We compute the $\barν$-invariant of homogeneous nearly-parallel $G_2$-structures on Aloff--Wallach spaces $N_{k,l} = SU(3)/S^1_{k,l}$. Using Goette's formulas for the $η$-invariants of homogeneous spaces, we derive an explicit expression for $\barν$ in terms of representation-theoretic data and show that for the two homogeneous nearly-parallel structures $φ^\pm$ on $N_{k,l}$ one has \[\barν(φ^\pm) = \mp 41.\] Additionally, we compare the $\barν$-invariants of the nearly-parallel $G_2$-structures arising from the 3-Sasakian structure.

Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback policies leads to intractable nonconvex problems. This is due to (i) products of functions involving the feedback law and risk allocation in the deterministic counterpart of the chance constraints, and (ii) the presence of the nonconvex Gaussian quantile (probit) function. Existing methods rely on two-stage optimization, which is nonconvex. To address this, we derive disjunctive convex chance constraints and select the feedback law from a set of precomputed candidates. The inherited compositions of the probit function are replaced with power- and exponential-cone representable approximations. The main advantage is that the problem can be formulated as a mixed-integer conic optimization problem and efficiently solved with off-the-shelf software. Moreover, the proposed formulations apply to general chance constraints with products of exclusive disjunctive and Gaussian variables. The proposed approaches are validated with a path-planning application.

We study braneworld cosmology in quasi-topological gravity (QTG) with an infinite tower of higher-curvature terms, focusing on the case in which the bulk admits regular black hole solutions. We derive the $\mathbb{Z}_2$-symmetric junction conditions for a FLRW brane moving in a static, spherically symmetric bulk geometry, and obtain the corresponding modified Friedmann equations for the scale factor. We prove that, in the small scale factor regime, the brane generically approaches a de Sitter phase characterized solely by the length scale $\sqrtα$ of the higher-derivative terms, while the standard Einstein-gravity braneworld dynamics is recovered in the low-energy regime. We further provide a universal estimate for the number of e-folds of the de Sitter phase in terms of the ratio between the black hole scale and the scale of new physics $r_g/\sqrtα$. The inflationary regime is fully independent of the brane matter content and hence avoids the problem of trans-Planckian matter densities. Numerical integrations for explicit regular bulk solutions (Dymnikova-like and Hayward black holes) confirm these estimates and illustrate how the bulk black hole sector controls the onset and termination of inflation. This framework leverages the powerful properties of QTGs, defined only in $D\ge 5$, to study consequences for a four-dimensional universe.

Assembling large-scale, defect-free Rydberg atom arrays is a key technology for neutral-atom quantum computation. Dynamic holographic optical tweezers enable the assembly and reconfiguration of such arrays, but phase mismatches between successive holograms can induce destructive interference and transient trap loss during spatial-light-modulator refresh. In this work, we introduce the weighted-projective Gerchberg--Saxton (WPGS) algorithm, a phase-stable approach to dynamic hologram updates for large-scale Rydberg atom-array reconfiguration. By enforcing inter-frame trap-phase continuity while retaining weighted intensity equalization, WPGS suppresses refresh-induced transient degradation. The phase-difference distribution between consecutive holograms further provides a simple diagnostic of transient robustness. Moreover, enforcing the phase constraint reduces the number of iterations required at each update step, thereby accelerating hologram generation. Numerical simulations of 2D and 3D reconfiguration with more than $10^3$ traps, including multilayer assembly and interlayer transport, show robust transient intensities and significantly faster updates than conventional methods. These results establish inter-frame phase continuity as a practical design principle for dynamic holographic control and scalable neutral-atom array reconfiguration.

We give a general methodology for constructing split exact sequences of amplified graph C*-algebras with sinks. This in turn allows us to construct explicit KK-equivalences with $\mathbb{C}^N$ for a large class of C*-algebras, including the quantum Grassmannian $\mathrm{Gr}_q(2,4)$. We discuss compatibility with known (quantum) CW-constructions and give an explicit KK-equivalence between the classical and quantum projective spaces $\mathbb{C}P^1$ and $\mathbb{C}P_q^1$.

We present a systematic numerical investigation of the "entanglement geometry gravity" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic foundation: the entanglement first law $δ\langle K\rangle=δS$ (slope=1.000), the encoding of geometry by mutual information (correlation=0.92), and the locality of holographic perturbations (3.3x). We also confirm that gravitational dynamics (JT gravity) does not emerge, identifying a sharp kinematics-dynamics boundary. Second, and more importantly, we discover that many-body localization (MBL) is the mechanism that protects emergent holographic geometry from thermalization. Replacing Haar-random evolution (geometry lifetime $t\sim6$) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength $W_c\approx10-12$ above which mutual-information-lattice correlations persist indefinitely ($r>0.5$ for $t>50$). We map the full parameter space: the optimal regime is a near-Ising anisotropy $Δ\approx50$ with $W=30$ yielding $r=0.779\pm0.002$ (confirmed by a fine scan over $Δ\in[30,70]$); only holographic (RTN) initial states sustain geometry, while product, Néel, and Bell-pair states do not. MBL preserves the spatial structure of entanglement (adjacent/non-adjacent MI ratio ~2.6-4.2x vs. 1.0x in the thermal phase), rather than its total amount. A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy: classical systems achieve spatial structure only at the cost of negligible mutual information, while MBL sustains both.

Transimpedance amplifiers (TIAs) are essential in sensor electronics, converting input currents into output voltages. Conventional TIAs utilize fixed-gain resistors, which saturate under high input currents and consequently result in undesirable recovery times. To overcome this limitation, volatile resistive switching devices have emerged as a promising alternative, offering intrinsic automatic gain control (AGC). Among these, vanadium dioxide (VO2) devices stand out for their reversible insulator-metal transition (IMT), producing abrupt, energy-efficient resistance changes near the transition temperature (67 C). In this work, a switching device was fabricated by sputtering a VO2 thin film and patterning 200 nm electrode gaps atop it. Before integrating this device into the TIA circuit, its switching dynamics were characterized under electrical pulse excitation. Slightly exceeding the temperature-dependent IMT threshold voltage (Vth) yielded fast and reproducible switching. Complementary pump-probe measurements showed that operating well below TC effectively suppresses short-term memory effects linked to the stochastic nature of the first-order transition. Leveraging these insights, a custom VO2-based TIA was developed, demonstrating variable gain and AGC functionality. Furthermore, applying a constant DC current bias during switching induced self-sustained oscillations (2 pJ per spike) with frequencies up to 60 MHz, consistent with the thermal timescale of the VO2 devices. Overall, these results provide a detailed understanding of VO2 switching dynamics and demonstrate their potential for enabling compact, energy-efficient AGC in high-speed TIAs for advanced sensing applications.

For $k$-summand base-$N$ addition, the carry process is a Markov chain on $\{0,\ldots,k-1\}$ whose transition matrix--the Holte matrix $T$--has eigenvalues $\{N^{-j}\}_{j=0}^{k-1}$, all simple and independent of $N$. We give the complete biorthogonal eigenvector system. The left eigenvectors factor as $\sum_i u_j[i] x^i = c_{k,j} (x-1)^j A_{k-j}(x)$, where $c_{k,j} = |s(k,k-j)|/k!$ involves unsigned Stirling numbers and $A_n(x)$ is the Eulerian polynomial. The right eigenvectors satisfy $\sum_i \binom{k-1}{i} v_j[i] x^i = (1+x)^{k-1-j} Q_j(x)$, where the quotient polynomials $Q_j$ have palindrome symmetry $x^j Q_j(1/x) = (-1)^j Q_j(x)$ and converge to $(1-x)^j$ as $k \to \infty$; for $j \le 3$, we give explicit closed forms in terms of $k$. The cascade-free avoidance count satisfies $a(L) = (\sqrt{d})^L U_L(x)$ (Chebyshev polynomial of the second kind) whenever the restricted transfer matrix has dimension $d \le 2$; we prove this is sharp: for $k$-summand addition, Chebyshev form holds for $k = 3$ and fails for $k \ge 4$. The proof uses oscillatory matrix theory to establish non-vanishing of all spectral residues. The characteristic polynomial of the restricted transfer matrix is determined in closed form by a Stirling-weighted Lagrange interpolation at the Holte eigenvalues. Two systems with binary carry state spaces are shadow-equivalent if and only if they share the pair $(N, d)$. The general classification for $k$-state systems reduces to the characteristic polynomial of $T$.

This paper deals with the mathematical modelling of signal propagation in nerve fibres. Due to the complexity of the processes where electrical, mechanical, and thermal effects are coupled, a phenomenological approach helps to build mathematical models. The ideas of phenomenology are briefly presented, and their application is described. These applications cover the modelling of ion currents (the Hodgkin-Huxley model), temperature effects, and inductance. This means that the ion currents through the biomembrane, the influence of endo- and exothermic reactions on temperature, and the influence of energy in a non-electrical form are taken into account using phenomenological variables, i.e., observables. Such an approach brings the mathematical models closer to reality. Using the concept of phenomenological inductance helps us better understand the propagation of an action potential in myelinated axons. In principle, contemporary mathematical models describing the process in axons are hybrid in nature, combining physical laws with phenomenology, i.e., with observables.

For a finite group $G$, let $ω(G)$ be the set of element orders of $G$ and let $h(G)$ be the number of pairwise nonisomorphic finite groups $H$ with $ω(H)=ω(G)$. We say that the recognition problem is solved for $G$ if the number $h(G)$ is known, and if $h(G)$ is finite, then all finite groups $H$ with $ω(H)=ω(G)$ are described. We complete the solution of the recognition problem for the finite simple linear and unitary groups.

This work proposes the use of orbital angular momentum (OAM) waves to improve the performance of a computational imaging (CI) system. Specifically, in contrast to a solely frequency-diverse operation, leveraging multiple OAM waves leads to a significant increase in the diversity of the measurement modes of a CI system. This significantly reduces the frequency bandwidth required to achieve high-quality image reconstructions. A proof-of-concept prototype working at Ka-band frequencies is used to validate the proposed approach. The prototype consists of two metalized three-dimensional (3D) printed cavities, with fully-dielectric transmitarrays inside that generate OAM waves. Imaging results from various targets reveal that the CI system achieves superior imaging quality when multiple OAM waves are considered, compared to when it solely relies on frequency-diversity. This is specially noticeable in the case of complex distributed targets, which can only be reconstructed with the prototype when multiple OAM waves are used. Furthermore, it is shown that accurate image reconstructions can be obtained employing only one eighth of the operational bandwidth of the frequency-diverse system.

In recently proposed framework of non-holomorphic modular symmetry introduces the concept of negative and zero modular weight of Yukawa couplings. These Yukawa couplings are function of complex modulus $τ$, which is responsible for the CP asymmetry produced during leptogenesis. In this work, we restrict the $τ$ on the fixed points of modular symmetry rather than its fundamental domain in such manner Yukawa couplings are also get fixed. We have adopt this framework and propose a type III seesaw mechanism. The model is tested against neutrino oscillation data through a $χ^2$ analysis using NuFIT~6.1. To test the stability of these predictions, we also analyze regions near each fixed point by introducing a deviation $τ\rightarrow τ_{\rm fixed}(1 + εe^{iϕ})$ with $ε\in (0,0.1)$ and $ϕ\in (-π,π)$. Our results show that certain fixed points, along with their nearby regions, are capable of producing viable neutrino phenomenology while also generating the observed baryon asymmetry of the Universe.

The emergence of triaxiality in the low-lying collective bands of $^{166}$Er is systematically explored within the SU3-IBM. In this framework, SU(3) higher-order interactions are included, which enable the descriptions of various quadrupole deformations. The triaxiality of $^{166}$Er is described with a triaxiality angle $γ=9.7^{\circ}$. In addition, the calculated energy spectra, $B(E2)$ transition strengths, and quadrupole moments show excellent agreement with experimental data. These results provide further evidence supporting the SU(3) triaxial interpretation of $^{166}$Er and confirm its triaxial deformation rather than the prolate shape.

What makes a public talk resonate with large audiences? While prior research has emphasized speaker delivery or topic novelty, we reasoned that a core driver of engagement is linguistic clarity. This aligns with theories of processing fluency and cognitive load, which posit that audiences reward speakers who present complex ideas accessibly. We leveraged artificial intelligence to analyze 1,239 TED Talk transcripts (2006--2013), supplemented by a later-phase longitudinal sample. Each transcript was evaluated across 50 independent large language model runs on two dimensions, clarity of explanation and structural organization, and linked to YouTube engagement metrics (likes and views).Clarity emerged as the strongest predictor of audience responses ($β= .339$ for likes; $β= .314$ for views), contributing substantial incremental variance ($ΔR^{2} \approx .095$) beyond duration, topic, and scientific status. The full model explained 29\% of variance in likes and 22.5\% in views. This effect was domain-general, remaining invariant across content categories and between scientific and non-scientific talks. Notably, clarity outperformed traditional readability metrics, indicating that discourse coherence predicts engagement more powerfully than surface-level linguistic simplicity. Longitudinal analyses further revealed standardization within TED, characterized by increasing clarity and reduced variability over time. Theoretically, these results support processing fluency accounts: clearer communication reduces cognitive friction and elicits more positive evaluative responses. Practically, transcript-based clarity represents a scalable and trainable strategy for improving public discourse. By demonstrating that language models can reliably capture latent communicative qualities, this study paves the way for feedback systems in education, science communication, and public speaking.

We perform a comparative phase space analysis of the light mass Galileon model and standard Quintessence in the context of late--time cosmic acceleration. Focusing on a spatially flat FLRW background, we consider a cubic Galileon interaction supplemented by a scalar potential and examine three representative choices of the potential: a generalized cosh potential, a simple cosh potential, and a linear potential. By introducing suitable dimensionless variables, the cosmological field equations are reformulated as an autonomous dynamical system, allowing a systematic investigation of the stationary points and their stability properties. For the light mass Galileon scenario, we find that although the phase space admits scalar field dominated solutions, all critical points are of saddle type for the potentials considered. In particular, no stable late-time accelerating attractor emerges, even in the presence of de-Sitter like configurations. In contrast, the Quintessence limit admits stable de-Sitter attractors for cosh potentials, providing a viable description of the observed late--time acceleration. Our results highlight a key qualitative distinction between Galileon and Quintessence cosmologies and indicate that, within the light mass Galileon framework, the higher-order Galileon interactions may be required to realize a stable accelerating Universe.

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate subrings. Our aim is to develop a general framework for the sum-product phenomenon that applies uniformly across arbitrary rings. The main result identifies nilpotent quotients as the fundamental obstruction to growth under both addition and multiplication. Another application of the main structure theorem is a ring-theoretic counterpart of Gromov's theorem on groups of polynomial growth. The principal tool in the proof is the existence of definable locally compact models for arbitrary approximate subrings from [Kru24]. This existence theorem extends beyond the finite (and pseudofinite) setting. To illustrate the scope of the method, we also establish a structure theorem for uniformly discrete approximate subrings of semi-simple real algebras, generalizing a classical sum-product result of Meyer.

Software engineers resolving repository-level issues do not treat existing tests as immutable correctness oracles. Instead, they iteratively refine both code and the tests used to characterize intended behavior, as new modifications expose missing assumptions or misinterpreted failure conditions. In contrast, most existing large language model (LLM)-based repair systems adopt a linear pipeline in which tests or other validation signals act mostly as post-hoc filters, treating behavioral constraints as fixed during repair. This formulation reduces repair to optimizing code under static and potentially misaligned constraints, leading to under-constrained search and brittle or overfitted fixes. We argue that repository-level issue resolution is fundamentally not optimization under fixed tests, but search over evolving behavioral constraints. To operationalize this view, we propose Agent-CoEvo, a coevolutionary multi-agent framework in which candidate code patches and test patches are jointly explored and iteratively refined. Rather than treating tests as immutable oracles, our framework models them as dynamic constraints that both guide and are revised by the repair process. Through mutual evaluation and semantic recombination, code and test candidates progressively narrow the space of behavior consistent with the issue description. Evaluated on SWE-bench Lite and SWT-bench Lite, Agent-CoEvo consistently outperforms state-of-the-art agent-based and agentless baselines in both repair success and test reproduction quality. Our findings suggest that enabling repair agents to revise behavioral constraints during search is critical for reliable issue resolution, pointing toward a shift from code-only optimization to coevolution of implementation and specification.

Low-energy electron diffraction (LEED) is a cornerstone technique for determining surface atomic structures[heldStructureDeterminationLowenergy2025], yet the quantitative analysis of electron diffraction intensity as a function of incident electron energy -- that is, LEED-\textit{I(V)} analysis -- remains a complex inverse problem. In this work, we tackle quantitative LEED-\textit{I(V)} analysis based on physics-informed Bayesian optimization (BO). By embedding multiple scattering LEED forward models directly into a trust-region BO loop, our approach simultaneously optimizes both structural and experimental parameters, adaptively adjusting trust regions for efficient exploration of complex non-convex parameter spaces without manual intervention. The robustness and scalability of the approach are demonstrated using the Ag(100)-(1$\time$1) and Fe\textsubscript{2}O\textsubscript{3}(1$\overline{1}$02)-(1$\time$1) surfaces as examples. Our work establishes a general framework for solving inverse problems in various characterization techniques, unlocking a physics-informed efficient, reproducible, and autonomous paradigm.

Compact, steep-spectrum radio sources are key tracers of exotic astrophysical objects such as pulsars and high-redshift radio galaxies. All-sky radio surveys at different frequencies, like the TIFR-GMRT Sky Survey (TGSS) and the NRAO VLA Sky Survey (NVSS), have been usually exploited to identify such tracers. The more recent imaging survey, Rapid ASKAP Continuum Survey (RACS), with higher angular resolution and better sensitivity offers an avenue for a far better identification and characterization of compact, steep-spectrum sources. In this work, using publicly available RACS images at 887 MHz and 1.4 GHz, we present an image-domain characterization of 171 compact source candidates between declinations -40 degrees and +41 degrees, that were detected and appeared compact at 147 MHz in TGSS but not detected at 1.4 GHz in NVSS. Our detailed characterization resulted in the identification of 66 compact sources, 87 non-compact, diffuse or resolved sources, and 18 sources that are not detected in either of the RACS or NVSS images, implying spectral indices steeper than -2.0. Out of the 66 compact sources, 34 have spectral indices steeper than -1.5. We demonstrate that a large fraction of the sources in our sample were earlier not detected and resulted in incorrect spectral index limits due to poor imaging quality of NVSS in the Galactic plane. We present the spectral indices and morphological classification of all the sources in our sample and discuss their usefulness in identifying and studying interesting sources such as radio pulsars, high-redshift radio galaxies, and other extragalactic sources.

Privacy has always been a critical issue in the digital era, particularly with the increasing use of Internet of Things (IoT) devices. As the IoT continues to transform industries such as healthcare, smart cities, and home automation, it has also introduced serious challenges regarding the security of sensitive and private data. This paper examines the complex landscape of digital privacy in IoT ecosystems, highlighting the need to protect personally identifiable information (PII) of individuals and uphold their rights to digital independence. Global events, such as the COVID-19 pandemic, have accelerated the adoption of IoT, raising concerns about privacy and data protection. This paper provides an in-depth examination of digital privacy risks in the IoT domain and introduces a clear taxonomy for evaluating them using the IEEE Digital Privacy Model. The proposed framework categorizes privacy risks into five types: identity-oriented, behavioral, inference, data manipulation, and regulatory risks. We review existing digital privacy solutions, including encryption technologies, blockchain, federated learning, differential privacy, reinforcement learning, AI, and dynamic consent mechanisms, to mitigate these risks. We also highlight how these privacy-enhancing technologies (PETs) help with data confidentiality, access control, and trust management. Additionally, this study presents AURA-IoT, a futuristic framework that tackles AI-driven privacy risks through a multi-layered structure. AURA-IoT integrates adversarial robustness, explainability, transparency, fairness, compliance, dynamic consent, and policy enforcement mechanisms to ensure digital privacy, security, and accountable IoT operations. Finally, we discuss ongoing challenges and potential research directions for integrating AI and encryption-based privacy solutions to achieve comprehensive digital privacy in future IoT systems.

In gauge theories, the mass of a field has been regarded as a purely on-shell concept: the pole mass is gauge-invariant, but the off-shell propagator has had no gauge-invariant definition of mass. We show that renormalization defines a gauge-invariant mass function at every virtuality, together with a gauge-invariant vertex. The virtual particle becomes as well defined as the on-shell one: the distinction is not dynamical but purely kinematic.

We study spontaneously vectorized black holes in Einstein-vector-Gauss-Bonnet theory with a quadratic coupling function. Besides the static, spherically symmetric black holes carrying an electric charge, there are uncharged static, axially symmetric black holes that possess a magnetic dipole moment. Both types possess radial excitations. The magnetic black holes are prolate. They are hotter than the Schwarzschild black holes and possess lower free energy. The domain of existence of the rotating vectorized black holes is bounded by the Kerr black holes, the spherically and axially symmetric static black holes, and the critical solutions.

We develop a systematic and fully explicit approach to the evaluation of binomial sums involving reciprocals of binomial coefficients based on Beta integral techniques. Starting from a simple integral representation, we provide a derivation of classical identities, including Frisch's formula, with all intermediate transformations rigorously justified. This framework naturally extends to parametric sums, yielding integral representations that lead to closed forms in terms of hypergeometric functions. In particular, we establish connections with terminating ${}_2F_1$ and generalized ${}_3F_2$ series, thereby linking discrete combinatorial sums with the analytic theory of special functions. We further derive explicit finite expansions suitable for symbolic and numerical computation, as well as higher-order extensions involving Pochhammer symbols. In addition, we present new families of identities, including shifted reciprocal sums and weighted sums involving powers of the summation index, which admit unified hypergeometric representations. Overall, the Beta integral method provides a versatile and unifying framework bridging combinatorial identities, integral representations, and hypergeometric analysis, and opens the way to further generalizations in combinatorics and special function theory.

Compact astrophysical objects, such as neutron stars, can provide a unique environment where the interplay between strongly interacting nuclear matter and dark matter (DM) can yield possible observable signatures. We investigate here the impact of fermionic DM interacting with nucleons via a vector mediator ($Z^\prime$) portal inside neutron stars using the relativistic mean field (RMF) framework. Unlike scalar portal DM models, which primarily modify the effective nucleon mass through scalar interactions, vector mediators introduce additional repulsive interactions that directly affect the baryonic chemical potential and the pressure of dense matter. We show that the precise measurements of neutron star properties, including the mass radius relation and tidal deformability from gravitational wave observations, X-ray and radio observations of pulsars, can shed light on properties of DM. We study the gross structural properties of a neutron star using the Tolman Oppenheimer Volkoff (TOV) equations, employing an equation of state (EOS) for neutron star matter in the presence of vector portal-assisted DM. The resulting stellar configurations consistent with observational bounds from gravitational wave observations in LIGO/Virgo, and X-ray observations of pulsars in NICER, are shown to constrain the vector portal DM parameters. It is observed that, while large portal mass can soften the EOS of the DM admixed neutron star matter, the light portal mass can make the EOS stiffer at large densities resulting in distinct mass-radius relation and the tidal deformability between the two scenarios. The vector portal DM scenario, with DM interaction with quarks via $Z^\prime$ vector boson, can establish a direct connection to terrestrial searches, including direct and indirect detection and collider searches for the $Z^\prime$ boson.

The interaction of a spark-generated cavitation bubble with an initially perturbed free surface is investigated experimentally, numerically, and analytically. By exploiting contact-line pinning, we accurately prescribe an initial meniscus with a thin, hydrophilic-coated rod inserted into the liquid. A pronounced surface cavity, driven by the oscillating bubble, forms and penetrates downward to a scale comparable to the bubble itself. The coupled cavity-bubble system exhibits two distinct regimes -- coalescence and non-coalescence -- separated by a critical condition governed by the non-dimensional stand-off parameter $γ$ and the initial meniscus height $h_m$. In the non-coalescence regime, the cavity evolves through inception, expansion, and rebound/jetting. The maximum cavity length $h_c$ follows a power-law scaling $h_c\proptoγ^α$ with $α=-2.7$ (experiments) and $α=-2.6$ (simulations) for $1.5\lesssimγ\lesssim3$, where inertia dominates. Deviations emerge for $γ\lesssim1.5$ (strong nonlinearity) and $γ\gtrsim3$ (surface tension and viscosity become noticeable). An analytical model based on the Rayleigh-Plesset equation combined with nonlinear Rayleigh-Taylor instability theory captures the trend and confirms that $h_m$ plays only a secondary role relative to $γ$. In the coalescence regime, atmospheric air vents into the bubble through the merged cavity, weakening the collapse intensity and reducing the associated pressure peak. We also examine air/liquid compressibility and boundary layer effects, whose significance grows as $γ$ decreases. These findings are relevant to surface-jetting technologies, cavitation-erosion mitigation, and underwater-noise suppression.

NBI-Slurm is a Perl package that provides a simplified, user-friendly interface for submitting and managing jobs on SLURM high-performance computing (HPC) clusters. It offers both a library of Perl modules for programmatic job management and a suite of command-line tools designed to reduce the cognitive overhead of SLURM's native interface. Distinctive features of NBI-Slurm are (a) TUI applications to view and cancel jobs, (b) the possibility to generate tool-specific wrappers for (bioinformatic) tools and (c) an energy-aware scheduling mode -- "eco mode" -- that automatically defers flexible jobs to off-peak periods, helping research institutions reduce their computational carbon footprint without requiring users to manually plan submission times.

Yttrium iron garnet (Y3Fe5O12) is a prototypical ferrimagnetic insulator widely used in spin-wave and magnonic devices owing to its extremely low magnetic damping and long magnon propagation length, and recent experiments suggest that lattice vibrations can influence magnetic properties, motivating a microscopic understanding of how phonons modify exchange interactions. In this work, phonon-driven tuning of exchange interactions in Y3Fe5O12 is investigated from a mode-resolved perspective based on first-principles calculations. We focus on how optical phonons modify the dominant superexchange pathways and how lattice distortions affect the Fe-O-Fe bond geometry that governs the exchange interaction. To this end, phonon modes are computed from density functional theory, and the exchange interactions are evaluated from a Wannier-based tight-binding model and mapped onto a spin Hamiltonian, while displaced structures along individual infrared-active modes are used to quantify their impact on the magnetic interactions.

We propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing through factorization homology of $\mathbb{E}_n$-algebras and the derived algebraic geometry of character stacks. We conjecture that the modular tensor category underlying the RT construction arises as the $\mathbb{E}_2$-category from BV-BFV quantization of Chern-Simons theory on the disk, with the derived character stack $\mathrm{Loc}_G(Σ)$ and its shifted symplectic structure mediating the proposed identification. We formulate seven conjectures, including a main conjecture asserting natural equivalence of the BV-BFV and RT constructions as (3-2-1)-extended topological quantum field theories, develop a proof strategy via deformation quantization of shifted symplectic stacks, and clarify the role of $\mathbb{E}_n$-Koszul duality in translating between perturbative and non-perturbative data. Supporting evidence is examined in the abelian, low-genus, and Seifert fibered cases. Connections to resurgence, categorification, and the geometric Langlands program are discussed as further motivation, though significant technical gaps remain open.

Magnetic straintronics, the strain-mediated control of magnetic anisotropy, has emerged as a key direction for next-generation energy-efficient technologies. In multiferroic heterostructures, magnetoelectric coupling is typically achieved by applying an electric field on a ferroelectric phase, inducing strain through the converse piezoelectric effect, which is then transferred to the adjacent ferromagnetic phase. As an alternative, strain can be remotely modulated through the photostrictive effect induced by light. While light-driven control of magnetic anisotropy has been explored, optical modulation of more complex phenomena such as exchange bias remains largely unaddressed. Here, we demonstrate significant light-induced modulation of exchange bias and magnetization switching at room temperature in a Pb(Mg1/3Nb2/3)O3-Pb(Zr,Ti)O3 (PMN-PZT)/Fe80Ga20(FeGa)/Ir20Mn80(IrMn) multiferroic heterostructure, driven by visible-light-photostriction. The magnetization state correlates with the light intensity, enabling multi-level states with light power densities as low as 0.1 W cm-2. These findings suggest a promising route toward low-power, multistate, and wireless opto-magnetic memory applications.

Kosek, Robertson, Sabo, and Schaal studied the minimum number \(M_k(n)\) of monochromatic solutions to the strict Schur inequality system $x_1\le x_2\le x_3$ and $x_1+x_2<x_3$ in \(2\)-colorings of \([k+1,k+n]\). They proved that for every fixed \(k\ge 0\), $M_k(n)= \frac{n^3}{12(1+2\sqrt2)^2}(1+o_k(1)),$ and left open the case \(k\le -2\). In this paper, we resolve that remaining range.