Ride-hailing platforms increasingly face uncertain driver acceptance, which makes traditional one-to-one 'exclusive dispatch (ED)' less efficient: rejections and timeouts force sequential retries and lengthen rider wait times, which in turn creates friction in the marketplace. 'Non-exclusive dispatch (NED)' mitigates this friction by broadcasting a request to multiple drivers in parallel. While NED can reduce latency, it introduces new design challenges -- most notably, how to choose notification sets and how to resolve driver contention (when multiple drivers accept the same ride). In this paper -- the second in a two-part collaboration with Lyft -- we develop a theoretically grounded framework to evaluate the long-run performance and marketplace effects of transitioning from ED to NED. We bridge theory and practice by combining (i) an optimization model that formulates NED as a constrained welfare maximization problem with (ii) large-scale discrete-event simulations on proprietary Lyft traces and (iii) a stylized macroscopic equilibrium model. Across simulation and equilibrium analysis, we find that NED improves key fulfillment metrics relative to ED: it reduces match time (and hence rider reneging) while increasing both the number and the average quality of completed matches. We also quantify the speed--quality trade-off between two common contention resolution rules, 'First-Accept' and 'Best-Accept': First-Accept maximizes speed and throughput, whereas Best-Accept is required to maximize per-match quality. Finally, we show that slightly conservative notification heuristics can improve long-run efficiency by avoiding excessive locking of high-value drivers and preserving future availability.

The evolution toward next-generation intelligent sensing requires microwave systems to move beyond static detection and achieve high-speed and adaptive perception of dynamic scenes. However, the existing microwave sensing systems have bottlenecks owing to their sequential digital processing chain, limiting the refresh rates to hundreds of hertz, while the existing integrated microwave processors are lack of programmable and scalable capabilities for robust and open-world deployment. To break the bottlenecks, here we report a programmable surface plasmonic neural network (P-SPNN) that enables real-time microwave sensing and automatic recognition of dynamic objects in open-world environment. With a perception latency of 25 ns and a refresh rate exceeding 10 kHz, the P-SPNN system operates more than two orders of magnitude faster than the conventional millimeter-wave sensors, while achieving an energy efficiency of 17 TOPS per W. With 288 programmable phase-modulated neurons, we demonstrate real time and robust classification of persons and cars with 91-97% accuracy in the open road scenarios. By further integrating beam-scanning function, P-SPNN enables multi-dimensional spatial temporal frequency sensing without the digital preprocessing. These results establish P-SPNN as a programmable, scalable, and low-power platform for high-speed perception tasks in realistic world, with broad implications for autonomous driving, intelligent sensing, and next-generation artificial intelligence hardware.

The chromosphere is a complex solar atmosphere that hosts a variety of transients and transports significant free energy to heat the corona. However, due to the limited sensitivity of polarization measurement and the influence of spectral line broadening, the basic magnetic field configuration in the chromosphere has not yet been fully revealed to correspond to the observed phenomena. In this work, we investigated the validity and application of the magnetic field inversion method for the H$_β$~4861~Å spectral line with non-local thermodynamic equilibrium approximations. We generated synthetic spectra by incorporating magnetic fields into semi-empirical FAL models for quiet Sun and sunspots, and then performed inversions to obtain the magnetic fields, which were then compared with the magnetic fields in the models. In addition, we evaluated the accuracy of the magnetic fields obtained using the weak field approximations and the impact of using the WFA results as the initial guess model for non-LTE inversion on the final results. Our work validates the effectiveness of the inversion method for the measurement of line-of-sight magnetic field components, which significantly improved the accuracy in both weak field (0 -- 500~G) and strong field ($>$2000~G) regions, while maintaining accuracy in the intermediate field range of 500 -- 2000~G. This demonstrates that the inversion techniques we employed are capable of resolving Zeeman-sensitive spectral lines in the chromosphere, which can be applied to the H$_β$ observational data from the new generation Solar Full-disk Multi-layer Magnetograph at GanYu Solar Station to provide full disk chromospheric magnetic field information.

In this work, we establish that Nesterov's accelerated gradient method, applied to $C^2$ functions satisfying the Polyak--Łojasiewicz inequality around local minimizers, achieves the optimal local linear convergence rate $ρ=\frac{\sqrt{3L+μ}-2\sqrtμ}{\sqrt{3L+μ}}+\varepsilon$, where $\varepsilon$ is an arbitrarily small constant. Our analysis requires neither higher-order smoothness beyond $C^2$ of the objective function nor any additional geometric regularity of the submanifold of local minimizers. The key novelty lies in a two-stage argument: we first establish a coarse yet valid local linear convergence rate and then, building upon this a priori convergence guarantee, obtain a refined characterization of the linearized iteration operator, which yields the optimal rate. As a result, we only need to slightly strengthen the standard $C^{1,1}$ assumption, which is commonly required in theoretical analyses of linear convergence for first-order methods, to $C^2$ smoothness. Moreover, the same analytical framework allows us to recover, under identical conditions, the optimal local exponential convergence rate $\sqrtμ$ for the continuous-time Heavy Ball dynamics. Finally, a representative numerical experiment corroborates our theoretical findings.

To comply with data protection regulations such as the EU General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA), websites widely deploy cookie consent banners to collect users' privacy preferences. In practice, however, these interfaces often embed dark patterns that undermine informed and freely given consent. As regulatory scrutiny increases, such patterns have not disappeared but have evolved into subtler and more legally ambiguous forms, making existing detection approaches outdated. We present UMBRA, a consent management platform (CMP)-agnostic system that detects both previously studied patterns (DP1-DP10) and nine newly evolved patterns (DP11-DP19) targeting information disclosure, consent revocation, and legal ambiguity, including pay-to-opt-out schemes, revocation barriers, and fake opt-outs. UMBRA combines text analysis, visual heuristics, interaction tracing, and cookie-state monitoring to capture multi-step consent flows missed by prior tools. We evaluate UMBRA on a manually annotated ground-truth dataset and achieve 99% detection accuracy. We further conduct a large-scale compliance-oriented measurement across 14,000 websites spanning the EU, the US, and top-ranked global domains. Our results show that evolved dark patterns are pervasive: revocation is often obstructed, cookies are set before consent or despite explicit rejection, and opt-out interfaces often fail to prevent third-party tracking. On sites with revocation barriers, cookies increase by 25% on average, and many use insecure attributes that increase exposure to attacks such as XSS and CSRF. Overall, our findings provide evidence of systematic non-compliance and show how evolving consent manipulation erodes user autonomy while amplifying privacy and security risks.

The widespread adoption of renewable energy poses a challenge in maintaining a feasible operating point in highly variable scenarios. This paper demonstrates that, within a feasible region of a power system that meets practical stability requirements, the power flow equations define a smooth bijection between nodal voltage phasors (angle and magnitude) and nodal active/reactive power injections. Based on this theoretical foundation, this paper proposes a data-based power flow evaluation method that can imply the associated power flow manifold from a limited number of data points around a single operating point. Using techniques from differential geometry and analytic functions, we represent geodesic curves in the associated power flow manifold as analytic functions at the initial point. Then, a special algebraic structure of the power flow problem is revealed and applied to reduce the computation of all higher-order partial derivatives to that of the first-order ones. Integrating these techniques yields the proposed data-based evaluation method, suggesting that a small number of local measurements around a single operating point is sufficient to imply the entire associated power flow manifold. Numerical cases with arbitrary directional variations are tested, certifying the efficacy of the proposed method.

Quantum spin liquids exhibit fractionalized spin excitations as a consequence of strong quantum many-body effects. The kagome antiferromagnetic Heisenberg model is a promising candidate for a quantum spin-liquid ground state; however, the nature of its excitation spectrum remains controversial, particularly regarding the presence of a spin gap and the gauge structure coupled to fractional quasiparticles. To address these issues, parton approaches have been extensively employed, where spin operators are represented in terms of fermionic or bosonic quasiparticles within the Abrikosov fermion and Schwinger boson frameworks. Thus far, these approaches have been pursued independently, and it has remained unclear how the results obtained from these frameworks compare, particularly with respect to the spin dynamics and gauge structure of the kagome antiferromagnet. Here, we investigate the dynamical spin structure factor of the antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on the kagome lattice, relevant to herbertsmithite, by employing both approaches. We find that the dynamical spin structure factor obtained from the Abrikosov fermion mean-field theory exhibits dome-shaped features, and that its continuum structure significantly depends on the gauge structure of the spin-liquid ansatz. On the other hand, the Schwinger boson mean-field theory yields a concave-down structure in the low-energy region, distinct from that obtained using the Abrikosov fermion approach. Moreover, incorporating many-body effects beyond the mean-field approximation substantially reduces the low-energy gap and enhances the low-energy spectral weight, consistent with experimental observations. Our results suggest the importance of many-body effects in the Schwinger boson theory for capturing the low-energy spin dynamics of kagome antiferromagnets.

This work addresses the reconstruction of a scatterer's shape from phaseless far field-intensity data arising from multiple incident waves interacting with the scatterer. We formulate the reconstruction as a statistical inverse scattering problem and adopt a Bayesian inference framework, which can readily be used to compute statistical moments for quantification of uncertainties in the shape reconstruction that arise from noise in the data due to measurement constraints. The shape of the scatterer is represented by a spline-based prior, with Bayesian parameters defined at the spline's knots. To efficiently evaluate the Bayesian likelihood across thousands of sampling points, we develop the intensity property inspired neural network (IPINN) surrogate. This surrogate incorporates the Helmholtz equation in the unbounded domain, exterior to each sampled scatterer, along with the radiation condition at infinity, enabling fast and accurate simulation of the acoustic far-field intensity. Importantly, the IPINN surrogate is trained independently of the observed data and requires only a single incident wave for training. We demonstrate that this surrogate approach yields a speed-up of several orders of magnitude. The resulting IPINN-Bayesian framework offers an efficient solution for shape reconstruction in unbounded domains with multiple incident wave boundary conditions, while exactly enforcing the radiation condition. Numerical experiments confirm the efficiency and effectiveness of the proposed algorithm.

Current studies on activity space are limited by the conceptualization of absolute physical space that fails to consider the heterogeneity of relational spaces reconstructed from spatial interactions of human movements between locations and falls short in incorporating the inherent hierarchical property of human mobility. Consequently, these approaches cannot faithfully reflect how people interact with urban spaces through travels. From the lens of relational space, this study proposes the new Hierarchical Activity Region Model (HARM) to derive the space and hierarchical properties of activity spaces perceived by various urban groups. We demonstrate the enhanced validity of our model on travel behavior in Manhattan, New York City, before, during, and after Hurricane Sandy on the basis of taxi data. Empirical results show that intra-urban travel retains clear hierarchical organization, even under disruption of a major weather event. Yet, travel undergoes a compression effect in travel hierarchies, characterized by fewer hierarchical levels and enlarged characteristic scales, followed by a rebound. Clustering the derived hierarchies reveals pronounced heterogeneity that stems from differences in population profiles; some groups sustain deeper structures or recover quickly, while others experience a persistent loss of levels. This study provides valuable insights into the functional hierarchies of urban mobility, which could inform more sustainable, resilient and equitable urban planning. The proposed methodological framework is generic for studying human mobility in broader contexts.

We generalize to $\mathrm{GL}(3,\mathbb{Q})$ the Poisson Summation method developed by Altuğ for $\mathrm{GL}(2, \mathbb{Q})$ for the strategy of Beyond Endoscopy. Concretely, assuming Conjecture A, we isolate the contribution of the trivial representation from the regular elliptic part of the trace formula and obtain a concrete expansion of \[ \mathrm{I}_{\mathrm{ell}}(f)-\mathrm{Tr}(\mathbf{1}(f)). \] Our starting point is a reformulation of the regular elliptic part in terms of cubic orders attached to characteristic polynomials. To these orders we associate a zeta function, defined through their overorders, prove a functional equation for its completion, and apply an approximate functional equation to rewrite the elliptic term in a form suitable for Poisson Summation. A key arithmetic input is a periodicity theorem showing that the relevant coefficients depend only on the parameters modulo a finite modulus. This makes it possible to perform Poisson Summation on the integral parameters indexed by the cubic data. The resulting main terms are governed by Kloosterman-type sums and an associated double Dirichlet series, which we evaluate explicitly. From this evaluation we are able to apply the residue theorem and find the trace of the trivial representation as a residue. We also recover the contribution of the \say{special} representation.

Most AI agents remain confined to an instrumental "command-execution" model, resulting in unequal, one-sided interactions. While recent works attempt to build relationships through hidden memory backends, these invisible processes often fail to break the instrumental bias. In this paper, we argue that true relational equality requires agents to have an independent, observable existence. We introduce the \textit{Observable Life Spaces} paradigm, where agents inhabit a continuous virtual environment, engage in daily activities, and form social relationships that users can directly observe. Through a mixed-methods study ($N=24$), we demonstrate that only when agents are endowed with a socialized life space that is visually observable to humans can the perceived equality during interaction be significantly enhanced ($p = 0.015$). Our findings suggest that visually representing an agent's social life space can effectively shift the human-agent dynamic from a purely instrumental relationship to one characterized by perceived equality.

Accurate prediction of protein-ligand binding affinity remains a central challenge in structure-based drug discovery. The effectiveness of machine learning models critically depends on the quality of molecular descriptors, for which advanced mathematical frameworks provide powerful tools. In this work, we employ a novel mathematical theory, termed the persistent local Laplacian (PLL), to construct molecular descriptors that capture localized geometric and topological features of biomolecular structures. The PLL framework addresses key limitations of traditional topological data analysis methods, such as persistent homology and the persistent Laplacian, which are often insensitive to local structural variations, while maintaining high computational efficiency. The resulting molecular descriptors are integrated with advanced machine learning algorithms to develop accurate predictive models for protein-ligand binding affinity. The proposed models are systematically evaluated on three well-established benchmark datasets, demonstrating consistently strong and competitive predictive performance. Computational results show that the PLL-based models outperform existing approaches, highlighting their potential as a powerful tool for drug discovery, protein engineering, and broader applications in science and engineering.

Public perceptions and expectations of inflation shape household spending, wage bargaining, and policy support, making them key determinants of macroeconomic outcomes. However, current measures rely on infrequent surveys and offer limited insight into underlying narratives and sector-specific concerns. This paper presents a novel approach to measuring public perception of inflation, using lightweight large language models (LLMs) fine-tuned on domain-specific Reddit data. We created an inflation classifier trained on posts related to components of the U.S. Consumer Price Index (CPI). When applied to more than 10 years of Reddit discussions (2012-2022), this classifier produces monthly Reddit inflation scores (RIS), which we validated against actual economic indicators. Our results show that fine-tuned lightweight LLMs perform well even with smaller training datasets, and the Reddit inflation scores strongly correlate with CPI (r=0.91) and closely align with the University of Michigan: Inflation Expectation (MICH). Importantly, Granger causality tests suggested that social media-based inflation scores often precede movements in both CPI and MICH, indicating their potential as predictive, forward-looking economic signals. Furthermore, change-point and lexical analyses uncovered shifts in inflation-related narratives across sectors like groceries, transportation, and housing, revealing dimensions of inflation concern that are not directly observable in aggregate price indices. By complementing traditional economic indicators with narrative-rich signals, this study demonstrates how NLP-based measures can facilitate earlier detection of inflationary pressures and policy responses.

Quantum error correcting codes (QECC) are essential for constructing large-scale quantum computers that deliver faithful results. As strong competitors to the conventional surface code, quantum low-density parity-check (qLDPC) codes are emerging rapidly: they offer high encoding rates while maintaining reasonable physical-qubit connectivity requirements. Despite the existence of numerous code constructions, a notable gap persists between these designs -- some of which remain purely theoretical -- and their circuit-level deployment. In this work, we propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. ASC leverages the sparsity of parity-check matrices and exploits the commutativity of X and Z stabilizer measurement subroutines to search for optimal compilation schemes. By iteratively invoking an SMT solver, ASC returns a depth-optimal solution if a satisfying assignment is found, and a near-optimal solution in cases of solver timeouts. Notably, ASC provides the first definitive answer to one of IBM's open problems: for all instances of bivariate bicycle (BB) code reported in their work, our compiler certifies that no depth-6 syndrome extraction circuit exists. Furthermore, by integrating ASC with an end-to-end evaluation framework -- one that assesses different compilation settings under a circuit-level noise model -- ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes, compared with as-soon-as-possible (ASAP) and coloration-based scheduling. ASC thus substantially reduces manual design overhead and demonstrates its strong potential to serve as a key component in accelerating hardware deployment of qLDPC codes.

Against the backdrop of the global drive to advance the green transformation of the information and communications technology (ICT) industry and leverage technological innovation to facilitate the achievement of Net-Zero carbon goals, research into Rydberg atomic receivers (RAREs) is gaining significant interest. RAREs leverage the electron transition phenomenon for signal reception, offering significant advantages over conventional radio frequency receivers in terms of miniaturized antenna design, high sensitivity, robust interference resistance, and compact form factors, which positions them as a competitive alternative for meeting zero-carbon communication demands. This article systematically elaborates on the basic principle, state-of-the-art progress, and novel experiments of RAREs in quantum wireless communication and sensing. In this first-of-its-kind work, we experimentally verify the RARE-based orthogonal frequency division multiplexing transmission and reveal the potential of deep learning design in optimizing quantum wireless systems. Finally, we delve into the prospect of integrating RARE with existing cutting-edge application scenarios, while mapping out critical pathways for developing Rydberg-based wireless systems.

The rapid evolution of next-generation communications and the Internet of Things (IoT) has catalyzed an urgent demand for governing expansive spatial environments as functional electromagnetic (EM) entities. However, deterministically programming such open EM spaces remains a formidable challenge, as current methodologies are largely confined to localized interfaces that lack the collective coordination required to orchestrate unbounded environments. Here, we introduce a general framework for the deterministic programming of EM space via cooperative metasurface clusters, achieved by mapping volumetric field interference landscapes onto a virtual nodal network. By representing excitations and meta-atoms as fully interconnected nodes, we transform intricate non-local interactions into tractable nodal states, enabling the precise quantitative synthesis of spatial scattering. This framework bridges local meta-atoms with global EM environment to program space as a functional entity, as demonstrated by a deeply coupled meta-emitter for programmable collective radiation and metasurface clusters that sculpt angle-resolved illusion spaces. By transitioning from individual components to cooperative multi-body assemblies, our work provides a scalable foundation for next-generation wireless networks, wave-based analog computing, and ambient intelligence, where space itself becomes a coherent functional and reconfigurable entity capable of holistic information management.

We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to prove that $ζ(σ+ it)\ne 0$ whenever $t\geq 3$ and $σ\geq 1- 1/(4.896\log t)$.

Topological concepts have been at the forefront of materials research in recent years, driving a revolution in our understanding of the response of quantum materials and enabling new ways to manipulate light and sound in topological metamaterials. Topological defects and topological boundaries of different dimensions have driven a paradigm shift in photonics, where topological photonic crystals and metamaterials can be engineered to create one-way flow of energy robust to defects or to control such flows with synthetic degrees of freedom along topological domain walls. More recently, topological point singularities encoded into photonic structures have been shown to enable confinement of optical modes with the topologically nontrivial nature of the cavity imprinted into the vorticity of optical far fields. Here we demonstrate that the two latter concepts - domain wall and point singularities - can be unified into an even more powerful tool to enable arbitrarily shaped resonant cavities of any dimension supporting spectrally stable zero-energy modes. We experimentally confirm that such modes, whose existence is guaranteed by topological principles, allow an unprecedented degree of control over the optical field, which appears to have no phase modulation across space, can have any desirable radiation pattern, and enables spectral stability regardless of shape or length.

We investigate CP-violation in the complex singlet extension of the general Two Higgs Doublet Model (2HDM) with Yukawa alignment condition. We first explore the possibility of explicit CP-violation in the extended scalar sector while the 125 GeV Higgs remains exactly Standard Model (SM)-like. We identify an additional source of CP violation in the complex singlet extension compared to the 2HDM, which allows this model a substantially greater freedom in satisfying the stringent EDM constraints. We also incorporate dark matter in this model and investigate the impacts of constraints from the dark sector on the model parameter space and its interplay with CP-violation phases. We further explore the possibility of detecting such a scenario at future collider experiments via CP-violating trilinear couplings among the non-standard scalars. Finally, we also deviate from the exact alignment limit and investigate the CP-properties of the observed Higgs boson in the context of our model. We demonstrate the strong model-dependent nature of the detection prospects of the CP-phase of the Higgs boson at future experiments, exploring both fermion couplings as well as the trilinear self-coupling of the Higgs boson.

Large Language Models (LLMs) have shown promising potential in E-commerce community recommendation. While LLMs and Multimodal LLMs (MLLMs) are widely used to encode notes into implicit embeddings, leveraging their generative capabilities to represent notes with interpretable tags remains unexplored. In the field of tag generation, traditional close-ended methods heavily rely on the design of tag pools, while existing open-ended methods applied directly to note recommendations face two limitations: (1) MLLMs lack guidance during generation, resulting in redundant tags that fail to capture user interests; (2) The generated tags are often coarse and lack fine-grained representation of notes, interfering with downstream recommendations. To address these limitations, we propose TagLLM, a fine-grained tag generation method for note recommendation. TagLLM captures user interests across note categories through a User Interest Handbook and constructs fine-grained tag data using multimodal CoT Extraction. A Tag Knowledge Distillation method is developed to equip small models with competitive generation capabilities, enhancing inference efficiency. In online A/B test, TagLLM increases average view duration per user by 0.31%, average interactions per user by 0.96%, and page view click-through rate in cold-start scenario by 32.37%, demonstrating its effectiveness.

The Schur $P$-, $Q$-multiple zeta functions were defined by Nakasuji and Takeda inspired by the tableau representation of Schur $P$-, $Q$-functions. While a product of two Schur $P$-functions expands as a linear combination of Schur $P$-functions, we obtain a similar expansion formula for the Schur $P$-multiple zeta functions by taking summation over the symmetric group permutating all the variables. We also introduce a expansion formula of skew Schur $Q$-multiple zeta functions by taking summation over the symmetric group. Furthermore, this skew type formula can be refined by restricting the symmetric group to its specific subgroup.

We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and Halperin. This theory is expected to describe dynamic scaling near the lambda transition in liquid $^4$He, Bose-Einstein condensation in ultracold atomic gases, and the superfluid transition in the unitary Fermi gas. Our simulation is based on a Metropolis algorithm previously applied to the critical endpoint of the liquid-gas phase transition in ordinary fluids. In the model E truncation of model F we obtain the expected dynamical exponent $z\simeq 3/2$. We observe the emergence of a propagating second sound mode at the phase transition. The second sound diffusivity $D_s$ is consistent with the scaling relation $D_s\sim ξ^{x_κ}$, where $ξ$ is the correlation length and $x_κ=1/2$.

We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a factorization of the far-field operator for the supported plate boundary conditions, and we analyze its range properties to justify both the linear sampling method (LSM) and the direct sampling method (DSM). Numerical experiments assess the performance of LSM and DSM under noise, a limited amount of data, multiple scattering, and variations in the Poisson's ratio. The results show that both methods robustly recover the obstacle's location and convex hull, with DSM offering improved stability and reduced computational cost.

Real-world potential of stop-and-go wave smoothing at scale remains largely unquantified. Smoothing freeway traffic waves requires creating a gap so the wave can dissipate, but the gap suggested is often too large and impractical. We propose a counterfactual wave smoothing benchmark that reconstructs a smooth and feasible trajectory from each empirical trajectory by solving a quadratic program with fixed boundary conditions and a maximum allowable gap constraint. We estimate the emission reduction potential from trajectories using the MOVES model. Applying the framework to nine weeks of weekday peak traffic data, featuring rich day-to-day stop-and-go wave dynamics, from the I-24 MOTION testbed, we find meaningful reduction potential under a 0.1-mile maximum gap: average CO2 reductions of 7.92% to 12.04% across lanes, with concurrent reductions of 14.30% to 28.91% CO, 23.15% to 29.42% HC, and 24.37% to 30.98% NOx. Our analysis also quantifies the trade-off between maximum allowable gap opening and emissions benefits.

It is shown that Schrödinger maximal inequalities over fractals are equivalent to the $L^2$ decay rates of Fourier transforms of fractal measures over the paraboloid. A similar connection is shown between the wave equation and cone averages. One implication is well-known and follows from the Kolmogorov-Seliverstov-Plessner method, but the other implication is nontrivial and relies on a variant of the Marstrand projection theorem. The idea of the proof is to insert an extra averaging parameter into a proof of Lucà and Rogers, which used a quantitative ergodic lemma instead of the Marstrand projection theorem. Lucà and Rogers gave a second proof of Bourgain's necessary condition $s\geq \frac{n}{2(n+1)}$ for Schrödinger solutions in $\mathbb{R}^{n+1}$ to converge pointwise a.e. back to the initial data as time tends to zero. One application of the main theorem in this article is a proof of Bourgain's necessary condition which does not use ergodic theory or number theory.

We define and study an integral refinement of the inverse of the Bloch-Kato exponential map which we call the de Rham logarithm. Our main tool to analyze the de Rham logarithm is the syntomic logarithm, a certain limit construction based on the theory of filtered prismatic cohomology initiated by Antieau, Krause and Nikolaus. We use the syntomic logarithm to prove a version of the Beilinson fibre square for all quasicompact, quasiseparated derived formal schemes. We also use our techniques to prove Conjecture $C_{EP}(\bq_p(n))$ of Fontaine and Perrin-Riou for all local fields $K/\bq_p$ and to compute the correction factor $C(X,n)$ introduced by Flach and Morin in their reformulation of the Bloch-Kato Tamagawa number conjecture for the Zeta function of a smooth projective scheme $X$ over a number ring.

Although beneficial information abounds on social media, the dissemination of harmful information such as so-called ``fake news'' has become a serious issue. Therefore, many researchers have devoted considerable effort to limiting the diffusion of harmful information. A promising approach to limiting diffusion of such information is link deletion methods in social networks. Link deletion methods have been shown to be effective in reducing the size of information diffusion cascades generated by synthetic models on a given social network. In this study, we evaluate the effectiveness of link deletion methods by using actual logs of retweet cascades, rather than by using synthetic diffusion models. Our results show that even after deleting 10\%--50\% of links from a social network, the size of cascades after link deletion is estimated to be only 50\% the original size under the optimistic estimation, which suggests that the effectiveness of the link deletion strategy for suppressing information diffusion is limited. Moreover, our results also show that there is a considerable number of cascades with many seed users, which renders link deletion methods inefficient.

In this work, we identify a set of side-channels in our Confidential Federated Compute platform that a hypothetical insider could exploit to circumvent differential privacy (DP) guarantees. We show how DP can mitigate two of the side-channels, one of which has been implemented in our open-source library.

We investigate two distinct formulations of Laurent multiple orthogonal polynomials on the unit circle, introduced in arXiv:2410.12094 and arXiv:2601.04783 respectively. For the first formulation, we prove that all zeros lie strictly within the complex open unit disk for any Angelesco or AT system. For the second formulation, we establish normality of all indices of the form $(\bm{n};\bm{n})$, $(\bm{n}+\bm{e}_j;\bm{n})$, and $(\bm{n};\bm{n}+\bm{e}_j)$ for any Angelesco or AT system, thereby enabling the full application of the Szegő mapping and Geronimus relations from arXiv:2601.04783 in the multiple orthogonality setting.

We report diffuse extended radio-continuum emission spatially coinciding with the IR source WISEA J094409.17-751012.8, and a semi-variable star, V687 Carinae. We use 944 MHz radio data from the large-scale Evolutionary Map of the Universe (EMU) survey to analyse this diffuse emission (EMU J094412-751016), which we nickname "Anglerfish". We investigate if the spatially correlated infrared (IR) source, WISEA J094409.17-751012.8, is physically related to Anglerfish. The IR colours of WISEA J094409.17-751012.8 are indicative of an elliptical galaxy, raising the possibility that Anglerfish may belong to the newly-discovered class of extragalactic radio sources known as Odd Radio Circles (ORCs) with WISEA J094409.17-751012.8 as the host galaxy. We also investigate the possibility that Anglerfish is physically related to the star, V687 Carinae, and whether it may be a remnant from a previous epoch of stellar mass-loss. We determine that a physical association between the radio emission and the star is unlikely due to the emission's non-thermal nature and the star's weak stellar winds compared to the theoretical expansion velocity of the 'shell'. It is possible that Anglerfish may be a Galactic high-latitude supernova remnant (SNR); however, we find that the observed size and luminosity are not consistent with this scenario. We also investigate the ORC scenario, which we deem the most likely scenario based on the Anglerfish's observed properties such as size, brightness, lack of other frequency detections, and spectral index. We therefore propose Anglerfish as an ORC candidate, but note that additional radio and optical observations are vital to further constrain the properties and confirm this classification.