By median we mean a scheme that inputs three element of a lattice, and outputs an element that is an average of the three inputs in a certain sense. The medians of a given finite lattice form a new lattice that is usually larger than the original, but generates a (not necessarily strictly) smaller variety. A median is called inner if it is a term function. The inner median lattice is closely related to the symmetric part of the equational basis of the lattice. We determine the outer and inner median lattices of all lattices of at most six elements.

Scholarly reading often involves engaging with various supplementary materials beyond PDFs to support understanding. In practice, scholars frequently incorporate such external materials into their reading workflow through annotation. However, most existing PDF annotation tools support only a limited range of media types for embedding annotations in PDF documents. This paper investigates cross-media annotation as a design space for augmenting academic reading. We present a design exploration of a cross-media annotation tool that allows scholars to easily link PDF content with other documents and materials such as audio, video or web pages. The proposed design has the potential to enrich reading practices and enable scholars to guide and support other researchers' reading experiences.

As early as 1935, Schrödinger recognized entanglement as ``not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought''. Indeed, most remarkable phenomena in quantum information science, such as quantum computing and quantum teleportation, spring from clever uses of entanglement. Among them, pseudotelepathy enables two or more players to win systematically at some cooperative games with no need for communication between them, a restriction that would make the task impossible in a classical world. We investigate the power of multipartite entanglement for pseudotelepathy. Some known games that can be won with tripartite entanglement cannot be won with bipartite entanglement, but they can be won with bipartite nonsignalling resources such as the so-called Popescu--Rohrlich nonlocal box. We exhibit a five-player game that can be won with tripartite entanglement, but not with arbitrary bipartite nonsignalling resources even in the presence of arbitrary five-partite classical resources. This illustrates both the power of bipartite nonsignalling resources (over bipartite entanglement) and the even superior power of tripartite entanglement.

This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families of uncertainty sets that capture ambiguity. Two complementary mechanisms generate robust quasi-convex measures: in the first, quasi-convexity is inherited from the initial risk measure under convex uncertainty sets; in the second it comes from the quasi-convex (or c-quasi-convex) structure of the uncertainty sets themselves. Building on Cerreia-Vioglio et al. (2011); Frittelli and Maggis (2011), we derive dual (penalty-type) representations for robust quasi-convex and cash-subadditive risk measures, showing that the classical convex cash-additive case arises as a special instance. We further analyze acceptance families and capital allocation rules under robustification, highlighting how ambiguity affects acceptability and the distribution of capital.

This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of conventional approaches. By leveraging a single ancillary qubit to control real-time evolution operators and employing Fourier analysis, WQTE enables parallel resolution of multiple eigen-energies. Theoretical analysis demonstrates that the algorithm achieves Heisenberg-limited precision and operates with only a non-zero wavefunction overlap between the reference state and target eigenstates, significantly reducing initialization complexity. Numerical simulations validate the algorithm's effectiveness in molecular systems (e.g., H4 chains) and lattice models (e.g., Heisenberg spin systems), confirming that computational error scales inversely with maximum evolution time while maintaining robustness against sampling errors and quantum noise. Experimental implementation on an NMR quantum processor further verifies its feasibility in real-world noisy environments. Compared to existing quantum algorithms (e.g., VQE, QPE and their variants), WQTE exhibits superior circuit depth efficiency, resource economy, and noise resilience, making it a promising solution for eigen-energy computation on noisy intermediate-scale quantum (NISQ) devices.

The COHERENT collaboration reports the most precise measurement of the coherent elastic neutrino-nucleus scattering cross section to date. This measurement was performed with COHERENT's germanium detector array, Ge-Mini, at the Spallation Neutron Source at Oak Ridge National Laboratory. A cumulative exposure of $4.68\times10^{22}$ protons on target yielded a total number of observed counts of $124^{+14}_{-12}$ and a flux-averaged cross section of $1.00 \pm 0.10 \mathrm{(statistical)} \pm 0.10 \mathrm{(systematic)}$ relative to the standard-model expectation of $5.9\times10^{-39} \mathrm{cm}^2$. The well-understood energy and timing distributions of the neutrino source allow for independent measurements of muon- and electron-neutrino scattering rates. This information is used to improve constraints on non-standard neutrino interactions mediated by heavy particles.

Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling behavior and possible explanations for this behavior have been under intense debate for two centuries. This review synthesizes empirical findings and theoretical frameworks on the energetics of living systems from an interdisciplinary perspective, with a focus on physical concepts. A general thermodynamic framework to study metabolism is laid out, together with a coarse-grained description of metabolic biochemistry. The rich history of experimental work in this field is surveyed, revealing a variety of metabolic scaling patterns at different levels of biological organization, from individual cells to whole populations. Several biophysical models proposed to explain the sublinear scaling of metabolic rate with body mass are summarized. Though the traditional focus has been on adult organisms, the review also highlights recent advances that probe metabolism during development. Improvements in experimental techniques, extensive datasets, and a host of open questions, suggest the field will continue gaining momentum in the near term. The review concludes with an outlook for this future progress: an interdisciplinary approach to elucidate metabolic scaling across different developmental stages and organism sizes.

Assume $κ= κ^{< κ}$ (usually $\aleph_0$ or an inaccessible). We shall deal with iterated forcings preserving ${}^{κ>}{\rm Ord}$ and not collapsing cardinals along a linear order $L$. A sufficient condition for this, which we will focus on, is for the forcings to have support $<κ$ and the $κ^+$-cc, and be strategically $<κ$-complete. The aim is to have homogeneous forcings, so that the iteration has many automorphisms. In addition to the inherent interest, such iterations are helpful for considering some natural ideals on ${}^\kappa2$, in order to get a model of ${\rm ZF} + {\rm DC}_κ +$ ``modulo this ideal, every set is equivalent to a $κ$-Borel one." But here we only have many automorphisms of the index set $L$ and therefore of the iteration of iterands $\mathbb{Q} $; we do not necessarily have homogeneity of $\mathbb{Q} $, and we do not have automorphisms mapping other names of $\mathbb{Q} $-reals onto each other. %\notemgrimes{What are the other names? Where do they come from?} However, for some reasonable forcing notions, there are no other $\mathbb{Q} $-reals! This was the reason for introducing and investigating saccharinity in earlier works with Jakob Kellner and with Haim Horowitz.

We present the full transseries of the strong-coupling expansion of the cusp anomalous dimension in ${\cal N}=4$ super Yang--Mills theory. This quantity admits an exact representation as a ratio of two determinants with particularly simple strong-coupling expansions. Nonperturbative contributions are classified by partitions into distinct non-negative odd integers and obey a universal structure. The corresponding Stokes constants are computed iteratively. The resulting resurgence pattern exhibits fermionic-type behavior.

Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay differential equations and identify the condition under which it applies. Using the linear chain trick, the distributed delay differential equations can be embedded into ordinary differential equations augmented with auxiliary variables, when the kernel function is characterized by a phase-type distribution. Employing the Schrödingerization method, the resulting equations can be embedded into the Schrödinger equation and efficiently solved by Hamiltonian simulation. Although this embedding requires the augmented differential equation to be semi-stable, we show that it is satisfied if and only if the original distributed-delay differential equations are semi-stable. The query complexity to obtain the normalized solution state of the $N$-dimensional delay system $|\mathbf{x}(t)\rangle\equiv\mathbf{x(t)}/\vert\vert\mathbf{x}(t)\vert\vert$ is $\mathcal{O}((st\vert\vert H\vert\vert_{\max}+\logε^{-1}/\log\logε^{-1})\vert\vert\mathbf{x}(0)\vert\vert/\vert\vert\mathbf{x}(t)\vert\vert)$ with $ε$, $g$, $H$, and $s$ being the allowable error, the dimension of the auxiliary variables associated with each kernel function, the Hamiltonian operator, and its sparsity, respectively. The gate complexity is given by this quantity multiplied by $\mathcal{O}(m+\log(N(1+gs)))$, where $m$ is the number of precision bits. To demonstrate the efficacy of our method, we present its applications to the generalized master equation and to the Redfield equation of the dephasing model.

In this paper, we investigate three specific subclasses of Ma-Minda type convex functions: namely, convex functions of order $α$, Janowski convex functions, and Robertson functions of normalized analytic functions defined in the open unit disk. For these classes, we establish logarithmic coefficient inequalities concerning both individual coefficient estimates and weighted series. The results presented here correct some earlier erroneous results and extend several previously known ones.

The classical Shafarevich conjecture predicts that the universal cover of a complex smooth projective variety $X$ is holomorphically convex. In this paper, we propose a refinement of this conjecture for varieties defined over the reals. In order to do this, we introduce the notions of real holomorphic convexity and transverse holomorphic convexity to capture the geometric differences dictated by the real locus $X(\mathbb{R})$ of $X$. Specifically, we conjecture that the universal cover is real holomorphically convex when $X(\mathbb{R}) \neq \emptyset$, and dianalytic holomorphically convex when $X(\mathbb{R}) = \emptyset$. We prove this refined conjecture in two main cases: when $X$ is a curve, and when the fundamental group of $X$ is nilpotent.

We identify overdamped gauge phonons as a new microscopic route to non-Fermi-liquid behaviour in Dirac materials. These phonons couple to electronic currents rather than densities, thereby realising a lattice analogue of transverse gauge-field mechanisms without requiring proximity to a quantum critical point. By computing the electronic self-energy with a phonon propagator dressed by electron-phonon interactions, we show that the low-energy behaviour is controlled by the orbital susceptibility chi and a dimensionless damping parameter alpha. In the overdamped regime, alpha >> 1, quasiparticles display strong deviations from Fermi-liquid theory. For chi > 0, Fermi-liquid behaviour persists only in a parametrically narrow infrared window before crossing over to non-Fermi-liquid scaling. For chi < 0, the Fermi-liquid regime is replaced by marginal-Fermi-liquid behaviour at the lowest energies, followed by a crossover to non-Fermi-liquid scaling. These results establish strain- induced gauge phonons as a promising source of anomalous metallic behaviour in systems such as twisted bilayer graphene.

We study the cross-resonance effect in capacitively-coupled fluxonium qubits and devise a simple formula for their maximum ZX interaction strength. By going beyond the perturbative regime, we find that a CNOT gate can generally be realized in under 200 ns with residual ZZ limited to 50 kHz, for fluxonium qubits with frequencies below 1 GHz. Our analysis relies on a semi-analytical method: we first numerically diagonalize the Floquet Hamiltonian of the strongly-driven control qubit and then perturbatively incorporate the weak qubit-qubit coupling to obtain an effective Hamiltonian. We also derive frequency collision windows around harmful control-target and control-spectator transitions. For large fluxonium devices, we predict a collision-free yield that is considerably less sensitive to junction variability compared to transmons in the same layout. These results support the viability of an all-fluxonium cross-resonance architecture with only capacitive couplings.

Choosing how much noise to add in Langevin dynamics is essential for making these algorithms effective in challenging optimization problems. One promising approach is to determine this noise by solving Hamilton-Jacobi-Bellman (HJB) equations and their exploratory variants. Though these ideas have been demonstrated to work well in one dimension, extension to high-dimensional minimization has been limited by two unresolved numerical challenges: setting reliable control bounds and stably computing the second-order information (Hessians) required by the equations. These issues and the broader impact of HJB parameters have not been systematically examined. This work provides the first such investigation. We introduce principled control bounds and develop a physics-informed neural network framework that embeds the structure of exploratory HJB equations directly into training, stabilizing computation, and enabling accurate estimation of state-dependent noise in high-dimensional problems. Numerical experiments demonstrate that the resulting method remains robust and effective well beyond low-dimensional test cases.

In this letter, we derive minimum-energy controls for a broad class of control-affine systems using a Lagrange multiplier fixed-point equation and a generally non-symmetric Gramian-like matrix. In feasible coercivity classes, this fixed point is unique and can be computed by standard Picard iteration. These iterates converge with factorial decay, yielding an implementable, highly scalable synthesis with an intrinsic energy bound. As a demonstration of concept, we use uniform complete controllability results for linear time-varying systems to derive a bracket-generating condition ensuring complete controllability for time-dependent planar control-affine systems with scalar inputs. Special treatment for the unicycle kinematic model is also provided, and numerical examples illustrate the approach's effectiveness.

In this work, we investigate the magnetic reconnection (MR) process as a mechanism for energy extraction from a rapidly rotating Buchdahl star (BS), one of the most compact horizonless objects that can, in principle, possess a spin parameter exceeding the extremal limit of a black hole (BH). We explore the energetics of the BS by focusing on the newly proposed MR mechanism developed by Comisso and Asenjo (the Comisso-Asenjo mechanism). Within this framework, we evaluate the energy extraction efficiency and the associated power output from a rapidly rotating BS. We show that the ergoregion of the BS exists only when the spin parameter satisfies $β>1/\sqrt{2}$. Consequently, the extraction of rotational energy through MR becomes possible only under this condition. Furthermore, we analyze the rate of energy extraction driven by fast magnetic reconnection and compare the resulting power with that predicted by the Blandford-Znajek mechanism. Our results indicate that the energy extraction rate increases significantly when the BS spin parameter exceeds the extremal limit for a BH, highlighting that MR can be substantially more efficient than the Blandford-Znajek mechanism. We demonstrate that MR can greatly enhance energy extraction efficiency from rapidly rotating BS with a large spin, making such an object potentially more efficient engines of high-energy astrophysical processes than BH.

Accurate software energy measurement is critical for optimizing energy, yet existing profilers force a trade-off between measurement accuracy and overhead due to tight coupling with supported specific hardware or languages. We present CodeGreen, a modular energy measurement platform that decouples instrumentation from measurement via an asynchronous producer-consumer architecture. We implement a Native Energy Measurement Backend (NEMB) that polls hardware sensors (Intel RAPL, NVIDIA NVML, AMD ROCm) independently, while lightweight timestamp markers enable tunable granularity. CodeGreen leverages Tree-sitter AST queries for automated instrumentation across Python, C++, C, and Java, with straightforward extension to any Tree-sitter-supported grammar, enabling developers to target specific scopes (loops, methods, classes) without manual intervention. Validation against "Computer Language Benchmarks Game" demonstrates $R^2 = 0.9934$ correlation with RAPL ground truth and $R^2 = 0.9997$ energy-workload linearity. By bridging fine-grained measurement precision with cross-platform portability, CodeGreen enables practical algorithmic energy optimization across heterogeneous environments. Source code, video demonstration, and documentation for the tool are publicly available at: https://smart-dal.github.io/codegreen/.

The rotational excitation of the three asymmetric-top molecular ion isotopologues H$_2$O$^+$, HDO$^+$, and D$_2$O$^+$ is studied theoretically using a combined framework of electron-molecule R-matrix scattering theory, multichannel quantum-defect theory, frame transformation theory, and the Coulomb-Born approximation. The latter two have been adapted here for asymmetric-top rotors. State-resolved cross sections and kinetic rate coefficients for transitions from the rotational ground state of the ions are presented. State-resolved rate coefficients for all calculated transitions $N=0\ldotstwo4$ are included as supplementary material and will be made available through the EMAA database.

A widely accepted picture of an accretion flow in the luminous soft spectral state of X-ray binary systems is a geometrically thin disc structure much like the classic analytic solution of Shakura \& Sunyaev. Although the analytic models are troubled by instabilities and miss important aspects of physics, such as magnetic fields, they are successfully used as a framework for interpreting observational data. Here, we compare the results of general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of optically thick, mildly sub-Eddington accretion on a stellar-mass black hole (the puffy disc) with established analytic and semi-analytic accretion models in the same regime. From the simulations, we find that the accretion flow is stabilised by the magnetic field, with a puffed-up, optically thick region resembling a warm corona surrounding a denser and cooler disc core. However, the stratified vertical structure of the disc significantly influences the observational picture of such a system. We analyse the inner disc structure, flow properties, effective viscosity, and inner edge position, and compare them to the predictions of standard models. We find that the simulated discs share some similarities with the models; however, they differ in several important aspects, most notably: the photosphere is geometrically thick, the inner edge is located closer to the central black hole than the analytic models assume, the surface density is significantly lower than analytically predicted, and the effective viscosity parameter is not constant but rises steeply in the innermost region.

(Abridged) Recently, streamers have been observed causing shocks at the outer edge of protoplanetary disks. The study of sulfur-bearing species can help us to understand the physical and chemical changes caused by infalling streamers toward their landing positions. We study the physical properties traced by SO$_2$ and SO toward the Class I protostar Per-emb 50, which is possibly related to the streamer infalling toward its disk. We present new NOEMA A-array observations as part of the large program "Protostars and Disks: Global Evolution" (PRODIGE). We analyzed the morphology of SO$_2$ and SO, and complement our interpretations with additional H_$2$CO and CO data from the same program. We compared the SO$_2$ and SO morphology with an infalling-rotating model. We applied Bayesian model selection to the brightest SO$_2$ line to disentangle the different kinematic components traced by this molecule. We used Local Thermodynamic Equilibrium (LTE) and non-LTE analyses to determine the temperature and density of the SO$_2$ emission. There are two separate peaks of SO$_2$ emission offset toward the southwest of Per-emb 50, one brighter (peak 1) at about 180 au from the protostar, and a weaker one (peak 2) at about 400 au. Peak 2 is blueshifted with respect to an infalling-rotating envelope. We propose that this peak is caused by the shock between the inner envelope and the streamer. Peak 1 is consistent with the expected envelope motion, and could thus be caused by shocks at the disk-envelope interface, but potential streamer influence cannot be neglected. Both peaks show abundance ratios consistent with a low velocity shock ($\sim 3-4$ \kms) when compared with shock models. Streamers can affect the physical and chemical structure of both disks and envelopes, suggesting that streamers can play an important role in shaping both structures in the embedded stages of star formation.

We consider the following generalization of the classic Binary Search Problem: a searcher is required to find a hidden target vertex $x$ in a graph $G$, by iteratively performing queries about vertices. A query to $v$ incurs a cost $c(v, x)$ and responds whether $v=x$ and if not, returns the connected component in $G-v$ containing $x$. The goal is to design a search strategy that minimizes the average-case search cost. Firstly, we consider the case when the cost of querying a vertex is independent of the target. We develop a $\br{4+ε}$-approximation FPTAS for trees running in $O(n^4/ε^2)$ time and an $O({\sqrt{\log n}})$-approximation for general graphs. Additionally, we give an FPTAS parametrized by the number of non-leaf vertices of the graph. On the hardness side we prove that the problem is NP-hard even when the input is a tree with bounded degree or bounded diameter. Secondly, we consider trees and assume $c(v, x)$ to be a monotone non-decreasing function with respect to $x$, i.e.\ if $u \in P_{v, x}$ then $c(u, x) \leq c(v, x)$. We give a $2$-approximation algorithm which can also be easily altered to work for the worst-case variant. This is the first constant factor approximation algorithm for both criterions. Previously known results only regard the worst-case search cost and include a parametrized PTAS as well as a $4$-approximation for paths. At last, we show that when the cost function is an arbitrary function of the queried vertex and the target, then the problem does not admit any constant factor approximation under the UGC, even when the input tree is a star.

We study the logarithmic equilibrium problem on the interval $[-1,1]$ in the presence of an external field generated by a uniform background charge supported on the same interval. For a real parameter $τ$, the external field is taken to be $τ$ times the logarithmic potential of the unit Lebesgue measure, and for all values of $τ$ we determine explicitly the unique equilibrium measure $μ_τ$, its support, its Cauchy transform, its logarithmic potential (when a closed expression is available), and the equilibrium constant. We show that the model exhibits three distinct regimes separated by critical values of $τ$. For sufficiently negative $τ$, the equilibrium support is a single symmetric subinterval strictly contained in $[-1,1]$. For an intermediate range of parameters, the support coincides with the full interval, and the equilibrium measure is an explicit linear combination of the Robin distribution and the Lebesgue measure. For large positive $τ$, the support becomes disconnected and consists of two symmetric outer intervals. In each regime, we find the equilibrium measure, its Cauchy transform, its potential (when a closed expression is available), and the equilibrium constant, using complex-analytic methods and singular integral techniques. These results yield a complete picture of how the support topology and the equilibrium density/constant evolve as $τ$ varies, including the transitions between one-cut, full-support, and two-cut configurations.

Runtime verification has gained popularity as a lightweight approach for increasing assurance in systems under scrutiny. Performing runtime checks enables dynamic monitoring and alerts for unexpected behavior, thereby improving reliability and correctness. Actor-based systems present significant challenges for runtime verification. Properties frequently span multiple actors with complex causal dependencies, while nondeterministic message interleavings can obscure execution semantics. Moreover, most existing monitoring tools are designed for single-process behavior. This paper presents ACTORCHESTRA, a runtime verification framework for Erlang that automatically tracks causality across multi-actor interactions. The framework instruments Erlang systems that comply with OTP guidelines via targeted code injection. This method establishes the orchestration infrastructure required to track causal relationships between actors without requiring manual modifications to the target system. To ease the specification of multi-actor properties, the framework provides WALTZ, a specification language that automatically compiles properties into executable Erlang monitors that integrate with the instrumented system. Three case studies demonstrate ACTORCHESTRA's effectiveness in detecting complex behavioral violations in real-world actor systems. A performance evaluation quantifies the runtime overhead of the monitoring infrastructure and analyzes the trade-offs between added safety guarantees and execution costs.

Laser frequency combs (LFCs) are a promising technology for wavelength calibration of astronomical high-resolution spectrographs requiring utmost accuracy and stability, since they directly translate the fundamental SI time standard from the radio frequency regime to optical frequencies. However, they have so far seen limited use in practice, due to their complexity, incomplete wavelength coverage, but also the challenges in the data analysis they imply. Here, we present a detailed test of a 34 GHz electro-optic modulation comb with the ESPRESSO spectrograph. Using thin-film lithum-niobate waveguides for broadening and harmonic generation, the setup provides partial coverage of the IR, visible, and near-UV spectral ranges. We focus on assessing the quality of the delivered spectra and their capability to facilitate accurate and stable wavelength calibration. We present a detailed analysis of the spectrally-diffuse background, the line width, and characterize the line-spread function over a broader width than possible with the ESPRESSO facility LFC. Comparing both combs, we find strong local discrepancies in the wavelength calibration accuracy up to 15m/s , which correlate with the echellogram structure. These do not originate from the lasers, but from misalignments in the ESPRESSO calibration unit, highlighting the strong need to make instrument fiber feeds more robust to light-injection effects. Nevertheless, we demonstrate excellent stability of the wavelength calibration, with a scatter of only 17cm/s . This, however, can only be achieved when accurately modeling the non-Gaussian line-spread function, showcasing the need for advanced data analysis techniques when dealing with LFC spectra.

Actionable recourse studies whether individuals can modify feasible features to overturn unfavorable outcomes produced by AI-assisted decision-support systems. However, many such systems operate in competitive settings, such as admission or hiring, where only a fraction of candidates can succeed. A fundamental question arises: what happens when actionable recourse is available to everyone in a competitive environment? This study proposes a framework that models recourse as a strategic interaction among candidates under a risk-based selection rule. Rejected individuals exert effort to improve actionable features along directions implied by the decision rule, while the success benchmark evolves endogenously as many candidates adjust simultaneously. This creates endogenous selection, in which both the decision rule and the selection threshold are determined by the population's current feature state. This interaction generates a closed-loop dynamical system linking candidate selection and strategic recourse. We show that the initially selected candidates determine both the benchmark of success and the direction of improvement, thereby amplifying initial disparities and producing persistent performance gaps across the population.

We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To ensure the divergence free property exactly, the velocity field is represented as the curl of a stream function in two dimensions and as the curl of a vector potential in three dimensions. Beyond classical stream-function or velocity-vorticity formulations, we further utilize the properties of the curl operator to derive two specific decoupled subproblems for the velocity (through the stream function or vector potential) and the pressure, respectively. The proposed formulations enable a sequential solution strategy, in which the velocity and pressure are solved independently. To resolve the inherent nonlinearity of the Navier-Stokes equations, we employ a Gauss-Newton linearization strategy, transforming the nonlinear velocity subproblem into a sequence of linear subproblems. These decoupled subproblems for velocity and pressure are subsequently solved using the TransNet framework. Compared with existing methods, the proposed approach reduces computational cost while strictly preserving the incompressibility constraint.

The candidate topological superconductor UTe$_2$ exhibits a complex phase diagram with multiple superconducting states, yet the nature of their coexistence has remained a central mystery. In particular, the apparent intersection of two second-order phase boundaries at a ``triple point'' in the pressure-temperature phase diagram is thermodynamically forbidden, suggesting hidden phase transitions or a fundamental misunderstanding of the superconductivity in UTe$_2$. Here, we use pulse-echo ultrasound to resolve this puzzle by discovering a new phase boundary that is characterized by a unique ``upward jump" in the sound velocity -- direct thermodynamic evidence for a re-entrant phase transition. Our results establish $\left(P^{\star},T^{\star}\right)$ as a tetracrtical point, beyond which the ambient and pressure-induced superconducting order parameters form a multi-component state. We use the measured phase diagram to construct a Ginzburg-Landau theory that shows that strong competition between the two superconducting order parameters drives the re-entrance and leads to phase locking that suppress superconducting fluctuations. These findings provide the definitive magnetic field-temperature-pressure phase diagram and establish a thermodynamic foundation for multi-component -- and potentially topological -- superconductivity in UTe$_2$.

Electrochemical water electrolysis, which produces clean energy carriers to mitigate carbon emissions, lacks suitable, low-cost electrodes for efficient oxygen evolution reaction (OER) in alkaline water splitting. To address this challenge, we developed Zn-Al alloy electrodes with varying Al contents up to 20 wt.% via powder metallurgy method and conducted electrochemical measurements of the OER in alkaline solution to investigate their catalytic performance. We also performed first-principles calculations to examine their thermodynamic phase stability and electronic structures. Both theoretical and experimental results indicated that incorporating $\geq 20$ wt.% Al into Zn led to thermodynamic phase instability and secondary-phase segregation in Al-rich regions, limiting reaction kinetics and reducing catalytic efficiency. Although the Al content of 5 wt.% into Zn exhibited favorable thermodynamic and electronic characteristics, but its electrochemical performance was inefficient and poor due to inadequate reaction active sites on the surface. In contrast, the 10 wt.% and 15 wt.% Al into Zn showed approximately three- and two-fold increases in anodic exchange current density relative to pure Zn, respectively. Additionally, the anodic overpotential losses ($η_{0,a}$) measured at a current density of 12 mAcm$^{-2}$ were 0.240 V for Zn$_{0.9}$Al$_{0.1}$ and 0.5603 V for Zn$_{0.85}$Al$_{0.15}$, significantly lower than that of pure Zn ($η_{0,a} = 1.086$ V). While Zn$_{0.9}$Al$_{0.1}$ and Zn$_{0.85}$Al$_{0.15}$ showed similar charge transfer resistance ($R_{\rm CT}$), Zn$_{0.9}$Al$_{0.1}$ demonstrated superior reaction kinetics and lower $η_{0,a}$ across all samples tested. Furthermore, the improved kinetics and reduced overpotential of the Zn-Al alloys favorably compare with those of other transition-metal-based catalysts, including Fe-Co-Ni-Mo alloys and Fe-doped CuO.

We present the first large-scale comparative analysis of Truth Social and the most popular conservative Reddit communities, r/Conservative, r/conservatives, and r/Republican. Using topic modeling with FASTopic and LLM-assisted refinement, we analyze topic prevalence, toxicity, and temporal dynamics across these communities during the first eight months of Truth Social. We find clear contrasts: Truth Social centers on grievance and narrative-driven content, while Reddit focuses more on policy debates. Toxicity is higher on Reddit and peaks in cultural and leader-focused topics. Despite similar event-driven participation shocks across platforms, Truth Social shows higher baseline proportions of users engaging with political topics. Our findings contribute to understanding how alternative right-leaning platforms reshape online discourse.