We present a dark fluid model described as a non-viscous, non-relativistic, rotating, and self-gravitating fluid. We assumed that the system has spherical symmetry and the matter can be described with the polytropic equation of state. The induced coupled non-linear partial differential equation system was solved by using a self-similar time-dependent ansatz introduced by L. Sedov and G. I. Taylor. These kinds of solutions were successfully used to describe blast waves induced by an explosion since the Guderley-Landau-Stanyukovich problem. We showed that these kinds of solutions can provide new solutions that are consistent with the Newtonian cosmological framework. We have found that such solutions can be applied to describe normal-to-dark energy on the cosmological scale.

Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber bundles. In this article we show that this ability of Kontsevich's classes is a manifestation of the following principle: the ``real blow-up'' construction on a smooth manifold essentially depends on its smooth structure and thus, given a smooth manifold (or smooth fiber bundle) $M$, the topological invariants of spaces constructed from $M$ by real blow-ups could potentially differentiate smooth structures on $M$. The main theorem says that Kontsevich's characteristic classes of a smooth framed bundle $π$ are determined by the topology of the 2-point configuration space bundle of $π$ and framing data.

The cognitive scientist Donald Hoffman argues that we don't perceive reality: spacetime, objects, colors, sounds, tastes, and so forth, are all merely an interface that we evolved to track evolutionary fitness rather than to perceive truths about external reality. In this paper, I expound on his argument, then I extend it, primarily, by looking at key ideas in physics that are quite germane to it. Among the topics in physics that I discuss are black holes, the holographic principle, string theory, duality, quantum gravity, and special relativity. I discuss these ideas from physics with an eye to their relevance for Hoffman's view.

We show that formamidinium lead bromide is unique among the halide perovskite crystals because its inorganic sub-lattice exhibits intrinsic local static disorder that co-exists with a well-defined average crystal structure. Our study combines THz-range Raman-scattering with single-crystal X-ray diffraction and first-principles calculations to probe the inorganic sub-lattice dynamics evolution with temperature in the range of 10-300 K. The temperature evolution of the Raman spectra shows that low-temperature, local static disorder strongly affects the crystal's structural dynamics and phase transitions at higher temperatures.

Off-the-shelf RDBMS typically expose only the query execution plan (QEP) of an SQL query, without presenting information about representative alternative query plans (AQPs) considered during plan selection in a user-friendly manner. Providing easy access to representative AQPs is valuable in database education, as it helps learners understand the plan choices made by a query optimizer, one of the several important components related to relational query processing. In this paper, we present a novel problem called the informative plan selection problem (TIPS), which aims to discover a set of k informative AQPs from the underlying plan space so that the plan informativeness of the set is maximized. Specifically, we explore two variants of the problem, batch TIPS and incremental TIPS, to cater to diverse learners. Due to the computational hardness of the problem, we present an approximation algorithm to address it efficiently while providing theoretical guarantees for the results. An extensive experimental study, including feedback from real-world learners and a three-year in-class evaluation of academic outcomes, demonstrates the effectiveness of our solutions for database education.

Implicit biases occur automatically and unintentionally and are particularly present when we have to make split second decisions. One such situations appears in refereeing, where referees have to make an instantaneous decision on a potential violation. In this work we revisit and extend some of the existing work on implicit biases in refereeing. In particular, we focus on refereeing in the NBA and examine three different types of implicit bias; (i) home-vs-away bias, (ii) bias towards individual players or teams, and, (iii) racial bias. For our study, we use play-by-play data and data from the Last Two Minutes reports the league office releases for games that were within 5 points in the last 2 minutes since the 2015 season. Our results indicate that the there is a bias towards the home team - particularly pronounced during the playoffs - but it has been reduced since the COVID-19 pandemic. Furthermore, there is robust statistical evidence that specific players benefit from referee decisions more than expected from pure chance. However, we find no evidence of negative bias towards individual players, or towards specific teams. Finally, our analysis on racial bias indicates the absence of any bias.

A rather general method for determining the spin density matrix of a multi-particle system from angular decay data is presented. The method is based on a Bloch parameterisation of the $d$-dimensional generalised Gell-Mann representation of $ρ$ and exploits the associated Wigner- and Weyl-transforms on the sphere. Each parameter of a (possibly multipartite) spin density matrix can be measured from a simple average over an appropriate set of experimental angular decay distributions. The general procedures for both projective and non-projective decays are described, and the Wigner $P$ and $Q$ symbols calculated for the cases of spin-half, spin-one, and spin-3/2 systems. The methods are used to examine Monte Carlo simulations of $pp$ collisions for bipartite systems: $pp\rightarrow W^+W^-$, $pp\rightarrow ZZ$, $pp\rightarrow ZW^+$, $pp\rightarrow W^+\bar{t}$, $t\bar{t}$, and those from the Higgs boson decays $H\rightarrow WW^{*}$ and $H\rightarrow ZZ^*$. Measurements are proposed for entanglement detection and Bell inequality violation in bipartite systems.

"An advanced city is not a place where the poor move about in cars, rather it's where even the rich use public transportation". This is what Enrique Penalosa, the celebrated ex-mayor of Bogota once said. However, in order to achieve this objective, one of the crucial properties that the public transportation systems need to satisfy is reliability. While reliability is often referenced with respect to on-schedule arrivals and departures, in this study we are interested in the ability of the system to satisfy the total passenger demand. This is crucial, since if the capacity of the system is not enough to satisfy all the passengers, then ridership will inevitably drop. However, quantifying this excess demand is not straightforward since public transit data, and in particular data from bus systems that we focus on in this study, only include information for people that got on the bus, and not those that were left behind at a stop due to a full bus. In this work, we design a framework for estimating this excess demand. Our framework includes a mechanism for identifying instances of potential excess demand, and a Poisson regression model for the demand for a given bus route and stop. These instances of potential excess demand are filtered out from the training phase of the Poisson regression. We show through simulated data that this filtering is able to remove the bias introduced by the censored data logged by the system. Failure to remove these data points leads to an underestimation of the excess demand. We then apply our approach on real data collected from the Pittsburgh Port Authority and estimate the excess demand over an one-year period.

Let $Y/S$ be a $p$-completely smooth morphism of $p$-torsion free $p$-adic formal schemes endowed with a Frobenius lift, and let $\overline Y/\overline S$ denote its reduction modulo $p$. We show that the category of crystals on the prismatic site of $\overline Y/S$ is equivalent to the category of $O_Y$-modules with integrable and quasi-nilpotent $p$-connection, and that the cohomology of such a crystal is computed by the associated $p$-de Rham complex. More generally, if $X$ is a closed subscheme of $\overline Y$, smooth over $\overline S$, then the prismatic envelope $Δ_X(Y)$ of $X$ in $Y$ admits such a $p$-connection, the category of prismatic crystals on $X/S$ is equivalent to the category of $O_ {Δ_X(Y)}$-modules with compatible integrable and quasi-nilpotent $p$-connection, and the cohomology of such a crystal is again computed by its $p$-de Rham complex. We also give a geometric construction of the ``prismatic Sen operator.'' Namely, we show that a lifting of $X$ (mod $p^2$) in $Y$ defines a vector field on the reduction modulo $p$ of $Δ_X(Y)$ and on a ``diffracted'' Higgs complex which calculates the mod $p$ prismatic and de Rham cohomologies of $X$. Surprisingly, this complex is not the reduction modulo $p$ of the afore-mentioned $p$-de Rham complexbut is rather its ``$α$-transform.'' As a consequence, we get a fairly explicit description of the action of the group scheme $G^γ$ on $RΓ(X, Ω^\bullet_{X/S})$, Drinfeld's strengthening of the Deligne-Illusie decomposition theorem. We also explain how earlier work by several authors relating Higgs fields, $p$-connections, and connections can be placed in the prismatic context.

Microfluidic devices offer unique opportunities to directly observe multiphase flow in porous media. However, as a direct representation of flow in geological pore networks, conventional microfluidics face several challenges. One is that simultaneous two-phase flow is not possible in a 2D network without fluctuation occupancy of pores. Nonetheless, such flow is possible in a microfluidic network if wetting phase can form a bridge across the gap between solid surfaces at a pore constriction while non-wetting phase flows through the constriction. We call this phenomenon "bridging". Here we consider the conditions under which this is possible as a function of capillary pressure and geometry of the constriction. Using the Surface Evolver program, we determine conditions for stable interfaces in a constriction, the range of capillary pressures at which bridging can occur, and those where the wetting phase would invade and block the constriction to the flow of the non-wetting phase ("snap-off"). We assume that the channels have uniform depth, vertical walls, and flat bottom and top surfaces, and that one phase perfectly wets the solid surfaces. If the constriction is long and straight, snap-off occurs at the same capillary pressure as bridging. For long, curved channels, snap-off happens as liquid imbibes before bridging can occur. For constrictions between cylindrical pillars, however, there is a range of capillary pressures at which bridging is stable; the range is greater the narrower the diameter of the cylinders relative to the width of the constriction. For smaller-diameter pillars, snap-off as non-wetting phase invades a downstream pore body is not possible. We relate these results to the shape of pore networks commonly used in microfluidic studies of two-phase flow to consider whether two-phase flow is possible in these networks without fluctuating pore occupancy.

The geometrically frustrated 3D pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a $\mathrm{U(1)}$ quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. In this work, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric $\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 $\mathrm{U(1)}$ spin liquids and 28 $\mathbb{Z}_2$ spin liquids that preserve pyrochlore space group symmetry while, upon further imposing time reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several $\mathrm{U(1)}$ spin liquid classes possess an unusual gapless multi-nodal-line structure ("nodal star") in the spinon bands, which is protected by the projective actions of the three-fold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form $C/T\sim \sqrt{T}+\sqrt{T}/\ln T$, in contrast to the form $C/T \sim T^2$ of the standard $\mathrm{U(1)}$ pyrochlore spin liquid with gapped spinons.

We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.

Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, and higher cliques). Current research aims at quantifying these hidden geometries by the algebraic topology methods and deep graph theory and understanding the dynamic processes on simplicial complexes. Here, we use the recently introduced model for geometrical self-assembly of cliques to grow nano-networks of triangles and study the filed-driven spin reversal processes on them. With the antiferromagnetic interactions between the Ising spins attached to the nodes, this assembly ideally supports the geometric frustration, which is recognized as the origin of some new phenomena in condensed matter physics. In the dynamical model, a gradual switching from the pairwise to triangle-based interactions is controlled by a parameter. Thus, the spin frustration effects on each triangle give way to the mesoscopic ordering conditioned by a complex arrangement of triangles. We show how the balance between these interactions changes the shape of the hysteresis loop. Meanwhile, the fluctuations in the accompanying Barkhausen noise exhibit robust indicators of self-organized criticality, which is induced by the network geometry alone without any magnetic disorder.

In this study we characterise the properties of foams used for varicose vein sclerotherapy. Their effectiveness is evaluated by predicting their yield stress and their flow profiles within a model of a vein. This information is represented using a Bingham number, which also takes into account the foam liquid fraction and the Sauter mean of the bubble size distribution. Based on this modelling, the most effective foams have a Bingham number B = 600 for a vein of diameter 2mm, in addition to a narrow bubble size distribution.

We simulate the quasi-static motion of a spherical particle through a stable, horizontal soap film. The soap film subtends a fixed contact angle, in the range $10-135^\circ$, where it meets the particle. The tension and pressure forces acting on the particle are calculated in two cases: when the film is held within a vertical cylinder, trapping a bubble but otherwise free to move vertically, and when the outer rim of the film is held in a fixed circular wire frame. Film deformation is greater in the second case, and the duration of the interaction therefore increases, increasing the contact time between particle and film. As the soap film returns towards its equilibrium shape following the passage of the particle a small bubble is trapped for contact angles below a threshold value of $90^\circ$. We show that this bubble is larger when the particle is larger and when the contact angle is smaller.

In the present paper, we explore various gravitational aspects such as energy extraction (via the Penrose process and Superradiance), particle collisions around a $\mathcal{N}=2$, $U(1)^2$ dyonic rotating black hole (BH) in the gauged supergravity model. The impact of the rotation parameter ($a$) and the gauge coupling constant ($g$) on the behaviour of horizon and ergoregion of the BH is studied. It is of interest to note that, compared with the extremal Kerr BH, the gauge coupling constant, under certain constraints, can enhance the maximum efficiency of energy extraction by the Penrose process almost double. Under the same constraints, we can extract approximately 60.75\% of the initial mass energy from the BH which is noticeably higher in contrast to the extremal Kerr BH. The limit of energy extraction in terms of the local speeds of the fragments is also examined with the help of the Wald inequality. We identify an upper limit on the gauge coupling constant up to which the phenomenon of Superradiance is likely to occur. Finally, we computed the center-of-mass energy ($E_{CM}$) of two particles with the same rest masses moving in the equatorial plane of the BH. Our study also aims to sensitize $E_{CM}$ to the rotation parameter and the gauge coupling constant for extremal and nonextremal spacetime as well. Especially, for the extremal case, an infinitely large amount of $E_{CM}$ can be achieved closer to the horizon which allows the BH to serve as a more powerful Planck-energy-scale collider as compared to Kerr and any other generalized BHs in the Kerr family explored so far in general relativity. However, $E_{CM}$ for the nonextremal spacetime is shown to be finite and has an upper bound.

We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network size diverges. We argue that a modification of ``stabilization'' conditions from the literature on geometric graphs provides a useful high-level formulation of weak dependence which we utilize to establish an abstract central limit theorem. Using results in branching process theory, we derive interpretable primitive conditions for stabilization. The main conditions restrict the strength of strategic interactions and equilibrium selection mechanism. We discuss practical inference procedures justified by our results.

In this paper we study a particular class of polynomials. We study the distribution of their zeros, including the zeros of their derivatives as well as the interaction between this two. We prove a weak variant of the sendov conjecture in the case the zeros are real and are of the same sign.

We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected simple cubic graphs for each $N$. Candidate structures are obtained by assigning different areas to the regions: for even $N$ there are $N/2$ regions of one area and $N/2$ regions of the other, and for odd $N$ we consider both cases, i.e. where the extra region takes either the larger or the smaller area. The perimeter of each candidate is found numerically for a few representative area ratios, and then the data is interpolated to give the conjectured least perimeter candidate for all possible area ratios. At larger $N$ we find that these candidates are best for a more limited range of the area ratio.

Recently a novel type of epithelial cell has been discovered and dubbed the "scutoid". It is induced by curvature of the bounding surfaces. We show by simulations and experiments that such cells are to be found in a dry foam subjected to this boundary condition.

We present simulations that show that an ideal two-dimensional foam with a finite contact angle develops an inhomogeneity for high liquid fraction $ϕ$. In liquid-liquid emulsions this inhomogeneity is known as flocculation. In the case of an ordered foam this requires a perturbation, but in a disordered foam inhomogeneity grows steadily and spontaneously with $ϕ$, as demonstrated in our simulations performed with the Surface Evolver.

By integrating the Young-Laplace equation, including the effects of gravity, we have calculated the equilibrium shape of the two-dimensional Plateau borders along which a vertical soap film contacts two flat, horizontal solid substrates of given wettability. We show that the Plateau borders, where most of a foam's liquid resides, can only exist if the values of the Bond number ${\rm Bo}$ and of the liquid contact angle $θ_c$ lie within certain domains in $(θ_c,{\rm Bo})$ space: under these conditions the substrate is foam-philic. For values outside these domains, the substrate cannot support a soap film and is foam-phobic. In other words, on a substrate of a given wettability, only Plateau borders of a certain range of sizes can form. For given $(θ_c,{\rm Bo})$, the top Plateau border can never have greater width or cross-sectional area than the bottom one. Moreover, the top Plateau border cannot exist in a steady state for contact angles above 90$^\circ$. Our conclusions are validated by comparison with both experimental and numerical (Surface Evolver) data. We conjecture that these results will hold, with slight modifications, for non-planar soap films and bubbles. Our results are also relevant to the motion of bubbles and foams in channels, where the friction force of the substrate on the Plateau borders plays an important role.

Efficient flexibility and higher system scalability call for enhanced network performance, better energy consumption, lower infrastructure cost, and effective resource utilization. To accomplish this, an architectural optimization and reconstruction of existing cellular network is required. Network slicing is considered to be one of the key enablers and an architectural answer of communication system of 2020 and beyond. Traditional mobile operators provide all types of services to various kinds of customers through a single network, however, with the deployment of network slicing operators are now able to divide entire network into different slices each with its own configuration and specific Quality of Service (QoS) requirements. In a slice-based network, each slice will be considered as a separate logical network. In this way, the infrastructure utilization and resource allocation will be much more energy and cost efficient in comparison to traditional network. In this paper, we provided a comprehensive discussion on concept and system architecture of network slicing with particular focus on its business aspect and profit modeling. We throughly discussed two different dimensions of profit modeling, so called Own-Slice Implementation and Resource Leasing for Outsourced Slices. We further addressed open research directions and existing challenges with the purpose of motivating new advances and adding realistic solutions to this emerging technology.

We consider a minimization problem of the form $P(φ, g, h):$ $$\min\left\{f(x):= φ(x) + g(x) - h(x) \colon x \in \mathbb{R}^n\right\},$$ where $φ$ is a differentiable function and $g,$ $h$ are convex functions, and introduce iterative methods to finding a critical point of $f$ when $f$ is differentiable. We show that the point computed by proximal point algorithm at each iteration can be used to determine a descent direction for the objective function at this point. This algorithm can be considered as a combination of proximal point algorithm together with a linesearch step that uses this descent direction. We also study convergence results of these algorithms and the inertial proximal methods proposed by Maing$\acute{e}$ and Moudafi (SIAM J. Optim. {\bf 19}(2008), 397--413) under the main assumption that the objective function satisfies the Kurdika--Łojasiewicz property. The proposed algorithm is then applied to solve the variable selection problem in linear regression.

We investigate the topological phase transitions of the deformed $\mathbb{Z}_3$ toric code, constructed by applying local deformations to the $\mathbb{Z}_3$ cluster state followed by projective measurements. Using the loop-gas and net configuration framework, we map the wavefunction norm to classical partition functions: the $Q=3$ Potts model for single-parameter deformations and a novel $\mathbb{Z}_3$ generalization of the Ashkin-Teller model (AT$_3$) for the general two-parameter case. The phase diagram, obtained via the projected entangled pair state (PEPS) representation and the variational uniform matrix product state (VUMPS) method, exhibits three phases -- the toric code phase, an $e$-confined phase, and an $e$-condensed phase -- separated by critical lines with central charges $c=4/5$ ($\mathbb{Z}_3$ parafermion conformal field theory) and $c=8/5$, along with isolated antiferromagnetic critical points at $c=1$ ($\mathbb{Z}_4$ parafermion conformal field theory). At these critical points, the system reduces to a square ice model with an emergent $U(1)$ 1-form symmetry, exhibiting Hilbert space fragmentation and quantum many-body scar states. Unlike the $\mathbb{Z}_2$ case, the absence of a sign-change duality leads to a richer phase structure.

Change detection (CD) has extensive applications and is a crucial method for identifying and localizing target changes. In recent years, various CD methods represented by convolutional neural network (CNN) and transformer have achieved significant success in effectively detecting difference areas in bi-temporal remote sensing images. However, CNN still exhibit limitations in local feature extraction when confronted with pseudo changes caused by different object types across global scales. Although transformers can effectively detect true change regions due to their long-range dependencies, the shadows cast by buildings under varying lighting conditions can introduce localized noise in these areas. To address these challenges, we propose the dynamically focused progressive fusion network (DFPF-Net) to simultaneously tackle global and local noise influences. On one hand, we utilize a pyramid vision transformer (PVT) as a weight-shared siamese network to implement change detection, efficiently fusing multi-level features extracted from the pyramid structure through a residual based progressive enhanced fusion module (PEFM). On the other hand, we propose the dynamic change focus module (DCFM), which employs attention mechanisms and edge detection algorithms to mitigate noise interference across varying ranges. Extensive experiments on four datasets demonstrate that DFPF-Net outperforms mainstream CD methods.

This paper investigates the dynamical behavior of steady spherical accretion onto a static, magnetically charged black hole embedded in a perfect fluid dark matter (PFDM) background. Using the shadow observations of M87* from the Event Horizon Telescope (EHT), we establish constraints on the parameter space for the magnetic charge and the PFDM parameter. Within this constrained range, we analyze the orbital dynamics of particles in a thin accretion disk surrounding the black hole and find that the black hole parameters significantly influence the effective potential, angular velocity, specific energy, and specific angular momentum of the particles. Subsequently, we calculate the radiative energy flux, temperature profile, and observed spectrum of the disk. Our results show that, while the local radiative flux and temperature at a given radius are lower for the charged-PFDM black hole compared to a Schwarzschild black hole, its overall radiative efficiency and total luminosity are higher. Finally, we explore the spherically symmetric, steady-state accretion process around the black hole, revealing how the parameters govern how the fluid velocity, density profile, and black hole mass accretion rate are influenced.

The emergence of Large Language Models (LLMs) has opened new opportunities to automate software engineering activities that traditionally require substantial manual effort. Among these, class diagram generation represents a critical yet resource-intensive phase in software design. This paper investigates the capabilities of state-of-the-art LLMs, including GPT-5, Claude Sonnet 4.0, Gemini 2.5 Flash Thinking, and Llama-3.1-8B-Instruct, to generate UML class diagrams from natural language requirements automatically. To evaluate the effectiveness and reliability of LLM-based model generation, we propose a comprehensive dual-validation framework that integrates an LLM-as-a-Judge methodology with human-in-the-loop assessment. Using eight heterogeneous datasets, we apply chain-of-thought prompting to extract domain entities, attributes, and associations, generating corresponding PlantUML representations. The resulting models are evaluated across five quality dimensions: completeness, correctness, conformance to standards, comprehensibility, and terminological alignment. Two independent LLM judges (Grok and Mistral) perform structured pairwise comparisons, and their judgments are further validated against expert evaluations. Our results demonstrate that LLMs can generate structurally coherent and semantically meaningful UML diagrams, achieving substantial alignment with human evaluators. The consistency observed between LLM-based and human-based assessments highlights the potential of LLMs not only as modeling assistants but also as reliable evaluators in automated requirements engineering workflows, offering practical insights into the capabilities and limitations of LLM-driven UML class diagram automation.

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary observations. We derive different stability estimates for determining the locations and the amplitudes of the sources in the space, the plane as well as in dimension one. The analysis employs a novel approach that combines several different arguments, including the improved regularity of the solutions, the application of Carleman estimates, time extension of solutions, and construction of explicit solutions to the adjoint equations. Further we provide numerical reconstructions to complement the theoretical findings.

Advances in quantum mechanics have long underpinned metrology by enabling practical realizations of units through quantum effects. With the 2019 SI revision, traceability is anchored in defined fundamental constants, reinforcing the quantum-mechanical basis of modern standards. In parallel, quantum technologies are transitioning from laboratory science to engineering and early industrial deployment, bringing familiar pressures for integration, reliability, cost reduction, supply-chain formation, and standardization. The direction of benefit is thus reversing: metrology and precision measurement are becoming enabling infrastructure for the industrialization of quantum technologies. Against this backdrop, this paper surveys the metrology and precision-measurement capabilities required across representative quantum-computing modalities and identifies where electrical and related metrology can contribute to the development, characterization, and reliable operation of quantum hardware. We then discuss cross-cutting measurement needs and standardization opportunities that recur across platforms, and note how similar frameworks can extend to emerging quantum-sensing applications.