We determine the number of local Arthur packets containing a certain fixed tempered representation for classical $p$-adic groups. More specifically, given a tempered extended multi-segment supported in the integers, we determine a count for all extended multi-segments which arise from it through applications of the operators arising from the theory of intersections of local Arthur packets.

We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced by a Lennard-Jones interaction. In addition to the pairwise force, the dynamics includes a nonlocal drift mediated by an environmental field, whose evolution is coupled to the particle configuration through a regularized empirical density. We then extend the analysis to a reaction model in which the switching (or killing) rate also depends on the field. An interlacing technique is considered for establishing the well-posedness of the full system. The model is motivated by the challenge to provide a stochastic microscopic description of the sulphation phenomenon in cultural heritage materials.

The transition to disaggregated and interoperable Open Radio Access Network (RAN) architectures and the introduction of RAN Intelligent Controllers (RICs) in O-RAN creates new resource optimization opportunities and fine-grained tuning and configuration of network components to save energy while fulfilling service demand. However, unlocking this potential requires fine-grained and accurate energy measurements across heterogeneous deployments. Three factors make this particularly challenging [...]. To address these challenges, we design the TENORAN framework, an automated measurement scaffold for fine-grained energy efficiency profiling of O-RAN deployments, and prototype it on a heterogeneous OpenShift cluster. TENORAN instruments an end-to-end deployment based on high-level specifications (e.g., gNB software stack and split options, traffic profiles), and collects synchronized performance metrics and power measurements for individual RAN components while the network is under controlled workloads including over-the-air traffic. Our experimental results demonstrate energy profiling of end-to-end experiments with xApps in the loop, energy efficiency differences between two RAN stacks, OpenAirInterface and srsRAN, in uplink and downlink, and core network power consumption trends.

We study subvarieties of very general complete intersections $X\subset \mathbb{P}^n$ of multidegree $(d_1,\dots,d_c)$, when $d:= d_1+\dots +d_c$ is sufficiently large. In a seminal paper Ein proved that if $d\geq 2n-c-k+2$, any $k$-dimensional subvariety of $X$ is of general type and has positive geometric genus. We strengthen this result by obtaining the optimal bound $d\geq 2n-c-k$, provided that $n> 2c+k$. As a consequence, we characterize algebraic hyperbolicity of very general complete intersections $X\subset \mathbb{P}^n$ of codimension $c\leq \frac{n-3}{2}$. For lower values of $d$, we prove that if $\frac{3n-c+2}{2}\leq d\leq 2n-c-2$ and $(d_1,\dots,d_c)$ satisfies an additional numerical condition, then the only curves in $X$ that are not of general type are lines. Moreover, we describe the locus where positive dimensional orbits of points under rational equivalence must lie. We obtain our results by proving that, under suitable numerical conditions, subvarieties of $X$ that are not of general type must lie in the locus of $X$ covered by lines. The proof of this result relies on a generalization of the approach and techniques developed for hypersurfaces by Voisin, Clemens-Ran and the second author, combined with a Grassmannian technique introduced by Riedl-Yang.

Urban mobility is a multi-entity system that involves travelers, transport modes, and infrastructure. Beyond conventional origin/destination analysis, this paper investigates how process mining can structure and interpret mobility behavior from event data. Using Call Detail Records (CDRs) from Oeiras in the Lisbon metropolitan area (Portugal), we construct both case-centric and object-centric event logs and discover models that summarize flows and typical durations. Results show that most trips are intra-municipal, while inter-municipal flows connect strongly to neighboring areas, with typical inter-parish travel times of about 20 minutes. The object-centric perspective explicitly links trips and transport modes, revealing mode-specific duration differences (e.g., bus vs. car) that inform multimodal planning. Our contributions are: (i) a reproducible pipeline to transform CDRs into process mining artifacts, (ii) empirical evidence that mobility data exhibit a process-like structure, and (iii) the added value of object-centric models for multimodal analysis. Limitations include the low spatial precision of CDRs (tower-sector level) and heuristic transport-mode labels. Future work will integrate transport-network context (e.g., stations and routes) and model object-centric logs as heterogeneous graphs to enable richer and more reliable analysis.

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights, possibly complemented by cross-diffusion terms that are homogeneous across links. In this work, we investigate the emergence of Turing patterns on Matrix Weighted Networks (MWNs), a recently introduced framework in which each edge is associated with a matrix weight. Focusing on the class of coherent MWNs, we provide a novel characterization of coherence in terms of node-dependent orthonormal matrices, showing that link transformations can be written as relative rotations between nodes. This representation allows us to deal with coherent MWNs of any size and to introduce an orthonormal change of variables capable to reduce diffusion on a coherent MWN to diffusion on a standard weighted network with scalar weights. Building on this, we extend the classical Turing instability analysis to MWNs and derive the conditions under which a homogeneous equilibrium of the local dynamics loses stability due to matrix-weighted diffusion. Our results show how network topology, scalar weights, and inter-node transformations jointly shape pattern formation, and provide a constructive framework to analyze and design Turing patterns on matrix-weighted and higher-order networked systems.

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver's ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

We force the Axiom of Choice over the least initial segment of a Nairian model satisfying ZF. In the forcing extension, square_kappa fails at all uncountable cardinals kappa, and every regular cardinal is omega-strongly measurable in HOD, as witnessed by the omega-club filter. Thus the failure of square everywhere is within the current reach of inner model theory, and the HOD Hypothesis is not provable in ZFC.

Task-based chatbots are software, typically embedded in real-world applications, that assist users in completing tasks through a conversational interface. As chatbots are gaining popularity, effectively assessing their quality has become crucial. Whereas traditional testing techniques fail to systematically exercise the conversational space of chatbots, several approaches specifically targeting chatbots have emerged from both industry and research. Although these techniques have shown advancements over the years, they still exhibit limitations, such as simplicity of the generated test scenarios and weakness in implemented oracles. In this paper, we conduct a confirmatory study to investigate such limitations by evaluating the effectiveness of state-of-the-art chatbot testing techniques on a curated selection of task-based chatbots from GitHub, developed using the most popular commercial and open-source platforms.

The transition to global synchronization in coupled dynamical systems is governed by the interplay between coupling strength and structural topology. Although abrupt, first-order-like synchronization transitions have been extensively reported in heterogeneous networks, it is unclear whether comparable accelerated onset behavior can emerge purely from coordination geometry in spatially homogeneous, regular lattices. In this study, we investigate large-scale ($N=10^5$) stochastic Stuart-Landau oscillator networks defined on regular lattices with controlled coordination number. Using topological data analysis (TDA), simplicial-complex characterization, and optimal-transport-based geometric diagnostics, we identify a coordination-controlled crossover in synchronization onset dynamics at approximately $z_{c} \approx 7$ within the class of regular lattices considered. Low-coordination lattices ($z < z_{c}$) exhibit persistent $H_2$ topological features in the dynamical amplitude field that correlate with delayed coherence and surface-limited propagation. In contrast, higher-coordination lattices ($z > z_{c}$) display rapid fragmentation of these features, reduced interface roughness, and predominantly positive Ricci curvature. This is consistent with enhanced path redundancy and improved transport efficiency. In this regime, the global order parameter exhibits accelerated exponential-like growth during the onset stage. Throughout this work, abrupt synchronization refers specifically to this exponential onset behavior rather than to thermodynamic first-order hysteresis. Our results demonstrate that increasing coordination density induces a qualitative reorganization of higher-order topological structure that strongly correlates with synchronization efficiency in regular lattice systems.

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

The Medium temperature (mid-T) baking of niobium superconducting radio-frequency cavities at 300 350&#8239; C in a vacuum furnace is known to enhance the quality factor (Q&#8320;). However, despite this improvement, cavities treated with this process often exhibit premature quench at relatively low accelerating fields. This limitation is suspected to arise from the formation of surface contaminants, such as niobium carbides, during the furnace bake at 350 C for 3 h. To investigate the influence of potential surface contamination, this study applied an ultralight chemical removal to 1.3&#8239;GHz and 650&#8239;MHz single-cell cavities that had undergone medium-temperature baking. The removal of the top RF surface layer led to a notable improvement in the quench field and Q&#8320;, indicating a beneficial effect of eliminating possible surface residues introduced during the bake.

We study the pair correlations of the logarithms of the integral values of quadratic norm forms at various scalings, proving the existence of pair correlation measures. We describe a surprising set of asymptotic behaviours when the scaling increases, passing from a punctual measure to a Poissonian behaviour through an exotic behaviour at the transition phase.

We present a classification algorithm for Calabi-Yau complete intersections arising from nef-partitions in fake weighted projective spaces, allowing us to determine all such complete intersections up to dimension five. Furthermore, we compute the Hodge pairs of the $3$-dimensional families obtained, and find twenty new Hodge pairs not realized by any toric Calabi-Yau hypersurface. Finally, we provide an explicit characterization for the families of maximal codimension.

Existing fundamental theorems for mean-square convergence of numerical methods for stochastic differential equations (SDEs) require globally or one-sided Lipschitz continuous coefficients, while strong convergence results under merely local Lipschitz conditions are largely restricted to Euler-Maruyama type methods. To address these limitations, we introduce a novel localized version of the fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients, which naturally arise in a wide range of applications. Specifically, we show that if a numerical scheme is locally consistent in the mean-square sense of order $q>1$, then it is locally mean-square convergent with rate $q-1$. Building on this result, we further prove that global mean-square convergence follows, provided that both the exact solution and its numerical approximation admit bounded $2p$th moments for some $p>1$. These new convergence results are illustrated on a class of locally Lipschitz SDEs of Hodgkin-Huxley type, characterized by a conditionally linear drift structure. For these systems, we construct different Lie-Trotter and Strang splitting methods exploiting their conditional linearity. The proposed convergence framework is then applied to these schemes, requiring innovative proofs of local consistency and boundedness of moments. In addition, we establish key structure-preserving properties of the splitting methods, in particular state-space preservation and geometric ergodicity. Numerical experiments support the theoretical results and demonstrate that the proposed splitting schemes significantly outperform Euler-Maruyama type methods in preserving the qualitative features of the model.

Interacting bosonic quasiparticles are the cornerstone for exploring many-body physics and nonlinear quantum phenomena in correlated light-matter systems. Strongly interacting dipolar excitons in van der Waals heterostructures have attracted significant interest due to their out-of-plane electric dipole moments and high tunability via the quantum-confined Stark effect (QCSE). However, leveraging these tunable dipolar excitons in strongly coupled exciton-photon systems to explore exotic many-body physics and macroscopic quantum phenomena remains experimentally elusive. Here, we report the strong coupling of dipolar excitons in a gated bilayer MoS2 device integrated with a one-dimensional photonic crystal hosting bound-states-in-continuum (BIC). The resulting polaritons hybridize cavity photons with a coherent superposition of two electrically tunable anti-aligned dipolar excitons, effectively binding them into composite quasiparticle states. By tuning the dipolar excitons into non-degenerate states via the QCSE, we realize in situ reconfiguration of the polariton wavefunction and observe an emergent polariton branch exhibiting non-monotonic Stark shifts. Notably, these tunable polaritons allow for customized control over nonlinear interactions through distinct excitonic hybridization and dipolar configurations. This in situ tunability offers a scalable pathway toward electrically programmable quantum fluids of light and correlated polariton phases in on-chip photonic integrated circuits.

The fundamental properties of ice have always attracted a lot of interest due to omnipresence of ice in many different natural contexts. Since cubic ice recently become experimentally accessible from a low-density gas hydrate precursor [1, 2], it has been possible to measure its density as a function of temperature in the whole thermodynamic range of metastability. We found strong analogies with respect to the other ice I polytype, i.e., hexagonal ice Ih [3], including the presence of a negative thermal expansion behavior at low temperature. Based on these results, a new enthalpy calculation quantifies the metastable nature of the cubic form and, consequently its inaccessibility from a "normal" ice Ih precursor.

Observational appearance of debris disks is largely controlled by collisional grinding of their dust grains. However, the mechanical strength of dust at sizes in the micrometer to millimeter range is poorly known. Recent studies suggested that dust particles in the Solar system might have a higher critical fragmentation energy $Q_{D}^*$ value than previously anticipated. Another recent study considered the Fomalhaut debris disk and found lower $Q_{D}^*$ values to provide better fits to the data. In order to constrain the mechanical strength of dust, we investigate collisional evolution of debris disks with $Q_{D}^*$ prescriptions differing by $\sim 3$ orders of magnitude. We find that, above a certain threshold $Q_{D}^*$ value, the disk's collisional evolution is dominated by rebounding -- rather than disruptive or cratering -- collisions. Rebounding (a.k.a. bouncing) collisions are those in which both impactors survive, being only slightly eroded and producing fragments that only carry a minor fraction of their mass. We show that disks dominated by rebounding collisions would have brightness profiles increasing outward outside the parent belt. Since such profiles are not observed, this places an upper limit on how hard the debris dust is allowed to be in order not to violate the observations. We derive an approximate analytic expression for this limit: $Q_{D}^* \approx (1/8) v_{K}^2(r)$ for grains close to the radiation pressure blowout size, where $v_{K}$ in the Keplerian circular speed at a distance $r$ from the star. This implies $Q_{D}^* \lesssim 10^{9...10} \,\hbox{erg}\,\hbox{g}^{-1}$ for micrometer-sized grains in typical debris disks. Even though rebounding collisions are not expected to affect debris disk evolution significantly, we emphasize that these collisions are actually much more frequent than disruptive and cratering ones in all debris disks.

While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a data-driven approach for learning FBP filters and projection weights directly from training data, with the goal of improving robustness without sacrificing computational efficiency. The resulting reconstructions adapt naturally to the noise level and acquisition geometry, while retaining the speed and simplicity of classical back-projection. The proposed method can be formulated as a regularized optimization problem for a linear inverse operator, which allows us to establish existence, uniqueness, and stability of the learned solution. From a spectral viewpoint, the learned filters act as data-adaptive gain functions that explicitly balance noise amplification and bias, in close analogy to a regularized pseudo-inverse. Experiments in both 2D and 3D show consistent improvements over conventional FBP and FDK in different case studies. Finally, we show that filters trained on synthetic laminography data generalize well to real-world measurements, delivering image quality comparable to advanced iterative methods without the high computational cost.

State-space models (SSM) are common in signal processing, where Kalman smoothing (KS) methods are state-of-the-art. However, traditional KS techniques lack expressivity as they do not incorporate spatial prior information. Recently, [1] proposed an ADMM algorithm that handles the state-space fidelity term with KS while regularizing the object via a sparsity-based prior with proximity operators. Plug-and-Play (PnP) methods are a popular type of iterative algorithms that replace proximal operators encoding prior knowledge with powerful denoisers such as deep neural networks. These methods are widely used in image processing, achieving state-of-the-art results. In this work, we build on the KS-ADMM method, combining it with deep learning to achieve higher expressivity. We propose a PnP algorithm based on KS-ADMM iterations, efficiently handling the SSM through KS, while enabling the use of powerful denoising networks. Simulations on a 2D+t imaging problem show that the proposed PnP-KS-ADMM algorithm improves the computational efficiency over standard PnP-ADMM for large numbers of timesteps.

Cities host most of the world population with diverse services and activities. One key challenge in urban modelling is the quantification of intra- and inter-city mobility patterns and the associated space-time dynamics of population density and anthropogenic activities. To address this, we apply the novel agent-based urban model DAVE (Dynamic Anthropogenic actiVities and feedback to Emissions) to simulate population behaviour and mobility in the Vaud and Geneva Cantons, a system of small- to medium-size cities in Switzerland. Simulation results provide detailed temporal (10 min) and spatial (500 m) population dynamics for different age groups and day types. DAVE further models the time-varying population distribution in 11 different microenvironments (e.g., home, work, leisure, outdoor) and the travel flows by different modes. Simulation results align with observations, confirming the possibility of driving urban system modelling with statistical information on residents' behaviour. Sustainability and health indicators like daily driving distance and walking time for each neighbourhood are also reflected by the model with urban-rural gradients displayed. This work serves as a foundation for future applications of DAVE to study bottom-up human-built environment interactions, from anthropogenic emissions and building energy to urban climate, exposure, and health in cities around the world.

$(1^a, 2^b)$-coloring is the problem of partitioning the vertex set of a graph into $a$ independent sets and $b$ 2-independent sets. This problem was recently introduced by Choi and Liu. We study the computational complexity and extremal properties of $(1^a, 2^b)$-coloring. We prove that this problem is NP-Complete even when restricted to certain classes of planar graphs, and we also investigate the extremal values of $b$ when $a$ is fixed and in some $(a + 1)$-colorable classes of graphs. In particular, we prove that $k$-degenerate graphs are $(1^k, 2^{O(\sqrt{n})})$-colorable, that triangle-free planar graphs are $(1^2, 2^{O(\sqrt{n})})$-colorable and that planar graphs are $(1^3, 2^{O(\sqrt{n})})$-colorable. All upper bounds obtained are tight up to a constant factor.

Modern time-domain surveys, such as the Zwicky Transient Facility (ZTF), detect far more extragalactic transients than can be spectroscopically classified. Photometric classification offers a scalable alternative, enabling the identification of larger, fainter, and higher-redshift supernova samples suitable for applications such as Type Ia supernova (SN Ia) cosmology. We present a feature-based photometric classifier for SNe detected by ZTF, with the primary goal of constructing a photometric SN Ia sample for cosmological analyses. Our approach utilises the autoencoder architecture of ParSNIP (Boone 2021) to capture the intrinsic diversity of SN light curves. We trained the model on a spectroscopically classified ZTF SN sample, incorporating a realistic noise augmentation procedure that simulates the flux uncertainties of fainter sources. Light curve features were used to train a gradient-boosted decision tree classifier, implemented in both binary (SN Ia vs. non-Ia) and multi-class configurations. We validated our classifier on independent, fainter ZTF data with and without noise augmentation. To evaluate real-time performance, we also applied our classifier to live ZTF alerts and conducted a spectroscopic classification survey within the ePESSTO+ collaboration. We found that noise augmentation significantly improves classification performance, particularly for fainter sources. Our binary classifier achieves an SN Ia recall of (98.1 $\pm$ 0.4)%, averaged across five train-test splits. SN Ia recall exceeds 98% for events with a peak apparent magnitude up to 20 and more than 10 detections, and remains above 96% up to magnitude 20.5. Overall, 95% of sources were correctly classified in both binary and multi-class modes. Our classifier performs efficiently on real ZTF data and enables construction of a large photometric SN Ia sample for cosmology.

The discovery of the ferroelectric nematic phase has brought with it a plethora of new polar liquid crystalline phases. One in particular is the anti-ferroelectric smectic A SmA\textsubscript{AF} phase. In this letter we show via observation and analysis of satellite peaks in the X-ray scattering pattern that the structure of the SmA\textsubscript{AF} phase involves a density modulation of $\approx$10-20 nm lateral to the smectic layer normal. Further, we demonstrate a previously undiscovered phase where the anti-ferroelectric order is maintained into a tilted smectic phase demonstrating the robustness of the underlying frustration that leads to the modulated structure. We suggest that the modulations are only in a single dimension and appear parallel to the tilt plane. This new phase also shows a significantly different and complex response to an electric field from other discovered polar LC phases due to the ability to modulate both tilt and polarisation direction.

We present a data-driven framework to infer phase-amplitude equations of coupled limit-cycle oscillators directly from waveform measurements. Exploiting the universality of the Stuart-Landau normal form near a supercritical Hopf bifurcation, we reconstruct a near-identity transformation from two independent observables of an isolated oscillator and infer the intrinsic Stuart-Landau parameters. Using this reconstructed transformation, we then estimate linear coupling coefficients from paired measurements. The method accurately recovers parameters for coupled van der Pol oscillators, providing a quantitative benchmark. Applied to a high-dimensional hydrodynamic system of two coupled collapsible-channel oscillators, the inferred Stuart-Landau model captures bistability between in-phase and anti-phase synchronization and reveals that the anti-phase state is destabilized through a Neimark-Sacker bifurcation. Our approach enables quantitative prediction of synchronization transitions involving amplitude dynamics from experimentally accessible waveform data.

The proactive Asset Administration Shell (AAS) enables bidirectional communication between assets. It uses the Language for I4.0 Components in VDI/VDE 2193 to facilitate negotiations, such as allocating products to available production resources. This paper investigates the efficiency of the negotiation, based on criteria, such as message load, for applications with a scaling number of assets. Currently, the focus of AAS standardization is on submodels and their security to enable interoperable data access. Their proactive behavior remains conceptual and is still a subject of scientific research. Existing studies examine proactive AAS architecture examples with a limited number of assets, raising questions about their scalability in industrial environments. To analyze proactive AAS for scaling applications, a scenario and evaluation criteria are introduced. A scalable implementation is developed using current architectures for proactive AAS, upon which experiments are conducted with a varying number of assets. The results reveal the performance limitations, communication overhead, and adaptability of the AAS-based negotiation mechanism scaling. This information can improve the further development and standardization of the AAS.

We consider the representation growth of split extensions of $SL_2^m(O)$. We prove that the corresponding representation zeta functions factor as a product of the representation zeta function of $SL_2^m(O)$ and the relative representation zeta function associated to the extension. We make use of our result by computing the zeta functions for two infinite families of split extensions of $SL_2^m(O)$ explicitly. Along the way, we compute the representation zeta functions of a large class of subgroups of $SL_2^m(O)$.

Quantum metrology exploits quantum mechanical effects to increase the precision of measurements of physical quantities. A wide variety of applications are currently being developed for scientific and technological purposes, however, most research relies on the use of highly entangled resource states that are challenging to generate and control in a given physical system. Here, we study the use of weighted graph states as more accessible resources for quantum metrology, which yield a favorable precision beyond the classical limit, approaching the Heisenberg limit. We find a notable robustness to variation in weights and less challenging weight requirements compared to standard graph states, which require a maximal weight at all edges. Both of these aspects reduce the practical demands in a physical setup, with the latter implying significantly less entanglement is required to gain a quantum advantage in metrology. We study the quantum Fisher information and optimized estimator variance of two identified sub classes of weighted graph states for an arbitrary number of N qubits, providing analytical forms and investigating their scaling. Our work opens up opportunities for using weakly entangled states in quantum-enhanced metrology.

This extended abstract is based on a talk given at the workshop and summer school ``Direct and Inverse Problems with Applications" in Ghent Analysis and PDE Centre in August 2024. It focuses on nonlinear diffusion equations of slow and fast types and their links with some geometric and functional inequalities in the framework of smooth metric measure spaces. The article presents some introduction in a summer school style as well as several new results.

The spherical nature of the wavefronts exhibited in the near-field of antenna arrays enables advanced beamforming capabilities, such as beampointing and beamnulling. In this paper, we exploit these properties to design a near-field beam pattern under a low exposure region constraint. We address the continuous region constraint through spatial discretization, which results in a large number of constraints that lead to prohibitive computational complexity. We propose a novel low-complexity algorithm that enables a computationally tractable beam pattern design. It uses a low-dimensional subspace representation of the low exposure region based on a singular value decomposition. Our approach achieves low complexity while providing a power received at a target user close to the optimal achievable power, yet with uniform power mitigation over the low exposure region.