ω, \ t>0, \end{align*} is considered under the assumptions that $D(1,s)=0$ and that $h(0,s)=h(1,s)=0$. Here, initial data $u_0$ and $v_0$ have suitable regularity and satisfy $0\le u_0\le 1$ and $v_0\ge 0$ with $\nabla v_0 \cdot ν|_{\partial Ω} = 0$. It is proved that there exists a global weak solution such that $0\le u\le 1$ and $v\ge 0$. Moreover, when $D(r,s) = D(r)$ for all $r\in[0,1]$ and $s\in[0,\infty)$ and additional conditions on $D$, $h$ and $g$ are assumed, uniqueness of global weak solutions with the mass conservation law $\int_Ωu(x,t) \, dx = \int_Ωu_0(x) \, dx$ is shown. Also, a flat-hump-shaped stationary solution is constructed in the one-dimensional setting

This work establishes oblique shocks in Massive Star Clusters (MSC) as a primary mechanism for accelerating cosmic rays (CR) up to the knee of the energy spectrum. We develop a model that incorporates the combined contribution of supernova and collective wind shocks, emphasizing the critical role of the shock obliquity angle in determining the maximum particle energy. We illustrate, within our model that oblique shocks can significantly enhance acceleration efficiency, allowing particles to reach multi-PeV energies in a rigidity-dependent manner. Our preferred model, which incorporates oblique shocks, reproduces the all-particle spectrum and composition observed by The Large High Altitude Air Shower Observatory (LHAASO), interpreting the knee as arising from a sequence of rigidity-dependent cutoffs. The model also predicts subdominant but detectable gamma-ray and neutrino emissions. This study provides an attempt at building a unified framework connecting MSC particle acceleration to the observed features of the cosmic-ray knee.