In this paper, we provide a sharp remainder term for the general weighted discrete $p$-Hardy inequality. By simply choosing weights and specifying $1<p<\infty$, we are able to recover the identity by Krej{č}i{ř}{\'ı}k-Štampach [KS22, Theorem 1], obtain the sharp form of the $p$-Hardy inequality by Fischer-Keller-Pogorzelski [FKP23, Theorem 1] and generalize the power weighted inequality by Gupta [Gup22, Theorem 2.1]{gupta2022discrete} with sharp remainder. In addition, we prove a quantitative stability result, thereby showing that any minimizing sequence of the discrete $p$-Hardy inequality must approach the family of non-trivial minimizers.

We consider a stopping problem and its application to the decision-making process regarding the optimal timing of organ transplantation for individual patients. At each decision period, the patient state is inspected and a decision is made whether to transplant. If the organ is transplanted, the process terminates; otherwise, the process continues until a transplant happens or the patient dies. Under suitable conditions, we show that there exists a control limit optimal policy. We propose a smoothed perturbation analysis (SPA) estimator for the gradient of the total expected discounted reward with respect to the control limit. Moreover, we show that the SPA estimator is asymptotically unbiased.

We review the literature on individual patient organ acceptance decision making by presenting a Markov Decision Process (MDP) model to formulate the organ acceptance decision process as a stochastic control problem. Under the umbrella of the MDP framework, we classify and summarize the major research streams and contributions. In particular, we focus on control limit-type policies, which are shown to be optimal under certain conditions and easy to implement in practice. Finally, we briefly discuss open problems and directions for future research.

This paper introduces a way of modeling the epidemic transmission rate using a stochastic process of the form $(β_t = φ(t)P_t : t \ge 0)$, where the positive deterministic function $φ(t)$ models the impact of a public health intervention and $P_t$ describes the stochastic evolution of the infection rate in the absence of any control measures. We establish general asymptotic results for an SI model governed by $(β_t : t \ge 0)$, showing that the asymptotic behavior is determined by the integrated intensity process $(H_t =\int_0^t β_s \, ds : t \ge 0)$. We study the intrinsically bounded Jacobi process and the Cox--Ingersoll--Ross (CIR) process as models for $(P_t : t \ge 0)$; both exhibit almost surely positive sample paths. We highlight that in the case of non-intervention $(φ\equiv 1)$, the process $(H_t : t \ge 0)$ is considerably more analytically tractable. Finally, we present numerical simulations for both models in two different scenarios: the case of non-intervention $(φ(t)=1)$ and the case of a successful intervention strategy (where $\int_0^\infty φ(t) \, dt < \infty$) modeled using exponential decay $φ(t) = e^{-αt}$ for both models.

This paper studies the empirical behaviour of the p-AVL tree, a probabilistic variant of the AVL tree in which each imbalance is repaired with probability $p$. This gives an exact continuous interpolation from $p = 0$, which recovers the BST endpoint, to $p = 1$, which recovers the standard AVL tree. Across random-order insertion experiments, we track rotations per node, total imbalance events, average depth, average height, and a global imbalance statistic $σ$. The main empirical result is that even small nonzero p already causes a strong structural change. The goal here is empirical rather than fully theoretical: to document the behaviour of the p-AVL family clearly and identify the main patterns.

Prior work on perceptual effectiveness has decomposed visualizations into smaller common units (e.g., channels such as angle, position, and length) to establish rankings. While useful, these decompositions lack the computational structure to predict performance for new visualization $\times$ task combinations, requiring new experiments for each. We propose an alternative unit of analysis: operationalizing quantitative visualization interpretation as sequences of composable visual decoding operators. Using probability density function (PDF) and cumulative distribution function (CDF) charts, we examine how chart-specific tasks can be decomposed into reusable, chart-agnostic perceptual operations and characterize their error profiles through hierarchical Bayesian modeling. We then test generalizability by composing learned operators to predict performance on a structurally different task: Moritz et al.'s [35] scatterplot mean-estimation experiment, where the chart type, chart dimensions, and analytic goal all differ from the learning conditions. With a pre-registered analysis plan, we compose operators under six candidate strategies and evaluate each against empirical data with no parameters fit to the response data. One strategy captures both bias and variance of observed responses; five alternatives fail in distinguishable ways. We argue that this decoding-operator-oriented approach to empirical visualization research and theory-building lays the groundwork for generative models that can predict a distribution of likely interpretations under different viewing conditions, new chart types, and new tasks. Free copy of this paper and supplemental materials: https://osf.io/prtfq; experiment interface: https://gleaming-dolphin-799fda.netlify.app/vis-decode-slider.

Ultra-narrow-linewidth lasers with suppressed high-frequency phase noise are critical for quantum control and precision metrology. While optical phase locking (OPL) is the standard technique for cloning the coherence of such sources, its effectiveness is often limited at high frequencies by feedback latency. We present a robust feedforward architecture that overcomes this limitation by recycling and demodulating the existing master-slave beat signal to drive a single electro-optic modulator for near-instantaneous noise cancellation. This approach eliminates the extraneous sidebands and transmission losses typical of more complex modulators. Through active stabilization of the beat amplitude and demodulation phase, we demonstrate robust suppression exceeding 30 dB from 10 kHz to 10 MHz. This hardware-efficient framework is readily compatible with standard OPL setups, offering a scalable solution for high-fidelity coherent control.

We discuss the amplitude and phase fluctuations of gravitational waves due to wave optics lensing in the presence of both a strong lens and cosmological weak lenses. By applying the geometric optics approximation to the strong lens and treating the weak lensing potential perturbatively, we obtain the amplification factor up to the second order in the weak lensing potential. Additionally, we establish a methodology to systematically evaluate the weak lensing effects based on diagrammatic rules. Based on the derived amplification factor, we evaluate the statistics of the fluctuations and demonstrate that the consistency relations originally established in the absence of a strong lens still hold in exactly the same form when a strong lens is present. The physical origin of these relations is also discussed. Furthermore, we demonstrate that for the mean of the weak lensing signal, both the magnification of the signal and the shift of the Fresnel scale to larger scales occur, consistent with the behavior observed in the variance.

This article is concerned with Kronecker flows on the infinite torus. The work is partly motivated by the fact that many Hamiltonian PDEs and systems on infinite lattices admit invariant tori, of possibly infinite dimension, on which the dynamics is linearizable. Finite-dimensional Kronecker flows are well understood: the dynamics can be reduced to a non-resonant flow on a subtorus, which is equivalent to being topologically transitive, to minimality, and to unique ergodicity in the projection. We prove that these properties still hold when the dimension of the torus is infinite if and only if the integer (finite) linear combinations of the frequencies form a free abelian group. Next, we construct a class of orbits whose closure is locally homeomorphic to the product of a ball and a Cantor set, extending a recent result by Sakbaev and Volovich. We also show that the Benjamin-Ono equation admits this type of solutions. Finally, we prove the equivalence between a classification problem for Kronecker flows and that for countable abelian groups without torsion.

Accurate phase estimation at the edge of data segments is crucial for EEG applications such as EEG-TMS in offline and real-time data analysis. Our research evaluates the phase estimation performance of four commonly used methods (Phastimate, SSPE, ETP, and PhastPadding) for accuracy and systemic biases, using data from young and elderly healthy controls and chronic stroke participants. To address the identified limitations of the established methods, we introduce Phase Estimation with Autoregressive Padding (PEAP), a method that prevents strong bandpass filtering-induced artifacts. Contrary to the established methods, PEAP does not show significant biases and improves accuracy by 3.2 to 9.2% for the continuous phase estimation. Our offline analysis demonstrates how established methods are systematically biased towards some estimates and how they induce phase shifts. We also show that differences between methods do not vary between clinical and control populations, supporting their translatability. This work indicates that systematic biases in established phase estimation methods may compromise the validity and comparability of phase-dependent findings. PEAP addresses these limitations and thus offers a more reliable and more accurate alternative method.

In this paper, we study the closed timelike geodesics of de-Sitter tori with one singularity and prove their uniqueness in their free homotopy class. We introduce the notion of timelike marked length spectrum of such a torus, and establish its rigidity with respect to the lengths of two homotopy classes of intersection number one. We also construct length-twist coordinates on the deformation space of de-Sitter tori with one singularity.

We investigate the properties of the intersection $\mathrm{Int}_{\mathfrak{F}}(G)$ of all $\mathfrak{F}$-maximal subgroups of a finite group $G$ for a hereditary formation $\mathfrak{F}$ of finite groups. We prove that $\mathrm{Int}_{\mathfrak{F}}(G/\mathrm{Int}_{\mathfrak{F}}(G))\simeq 1$ holds for any finite group $G$ if and only if $\mathfrak{F}$ contains every group $G$ all of whose $\mathfrak{F}$-subgroups are $\mathfrak{F}$-subnormal. As corollaries we obtain the results of A. N. Skiba (2011), J. C. Beidleman and H. Heineken (2011) about $\mathrm{Int}_{\mathfrak{F}}(G)$ for a hereditary saturated formation $\mathfrak{F}$.

3GPP Release 19 has initiated the standardization of integrated sensing and communications (ISAC), including a channel model for monostatic sensing, evaluation scenarios, and performance assessment methodologies. These common assumptions provide an important basis for ISAC evaluation, but reproducible end-to-end studies still require a transparent sensing implementation. This paper evaluates 5G New Radio (NR) base station (gNB)-based monostatic sensing for the Unmanned Aerial Vehicle (UAV) use case using a 5G NR downlink Cyclic Prefix-Orthogonal Frequency Division Multiplexing (CP-OFDM) waveform and positioning reference signals (PRS), following 3GPP Urban Macro-Aerial Vehicle (UMa-AV) scenario assumptions. We present an end-to-end processing chain for multi-target detection and 3D localization, achieving more than 70% detection probability with less than 5% false alarm rate, in the considered scenario. For correctly detected targets, localization errors are on the order of a few meters, with a 90th-percentile error of 4m and 6m in the vertical and horizontal directions, respectively. To support reproducible baseline studies and further research, we release the simulator 5GNRad, which reproduces our evaluation

We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making it difficult to simultaneously achieve computational efficiency and accurate constraint satisfaction. We propose a zeroth-order random-subspace sequential quadratic programming method (ZO-RS-SQP) that combines two-point directional estimation with low-dimensional SQP updates. At each iteration, the method samples a random low-dimensional subspace, estimates the projected objective gradient and constraint Jacobians using two-point evaluations, and solves a reduced quadratic program to compute the step. As a result, the per-iteration evaluation cost scales with the subspace dimension rather than the ambient dimension, while retaining the structured linearized-constraint treatment of SQP. We also consider an Armijo line-search variant that improves robustness in practice. Under standard smoothness and regularity assumptions, we establish convergence to first-order KKT points with high probability. Numerical experiments illustrate the effectiveness of the proposed approach on nonlinear constrained problems.

The multiplex network paradigm has been instrumental in revealing many unexpected phenomena and dynamical regimes in complex interacting systems. Nevertheless, most of the current research focuses on undirected multiplex structures, whereas real-world systems predominantly involve directed interactions. Here, we present an analytical framework for attaining optimal synchronization in directed multiplex networks composed of phase oscillators, considering both frustrated and non-frustrated regimes. A multiplex synchrony alignment function (MSAF) is introduced for this purpose, whose formulation integrates structural properties and dynamical characteristics of the individual directed layers. Using this function, we derive two classes of frequency distributions: one that yields perfect synchronization at a prescribed coupling strength in the presence of phase-lag, and another that optimizes synchronization over a broad range of coupling strengths. Numerical simulations on various directed duplex topologies demonstrate that both frequency sets substantially outperform conventional distributions. We also explore network optimization through a directed link rewiring strategy aimed at minimizing the MSAF, along with a swapping algorithm for optimally assigning fixed frequencies on both layers of a given directed duplex network. Examination of synchrony-optimized directed networks uncovers three notable correlations: a positive relationship between frequency and out-degree, a negative correlation between neighboring frequencies, and an anti-correlation between mirror node frequencies across directed layers.

Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.

We study what deterministic distributed algorithms can compute on random input graphs in extremely weak models of distributed computing: all nodes are anonymous, and in each communication round, nodes broadcast a message to all their neighbors, receive a (multi)set of messages from their neighbors, and update their local state. These correspond to the SB and MB models introduced by Hella et al. [PODC 2012] and are strictly weaker than the standard port-numbering PN and LOCAL models. We investigate what can be computed almost surely on random input graphs. We give a one-round deterministic SB-algorithm using $O(\log n)$-bit messages that computes unique identifiers with high probability on anonymous networks sampled from $G(n,p)$, where $n^{\varepsilon-1} \le p \le 1/2$ and $\varepsilon>0$ is an arbitrarily small constant. This algorithm is inspired by canonical labeling techniques in graph isomorphism testing and can be used to "anonymize" existing distributed graph algorithms designed for the broadcast CONGEST and LOCAL models. In particular, we give a new anonymous algorithm that finds a triangle in $O(1/\varepsilon)$ rounds on the above input distribution. We also investigate computational power of natural analogs of "Monte Carlo" and "Las Vegas" distributed graph algorithms in the random graph setting, and establish some new collapse and hierarchy results. For example, our work shows the collapse of the weak model hierarchy of Hella et al. on $G(n,p)$, as apart from a vanishingly small fraction of input graphs, the SB model is as powerful as LOCAL.

We study how artificial intelligence (AI) affects firms' incentives to pursue incremental versus radical knowledge recombinations. We develop a model of recombinant innovation embedded in a Schumpeterian quality-ladder framework, in which innovation arises from recombining ideas across varying distances in a knowledge space. R&D consists of multiple tasks, a fraction of which can be performed by AI. AI facilitates access to distant knowledge domains, but at the same time it also increases the aggregate rate of creative destruction, shortening the monopoly duration that rewards radical innovations. Moreover, excessive reliance on AI may reduce the originality of research and lead to duplication of research efforts. We obtain three main results. First, higher AI productivity encourages more distant recombinations, if the direct facilitation effect is stronger than the indirect effect due to intensified competition from rivals. Second, the effect of increasing the share of AI-automated R&D tasks is non-monotonic: firms initially target more radical innovations, but beyond a threshold of human-AI complementarity, they shift the focus toward incremental innovations. Third, in the limiting case of full automation, the model predicts that optimal recombination distance collapses to zero, suggesting that fully AI-driven research would undermine the very knowledge creation that it seeks to accelerate.

Probabilistic forecasts must sum to unity and cannot express ``I don't know.'' Possibility theory relaxes this constraint: a subnormal distribution explicitly measures how much of the plausibility budget remains unassigned, ignorance signal that probability cannot represent. This paper develops a verification framework for such forecasts, centred on a five-number scorecard that separately diagnoses whether the forecast pointed at the right outcome (depth-of-truth), how sharply (diffuseness, support margin), how confidently (ignorance), and how dominantly (conditional necessity). A possibility-to-probability conversion preserves ignorance for familiar frequency-based scoring; categorical threshold scores (POD, FAR, CSI, etc.) connect to operational practice. Together, these three complementary facets -- possibilistic, probabilistic, and categorical -- expose failure modes invisible to any single metric. Storm Prediction Center convective outlook categories serve as the running example throughout; a synthetic reforecast demonstrates diagnostic visualisations and scorecard interpretation. Ignorance is better expressed than repressed.

Given subvarieties $X, Y$ of a complex algebraic variety $S$ of complementary dimension, must they intersect? When $S$ is projective space, this is a consequence of the classical Bézout theorem, and an analogue for simple abelian varieties was established by Barth in 1968. Moreover, the moving lemma suggests that, after suitable translations, one may arrange for intersections of the expected dimension. In this work, we obtain variants for simple abelian varieties in the spirit of the completed Zilber--Pink philosophy. When $X$ and $Y$ have complementary dimension, we show that the intersections $X \cap [n]Y$ are zero-dimensional for all but finitely many integers $n$, and that these intersections collectively give rise to an analytically dense subset of $X$ as $n$ varies. We moreover control those $n$ for which $X \cap [n] Y$ has a positive dimensional component uniformly in $X, Y$ and $A$. When $\dim X + \dim Y < \dim A$, we show that $X \cap [n]Y = \varnothing$ for a set of integers $n$ of asymptotic density one, except in the presence of intersections at torsion points.

Fluid antenna systems (FAS) provide extra position agile spatial diversity for integrated sensing and communication (ISAC), by jointly optimizing the port selection and precoding. However, this optimization is challenging in air ground networks due to the intricate dual objective Pareto frontier, complex self-interference, and prohibitive channel state information overhead. To overcome these bottlenecks, this work proposes a novel grey box multi objective Bayesian optimization framework to address the joint design of discrete port selection and ISAC precoding. Unlike black box methods, this architecture explicitly leverages known physical system models to learn unknown channel constituents, dramatically reducing sample complexity. To navigate high dimensional combinatorial spaces, an adaptive trust region mechanism powered by expected hypervolume improvement (EHI) acquisition is implemented. Furthermore, the framework incorporates a spatio-temporal tracking strategy to handle the continuous mobility of users and targets, robustly capturing the drifting optimum in time varying environments. Simulations demonstrate that this framework achieves significantly faster convergence and discovers superior Pareto optimal configurations, validating its efficiency for dynamic real time FAS-ISAC deployments.

We have studied the antiferromagnetic Ising model on the icosahedral bcc lattice, as a model system of 1/1 approximant Tsai-type quasicrystals. We addressed thermal equilibrium properties of this system with Markov-chain Monte Carlo simulation supplemented with the parallel tempering technique to accelerate the relaxation dynamics. As a result, we found a second-order phase transition takes place to the magnetic ordered phase with ${\mathbb Z_3}\times {\mathbb Z_2}$ symmetry breaking. Despite the ordering, the low-temperature phase keeps macroscopic degeneracy as identified by finite residual entropy, $\mathcal{S}\sim0.1767/{\rm spin}$. Remarkably, the existence of residual entropy turns out to play a major role in the formation of magnetic order. Generation of domain wall is suppressed, as it reduces the residual entropy locally stored in icosahedra, beyond the gain of configurational entropy due to domain wall patterns. Magnetic order arises out of this competition as entropic crystallization, which manifest universal mechanism of strongly frustrated systems with large geometrical units.

We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of discrete spatial sampling patterns into an asymptotically unbiased spectral maximum-likelihood estimation method along with analytical uncertainty calculation. We illustrate the broad applicability of our modeling through synthetic and real data examples with sampling patterns that include irregularly bounded contiguous region(s) of interest, structured sweeps of instrumental measurements, and missing observations dispersed across the domain of a field, from which contiguous patches are generally favorable. We find through asymptotic studies that allocating samples following a growing-domain strategy rather than a densifying, infill scheme best reduces estimator bias and (co)variance, whether the field has been sampled regularly or not. As our modeling assumptions, too, shape how (well) an observed random field can be characterized, we study the effect of covariance parameters assumed a priori. We demonstrate the desirable behavior of the general Matern class and show how to interrogate goodness-of-fit criteria to detect departures from the null hypothesis of Gaussianity, stationarity, and isotropy.

Classical Distributed Model Predictive Control (DiMPC) requires multiple iterations to achieve convergence, leading to high computational and communication burdens. This work focuses on the improvement of an iteration-free distributed MPC methodology that minimizes computational effort and communication load. The aforementioned methodology leverages multiparametric programming to compute explicit control laws offline for each subsystem, enabling real-time control without iterative data exchanges between subsystems. Extending our previous work on iteration-free DiMPC, here we introduce a FAcet-based Critical region Exploration Technique for iteration-free DiMPC (FACET-DiMPC) that further reduces computational complexity by leveraging facet properties to do targeted critical region exploration. Simulation results demonstrate that the developed method achieves comparable control performance to centralized methods, while significantly reducing communication overhead and computation time. In particular, the proposed methodology offers substantial efficiency gains in terms of the average computation time reduction of 98% compared to classic iterative DiMPC methods and 42% compared to iteration-free DiMPC methods, making it well-suited for real-time control applications with tight latency and computation constraints.

Powerful approaches to squeeze the motional state of a harmonic oscillator rely on the stepwise modulation of its resonance frequency. Such protocols can be limited by forces that vary slowly between experimental runs but are constant during a single experimental shot. Such shot-to-shot noise gives rise to a spread in experimental outcomes that masks the uncertainty intrinsic to quantum theory. Taking inspiration from spin-echo protocols, we propose a decoupling technique that, under ideal conditions, perfectly cancels shot-to-shot force noise in squeezing experiments based on parametric modulation. We implement the protocol using an optically levitated nanoparticle, where shot-to-shot force noise arises from slowly varying stray fields acting on the charge carried by the particle. Using our oscillator-echo protocol, we demonstrate shot-to-shot noise suppression to the measurement-backaction limit.

This paper considers output reachability analysis for linear time-invariant systems with unknown state-space matrices and unknown observation map, given only noisy input-output measurements. The Cayley--Hamilton theorem is applied to eliminate the latent state algebraically, producing an autoregressive input-output model whose parameter uncertainty is enclosed in a matrix zonotope. Set-valued propagation of this model yields output reachable sets with deterministic containment guarantees under a bounded aggregated residual assumption. The conservatism inherent in the lifted matrix-zonotope product is then mitigated by a decoder-only Transformer trained on labels obtained through directional contraction of the formal envelope via an exterior non-reachability certificate. Split conformal prediction restores distribution-free coverage at both per-step and trajectory levels without access to the true reachable-set hull. The framework is validated on a five-dimensional system with multiple unknown observation matrices.

A relaxed baseline case, based on the SPARC Primary Reference Discharge (PRD) design point, is used to conduct a thorough investigation for the most unstable low-$n$ MHD instabilities for the first time. The simulations use the high-fidelity 3D extended-MHD code M3D-C1. The linear simulation, by scanning over the resistivity, identifies a dominant internal kink mode at the $q=1$ surface with a toroidal mode number $n=1$. Both the current and the pressure profiles are strongly affecting the kink instability in the baseline case. The linear growth rate is sensitive to the keV-level temperature profile and the on-axis $q_0$ around unity. A simplified 1D eigenvalue solver shows a good qualitative agreement for the observed pressure effects. In 3D nonlinear simulations, the marginally unstable case gives a moderate sawtooth crash soon after $q_0$ drops below unity, likely because of the lack of stabilizing effects in our simulations, such as heating and energetic particles. When both the current and the pressure drives exist (the baseline case), a strong sawtooth is observed, which features a magnetic reconnection event and a hollowed pressure profile. This can be explained by mixing both the Kadomtsev and Wesson models. The actual sawtooth crash may occur in SPARC before $q_0$ drops far below unity due to the sensitive changes of the instability around $q_0\sim 1$. The sawtooth-like oscillations shown in low-$β$ simulations also provides an opportunity to investigate periodic sawtoothing timescales in SPARC. This work forms a basis for understanding particle and heat transport under the influence of MHD instabilities, which can be essential for properly assessing the performance of the SPARC tokamak and future fusion pilot plants.

We show that dynamic coordination of distributed energy resources (DERs) can increase the capacity of low- and medium-voltage grids, improve reliability and power quality, and reduce solar curtailment. We develop three approaches to compute hosting capacity on a representative distribution grid with realistic scenarios. A deterministic iterative method provides insight into how dynamic operation and DER interactions enhance capacity and affect power flows, demonstrating clear gains over static methods even with low-to-moderate levels of storage and flexible demand. A stochastic programming approach jointly optimizes DER siting and sizing, showing that nodal colocation and complementary effects expand the feasible region of solar, heat pump, and battery penetrations by over 22X. This enables up to 200% solar, 100% battery, and 90% heat pump penetration. Batteries emerge as the most critical technology, followed by heat pumps and electric vehicles. A Monte Carlo-based extension shows that uncertainty significantly impacts hosting capacity and grid metrics, with 46% higher volatility under dynamic operation.

We present exact results for steady-state density correlation functions in conserved-mass transport processes with {\it anisotropic}, reflection-symmetric hopping on a $d-$dimensional hypercubic lattice. In addition to mass conservation, we consider center-of-mass (CoM) conservation, imposed either along a specific axis or along all axes. CoM-conserving dynamics is implemented through coordinated {\it multidirectional} hopping of two equal chunks of masses in {\it opposite} directions. While anisotropy and mass conservation are known to generate power-law density correlations $C({\bf x}) \sim 1/|{\bf x}|^d$ at large distance $|{\bf x}| \gg 1$ {\it [Phys. Rev. A {\bf 42}, 1954 (1990)]}, an additional CoM conservation can qualitatively alter the nature of the power law. Indeed, when CoM is conserved in {\it all} directions, the correlations decay faster $-$ typically as $C({\bf x}) \sim 1/|{\bf x}|^{(d+2)}$, regardless of the presence (or absence) of anisotropy. Consequently, the systems exhibit an extreme {\it hyperuniformity} (``class I''), where the long-wavelength density fluctuations, despite the slow power-law decay, are anomalously suppressed. When CoM is conserved along particular ({\it not} all) directions, the slower $1/|{\bf x}|^{d}$ power-law decay is recovered. The above behavior can be understood from an analogy between the correlation function and an electrostatic potential: While a (rank-$2$) quadrupolar charge distribution gives rise to the $1/|{\bf x}|^{d}$ power law, the $1/|{\bf x}|^{(d+2)}$ power law originates from a higher-order (rank-$4$) multipolar charge distribution. These findings reveal a rich interplay between anisotropy and CoM conservation in nonequilibrium steady states.

High-throughput solid-state nanopore experiments generate continuous MHz-rate data streams in which only a small fraction of data contains informative molecular information. This creates storage and processing bottlenecks that limit experimental scalability. We introduce Data Sieving, a GPU-accelerated acquisition framework that integrates real-time event detection directly into the measurement pipeline and selectively stores and allows real-time analysis of snapshots around molecular translocations. The system employs a lightweight rolling-average and min-max trigger to identify event candidates in parallel across channels. This architecture reduces stored data volume by up to 98% while preserving complete molecular signatures across a wide temporal range, from microsecond-scale protein dynamics to second-scale nucleic acid nanoparticle events. Continuous baseline monitoring enables autonomous closed-loop actuation; in high-concentration DNA experiments, automatic declogging restored pore conductance, reducing the time spent in a non-productive clogged state to near-zero and without interrupting parallel measurements. Validated across DNA, protein, and nucleic acid nanoparticle measurements, Data Sieving links data storage directly to molecular information content rather than experiment duration, enabling scalable, real-time operation of parallel nanopore sensors. The approach provides a hardware-agnostic foundation for long-duration, high-bandwidth single-molecule experiments and other event-driven sensing platforms. By using algorithms intrinsically compatible with low-latency digital architectures, this framework provides a clear path toward high-bandwidth, highly multiplexed recording across hundreds of individual nanopore channels in both solid-state and biological pores.