We give examples of K3 surfaces over $\mathbb{Q}$ of degree $10$ whose geometric Picard group has rank~$1$. These K3 surfaces are intersections in $\mathbb{P}^9$ of three hyperplanes, one quadric and the image of the Plücker embedding of the Grasmannian $\mathrm{Gr}(2,5)$. We also give an example of a K3 surface of degree $6$ over~$\mathbb{Q}$ whose Picard rank is $1$.

We provide simple ``left-inverse characterizations'' of the recently introduced singularity invariants $c(Z)$, $w(Z)$, and ${\rm HRH}(Z)$ of an equidimensional variety $Z$. Combining this with a trace morphism, we establish descent results of these invariants for finite surjective morphisms.

We investigate how the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian can emerge from a microscopic fermionic model based on half-filled Hubbard tripods. We first show that a single tripod hosts a robust threefold-degenerate low-energy manifold corresponding to an effective $S = 1$ degree of freedom. This manifold prevails over a broad range of interactions and remains stable against moderate disorder. We then combine exact diagonalization with fourth-order quasi-degenerate perturbation theory to derive an effective bilinear-biquadratic spin model for a pair of coupled tripods and identify coupling regimes where the target ratio is approached. In particular, tuning leg-center hopping together with two symmetry-inequivalent leg-leg hoppings yields the characteristic singlet-triplet degeneracy associated with a biquadratic-to-bilinear ratio close to 1/3. Extending the analysis to three tripods, we compare nonequivalent coupling geometries and find a strategy that suppresses unwanted longer-range and multispin terms while preserving the target nearest-neighbor couplings in the weak-coupling regime. These results establish a concrete bottom-up route from Hubbard clusters to valence-bond-solid spin physics in tunable quantum-dot arrays.

A random variable $ξ$ has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (λξ) <\infty$ for some $λ>0$, and has a {\it heavy-tailed} distribution (is heavy-tailed) if $\E \exp (λξ) = \infty$, for all $λ>0$. In \cite{LSK1}, the authors presented a particular example of a light-tailed random variable that is the minimum of two independent heavy-tailed random variables. In \cite{FKT}, it was shown that any light-tailed random variable with right-unbounded support may be represented as the minimum of two independent heavy-tailed random variables, with further generalisations of the result in a number of directions. We analyse an ``inverse'' question. Namely, we obtain necessary and sufficient conditions on the distribution of a heavy-tailed random variable, say $ξ_1$, that allow to find another independent heavy-tailed random variable, say $ξ_2$, such that their minimum $\min (ξ_1,ξ_2)$ is light-tailed. We also provide a number of extensions of this result

In this manuscript, we establish local Schauder estimates for flat viscosity solutions, that is, solutions with sufficiently small norms, to a class of fully nonlinear elliptic partial differential equations of the form \[ F(D^{2} u, x) + \langle \mathfrak{B}(x), D u \rangle = f(x) \quad \text{in} \quad \mathrm{B}_1 \subset \mathbb{R}^{n}, \] where the operator \(F\) is differentiable, though not necessarily convex or concave. In addition, we impose suitable Dini-type continuity assumptions on the data. Our methodology is based on geometric tangential techniques, combined with compactness and perturbative arguments. This approach is strongly motivated by recent advances in the theory of nonlinear elliptic equations and free boundary problems. As a byproduct of our analysis, we also obtain an Evans-Krylov type estimate. Our results can be viewed as an extension of the work by dos Prazeres and Teixeira (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 485-500), now within the framework of linear drift terms and Dini continuity assumptions. Finally, we apply our results to characterize the nodal sets of flat viscosity solutions of non-convex, fully nonlinear, uniformly elliptic PDEs.

It is known that a point in three-dimensional Euclidean space whose coordinates are equal to the cosines of the angles $\angle BDC, \angle ADC, \angle ADB$, where the point $D$ lies in the plane of a given triangle $ABC$, lies on the surface $\mathbb{BP}\subset [-1,1]^3$, given by the equation $1+2x_1x_2x_3-x_1^2-x_2^2-x_3^2 = 0$. It should be emphasized that the set of corresponding points essentially depends on the shape of triangle $ABC$. In this paper, we solve the following problem: For a fixed triangle $ABC$, for each point $U \in \mathbb{BP}$, determine the number of points $D$ from the plane of the triangle with the condition $U=(\cos \angle BDC, \cos \angle ADC, \cos \angle ADB)$. The problem of determining such points $D$ is known as the Snellius-Pothenot problem.

The optical response of two-dimensional materials is often significantly impacted by excitonic effects due to the reduced screening of attractive Coulomb interactions in low-dimensional systems. Accurate modeling of exciton formation and real-time dynamics is essential to understanding their ultrafast optical properties. In this study, we theoretically investigate the exciton dynamics in a two-dimensional hexagonal boron nitride (h-BN) and a germanium sulfide (GeS) monolayers exposed to an ultrashort laser pulse. We analyze the system's response to the external field in one- and two-photon excitation regimes. For our calculations, we combine a state-of-the-art ab initio approach to study exciton dynamics with a highly precise numerical scheme. We incorporate electron-hole interactions through a non-local self-energy operator derived from the many-body perturbation theory (MBPT) within the time-dependent adiabatic $GW$ (TD-a$GW$) approximation. We implement this approach using the full-electron LAPW+lo method in the all-electron exciting package. Our results elucidate the role of many-body effects in shaping ultrafast excitonic processes in two-dimensional materials, contributing to the fundamental understanding necessary for optoelectronic and photonic applications.

Given an o-minimal structure, we show that every definable (in this structure) mapping that is Lipschitz with respect to the inner metric can be approximated by $\mathscr{C}^1$ mappings that are Lipschitz with respect to the inner metric with arbitrarily close bounds for the derivative. When the o-minimal structure admits $\mathscr{C}^\infty$ cell decomposition, we show that the approximation can be required to be $\mathscr{C}^\infty$ and we extend this result to outer Lipschitz mappings. The proof involves the construction of partitions of unity with sharp bounds for the derivative, which can be useful for other approximation problems.

For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algorithm is tight. For unconstrained case, we can enlarge the upper bound to $\frac{1}{\sqrt{3}L}$ and show that this upper bound is also tight. The convergence analysis is carried out by using a new Lyapunov-type function.

We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum of the target cosmology is written as a rescaled reference spectrum plus a small difference, and the trispectrum is expanded perturbatively in this difference. For the external momentum configuration considered here, truncating the expansion at third order reproduces the full numerical result with sub-percent accuracy over the range of scales studied, while higher-order terms are strongly suppressed. This reorganization reduces the number of cosmology-independent building blocks that must be computed compared with direct basis decompositions of the linear power spectrum. This provides a practical route to faster evaluations of higher-loop and higher-multiplicity correlators in the Effective Field Theory of Large-Scale Structure.

Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. The wave itself is a weighted sum of the polynomial terms multiplied by the periodic functions. The integer weights are found to be a sum of partitions into a smaller set of integers implying the recursive structure of integer partitions.

Housing instability is a persistent challenge faced by households in cities across the United States. In worst-case scenarios, households are displaced from their residences and forced to start anew. In an effort to mitigate the harms of residential displacement, local policymakers have an interest in monitoring residential displacement within their communities. In this work, we propose a new strategy to estimate sub-county residential displacement within the Central Puget Sound Region using data from three household survey programs. We first estimate residential displacement between 2016-2023 from a local household travel survey using a Bayesian spatiotemporal model, and poststratify with data from the American Community Survey. We then benchmark these estimates to the American Housing Survey to ensure consistency across sources. The results reveal east-west and north-south differences in residential displacement rates within the region as well as a temporary moderation of displacement in the 2020-2021 cohort of movers. Our estimates are publicly available for interested stakeholders to further study trends in residential displacement in the Central Puget Sound Region, and our methodology is transportable to other jurisdictions with similar data contexts.

Strategic diagrams and co-word analysis are widely employed to examine the conceptual structure of scientific domains and their development over time. Yet a structural inconsistency characterises dominant longitudinal implementations: themes are detected through relational clustering in weighted networks, whereas their inter-temporal connections are commonly inferred from set-theoretic overlap among keywords or core documents. This study introduces a structurally integrated framework in which lineage reconstruction is embedded within the same weighted relational architecture that underpins cross-sectional detection. The approach models thematic continuity through graded document affiliation and a lineage-strength measure that combines directional coverage with centrality-weighted structural relevance, thereby conceptualising evolution as the reconfiguration of relational structures rather than simple lexical persistence. By aligning thematic detection and temporal modelling within a unified relational paradigm, the framework enhances the methodological coherence and interpretive robustness of longitudinal science mapping.

Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not yet fully understood, with profound consequences for phenomena ranging from landscape evolution to cellular unjamming during tumor metastasis. With this paper, we introduce tools from linear control theory that quantify system response to external input, and demonstrate their utility in elucidating the dynamics of jammed amorphous materials under stress. Our results indicate that average controllability, the response of a system to perturbation, strongly correlates with particle rearrangement in systems subject to quasistatic shear, implying that average controllability is an accurate predictor of rearrangement dynamics in certain contexts. Moreover, we show that the time scale over which average controllability is calculated can be tuned to optimize its predictive capacity for particle rearrangement. Values of the optimal time scale provide physical insight into the system; namely, that multiple rearranging particles participate on average in vibrational eigenmodes of lower and lower energy as the system is sheared until the rearrangement event. Broadly, our study demonstrates that linear control theory is a promising mathematical framework for predicting and designing mechanical response in disordered media.

Solar Energetic Particles (SEPs) are a signature of solar eruptions, and to link them to acceleration mechanisms many studies investigate their injection time at the Sun, $t_{sun}$. We assess velocity dispersion analysis (VDA), an often-used method to derive $t_{sun}$. We use full-orbit simulations of 1--100 MeV SEP protons in a novel model of the interplanetary magnetic turbulence superposed on a Parker Spiral magnetic field. The turbulence is described analytically as dominant transverse fluctuations that are 2D with respect to the mean field, supplemented with a minor contribution of asymptotically slab turbulence modes. We determine simulated SEP intensities for three turbulence strengths and use VDA to obtain $t_{sun}$ and the apparent path length $s$ of the SEPs, employing an SEP onset threshold to mimic a realistic energetic proton background before the SEP event. We find that turbulence strongly affects $t_{sun}$ and $s$. For weak and moderate turbulence, VDA estimates of $t_{sun}$ are 2-16 minutes after the actual solar injection time, and the path lengths are 0.2-0.3 au longer than the Parker spiral. For strong turbulence, the path lengths are $>5$ au, considerably longer than those typically obtained from SEP observations. We also investigate the effect of energy-dependence of the pre-event proton background, and find that different background spectra result in 5-20-minute difference in VDA injection times, depending on the heliolongitude. We conclude that in many cases VDA-derived injection times include a significant contribution from turbulence and/or the pre-event background and are not an accurate estimate of the acceleration time.

Let $f(x)=x^{2p}+ax^p+b^p$, where $p$ is a prime and $a,b\in {\mathbb Z}$ with $ab\ne 0$. If $f(x)$ is irreducible over ${\mathbb Q}$, we say that $f(x)$ is monogenic if $\{1,θ,θ^2,\ldots ,θ^{2p-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. In this article, we give a characterization of the monogenic trinomials $f(x)$ according to their Galois groups. These results extend prior investigations of the authors.

We confirm Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.

In optimal control, extending the class of admissible controls is a common strategy to guarantee the existence of optimal solutions. However, such extensions may introduce a gap between the infimum of the original problem and the minimum of the extended one, especially in the presence of endpoint constraints. Since Warga's seminal work, normality of first-order necessary conditions for extended minimizers has been recognized as a sufficient condition to avoid this phenomenon, though it is far from being necessary. In this paper, we consider impulsive extensions of control-affine systems with unbounded controls. We establish that a notion of \textit{higher-order normality}, based on iterated Lie brackets of the systems vector fields, suffices to prevent an infimum gap. The key novelty of this manuscript consists in showing that this holds under a local topology defined by the $L^1$-distance between controls, rather than the more common $L^\infty$-distance between trajectories. Among the reasons that motivate the interest in this issue, let us mention that a counterexample by R. B. Vinter shows that for a different extension -- based on convexification of the velocity set -- a local extended minimizer that is normal with respect to the $L^1$-norm of the controls may still exhibit a gap. Our method relies on set-separation techniques. Such an approach makes it possible to derive higher-order conditions and to exploit the corresponding notion of higher-order normality.

Recent predictions of orders of magnitude larger orbital current effects compared to spin currents have attracted significant interest. However, the full potential of giant orbital currents remains to be fully harnessed, since so far, the orbital currents need to be converted into spin currents before they can interact with the static magnetization that is dominated by spin angular momentum in conventional magnets. By using a magnet dominated by orbital angular momentum, we demonstrate a more than fifty-fold enhancement in orbital Hall magnetoresistance in CoO/Cu*, compared to conventional CoO/Pt. This is found to be driven by a unique interaction between dynamic orbital angular momentum from surface oxidized Cu* (i.e., the orbital current) and the static orbital angular momentum which constitutes the magnetic moments in the antiferromagnetic insulator CoO. A distinctive scattering mechanism for orbital currents at the CoO interface leads to a sign reversal in orbital magnetoresistance in CoO/Cu* compared to CoO/Pt. Our results show how by using orbital angular momentum-dominated materials such as CoO, we can harness the benefits of giant orbital currents that have not been possible using conventional spin-dominated magnets, for orbitronics-based devices, offering unprecedented energy efficiency for operations of antiferromagnets that combine ultimate stability with THz dynamics.

Security incident analysis (SIA) poses a major challenge for security operations centers, which must manage overwhelming alert volumes, large and diverse data sources, complex toolchains, and limited analyst expertise. These difficulties intensify because incidents evolve dynamically and require multi-step, multifaceted reasoning. Although organizations are eager to adopt Large Language Models (LLMs) to support SIA, the absence of rigorous benchmarking creates significant risks for assessing their effectiveness and guiding design decisions. Benchmarking is further complicated by: (i) the lack of an LLM-ready dataset covering a wide spectrum of SIA tasks; (ii) the continual emergence of new tasks reflecting the diversity of analyst responsibilities; and (iii) the rapid release of new LLMs that must be incorporated into evaluations. In this paper, we address these challenges by introducing SIABENCH, an agentic evaluation framework for security incident analysis. First, we construct a first-of-its-kind dataset comprising two major SIA task categories: (i) deep analysis workflows for security incidents (25 scenarios) and (ii) alert-triage tasks (135 scenarios). Second, we implement an agent capable of autonomously performing a broad spectrum of SIA tasks (including network and memory forensics, malware analysis across binary/code/PDF formats, phishing email and kit analysis, log analysis, and false-alert detection). Third, we benchmark 11 major LLMs (spanning both open- and closed-weight models) on these tasks, with extensibility to support emerging models and newly added analysis scenarios.

In this paper, we investigate rigid-ruling folding motions of crease-rule patterns, that is, conjugacy-preserving isometries of developable semi-discrete conjugate nets. We derive two conditions for the rigid-ruling foldability of pairs of curves and consider two applications. First, we introduce computations that enable the sequential construction of rigid-ruling foldable crease-rule patterns. Second, we examine combinations of planar and constant fold-angle creases. In particular, we show that constant fold-angle creases are only compatible with other constant fold-angle creases, and we provide a characterization of rigid-ruling foldable combinations of planar and constant fold-angle creases.

In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on dynamical systems, we continue this analysis focusing on what we believe is an unexplored (or, at least, not so explored! aspect of Heisenberg dynamics, related to the need for using vectors which are {\em brute-force normalized}. Our main interest is on conserved quantities, and on conditions which guarantee that some observables of the system, or their mean values, do not evolve in time.

We establish the existence of nontrivial nonnegative weak solutions to the following equation \begin{equation*} -Δ_γu + V(z)u = Q(z)f(u), \quad z\in \mathbb{R}^N, \end{equation*} where $Δ_γ$ denotes the so-called Grushin-type operator in $\mathbb{R}^N$. The potentials $V$ and $Q$ are assumed to be controlled below and above, respectively, by functions of type $(1+|z|)^a$, $a\in\mathbb{R}$. The main result is the embedded of the space $E_V^γ$ into the weighted Lebesgue space $L_Q^p(\mathbb{R}^N)$, under suitable conditions. Finally, we derive regularity results for the obtained weak solutions.

We introduce a stochastic nonlocal reaction--diffusion model arising in tumour dynamics. Spatial dispersal is described by the fractional Laplacian, accounting for anomalous diffusion and long--range relocation events. The system is perturbed by multiplicative fractional Brownian motion (fBm) with Hurst parameter $H>1/2$, which we interpret as temporally correlated fluctuations in the tumour microenvironment and host response. We first establish well--posedness and identify parameter regimes leading to global--in--time solutions or finite--time blow--up under general multiplicative fractional noise. We then focus on linear multiplicative noise and, via a Doss--Sussmann transformation, derive sharper results: explicit lower and upper bounds for the blow--up time together with quantitative estimates of the blow--up probability, clarifying how noise intensity can accelerate progression or, on favourable paths, enhance suppression consistent with extinction (loss of viability). Finally, one--dimensional simulations illustrate the interplay between anomalous diffusion, fractional noise, and the nonlocal reaction mechanism in shaping the long--time dynamics.

Semiconducting devices face persistent challenges in operating at high pressure, as the band theory predicts that materials transition to a more metallic state under compression. However, our findings with carbon chains in KFI substrates reveal a conditional deviation from this norm. We not only witness the transition from polyyne (semiconductor) to cumulene (metal) at medium pressure, but we also observe an unexpected re-entrance of the polyyne at high pressures, where the band gap in the polyyne increases with pressure. In addition, the synthesis of long cumulene chains has posed a longstanding challenge in the quest for high-temperature organic superconductivity. We have identified critical conditions for synthesizing extended cumulene chains within zeolite frameworks, highlighting the interplay between unconventional charge density waves and significant torsions. The KFI zeolite facilitates the formation of carbon chains exceeding 5,000 atoms, in stark contrast to around 100 other zeolites that are limited to ~10 atoms. The cumulene@KFI system demonstrates a superconducting transition temperature reaching ~62 K, surpassing the highest reported values for bulk iron-based superconductors. This interplay between carbon structures and superconductivity not only advances our understanding of charge density waves but also heralds a new era in the study of novel applications

In this work, we investigate the exponential stability of the viscous Saint-Venant equations by adding to the standard hyperbolic Saint-Venant equations a viscosity term coming from the higher order approximation of the Saint-Venant equations from Navier-Stokes equations. The inclusion of viscosity transforms these equations into more complex second-order partial differential equations, accurately modeling the behavior of real-world fluids that inherently possess viscosity. We construct an explicit quadratic Lyapunov function and demonstrate that it must be diagonal in physical coordinates, revealing that certain quadratic Lyapunov functions effective in non-viscous cases become inadequate when viscosity is introduced. We find explicit sufficient conditions on the parameters of the boundary conditions such that for small viscosities a quadratic Lyapunov function exists. This result ensures the exponential stability of the linearized system around the steady-state solutions in the $L^2$ norm.

The Hobby-Eberly Dark Energy Experiment (HETDEX) is an untargeted ~540 deg^2 spectroscopic survey of Lyα emission in the 1.9 < z < 3.5 Universe. In surface brightness, this survey reaches 1σ Lyα sensitivities of approximately 2-5 x 10^-18 erg s^-1 cm^-2 arcsec^-2, allowing large samples of extended Lyα nebulae (LAN) to be studied. We selected a sample of 70,691 Lyα-emitting galaxies (LAEs) with an emission-line signal-to-noise ratio greater than 6 and modeled the Lyα emission as a point-source component with an optional exponential envelope. Half (~47.5%) of the LAE sample (33,612 objects) exhibits significant extended emission and is best fit by the two-component model. The fraction of resolved sources increases with Lyα flux and luminosity. Their isophotal areas range from 10-130 arcsec^2 (median 15 arcsec^2), with integrated Lyα fluxes from 6-2000 x 10^-17 erg s^-1 cm^-2 (median 20 x 10^-17 erg s^-1 cm^-2). Comparison between point-spread-function-weighted and isophotal flux measurements shows that the HETDEX pipeline underestimates the total Lyα flux by ~30% on average, reflecting the substantial halo contribution in extended sources. Approximately 420 LANs are found per deg^2 over 79.5 deg^2 of non-contiguous sky. About 12% of resolved sources show active galactic nuclei signatures and are bright in Lyα and continuum. The remaining 88% span a wide range of morphologies and often lack continuum counterparts. Exponential scale lengths show no strong correlation with Lyα flux or luminosity (median 11.6 +/- 1.9 kpc). Only 2.9% of the full S/N > 6 LAE population with ancillary data have radio counterparts, but 64% of those are found to be extended, with the radio fraction increasing with Lyα size.

We present a spatially resolved stacked analysis of 287 LAEs at $z>4$ observed with JWST/NIRSpec prism spectroscopy. By constructing a two-dimensional stack from public surveys (CAPERS, CEERS, JADES, and RUBIES), we probe the average internal structure of typical LAEs on sub-kiloparsec scales. We find a clear radial decoupling between resonant and non-resonant emission: while EW(H$β$) and other optical lines decline with radius, EW(Ly$α$) increases toward the outskirts, and the Ly$α$ escape fraction rises from $\sim16\%$ in the center to $\gtrsim24\%$ at larger radii. This behavior indicates that resonant scattering redistributes Ly$α$ photons into lower-density outer regions, where escape becomes more efficient. Optical diagnostics and $T_e$ measurements reveal low metallicities ($12+\log(\rm O/H)\simeq7.7\pm0.2$), high ionization parameters, negligible dust attenuation, and systematically elevated N/O ratios ($\log({\rm N/O})\sim-0.4$). The latter place typical LAEs among the growing population of nitrogen-enhanced high-redshift galaxies, pointing to rapid and possibly feedback-driven chemical enrichment. The inferred ionizing photon production efficiency, $\log(ξ_{\rm ion}/{\rm Hz\,erg^{-1}})\simeq25.2$, together with the high Ly$α$ escape fractions, suggests that these systems are efficient, though not extreme, contributors to the ionizing photon budget. Comparison with SPICE radiation-hydrodynamic simulations shows that bursty supernova feedback models naturally reproduce the observed radial trends in Ly$α$ escape, UV slope, and emission-line equivalent widths, linking the spatial redistribution of Ly$α$ to stochastic star formation and feedback-driven gas flows. Our results demonstrate that Ly$α$ emission, chemical enrichment, and feedback are tightly connected in typical $z>4$ LAEs. (Shortened version for arXiv; full abstract in the paper)

A crucial aspect of research is understanding how real-world networks, such as transportation and information networks, are formed. A prominent model for such networks was introduced by \cite{fabrikant_network_2003} and extended by \cite{bilo_temporal_2023}, incorporating temporal graphs to better represent real-world networks. In this model, there is a given host graph with $n$ agents (represented by nodes) and time labels on the edges. Each agent can establish connections by purchasing edges. This makes the edges present at the time steps given by the time labels of the host graph. The goal of each agent is to reach as many other agents as possible while minimizing the number of edges bought. However, this model makes the simplifying assumption that each edge comes with predetermined time steps. We address this deficiency by extending the model of Bilo et al. \cite{bilo_temporal_2023} to allow agents to purchase edges and to decide when they appear. To capture a variety of real-world applications, we study two reachability models and several cost functions based on the label an agent assigns to an edge. For these settings, we provide proofs of existence of Nash equilibria, as well as lower and upper bounds on the Price of Anarchy and Price of Stability.

Recently, out-of-home advertising has become a popular marketing technique, due to its higher return on investment. E-commerce houses approach the influence provider to achieve effective advertising through their tags (advertising content), influence demand, and budgets. The influence provider's goal will be to make proper tag allocations, meet the required influence demand within the budget constraint, and minimize total regret. We formalize this as a combinatorial optimization problem and refer to it as \textsc{Tag-specific Regret Minimization in Outdoor Advertising (TRMOA)}. We show that TRMOA is NP-hard and inapproximable within a constant factor. The regret model we consider is non-monotone and non-submodular, and the simple greedy approach is ineffective. We introduce a fairness-aware greedy round-robin approach that reduces regret with balanced allocation across advertisers. To improve, we also introduce randomized greedy and local search algorithms. We have experimented with all the methodologies using real-world trajectory and billboard datasets to show the effectiveness and efficiency of the solution methodologies.