The development of large-scale quantum systems increasingly relies on the close integration of heterogeneous components such as qubits, control electronics, and readout circuits, making thermal management at cryogenic temperatures a central challenge in such architectures. In this work, we present an experimental thermal study of two building blocks of such systems: the substrate and the on-chip routing. We first investigate the sub-kelvin thermal conductivity of four substrate materials: high-resistivity silicon, low-resistivity silicon, borosilicate, and sapphire. We report that high-resistivity silicon exhibits the highest thermal conductivity among the substrates studied ($5\cdot10^{-2}$~W/m$\cdot$K at 300~mK), while low-resistivity silicon, borosilicate, and sapphire show lower values ($8\cdot10^{-4}$~W/m$\cdot$K, 2$\cdot10^{-3}$~W/m$\cdot$K, and 2$\cdot10^{-3}$~W/m$\cdot$K at 300~mK, respectively). Ballistic conductance evaluation using a finite-element non-equilibrium Green's function approach further allows us to extract the phonon mean free path in each substrate and gives insights into the involved scattering mechanisms. Additionally, we employ a dedicated test vehicle to evaluate the impact of on-chip routing on the thermal conductance of the system. Our measurements with superconducting Nb routing lines reveal that the routing increases the in-plane thermal conductance of the system, but the substrate remains the dominant heat path. These results highlight the critical role of the substrate choice within quantum systems and underscore the importance of function partitioning through 3D integration approaches for more efficient thermal management in quantum architectures.

Mixing of miscible liquids is an essential process in multiple industrial settings, usually with the intent to homogenize the product. This seemingly simple process is in fact a complex hydrodynamic problem that has a direct impact on the product quality. In this study, numerical simulations of a stirred tank were performed with a 50/50 ratio of liquids and systematically varied the Reynolds and Richardson numbers. A positive correlation between the mixing time and the Richardson number was observed, as reported in the literature. The influence of the Reynolds number was not as pronounced and clear. Based on the Power, Froude and Richardson numbers, we were able to derive an exponential scaling for the dimensionless mixing time that collapsed all our data onto one master curve.

The density dependence of the nuclear symmetry energy remains one of the key uncertainties in contemporary nuclear physics, with significant implications for the structure of exotic nuclei, the dynamics of heavy-ion collisions, and the properties of astrophysical objects such as neutron stars and core-collapse supernovae. However, extracting robust constraints requires observables that are minimally affected by final-state interactions and are reliably predicted by transport models. This review synthesizes recent theoretical and experimental advancements in constraining the symmetry energy by leveraging isospin diffusion in heavy-ion reactions within the Fermi energy domain. Recent results from the INDRA-FAZIA collaboration, including isospin transport ratio data, and Boltzmann-Uehling-Uhlenbeck (BUU) transport model calculations are highlighted. Confidence regions for the symmetry energy are extracted from isospin transport ratios and isospin diffusion currents by utilizing state-of-the-art nuclear functionals, including both ab initio and phenomenological approaches, with a particular focus on the density regions probed by these experiments. The resulting constraints will aid future Bayesian studies of the nuclear equation of state and contribute to a more unified understanding of dense matter in both terrestrial experiments and astrophysical environments.

Ultraluminous X-ray sources (ULXs) are mostly extragalactic non-nuclear point sources having X-ray luminosity exceeding the Eddington luminosity of 10 $M_\odot$ black hole i.e., $L_X \geq $ 10$^{39}$ erg ~s$^{-1}$. They are observed in all types of galaxies; spirals, ellipticals and dwarf irregulars. But the rate of occurrence of ULXs per galaxy varies, some might host a single ULX, whereas some host a large number. In this work we attempt to identify possible differences in ULX properties between two extreme categories in spirals and ellipticals, i.e. ULXs occurring at a rate of one per galaxy ($N=1$) and those occurring at larger rate. We adopt an effective scheme to generate flux limited, credible samples corresponding to the two groups in spirals and ellipticals. From this study, we infer the presence of a separate population of ULXs in the $N=1$ spiral group which contains a reasonable fraction of both soft and hard sources, while the remaining categories contain mostly harder sources. We also find six ULXs in $N=1$ ellipticals with globular cluster association. In addition, we identify few luminous candidates likely hosting massive accretors. This study provides crucial hints of a potential link between ULX types and their occurrence rates and host morphology, a finding that warrants validation via targeted observations and detailed spectral analysis of these sources.

Shock solutions for multi-temperature Euler equations are inherently ambiguous due to the loss of microscopic physical detail during model reduction and occurrence of non-conservative terms. This paper presents a detailed analytical study of shock structures in such models. We derive two distinct Hugoniot relations, each corresponding to a physically admissible shock solution: one for the general multi-temperature case and one for two-temperature plasma flows. Through classical analysis à la Courant--Friedrichs, we demonstrate that both satisfy admissibility conditions, revealing a fundamental non-uniqueness in shock structures. By relating these solutions to existing numerical schemes, the structure preserving and vanishing viscosity approaches, we provide physically justified references for constructing and evaluating discontinuous numerical approximations. In particular, we emphasize that the Hugoniot relation is not uniquely determined by the macroscopic PDEs alone, but must be supplied from external sources such as experiments or first-principles simulations. This insight demonstrates the essential role of microscopic physics in resolving shock ambiguity and contributes to the theoretical foundation for modeling discontinuous plasma flows.

We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fejér monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean and almost surely, under an abstract stochastic regularity assumption, derived from previous work of Kohlenbach, López-Acedo and Nicolae [Isr. J. Math. 232(1), pp. 261-297, 2019] on such notions in a deterministic context. Our notion of regularity extends and unifies many common conditions from the literature, such as generalized contractivity for self maps, weak sharp minima and error bounds for real-valued functions, uniform monotonicity and global metric subregularity for set-valued operators, related Polyak-Łojasiewicz or Kurdyka-Łojasiewicz conditions, as well as expected sharp growth as e.g. studied by Asi and Duchi [SIAM J. Optim. 29(3), pp. 2257-2290, 2019]. The rate is moreover highly uniform, depending only on very few data of the surrounding objects. We also discuss special cases which allow for the construction of fast rates in the form of linear non-asymptotic guarantees. We conclude by presenting three concrete methods from stochastic approximation where our results yield new rates of convergence, including the classical example of the stochastic proximal point method, a randomized variant of the Krasnoselskii-Mann scheme for solving stochastic fixed-point equations, and a Busemann subgradient method recently introduced by Goodwin, Lewis, López-Acedo and Nicolae [Math. Program., to appear], all of which make use of our metric generality by being formulated over complete geodesic metric spaces of nonpositive curvature.

Open-Vocabulary Multimodal Emotion Recognition (OV-MER) aims to predict emotions without being constrained by predefined label spaces, thereby enabling fine-grained emotion understanding. Unlike traditional discriminative methods, OV-MER leverages generative models to capture the full spectrum of emotions and employs emotion wheels (EWs) for metric calculation. Previous approaches primarily rely on token-level loss during training. However, this objective is misaligned with the metrics used in OV-MER, and these metrics cannot be directly optimized via gradient backpropagation. To address this limitation, we turn our attention to reinforcement learning, as this strategy can optimize non-differentiable objectives. We term this framework AffectGPT-RL. Furthermore, we conduct extensive experiments to elucidate the role of reinforcement learning in this task, revealing the necessity of the reasoning process, the impact of different rewards, and the generalizability to other emotion tasks such as sentiment analysis and basic emotion recognition. Experimental results demonstrate that AffectGPT-RL yields significant performance improvements on OV-MER. Beyond this task, we also achieve remarkable performance gains on basic emotion recognition, attaining state-of-the-art results on MER-UniBench. To the best of our knowledge, this is the pioneering work exploring the role of reinforcement learning in OV-MER, providing valuable guidance for subsequent researchers. Our code is provided in the supplementary material and will be released to facilitate future research.

As production code evolves, the test suite must co-evolve to remain effective. Existing benchmarks for test evolution operate at method-level granularity with pre-paired inputs, bypassing the task of locating affected tests from the full project and excluding the need for new tests entirely. We present TEBench, the first project-level benchmark for test evolution. Given a project repository and a code-changing commit, TEBench requires systems to autonomously identify tests requiring modification, determine where new tests are needed, and produce the corresponding test patch. We construct TEBench through a four-stage pipeline over Defects4J projects, curating 314 task instances from 10 projects with developer-written ground truth. Each instance is annotated with one or more of three evolution types: Test-Breaking (tests that fail), Test-Stale (tests that pass but no longer meaningfully validate updated behavior), and Test-Missing (new tests needed for introduced behavior). We evaluate seven configurations spanning three industrial agent frameworks (Claude Code, Codex CLI, OpenCode) and six base models, alongside a heuristic baseline. All seven configurations converge on an identification F1 of 45.7% to 49.4%, revealing a shared performance ceiling across both frameworks and base models. Test-Stale is the most challenging type, averaging F1 around 36%, since configurations rely on execution failure signals and lack proactive semantic reasoning. On the update task, configurations produce highly executable test modifications whose surface form diverges substantially from ground truth. Trajectory analysis reveals a reactive "execute-fail-fix" loop that succeeds for breaking tests but structurally cannot address stale or missing tests. TEBench is available at https://github.com/iSEngLab/TEBench with a leaderboard at https://tebench-leadership.vercel.app.

Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.

Let $\mathfrak{J}$ be a JB$^*$-algebra with no quotients isomorphic to $S_2(\mathbb{C})$. Let $μ$ be a local quasi-linear Jordan functional on $\mathfrak{J}_{sa}$. We show that $μ$ is a linear functional on $\mathfrak{J}_{sa}$ if and only if the restriction of $μ$ to the closed unit ball of $\mathfrak{J}_{sa}$ is uniformly weakly continuous.

We present TACO, a toolsuite for the development and automatic verification of fault-tolerant and threshold-based distributed algorithms. Our toolsuite implements three approaches for model checking threshold automata in different decidable fragments known from the literature and two semi-decision procedures going beyond these decidable fragments. Moreover, TACO is a modular, extensible, and well-documented framework for developing algorithms and tools for threshold automata. We present important features, give an overview of the implemented algorithms, and evaluate their performance experimentally.

Plasticity in body-centered cubic (BCC) nanocrystals is often associated with twin nucleation phenomena under extreme loading conditions. Here, we reveal unconventional twinning pathways that operate at the intersection of crystal plasticity and structural phase transitions. We show that the classical shear-driven twinning mode becomes progressively suppressed with increasing pressure, giving rise to transformation-mediated twinning pathways involving transient HCP or FCC phases. In BCC Fe, Ta, and Nb nanocrystals of moderate elastic stiffness, plasticity is consistently initiated by an elastic instability that triggers a dual-shuffle process mediated by stable or metastable hexagonal closed-packed (HCP) phases. This pathway operates independently of the characteristic {112} twin boundary planes and is driven by compression, challenging the conceptual paradigm for metal plasticity in which plastic deformation arises from shear stresses resolved on specific planes. By contrast, in the archetypal elastically stiffer BCC Mo and W nanocrystals, plastic deformation proceeds via two alternative twinning pathways associated with shear-driven elastic instabilities mediated by highly-distorted face-centered cubic (FCC) phases. Comprehensive analyses of the energy landscapes to the competing nanoscale twinning modes provide mechanistic insight into their activation, establishing a unified framework for transformation-mediated twinning in BCC nanocrystals across a broad range of loading conditions.

Intrinsic defects govern carrier trapping and recombination in two-dimensional semiconductors, yet the microscopic origin of defect-dependent capture dynamics remains unclear. Here, we compute carrier capture coefficients of vacancy defects, treating monolayer MoS$_2$ as a prototype, from first principles. We find that the single Sulphur vacancy forms a shallow defect with a small capture coefficient of $\sim 10^{-16}\ \mathrm{cm}^3/\mathrm{s}$, whereas the Sulphur divacancy exhibits a capture coefficient larger by seven orders of magnitude, $\sim 10^{-9}\ \mathrm{cm}^3/\mathrm{s}$, despite being only moderately deeper in energy. This enhancement originates from strong lattice relaxation enabling efficient multiphonon capture. Consequently, single vacancies contribute weakly to trapping, while Sulphur divacancies dominate nonradiative recombination and reduce quantum yield. In contrast, molybdenum vacancies and Sulphur antisites, although deep, show much smaller capture coefficients, indicating a limited role in carrier trapping in n-type devices.

Recently, neural directional filtering (NDF) has been introduced as a flexible approach for reconstructing a virtual directional microphone (VDM) with a desired directivity pattern for spatial sound capture. Building on this idea, we propose NDF+, which enables joint neural directional filtering and diffuse sound extraction. NDF+ reformulates VDM estimation into two coupled subtasks: dereverberated VDM reconstruction and diffuse sound extraction. This reformulation enables NDF+ to manipulate diffuse components in the final reconstructed VDM output. We evaluated NDF+ under reverberant conditions and compared it with representative conventional baselines. Results show that NDF+ consistently outperforms the baselines on both subtasks, while maintaining VDM reconstruction quality comparable to that of the original single-task NDF model. These findings indicate that NDF+ introduces an additional degree of freedom for diffuse sound control in the VDM reconstruction. In a stereo recording application, NDF+ provides controllable inter-channel level differences between left and right channels by adjusting the estimated diffuse component.

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) extend conventional diagonal RISs by allowing inter-element coupling, thereby enlarging the set of attainable scattering matrices and improving the achievable signal-to-noise ratio (SNR). On the other hand, hybrid active/passive RISs use reflect-type power amplifiers in a fraction of the elements to alleviate the multiplicative path loss. In this paper, we bring these two ideas together and introduce a \emph{family of hybrid BD-RIS architectures}, in which the surface is partitioned into two reflecting subsurfaces (RSs), each adopting either a passive or an active group-connected BD-RIS design. We derive a closed-form SNR-maximizing solution that combines, for every BD-RIS group, Takagi's factorization of a certain complex symmetric matrix with an optimal per-group amplification factor that satisfies the reflect-power budget. Three architectures within the proposed family (active/passive, fully-connected-active/sub-connected-active, and sub-connected-active/sub-connected-active hybrid BD-RIS) are studied. Numerical results in a single-input single-output (SISO) link with blocked direct path show that the proposed hybrid BD-RIS architectures attain the same or higher receive SNR than their diagonal counterparts while using significantly fewer reflect-type amplifiers.

We derive lower and upper bounds on the identification capacity of inverse Gaussian channels, a fundamental model for molecular communications in fluid environments. The analysis considers deterministic encoding schemes under a peak time constraint and characterizes the asymptotic growth of codebook sizes. A central result reveals that, under a mild regularity condition on the noise, i.e., the stochastic first arrival time of an information-carrying molecule propagating via diffusion and drift to the receiver, the identification capacity exhibits super-exponential growth in the codeword length, $n,$ i.e., $\sim 2^{(n \log n)R},$ where $R$ is the coding rate.

We study families $u_s$ of functions satisfying the equations $(-Δ)^s u_s=0$, $s \in (0,1)$ in a smooth bounded open set $Ω\subset \mathbb{R}^N$. The main purpose of this paper is twofold. First, we provide a detailed analysis of the asymptotics of these families in the zero order limit $s \to 0^+$. Second, we study the differentiability of $u_s$ as a function of $s$. Most of our results are devoted to the associated Poisson problem, where the family $u_s$ is determined by the exterior condition $u_s = g$ in $\mathbb{R}^N \setminus Ω$ for some fixed function $g \in L^\infty(\mathbb{R}^N \setminus Ω)$. Our results show that both the zero order asymptotics and the differentiability properties of $u_s$ can be expressed in terms of the logarithmic Laplacian of suitable extensions of $g$. This allows to deduce pointwise monotonicity properties of $u_s$ in the order parameter $s$ for a large class of functions $g$.

Quantum error correction (QEC) enables fault-tolerant quantum computation but requires operating quantum hardware at physical error rates below code-dependent thresholds, which remains challenging for current devices. We introduce syndrome resampling, a general method that increases QEC thresholds of any decoder and suppresses logical errors without additional hardware, decoding modifications, or code-specific assumptions beyond syndrome statistics. The method exploits the fact that syndromes with low probability are likely to lead to logical failure, therefore biasing syndrome averages towards most likely syndromes effectively increases logical fidelities. We establish a direct connection between the Rényi coherent information (RCI) and powers of the syndrome probability distribution, showing that resampling syndromes according to these powers combined with maximum likelihood decoding (MLD) realizes a family of optimal thresholds associated with phase transitions in the RCI. Numerical simulations of surface codes demonstrate that syndrome resampling substantially increases thresholds for both optimal and suboptimal decoders and reduces logical error rates by up to four orders of magnitude in experimentally relevant regimes. We further show that syndrome resampling can be effectively implemented from finite data and combined with decoding-based post-selection to achieve additional gains. Finally, applying the method to existing experimental QEC data yields up to two orders of magnitude reduction in logical error rates without requiring additional measurements. Our results provide a practical and decoder-agnostic route to improved logical fidelities in near-term QEC experiments.

The non-relativistic limit of a generalized relativistic Pauli operator\[H_c^{S,α}=\left(2c^β\bigl(σ\cdot(-i\nabla-a)\bigr)^2+(mc^γ)^{2/α}\right)^{α/2}-mc^γ+V\]on $L^2(\mathbb{R}^3;\mathbb{C}^2)$ is investigated under the constraint$2α=γβ+γ^2$.This operator generalizes the relativistic Pauli operator within the framework of Bernstein functions.The associated heat semigroup $e^{-tH_c^{S,α}}$ admits a Feynman--Kac representation involving Brownian motion, a subordinator, and a Poisson process.Using this representation, we prove that the semigroup $e^{-tH_c^{S,α}}$ converges strongly to $e^{-tH^{S,α}}$ as $c\to\infty$, where the limiting generator is given by\[H^{S,α}=\fracα{2m^{\frac{2}α-1}}\bigl(σ\cdot(-i\nabla-a)\bigr)^2+V.\]The non-relativistic limit of a generalized relativistic Schrödinger operator is also investigated.

The automated recognition of algorithm implementations can support many software maintenance and re-engineering activities by providing knowledge about the concerns present in the code base. Moreover, recognizing inefficient algorithms like Bubble Sort and suggesting superior alternatives from a library can help in assessing and improving the quality of a system. Approaches from related work suffer from usability as well as scalability issues and their accuracy is not evaluated. In this paper, we investigate how well our approach based on the abstract syntax tree of a program performs for automatic algorithm recognition. To this end, we have implemented a prototype consisting of: A domain-specific language designed to capture the key features of an algorithm and used to express a search pattern on the abstract syntax tree, a matching algorithm to find these features, and an initial catalog of "ready to use" patterns. To create our search patterns we performed a web search using the algorithm name and described key features of the found reference implementations with our domain-specific language. We evaluate our prototype on a subset of the BigCloneEval benchmark containing algorithms like Fibonacci, Bubble Sort, and Binary Search. We achieve an average F1-score of 0.74 outperforming the large language model Codellama which attains 0.35. Additionally, we use multiple code clone detection tools as a baseline for comparison, achieving a recall of 0.62 while the best-performing tool reaches 0.20.

This paper establishes absolute stability conditions for nonlinear negative imaginary (NI) systems interconnected with static nonlinear feedback. We first show that the NI property is preserved when the feedback nonlinearity can be expressed as the gradient of a continuously differentiable function, and the composite storage of the resulting system remains positive definite. This condition provides a direct connection between nonlinear static feedback and storage-function shaping along the measured output channels. Building on this result, conditions are derived for absolute stability of the closed-loop system under mild assumptions. The linear specialization of the results strictly generalizes prior absolute stability results for linear NI systems, allowing coupled nonlinearities not covered by existing slope-restricted or sector-bounded frameworks. Finally, the proposed theory is illustrated through a linear example highlighting this generalization and a nonlinear example that shows the utility of the proposed results in potential energy shaping.

We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism, which provides a relational notion of dynamics by conditioning the global state on a clock subsystem. Using Misner variables, the WDW equation assumes a Klein-Gordon (KG) type form. Its general solution is constructed as a Gaussian superposition of momentum eigenstates, resulting in an entangled global state between the clock and the remaining subsystem. Within this relational framework, we construct conditional states and obtain the corresponding probability density consistent with the KG-type inner product. The resulting conditional probability density vanishes in the limit of zero volume for all clock values, indicating quantum resolution of the classical singularity. We further show that positivity of the probability density imposes constraints on the admissible clock values, which depend on the parameters of the Gaussian wavepacket. These results highlight the essential role of quantum correlations in the emergence of relational dynamics, and demonstrate that the Page-Wootters formalism provides a consistent and nonsingular probabilistic description of quantum cosmology.

We study the $φ$-Verma modules of the Heisenberg subalgebra $\mathcal{H}_m$ of the universal central extension of $\mathfrak{sl}_2 \otimes A_m$, where $A_m$ is the coordinate ring of the superelliptic curve $u^m = P(t)$, and ask how the orthogonal polynomial families that arise in the centre relations are controlled by the module theory of $\mathcal{H}_m$. Our main results are proved unconditionally for the hyperelliptic case $m=2$, $r=1$; corresponding statements for $m \ge 3$ are recorded as conjectures. In the hyperelliptic case we prove three theorems. First, the canonical contravariant (Shapovalov) form on $M(φ)$ is diagonal in the polynomial basis $\{\tilde{P}_n\}_{n \ge 0}$ determined by the cocycle, with Legendre squared norms $h_n = 2/(2n+1)$. Second, $M(φ)$ is irreducible if and only if $φ$ is $p$-admissible, and this is equivalent to non-degeneracy of the Shapovalov form. Third, there is an explicit intertwiner $Φ\colon M(φ) \to \mathbb{C}[x]$ which sends the free-boson Sugawara zero mode $Ω= -L_0(L_0 + \mathrm{Id}) \in \widetilde{U(\mathcal{H}_m)}$ to the classical Legendre differential operator $L = (1-x^2)\partial_x^2 - 2x\partial_x$, the level-$n$ image of the highest-weight vector to the Legendre polynomial $P_n(x)$, and the Casimir tower $\{Ω^r\}_{r \ge 1}$ to $\{L^r\}_{r \ge 1}$. As a companion result, $M(φ)$ is canonically isomorphic to a bosonic Fock space with the Shapovalov form identified with the Fock inner product.

Many-body localized (MBL) systems are known to thermalize in periodically driven systems. In this work, we demonstrate that under proper driving protocol, this thermalization this thermalization can be resisted such that the MBL phase turns into a non-ergodic extended phase, known as the many-body critical (MBC) phase. Considering a kicked quasiperiodic Ising chain, we show that while at high-frequency driving the ergodic, MBL, and the MBC phases coexist, at moderate driving frequencies the MBL phase is completely suppressed and the MBC phase proliferates in the parameter space. Using quasienergy statistics, Floquet eigenstates, autocorrelation dynamics, and entanglement growth, we characterize the emergent phases and identify non-monotonic signatures revealing richness of the nonergodic phases. Our results establish Floquet driving as a powerful route to stabilizing nonergodic extended many-body phases beyond the conventional Floquet-MBL paradigm.

Astrophysical current layers, e.g., in pulsar winds, can be electrically charged, while the plasma is charge-symmetric, $e^\pm$. Using PIC simulations, we investigate dynamics and plasmoid formation (tearing instability) in charged Harris-type and rotational current layers. Electrically charged current layers, initially in global force-balance, are electrostatically unstable: the resulting dynamics is an intricate interplay between electrostatic Bernstein waves (BWs) and the current tearing mode. Besides overall density and magnetic field, plasma temperature is an important factor. In the charged Harris sheet set-up, the quickly generated BW are trapped within the layers (internally reflected at the upper hybrid resonance). BWs quickly redistribute the charge modifying the initial stage of tearing, but without strongly affecting overall plasmoid growth; resulting plasmoids are mildly charged. In rotational current layers: (i) even initially overall uncharged configurations develop large fluctuations of charge density; (ii) overall dynamics depends on the initial overall temperature; (iii) for certain combination of parameters tearing rate is greatly increased in the charged case.

For the Heun differential equation and all of its confluent equations, we derive formal series expansions of the accessory parameters using the Voros periods. We then compare these expansions with the classical conformal blocks recently obtained by Bonelli--Shchechkin--Tanzini, and examine the Zamolodchikov-type conjecture expected to hold between them, allowing for irregular singularities. In particular, as an extension of the previous works of Mironov--Morozov, Piatek--Pietrykowski and Lisovyy--Naidiuk, we provide a detailed prescription for choosing cycles on the spectral curve that yield the Voros period which corresponds to the classical (regular or irregular) conformal blocks through the accessory parameter.

Inspired by the work of Cordero-Erausquin, McCann and Schmuckenschläger [{\it Invent. Math.,} 2001], we derive an explicit expression for the Jacobian determinant of the normal exponential map on a submanifold, establishing a relationship with its ambient counterpart. This formula leads to a new comparison theorem which is closely related to the comparison theorem of Heintze-Karcher [{\it Ann. Sci. École Norm. Sup.,} 1978] and the esitimate of Brendle [{\it Comm. Pure Appl. Math.,} 2023]. As applications, inspired by Wang [{\it Ann. Fac. Sci. Toulouse Math.,} 2023] (and hence also by Heintze-Karcher), we obtain a Fenchel-Borsuk-Chern-Lashof-type inequality and a Willmore-Chen-type inequality on closed submanifolds in complete noncompact manifolds with nonnegative curvature and Euclidean volume growth.

We develop a model-independent framework to quantify phase-space "crystallization", the degree of ordered radial and kinematic substructure, in 79 Galactic globular clusters using the Gaia EDR3-based membership catalogue of E. Vasiliev & H. Baumgardt (2021a). We construct a scalar crystallization index, C_index, by combining a radial inhomogeneity metric (z_rad) and a local, cluster-centric tangential-velocity metric (z_vel) standardized against empirical nulls. The population distribution is strongly non-Gaussian: most clusters are consistent with smooth, equilibrium expectations, while a small high-C tail (C_index >= 2) identifies dynamically complex systems, including NGC 5139 (ωCen) and NGC 104 (47 Tuc). Correlation and fixed-N tests show that sample size affects detectability, but does not by itself explain all high-rank objects. Through synthetic injection tests in dynamically "quiet" control clusters, we demonstrate sensitivity to ultra-cold, shell-confined kinematic components, ruling out single-shell structures comprising more than a few to ~ 10-20% of core stars in the best-sampled control clusters. We find no evidence, within the sensitivity of the adopted diagnostics, for phase-space structures that require explanations beyond known dynamical processes. However, C_index provides a useful tool for ranking clusters by dynamical extremeness, serving both as a diagnostic for internal complexity and as a quantitative metric for prioritizing follow-up dynamical or technosignature-oriented observations.

Competing interactions, non-trivial electronic band topology, quantum fluctuations, and the interplay between emergent degrees of freedom in frustrated quantum materials can give rise to a wide range of exotic phenomena. Glassy dynamics, originally studied in amorphous materials and biological systems, has recently attracted considerable interest in quantum condensed matter, particularly in relation to the collective behavior of spins, quasiparticle excitations, and topological spin textures. Here, we investigate the emergence of unconventional glassy spin dynamics in a broad class of frustrated quantum materials, where spin freezing exhibit distinct signatures in both thermodynamic and microscopic measurements. Using a comprehensive set of experimental probes, including thermodynamic, NMR, ($μ$SR), and neutron scattering, we identify characteristic signatures of topological spin-glass behavior and these complementary techniques reveal unconventional spin dynamics, short-range spin correlations, emergent low-energy excitations, and glassy behavior of topological origins, distinguishing these states from conventional spin glasses and disordered magnets. Furthermore, we discuss the role of hydrodynamic spin modes in governing glassy dynamics and the emergence of spin-jam states in frustrated lattices, providing a unified framework for understanding unconventional spin freezing of topological origin and bridging experimental observations with theoretical models. This review aims to advance our understanding of collective many-body phenomena arising from competing interactions, topological defects, collective excitations, quantum entanglement, and symmetry constraints. Such insights may facilitate the discovery and design of novel quantum materials and help address fundamental questions in contemporary condensed matter physics, with potential implications for future quantum technologies.

We introduce EventColumn, a new column type that integrates event-sequence data with heterogeneous tabular attributes into a single unified table. EventColumn lets analysts compare event sequences alongside numerical, categorical, and temporal attributes at both instance and group levels, offering a compressed overview, heatmap group summaries, alignment by event types, and boxplots of similar historical items. We developed EventColumn together with collaborators from the steel industry to facilitate the analysis of production events and warehouse logistics, but the solution generalizes to a wide range of event sequence datasets with additional tabular attributes. Unlike most existing approaches that compare either event sequences or tables, EventColumn supports simultaneous comparison of both. We demonstrate its integration with Taggle and Microsoft Power BI on data from steel production logistics and on a public e-commerce dataset.