Recent observations from the DESI Collaboration indicate a preference for quintom dark energy, i.e., its equation of state evolves across the cosmological constant boundary $w=-1$. It is well known that models with single perfect fluid or single scalar field minimally coupled to Einstein gravity develop perturbative instabilities around the crossing, thereby cannot realize the quintom scenario. In this paper, we propose a method to circumvent the instability problem of these models by considering the coupling of dark energy to the Nieh-Yan density within the framework of teleparallel gravity. We show that with this coupling the background evolution is not affected, but the dark energy perturbation is removed from the menu of dynamical degrees of freedom, thus avoiding the inherent difficulties in the old models. Furthermore, the Nieh-Yan coupling causes parity violation in gravitational waves, and this can be considered as a clear prediction of this mechanism.

This paper considers the asymptotic behavior in $β$-Hölder spaces, and under $L^p$ loss, of the non-modified gamma kernel density estimator introduced by Chen [Ann. Inst. Statist. Math. 52 (2000), 471-480] for the analysis of nonnegative data, in the situation where the target may have a finite effective or true upper endpoint but the estimator itself is left untruncated and treats the support as $[0,\infty)$. The finite endpoint is used as an analytical device in the definition of the function class and the risk, not as information supplied to the estimator. The functional classes are chosen so that the target density matches smoothly to zero at the upper endpoint, which isolates the behavior at the origin and avoids an additional upper-endpoint leakage bias. It is shown that this estimator can achieve the minimax rate asymptotically for a suitable choice of bandwidth whenever $(p,β)\in [1,3)\times(0,2]$, or whenever $3 \leq p < 4$ and $(p-3)/(p-2) < β\leq 2$. It is also shown that this estimator cannot be minimax when either $p\in [4,\infty)$ or $β\in (2,\infty)$. The remaining region $\left\{(p,β): 3 < p < 4,\ 0 < β\leq (p-3)/(p-2)\right\}$ is an open case.

Establishing a complete electronic phase diagram for REFeAsO (RE = rare earth, RE1111) ironbased superconductors has remained experimentally challenging. Here, we report a systematic investigation of PrFeAsO1-xFx over the full nominal fluorine-doping range 0 to 1 and construct the first comprehensive electronic phase diagram for this system. The evolution from the nonsuperconducting parent compound to the fluorine-rich limit reveals a broad dome shaped superconducting region. Structural refinement demonstrates a systematic lattice contraction with increasing fluorine content (x), corroborated by Raman spectroscopy through softening of the Pr(A1g) phonon mode and hardening of the Fe(B1g) mode, confirming effective fluorine incorporation at the oxygen sites. The maximum superconducting transition temperature (Tc) reaches up to 52.3 K, approximately 5 K higher than previous reports for Pr1111. Magnetotransport measurements yield large upper critical fields Hc2(0) exceeding 100 T, while analysis of resistive transition broadening reveals thermally activated flux flow with a crossover from single-vortex to collective pinning regimes. Specific-heat measurements exhibit a reduced jump deltaC/γTc < 1.43, reflecting strong superconducting fluctuations and multiband pairing. These results establish clear structure property correlations and provide a unified description of superconductivity across the entire doping range of the Pr1111 system.

We propose a new double-bridge mechanism to significantly enhance $T_c$ in ionic oxide superconductors. Based on our recently proposed ionic-bond-driven O/Cu-bridged (bridge-I) pairing e$^-$-O-e$^-$/h$^+$-Cu-h$^+$ formed in the pseudogap phase ($T_c<T<T^*$), we reveal a key bridge-II Cu/O-mediated inter-pair attraction that overcomes direct Coulomb repulsion and drives coherent Bose-Einstein condensation (BEC) of preformed Cooper pairs. Within the BEC framework (Eq.(3)), $T_c$ follows the Uemura scaling $(n_{\rm pair}^{\rm 3D})^{2/3}/m_{\rm pair}^*$ or $n_{\rm pair}^{\rm 2D}/m_{\rm pair}^*$ and increases linearly with the attractive scattering length $a<0$. Strengthening bridge-II attraction, minimizing $m_{\rm pair}^*$, and optimizing $n_{\rm pair}^{\rm 3D}$ are the key to maximizing $T_c$. This double-bridge mechanism unifies the \textbf{eV-scale} strong pairing at room temperature and BEC, provides a universal route toward higher $T_c$, and guides the design of next-generation superconductors.

We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes and magnetohydrodynamic (MHD) equations on the whole plane under a suitably small initial energy. The solutions constructed here admit far-field vacuum and unbounded densities. Moreover, they possess an intermediate regularity regime between the finite-energy weak solutions of Lions-Feireisl and the framework of Hoff. This particularly extends our previous half-plane case with Dirichlet boundary conditions (arXiv:2601.11852) to the whole-plane MHD coupling, and we also generalize the works of Hoff (Comm. Pure Appl. Math. 55 (2002), pp. 1365-1407) and Suen and Hoff (Arch. Ration. Mech. Anal. 205 (2012), pp. 27-58) by allowing vacuum states and unbounded density. Our analysis lies in a new perspective that exploits the spatial integrability of the density and the resulting integrability of the pressure, together with the specific structure of the MHD system.

Despite decades of research, the microscopic origin of sublattice melting and fast ion transport in superionic conductors remains elusive. Here, we introduce a chemically neutral minimal binary model consisting of a rigid host lattice stabilized by short-range steric repulsion and a soft carrier sublattice interacting via long-range Wigner-type forces. This contrast naturally produces distinct melting temperatures and an intermediate sublattice-melting phase in which carriers become fluidlike while the host remains crystalline. Molecular dynamics simulations identify three dynamical regimes-crystalline, sublattice-melt, and fully molten-marked by sharp changes in diffusivity, structural correlations, and dynamical heterogeneity. Near sublattice melting, carrier motion is strongly anharmonic and spatially heterogeneous, beyond mean-field hopping descriptions. By tuning the density, we demonstrate that sublattice melting can be continuously controlled, establishing a direct link between lattice softness, anharmonicity, and collective ion transport. Comparison with conventional long-range Coulombic models confirms that our minimal model reproduces the key dynamical signatures of superionicity, providing a unified microscopic foundation for designing mechanically robust superionic conductors.

Automated unit test generation using large language models (LLMs) holds great promise but often struggles with generating tests that are both correct and maintainable in real-world projects. This paper presents KTester, a novel framework that integrates project-specific knowledge and testing domain knowledge to enhance LLM-based test generation. Our approach first extracts project structure and usage knowledge through static analysis, which provides rich context for the model. It then employs a testing-domain-knowledge-guided separation of test case design and test method generation, combined with a multi-perspective prompting strategy that guides the LLM to consider diverse testing heuristics. The generated tests follow structured templates, improving clarity and maintainability. We evaluate KTester on multiple open-source projects, comparing it against state-of-the-art LLM-based baselines using automatic correctness and coverage metrics, as well as a human study assessing readability and maintainability. Results demonstrate that KTester significantly outperforms existing methods across six key metrics, improving execution pass rate by 5.69% and line coverage by 8.83% over the strongest baseline, while requiring less time and generating fewer test cases. Human evaluators also rate the tests produced by KTester significantly higher in terms of correctness, readability, and maintainability, confirming the practical advantages of our knowledge-driven framework.

This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly-attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.

We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-wise eigenvalues, instead of scalar eigenvalues as in the classical case, that have corresponding eigenvectors with all components nontrivial and localized by their norm. We also show that, when applied to nonlinear eigenvalue problems for differential equations, this localization property of the eigenvectors provides, in turn, qualitative properties of the solutions. This is illustrated in two contexts of systems of PDEs and ODEs. We show the applicability of our theoretical results with two explicit examples.

Interface roughness scattering is an important limiting factor for achieving high performance Quantum Cascade Lasers. Following recent results, we study the growth conditions for a strain-compensated QCL emitting around 4.6 μm grown on a (511)A InP substrate using AFM and XRD measurements. We find that modulating the arsenic flux and correctly tailoring the III/V ratio is fundamental to achieve a good quality material. We report the first lasing device on such a platform with a current density threshold of 1.34 kA/cm2 and a slope efficiency of 1.1 W/A, which result suboptimal compared to the (100) reference. Finally, we find a 7% redshift of the (511)A spectrum which we attribute to an impurity scattering due to the increased incorporation along the exposed (111) direction. We validate this statement by verifying that the change in CBO and effective electron mass due to strain along a non-trivial direction cannot cause such a shift by using the k-p method generalized to arbitrary growth directions

Passive qubit reset is a key primitive for quantum information processing, whereby qubits are initialized by allowing them to relax to their ground state through natural dissipation, without the need for active control or feedback. However, passive reset occurs on timescales that are much longer than those of gate operations and measurements, making it a significant bottleneck for algorithmic execution. Here, we show that this limitation can be overcome by exploiting the Mpemba effect, originally indicating the faster cooling of hot systems compared to cooler ones. Focusing on the regime where coherence times exceed energy relaxation times ($T_2 > T_1$), we propose a simple protocol based on a single entangling two-qubit gate that converts local single-qubit coherences into fast-decaying global two-qubit coherences. This removes their overlap with the slowest decaying Liouvillian mode and enables a substantially faster relaxation to the ground state. For realistic parameters, we find that our protocol can reduce reset times by up to $50\%$ compared to standard passive reset. We analyze the robustness of the protocol under non-Markovian noise, imperfect coherent control and finite temperature, finding that the accelerated reset persists across a broad range of realistic error sources. Finally, we present an experimental implementation of our protocol on an IQM superconducting quantum processor. Our results demonstrate how Mpemba-like accelerated relaxation can be harnessed as a practical tool for fast and accurate qubit initialization.

We investigated how Gamma-Ray Burst (GRB) prompt emission measurements are affected by increasing distance to the source. We selected a sample of 26 bright GRBs with measured redshifts $z<1$ observed by the Burst Alert Telescope (BAT) on board the Neil Gehrels Swift Observatory (Swift) and simulated what BAT would have observed if the GRBs were at larger redshifts. We measured the durations of the simulated gamma-ray signals using a Bayesian block approach and calculated the enclosed fluences and peak fluxes. As expected, we found that almost all durations (fluences) measured for simulated high-$z$ GRBs were shorter (less) than their true durations (energies) due to low signal-to-noise ratio emission becoming completely dominated by background, i.e., the ``tip-of-the-iceberg'' effect. This effect strongly depends on the profile and intensity of the source light curve. Due to the uniqueness of GRB light curves, there is no common behavior in the evolution of measured durations with redshift. We compared our synthetic high-$z$ (i.e., $z>3$) GRBs to a sample of 72 observed high-$z$ bursts and found that the two samples were not inconsistent with being drawn from the same underlying population. We conclude that: (i) prompt emission durations (fluences) of high-$z$ GRBs observed by Swift/BAT are most likely underestimations, sometimes by factors of $\sim$several tens ($\sim2$), and (ii) changes in the average GRB prompt emission duration and fluence with increasing redshift are consistent with the tip-of-the-iceberg effect.

Large Language Models (LLMs) are rapidly becoming critical infrastructure for enterprise applications, driving unprecedented demand for GPU-based inference services. A key operational challenge arises from the two-phase nature of LLM inference: a compute-intensive \emph{prefill} phase that processes user input, followed by a memory-bound \emph{decode} phase that generates output tokens. When these phases share GPU resources, prefill tasks throttle the processing speed of concurrent decodes, creating state-dependent contention. This contention is further complicated by workload heterogeneity, as different applications exhibit vastly different input and output lengths. We develop a stochastic control framework for scheduling heterogeneous LLM workloads across large GPU clusters. We formulate LLM inference as a multiclass many-server queueing network with state-dependent service rates, grounded in empirical iteration-time measurements. We analyze the fluid approximation of this system and solve steady-state linear programs that characterize optimal resource allocation. We design gate-and-route policies that regulate prefill admission and decode routing, and prove that they are asymptotically optimal in the many-GPU limit under both bundled and separate token-pricing schemes. We further extend the framework to incorporate Service Level Indicators (SLIs) such as latency and fairness, providing a general approach to constrained scheduling. Numerical experiments calibrated to empirical iteration-time data demonstrate that our policies outperform standard serving heuristics.

We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations and repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x. Our code is available at https://github.com/BehroozZare/fast-permute.

We present a physics-informed classical-quantum machine learning framework for discriminating pristine CaF$_2$ from Er-doped CaF$_2$ using first-principles optical descriptors. Finite Ca$_8$F$_{16}$ and Ca$_7$ErF$_{16}$ clusters were constructed from the fluorite structure (a=5.46~$Å$) and treated using density functional theory (DFT) and linear-response time-dependent DFT (LR-TDDFT) within the GPAW code. Geometry optimization was performed in LCAO mode with a DZP basis and PBE exchange-correlation functional, followed by real-space finite-difference ground-state calculations with grid spacing h=0.30~$Å$ and N$_{bands}$=N$_{occ}$+20. Optical excitations up to 10~eV were obtained via the Casida formalism and converted into continuous absorption spectra using Gaussian broadening ($σ$=0.1-0.2~eV). From 1,589 energy-resolved points per system, physically interpretable descriptors including transition energy $E$, extinction coefficient $κ$, and absorption coefficient $α$ were extracted. A classical RBF-kernel support vector machine (SVM) achieves a test accuracy (ACC) of 0.983 and ROC-AUC of 0.999. Quantum support vector machines (QSVMs) evaluated on statevector and noisy simulators reach accuracies of 0.851 and 0.817, respectively, while execution on IBM quantum hardware yields a test-slice accuracy of 0.733 under finite-shot and decoherence constraints. A hybrid quantum neural network (QNN) with a 3-qubit feature map and depth-4 ansatz achieves a test accuracy of 0.93 and AUC of 0.96. Results here demonstrate that dopant-induced optical fingerprints form a robust, physically grounded feature space for benchmarking near-term quantum learning models against strong classical baselines.

We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs, intermediate buffers, and device-host synchronization, our approach minimizes memory traffic and enables efficient differentiation under both static and dynamically changing sparsity. Our programming model lets users express energy terms over mesh neighborhoods, while our system automatically manages parallel execution, derivative propagation, sparse assembly, and matrix-free operations such as Hessian-vector products. Our system supports both scalar- and vector-valued objectives, dynamic interaction-driven sparsity updates, and seamless integration with external GPU sparse linear solvers. We evaluate our system on applications including elastic and cloth simulation, surface parameterization, mesh smoothing, frame field design, ARAP deformation, and spherical manifold optimization. Across these tasks, our system consistently outperforms state-of-the-art differentiation frameworks, including PyTorch, JAX, Warp, DrJIT, EnzymeAD, and Thallo. We demonstrate speedups across a range of solver types, from Newton and Gauss-Newton for nonlinear least squares to L-BFGS and gradient descent, and across different derivative usage modes, including Hessian-vector products as well as full sparse Hessian and Jacobian construction. Our system is available as open source at https://github.com/owensgroup/RXMesh.

Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over $\mathbb{Q}$ for which the strong Birch-Swinnerton-Dyer (BSD) conjecture holds. Building on their results, we encode the required hypotheses into an explicit algorithm and apply it to the database of elliptic curves in the $L$-functions and Modular Forms Database (LMFDB), identifying all elliptic curves $E$ of conductor at most $500{,}000$ that admit infinitely many quadratic twists satisfying the strong BSD conjecture. Our computations provide certain numerical evidence for a conjecture of Radziwiłł and Soundararajan predicting Gaussian behavior in the analytic order of the Shafarevich-Tate group, while also observing a systematic positive bias within the BSD-satisfying subfamily.

We study the entanglement produced in transverse momentum by two-particle scattering at high energy. Employing the S-matrix framework for the derivation of reduced density matrices, we formulate the entanglement entropy for an inelastic scattering as well as an elastic one. We display the formulas of the entanglement entropy in terms of two-body cross sections. We also derive the entanglement density as a function of the transverse momentum. As an application, we then focus on both forward elastic ($pn \to pn$) and inelastic ($pn \to np$) channels scattering allowing for a fruitful comparison of the two reactions with the same proton-neutron content. We evaluate the elastic and inelastic entanglement entropy by using known parameterizations of experimental data for neutron-proton reactions. Comparing those entanglement entropies, we observe that the inelastic scattering produces more overall entanglement than the elastic one in the $pn$ sector.

A new direct measurement of the 59Cu(p,a)56Ni excitation function from 2.43-5.88 MeV in the center-of-mass was performed in inverse kinematics using the high-efficiency MUSIC active-target detector at FRIB. This reaction plays a critical role in constraining the strength of the NiCu cycle in different explosive astrophysical scenarios such as Type I X-ray bursts and the nu-p process in neutrino-driven winds after a core-collapse supernova. The newly derived stellar rate is systematically lower than previous estimates, suppressing NiCu cycle recycling in X-ray bursts to below 3% and enhancing nu-p process efficiency throughout the relevant temperature range, potentially extending its effective operation to temperatures as high as T9 = 3.94 (+0.99/-0.85).

Volume polynomials form a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties. I will survey realization problems related to them, review fundamental inequalities they satisfy, and discuss applications to the combinatorics of algebraic matroids. These notes are based on lectures given at the 2025 Summer Research Institute in Algebraic Geometry at Colorado State University.

This paper establishes an asymptotic expansion for expanding sector average on compact quotients of real rank-one Lie groups, with $SO(n,1)$ as a model case. Using tools from harmonic analysis and representation theory, the problem is reduced, via the action of the Casimir operator, to an ordinary differential equation(ODE) governing the evolution along the expanding $A$-direction. The asymptotic expansion is then derived from the analysis of this ODE.

We study the extraction of quantum coherence by three static Unruh-DeWitt (UDW) detectors that interact locally with a massless scalar vacuum field in the vicinity of an infinite perfectly reflecting boundary. Depending on the setup, the detectors are positioned either parallel or orthogonal to the boundary, with their energy gaps chosen to satisfy the hierarchy $Ω_C\geq Ω_B\geq Ω_A$. Our analysis reveals that decreasing the detector-boundary separation leads to a monotonic degradation of quantum coherence, whereas the same boundary effect can simultaneously preserve and even amplify the harvested quantum entanglement. Moreover, when the detectors possess distinct energy gaps, coherence extraction is further inhibited; strikingly, such non-identical configurations substantially enhance the efficiency of entanglement harvesting and markedly extend the range of detector separations over which non-negligible entanglement can be generated. Nevertheless, the harvesting of nonlocal quantum coherence is achievable over a significantly broader range of detector separations than that of quantum entanglement. Despite exhibiting similar overall behavior, orthogonal detector configurations outperform parallel ones in coherence harvesting, highlighting the quantitative influence of detector geometry. Overall, our study reveals a hierarchical distinction between quantum coherence and entanglement as operational resources in structured vacuum fields: quantum coherence is not only more readily accessible across space but also more robust than entanglement, whereas entanglement exhibits richer features and can be selectively activated and enhanced through boundary effects and detector non-uniformity.

A $(v,k,λ, μ)$-partial difference set (PDS) is a subset $D$ of size $k$ of a group $G$ of order $v$ such that every nonidentity element $g$ of $G$ can be expressed in either $λ$ or $μ$ different ways as a product $xy^{-1}$, $x, y \in D$, depending on whether or not $g$ is in $D$. If $D$ is inverse closed and $1 \notin D$, then the Cayley graph ${\rm Cay}(G,D)$ is a $(v,k,λ, μ)$-strongly regular graph (SRG). PDSs have been studied extensively over the years, especially in abelian groups, where techniques from character theory have proven to be particularly effective. Recently, there has been considerable interest in studying PDSs in nonabelian groups, and the purpose of this paper is develop character theoretic techniques that apply in the nonabelian setting. We prove that analogues of character theoretic results of Ott about generalized quadrangles of order $s$ also hold in the general PDS setting, and we are able to use these techniques to compute the intersection of a putative PDS with the conjugacy classes of the parent group in many instances. With these techniques, we are able to prove the nonexistence of PDSs in numerous instances and provide severe restrictions in cases when such PDSs may still exist. Furthermore, we are able to use these techniques constructively, computing several examples of PDSs in nonabelian groups not previously recognized in the literature, including an infinite family of genuinely nonabelian PDSs associated to the block-regular Steiner triple systems originally studied by Clapham and related infinite families of genuinely nonabelian PDSs associated to the block-regular Steiner $2$-designs first studied by Wilson.

Compton scattering of photons off high-energy electrons is a fundamental quantum mechanical process widely utilized to produce a $γ$-ray beam for scientific research. Instead of injecting laser light into a storage ring as a conventional way, we have developed an innovative method to achieve drastically higher energies approaching the ring energy by the backward Compton scattering of extreme ultraviolet (EUV) light. In this method, $92$ $\mathrm{eV}$ photons obtained from an undulator in a storage ring were reflected back to the original ring using a Mo/Si multilayer mirror. Consequently, $γ$-ray beam production through the EUV light Compton scattering using reflected synchrotron radiation was observed for the first time in a demonstration experiment conducted at the $1$ $\mathrm{GeV}$ ring, NewSUBARU. The measured energy spectrum was well reproduced by a theoretical calculation with the maximum energy of $0.543$ $\mathrm{GeV}$. The production rate was $1.4 \pm 0.1$ kcps for the energies above $0.160$ $\mathrm{GeV}$. This rate was quantitatively explained by the luminosity and the scattering cross section. The present work paved the way to create a new $γ$-ray beam source for future applications such as hadron photoproduction experiments.

We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and nonstationary Hamiltonians, corresponding to geodesic and nongeodesic trajectories. We formulate Krylov complexity in geometric terms, both instantaneously and in a time-averaged sense, and contrast it with an IG complexity of quantum evolutions characterized in terms of efficiency and curvature. We show that the two measures reflect fundamentally different aspects of quantum dynamics: Krylov's state complexity quantifies the directional spread of the evolving state relative to the initial state, whereas the IG complexity captures the effective volume explored along the trajectory on the Bloch sphere. This geometric distinction explains their inequivalent behavior and highlights the complementary nature of state-based and information-geometric notions of complexity in quantum systems.

Ice melting into saline water plays a fundamental role in the dynamics near the ice-ocean interface in polar oceans. The physics of ice melting involves a non-trivial interplay between thermodynamics at the interface, hydrodynamic transport in the bulk and the properties of the ambient ocean. The key control parameters are the density ratio $R_ρ$ proportional to the ambient ocean salinity and the Lewis number $Le = κ_T/κ_S$, which compares the thermal and salt diffusivities. Increasing the salinity is known to slow down melting, with the melt rate transitioning from subdiffusive to diffusive as $R_ρ$ increases. Here, we ssess the role of turbulence in this transition, using highly-resolved numerical simulations of the two-dimensional Boussinesq equations with a slowly melting upper boundary. We analyse the non-stationary growth of the temperature and meltwater mixing layers, varying the Lewis number and the density ratio. While meltwater is continuously entrained by convection inside the bulk, we identify a transition from convection to diffusion close to the interface. This transition is reflected by the formation of an interfacial boundary layer that regulates the flux of meltwater pouring into the turbulent bulk for $R_ρ\gtrsim 10$. Using mixing-layer diagnostics based on meltwater-concentration thresholds, we observe that the turbulent layer grows super-diffusively $\propto t^{1.33}$, while the interfacial boundary layer expands diffusively $\propto t^{0.5}$ but with a non-universal prefactor. These results indicate that double-diffusive effects are here confined to the interface, and highlight potential limitations of diagnostics based on fixed concentration thresholds in oceanographic applications.

By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$-Laplace equation in $\mathbb{R}^n$, with $n\geq 3$, and whose infimum over a ball behaves properly must be a bubble.

In this work, we present a theoretical analysis of null geodesics, critical photon orbits, and shadow formation associated with a wormhole generated by a geometric defect. The propagation of light in this spacetime is examined through the deflection angle in both weak- and strong-field regimes. Analytical expansions are derived in each regime and employed to characterize gravitational lensing observables. By varying the global monopole charge, we evaluate its impact on these observables and determine parameter ranges that may be accessible to current or future observational probes. Finally, we calculate the quasinormal modes as well as the time-domain solution for scalar perturbations as well.

Side-channel attacks (SCAs) pose a serious threat to system security by extracting secret keys through physical leakages such as power consumption, timing variations, and electromagnetic emissions. Among existing countermeasures, artificial noise injection is recognized as one of the most effective techniques. However, its high power consumption poses a major challenge for resource-constrained systems such as Internet of Things (IoT) devices, motivating the development of more efficient protection schemes. In this paper, we model SCAs as a communication channel and aim to suppress information leakage by minimizing the mutual information between the secret information and side-channel observations, subject to a power constraint on the artificial noise. We first consider the Gaussian input case, where the mutual information becomes the channel capacity, which is one way to quantify the information leakage. We then extend the framework to arbitrary input distributions by identifying conditions under which the optimization remains convex and by leveraging the fundamental I-MMSE relationship to derive the optimal noise allocation. Numerical results show that the proposed methods substantially reduce mutual information compared with conventional techniques, demonstrating their effectiveness for security-critical systems operating under tight power constraints.

We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately predict the behaviour at these critical points, which are challenging for conventional computational methods. Based on our numerical calculations, we identify with a high degree of confidence the point at which the spectrum turns from continuous to discrete and the point at which oscillations turn from having asymptotically infinite amplitudes to finite amplitudes. Furthermore, we numerically investigate the behaviour in the large $n$ regime and provide an intuitive explanation that coincides with the numerical results.