X-ray Photoelectron Spectroscopy (XPS) is a crucial technique for material surface analysis, yet interpreting its spectra is often challenging for both human analysts and automated methods due to the prevalence of variable spectral shifts and overlapping peaks. This project introduces a machine learning solution using a Spatial Transformer Network (STN), a type of neural network that implicitly learns to align spectra. An STN model was designed to classify the chemical environments present in an input spectrum, using functional groups as a proxy. The model was trained and tested on a large synthetic dataset of 100,000 spectra, created by linearly combining real experimental data from a library of 104 polymers. \cite{RN22} To simulate experimental variability, random uniform shifts and broadening were applied to the data. The STN was found to effectively correct for random electrostatic shifts (up to 3.0 eV) and achieved relatively high accuracy ($\sim$ 82\%) in identifying functional groups, despite utilizing a much simpler architecture than previous work. These findings demonstrate that neural networks can effectively learn the underlying relationships between spectral features and chemical composition when they are able to intrinsically account for variable shifts. This work advances the development of more reliable automated XPS analysis, offering potential as an assistive tool for researchers and as a core component in future autonomous systems like self-driving laboratories.

We present a quantum-classical hybrid implementation of the Liouvillian recursion method to compute many-body Green's functions using a quantum computer. From an approximate ground state preparation circuit, this algorithm produces the local ($r=r'$) and inter-site ($r\neq r'$) Green's functions $G_{rr'}(ω)$ by measuring observables generated recursively. We demonstrate the approach on a superconducting quantum processor for the open-boundary four-site Hubbard model. We then use the computed Green's functions as input to the Galitskii-Migdal formula to produce better ground state energy estimation than the expectation value of the Hamiltonian for the approximate circuit. Empirical results indicate exponential convergence in the number of iterations, yielding a computational complexity polynomial in the Green's-function accuracy, as measured with the Wasserstein distance. Our results also indicate significant robustness to noise and to inaccuracies of the ground state preparation, providing evidence that Liouvillian recursion is well adapted to the constraints of near-term quantum computing.

High harmonic generation (HHG) in solids results from an interplay between intraband acceleration and electron-hole recombination driven by a high-intensity laser pulse. Here, we theoretically reveal that the driving pulse duration can play a major role in extending HHG to higher photon energies by promoting higher conduction band excitations. The effect is present in a conventional semiconductor as Si, restricted in a large-gap insulator as MgO, and most prominent in RhSi, a prototypical chiral Weyl semimetal presenting numerous band crossings. Further, we elucidate the HHG selection rules in RhSi required for the synthesis of attosecond locally chiral light. The chiral crystal structure enables the generation of a local 3D electric field exhibiting an asymmetric instantaneous torsion on attosecond timescales. A pronounced circular dichroism emerges when the driving helicity is either aligned with or opposite to the crystal handedness. Our findings motivate future experiments in chiral Weyl semimetals to track high-energy band crossings and in-situ locally chiral light, paving the way for chiral compact light sources and light-wave driven topological electronics.

The Microchannel X-ray Telescope on board the Space-based multi-band astronomical Variable Objects Monitor (SVOM) satellite detects and localizes the X-ray afterglow of gamma-ray bursts. One year after the launch, this paper presents the in-flight performance of the scientific analyses conducted by the on-board computer. After summarizing the analysis steps, the paper reviews the on-board results obtained with 15 gamma-ray burst afterglows detected by the telescope between October 2024 and August 2025. For all bursts, the localization uncertainty is estimated to be below 2 arcmin, as required by the mission design. On average, the measured position is found to be 40 arcsec away from the position measured by other experiments with a better sky resolution. Moreover, we show that the on-board analysis provides a precise sky location for the burst only a few seconds after the beginning of the observation. Taking advantage of an efficient very-high-frequency antenna network, this information is quickly collected on the ground and disseminated to other observation facilities. This low-latency strategy is critical for the multi-wavelength and multi-instrument follow-up program of SVOM.

The quantum Hall effect (QHE) is theoretically understood as a superfluid condensate of composite bosons (CBs) -- bound states of electrons and magnetic flux quanta. While dissipationless transport is consistent with this picture, other signatures of superfluidity, such as the Meissner effect, remain elusive. Here, we present direct experimental evidence for CB superfluidity by probing the system's response to a controlled, time-varying magnetic field in Corbino disk geometries. We simultaneously observe the quantized Laughlin charge pumping and a new, quantized charge accumulation phenomenon, governed by the relation $ΔQ_{\rm a}/e = ν\,(ΔΦ/Φ_0)$. This relation signifies that the system actively maintains the fixed electron-to-flux ratio that defines the CBs, neutralizing excess flux by drawing in a precise number of electrons. Crucially, devices with multiple concentric top gates reveal that this charge accumulation is uniformly distributed across the bulk of the QHE fluid, demonstrating that it is a collective, bulk property rather than an edge effect -- a key signature of a superfluid condensate. Furthermore, the presence of a top gate determines the screening mechanism: in a "grand canonical" setting with a gate, low Coulomb energy favors a charge-mediated screening (generalized Meissner effect); without a gate, the system enters a "canonical" regime, exhibiting fixed electron density like type-II superconductors. These observations confirm the CB superfluid nature of the QHE ground state and establish a versatile platform for studying macroscopic quantum coherence and its screening transitions in two dimensions.

We consider colored variants of a class of geometric-combinatorial questions on $k$-gons and empty $k$-gons that have been started around 1935 by Erdős and Szekeres. In our setting we have $n$ points in general position in the plane, each one colored either red or blue. A structure on $k$ points is a geometric graph where the edges are spanned by (some of) these points and is called monochromatic if all $k$ points have the same color. Already for $k=4$ there exist interesting open problems. Most prominently, it is still open whether for any sufficiently large bichromatic set there always exists a convex empty, monochromatic quadrilateral. In order to shed more light on the underlying geometry we study the existence of five different monochromatic structures that all use exactly 4 points of a bichromatic point set. We provide several improved lower and upper bounds on the smallest $n$ such that every bichromatic set of at least $n$ points contains (some of) those monochromatic structures.

Many models of opinion dynamics include measures of distance between opinions. Such models are susceptible to boundary effects where the choice of the topology of the opinion space may influence the dynamics. In this paper we study an opinion dynamics model following the seminal model by Axelrod, with the goal of understanding the effect of a toroidal opinion space. To do this we systematically compare two versions of the model: one with toroidal opinion space and one with cubic opinion space. In their most basic form the two versions of our model result in similar dynamics (consensus is attained eventually). However, as we include bounded confidence and eventually per agent weighting of opinion elements the dynamics become quite contrasting. The toroidal opinion space consistently allows for a greater number of groups in steady state than the cubic opinion space model. Furthermore, the outcome of the dynamics in the toroidal opinion space model are more sensitive to the inclusion of extensions than in the cubic opinion space model.

We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and quadruple precision, with significantly smaller run times than other tools. This opens the door to evaluating higher complexity Feynman integrals on the fly in Monte Carlo generators, and enables a cheaper and easy to parallelise generation of grids for the topologies with prohibitive computational times. To show its performance, we test one- and two-loop integral families, achieving evaluation times in double precision of milliseconds and hundreds of milliseconds, respectively. We comment on the results and suggest room for improvement.

We apply the idea of using a combination of virial inequalities and Kato smoothing, previously applied to NLS and generalized KdV pure power equations to Euler-Poisson: we assume that a solution remains very close for all times to a soliton in an appropriate space and then we prove an asymptotic convergence to a soliton for $t\to +\infty$.

We study the resolution of discontinuous singularities in gas dynamics via multi-dimensional rarefaction waves. While the mechanism is well-understood in one spatial dimension, the rigorous construction in higher dimensions has remained a challenging open problem since Majda's proposal, primarily due to the characteristic nature of rarefaction fronts which leads to derivative losses in linearized estimates. In this paper, we establish the nonlinear stability of multi-dimensional rarefaction waves for the compressible Euler equations with ideal gas law. We prove that for initial data being small perturbations of the planar rarefaction wave in $H^s$ ($s > s_c$), there exists a unique global solution that converges asymptotically to the background rarefaction wave as $t \to \infty$. Our proof relies on a novel Geometric Weighted Energy Method (GWEM), which yields stable energy estimates without loss of derivatives in standard Sobolev spaces, overcoming the limitations of previous Nash-Moser schemes. A key ingredient is a detailed geometric description of the rarefaction wave fronts via the acoustical metric, where we identify a hidden extra vanishing structure in the top-order derivatives of the characteristic speed. This is the first paper in a series, providing the crucial a priori energy bounds. The existence of solutions and applications to the multi-dimensional Riemann problem will be addressed in the forthcoming companion paper.

In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing alignments over important classes of Petri nets. First, we show that the alignment problem is PSPACE-complete on the class of safe Petri nets and also on the class of safe and sound workflow nets. For live, bounded, free-choice systems, we prove the existence of optimal alignments of polynomial length which positions the alignment problem in NP for this class. We further show that computing alignments is NP-complete even on basic subclasses such as process trees and T-systems. We establish NP-completeness on several related classes as well, including acyclic systems. Finally, we demonstrate that on live, safe S-systems the alignment problem is solvable in P and that both assumptions (liveness and safeness) are crucial for this result.

We investigate the \(J/ψ\) direct production mechanism in the rare exclusive Higgs decay \(H\to J/ψ+γ\) within nonrelativistic QCD (NRQCD), which provides a clean probe for extracting the charm-quark Yukawa coupling to the Higgs boson. The Principle of Maximum Conformality (PMC) is used to remove conventional renormalization-scheme and scale ambiguities in the next-to-next-to-leading-order (N\(^2\)LO) perturbative QCD series. Large logarithmic contributions arising from Yukawa coupling renormalization are resummed, providing a reliable foundation for subsequent analyses. Using the experimentally measured leptonic decay width of \(J/ψ\) and the N\(^2\)LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element \(\langle J/ψ({\bm ε})|ψ^{\dagger}{\bm σ}\cdot{\bm ε}χ(μ_Λ) |0\rangle\). Combining this with the factorization-scale-dependent short-distance coefficient, we obtain a factorization-scale-invariant decay width for the channel. Compared with earlier predictions in the literature, our fixed-order result for \(Γ(H\to J/ψ+γ)\) is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find \(Γ(H\to J/ψ+γ) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}\) GeV, where the uncertainty is the quadratic sum of contributions from \(Δα_s(m_Z) = \pm 0.0009\), \(ΔΓ_{J/ψ\to e^+e^-} = \pm 0.10\ \text{GeV}\), \(Δ\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}\), and the estimated magnitude of N\(^3\)LO contributions from Bayesian analysis. This work demonstrates for the first time how the PMC can be applied to obtain fixed-order perturbative predictions that are invariant under both renormalization and factorization scale variations.

The Teichmüller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. Its complex structure follows from Lieb isomorphism. In this paper, we show the conformal naturality of Lieb isomorphism. We then study Douady-Earle section for these Teichmüller spaces. In particular, we study the real-analyticity of Douady-Earle section for classical Teichmüller spaces. We give two explicit examples of maximal holomorphic motions over simply connected complex Banach manifolds. As an application of the real-analyticity of the Douady-Earle section for the classical Teichmüller spaces of Riemann surfaces, we prove a new result showing that a family of Jordan curves varies real-analytically over a simply connected complex Banach manifold and as quasiconformal images of the one at the basepoint, provided that a finite number of marked points on the Jordan curves vary holomorphically over the same parameter space.

Symmetries are fundamental to both turbulence and differential equations. The large-eddy simulation (LES) equations inherit these symmetries provided the LES closure respects them. Classical LES closures based on eddy viscosity or scale similarity preserve many of the original symmetries by design. Recently, data-driven neural network closures have been applied to LES to improve accuracy, but stability and generalizability remain challenges, as symmetries are not automatically enforced. In this work, we compare approaches for constructing symmetry-preserving data-driven LES closures, including tensor-basis neural networks (TBNNs) and group-convolutional neural networks, alongside unconstrained convolutional networks. All three data-driven closures outperform classical models in both the functional sense (producing the right amount of dissipation) and the structural sense (stress tensor prediction). While unconstrained networks achieve comparable prediction accuracy, symmetry-preserving models produce more physically consistent velocity-gradient statistics, suggesting that enforcing symmetries improves the quality of the learned closure beyond what aggregate error metrics such as relative tensor prediction errors capture.

Immersive learning environments such as virtual classrooms in Virtual Reality (VR) offer learners unique learning experiences, yet providing effective learner support remains a challenge. While prior HCI research has explored in-lecture support for immersive learning, little research has been conducted to provide post-lecture support, despite being critical for sustained motivation, engagement, and learning outcomes. To address this, we present AttentiveLearn, a learning ecosystem that generates personalized quizzes on a mobile learning assistant based on learners' attention distribution inferred using eye-tracking in VR lectures. We evaluated the system in a four-week field study with 36 university students attending lectures on Bayesian data analysis. AttentiveLearn improved learners' reported motivation and engagement, without conclusive evidence of learning gains. Meanwhile, anecdotal evidence suggested improvements in attention for certain participants over time. Based on our findings of the field study, we provide empirical insights and design implications for personalized post-lecture support for immersive learning systems.

We present our updated results on the intrinsic width of the profile of the flux tube in (2+1)-dimensional Yang-Mills theory with SU(2) gauge group. We identify the intrinsic width as the characteristic length scale of the exponentially decaying tails of the profile of the flux tube. Inspecting a broad range of temperature, we check that this length does not depend on the length of the flux tube. Our estimations of the intrinsic width show a constant value at low temperature and a growing trend approaching the deconfinement temperature that can be understood from the universality class of the phase transition via the Svetitsky-Yaffe mapping.

Volatile elements - those that vaporize at low temperatures - are depleted in lunar rocks relative to terrestrial rocks. This systematic chemical depletion is evidence for vaporization and preferential removal of vapor from proto-lunar materials during the high-temperature processes accompanying lunar origin. Despite the robustness of these observations, the physical processes by which proto-lunar vapors were removed after the giant impact are not yet well-understood. Here, we show that toward the end of post-giant impact cooling history, Earth's atmosphere was dominated by carbon species (e.g., CO) and was spatially compact, behaving as a closed system retaining Earth's volatile inventory, whereas the proto-lunar disk atmosphere was dominated by H and H2 and was spatially extended, developing into a hydrodynamic outflow analogous to the solar wind. We find that equilibrium H2 recombination (2H->H2) in a partially-dissociated disk atmosphere produces a nearly isothermal structure, a feature known to activate outflows. The expected outflow was strong enough to propel proto-lunar volatiles from a Roche-interior (r < 3RE) disk out of Earth's gravity field and to establish a cometary tail composed of volatile elements transporting proto-lunar disk volatiles into interplanetary space. The proposed model suggests that the dichotomy in volatile element abundances between the silicate Earth and Moon is a natural outcome of the hydrodynamical behavior of magma ocean atmospheres and that lunar chemical and isotopic volatile abundances are diagnostic of the radial structure of the proto-lunar disk towards the end of its condensation.

Adolescents are directly affected by preventive health decisions such as vaccination, yet their perspectives are rarely solicited or supported. Most digital interventions for Human Papillomavirus (HPV) vaccination are designed exclusively for parents, implicitly treating adolescents as passive recipients rather than stakeholders with agency. We present the design and evaluation of a mobile intervention that gives adolescents a voice in HPV vaccination decisions alongside their parents. The system uses embodied conversational agents tailored to each audience: parents interact with an animated physician using education and motivational interviewing techniques, while adolescents can choose between an age-appropriate doctor or a narrative fantasy game that conveys HPV facts through play. We report findings from a clinic-based pilot study with 21 parent-adolescent dyads. Results indicate high satisfaction across both audiences, improved HPV knowledge, and increased intent to vaccinate. We discuss design implications for supporting adolescent participation, choice, and agency in decisions about their health.

Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be supplemented with a fast and accurate classical decoding algorithm. Standard techniques for measuring the parity-check operators of a quantum error-correcting code involve repeated measurements, which both increases the amount of data that needs to be processed by the decoder, and changes the nature of the decoding problem. Knill error correction is a technique that replaces repeated syndrome measurements with a single round of measurements, but requires an auxiliary logical Bell state. Here, we provide a theoretical and numerical investigation into Knill error correction from the perspective of decoding. We give a self-contained description of the protocol, prove its fault tolerance under locally decaying (circuit-level) noise, and numerically benchmark its performance for quantum low-density parity-check codes. We show analytically and numerically that the time-constrained decoding problem for Knill error correction can be solved using the same decoder used for the simpler code-capacity noise model, illustrating that Knill error correction may alleviate the stringent requirements on classical control required for building a large-scale quantum computer.

Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable Jordan curve and study some of its basic properties. Under further smoothness assumptions, we derive the associated Fokker-Planck-Kolmogorov equation, prove convergence towards the stationary Coulomb gas distribution, study large deviations at low temperature, and derive the limiting mean-field McKean--Vlasov equation in the many-particle limit.

We investigate the spectrum of $T_{ΥΥ}$ tetraquark candidates within a coupled-channels framework. The analysis includes all $L\leq2$ combinations of $Υ(1S)$, $Υ(2S)$, $η_b(1S)$, and $η_b(2S)$ in the $J^P = 0^\pm, 1^\pm, 2^\pm$ sectors. The meson-meson interaction is derived from an underlying constituent quark model through the resonating group method, and the properties of the states are obtained from poles of the scattering matrix. We find a rich spectrum of resonant, and virtual, states distributed between the $η_b(1S)η_b(1S)$ and $Υ(2S)Υ(2S)$ thresholds. The pattern of poles exhibits approximate heavy-quark spin symmetry multiplets. Several states are dominated by a single channel and can be associated with threshold-driven structures, while higher-mass resonances show sizable mixing among channels involving radially excited bottomonia. The predicted widths range from tens to several hundred MeV. Branching ratios indicate that many states couple predominantly to final states with at least one excited bottomonium, whereas only a subset of the spectrum is expected to be visible in the $η_b(1S)η_b(1S)$, $η_b(1S)Υ(1S)$ and $Υ(1S)Υ(1S)$ channels. These results provide quantitative guidance for experimental searches of fully heavy tetraquarks and offer a test of coupled-channel dynamics and heavy-quark spin symmetry in the $bb\bar b\bar b$ sector.

Based on spectroscopic and photometric observations, we have determined the fundamental parameters of the poorly studied star HD 188101 with a weak magnetic field. Its effective temperature $T_{\rm eff} = 14200 \pm 990$ K and surface gravity log g = 3.70 $\pm$ 0.16 are typical for main-sequence B9 stars. The He, C, O, Mg, Si, Ti, and Sr abundances have been determined by taking into account the departures from local thermodynamic equilibrium. Overabundances of Si, Ti, and Sr relative to their solar abundances have been revealed. The He abundance is lower than the solar one, but the difference is within the error limits. In addition to the photometric variability known from Kepler data, we have found changes in absorption for He I, Mg II, Si II, Si III, Ti II, and Fe II lines, with different He I and Mg II lines giving different abundances for the same phase of observations. The star HD 188101 is shown to belong to the group of chemically peculiar He-weak SiTiSr stars.

We investigate the extreme values of a sparse and equicorrelated Gaussian field on a triangle: the correlations on every vertical or horizontal line are all equal to a parameter $r \in [0,1/2]$ and are zero everywhere else. This problem is closely linked with various problems in high-dimensional statistics and extreme-value theory. We identify the threshold for $r$ at which the standard Gumbel law breaks down. Our result is based on a subtle application of the Chen-Stein method for Poisson approximation. As applications, we discuss the implication of our results on multiple testing and resolve several questions that were left open in \cite{heiny2024maximum}, \cite{tang2022asymptotic} and \cite{Jiang19}.

In short-baseline experiments such as LSND and MiniBooNE, an excess of electron neutrinos has been observed, originating from a muon neutrino beam. To address this anomaly, in the line of many works, we investigate various neutrino mixing schemes involving eV-scale sterile neutrinos alongside three active neutrinos. Using updated experimental and global fit data, we studied neutrinoless double beta decay for three different schemes such as 3+1, 1 + 3, and 2 + 2, which involve one sterile neutrino and three active neutrinos. We have done analysis of these schemes for normal hierarchy (NH) as well as for inverted hierarchy (IH) frameworks, and constrained the sterile neutrino mass in light of current and future neutrinoless double beta decay experiments. The 3+1 scheme is found to be the most viable and at the level of $3σ$ the mass of sterile neutrino with respect to the lightest neutrino mass ($m_{\text{lightest}}$) is restricted to $4.75~eV$ for the NH and $4.72~eV$ for the IH. Additionally, the limits on the sum of four neutrino masses are determined to be $4.81~eV$ for the normal hierarchy and $4.78~eV$ for the inverted hierarchy. The updated analysis of all these schemes would help us in understanding physics governing neutrinoless double beta decay and limit on the mass of sterile neutrinos.

We establish the theoretical foundations for embedding a correlated wave function in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation which equates two, in principle distinct, kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-DFT formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based DMRG-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (PDFT) instead of a semilocal GGA does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.

In this paper, we use the particle motion bijection introduced by Warnaar and developed by the two authors, Jouhet and Konan, to study q-series and partition identities of the Andrews--Gordon type with parity restrictions. These restrictions are of the type ``even (resp. odd) parts appear an even number of times". We prove $q$-series identities where a multisum equals a sum of products, which generalise identities of Andrews and Kim--Yee in a similar way that Stanton's identities generalised the Andrews--Gordon identities. As a consequence of our results, we obtain a simple proof of a recent identity of Chern--Li--Stanton--Xue--Yee related to Ariki--Koike algebras.

We study the Dirichlet problem for a class of fractional $p$-Laplacian operators of order $s \in (0,1)$ defined through the Riesz fractional gradient, which differs fundamentally from the standard fractional $p$-Laplacian. Our analysis combines the framework of Lions-Calderón spaces, Besov embeddings, and an adaptation of Nirenberg's difference quotient method, originally developed by Savaré, to the fractional Riesz setting. As a main result, we establish global Besov regularity estimates for weak solutions. Concretely, in the superquadratic regime $p \geq 2$, we prove $u \in \dot{B}_{p,\infty}^{s+1/p}(Ω)$ for $s \in [\frac{1}{p'},1)$, and $u \in \dot{B}_{p,\infty}^{s+\frac{s}{p-1}}(Ω)$ for $s \in (0,\frac{1}{p'})$. In the subquadratic case $1<p<2$, we show $u \in \dot{B}_{p,\infty}^{s+1/2}(Ω)$ for $s \in [\frac{1}{2},1)$, and $u \in \dot{B}_{p,\infty}^{2s}(Ω)$ for $s \in (0,\frac12)$, with quantitative bounds depending on the source data.

Electrowetting on textured and lubricant infused surfaces is conventionally expected to promote enhanced droplet spreading by reducing apparent contact angles. Contrary to this intuition, we report rapid tangential droplet ejection at applied DC voltages on specific microtextured, lubricant infused surfaces. Using high speed imaging and a precisely controlled electrowetting setup, we reveal the dependence of droplet dynamics on surface topology, wetting state, and the presence of a lubricant. On densely textured thick PDMS substrates of post spacing 5 to 10 um in a low hysteresis non-wetting Cassie state, and on all lubricant infused textured surfaces, droplets experience sudden lateral motion and eventual detachment. We attribute this counterintuitive phenomenon to unbalanced electrocapillary forces at the contact line combined with minimal pinning, which allows asymmetries in electric stresses to translate directly into net lateral motion. In contrast, Wenzel state droplets or surfaces with larger texture spacing exhibit conventional spreading with strong adhesion. By capturing the fundamental interplay among electrostatic driving forces, contact line pinning, and interfacial mobility, our results provide a new paradigm for controlled droplet transport and ejection in electrowetting systems mediated by dense micro posts and lubricant induced interfaces.

The notion of a tropical vector bundle on a toric variety was recently introduced by Khan-Maclagan and Kaveh-Manon. In this paper, we study the Euler characteristic and rank of global sections for tropical vector bundles. We associate a convex chain (a finite integer linear combination of indicator functions of convex polytopes) to a tropical vector bundle encoding its Euler characteristic. We then see that the Khovanskii-Pukhlikov theory of convex chains gives a combinatorial Hirzebruch-Riemann-Roch theorem for tropical vector bundles. This, in particular, applies to toric vector bundles. Also, we extend Klyachko's resolution of a toric vector bundle by split toric vector bundles to tropical vector bundles. As shown by Kaveh-Manon, every matroid comes with a tautological tropical vector bundle. We answer positively a question posed by Kaveh-Manon about equality of Euler characteristic with rank of space of global sections (in other words, vanishing of higher cohomologies) for the tautological bundle of a matroid.

A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations, each with a sensing region of adjustable range; how should we adjust the individual sensor ranges in order to optimize energy consumption? We provide both negative theoretical and positive practical results for this important and natural challenge. On the theoretical side, we show that even if all objects move at constant speed along straight lines, no polynomial-time algorithm can guarantee optimal coverage for a given starting solution. On the practical side, we present an algorithm based on geometric insights that is able to find optimal solutions for the $\min \max$ variant of the problem, which aims at minimizing peak power consumption. Runtimes for instances with 500 moving objects and 25 stations are in the order of seconds for scenarios that take minutes to play out in the real world, demonstrating real-time capability of our methods.