The anti-concentration phenomenon in probability theory has been intensively studied in recent years, with applications across many areas of mathematics. In most existing works, the ambient probability space is a product space generated by independent random variables. In this paper, we initiate a systematic study of anti-concentration when the ambient space is the symmetric group, equipped with the uniform measure. Concretely, we focus on the random sum $S_π = \sum_{i=1}^{n} w_i\, v_{π(i)}$, where $w=(w_1,\dots,w_n)$ and $v=(v_1,\dots,v_n)$ are fixed vectors and $π$ is a uniformly random permutation. The paper contains several new results, addressing both discrete and continuous anti-concentration phenomena. On the discrete side, we establish a near-optimal structural characterization of the vectors $w$ and $v$ under the assumption that the concentration probability $\sup_x P(S_π=x)$ is polynomially large. On the continuous side, we study the small-ball event $|S_π-L|\le δ$. Our results exhibit sub-gaussian decay in $L$. Our results have applications in various areas. First, we use our inverse theorems to derive and strengthen a number of previous anti-concentration bounds. In particular, we show that if both $w$ and $v$ have distinct entries, then $\sup_x P(S_π=x) \le n^{-5/2+o(1)}$. Next, we apply our new results to study random polynomials, and prove that the number of extremal points of random permutation polynomials is bounded by $O(\log n)$, extending results of S{ö}ze~\cite{Soze1, Soze2}. In the final application, we prove that random matrices whose rows are independent random permutations of a fixed non-degenerate vector are nonsingular with high probability.

In this paper we generalize Vasiliev's higher-spin gravity theory in 3d into $\mathcal{N} = (0, 2)$ case, by which we mean that the asymptotic symmetry of such a gravity theory have the structure of 2d $\mathcal{N} = (0, 2)$ superconformal algebra. While the construction is limited to linearized level, asymptotic symmetry and possible matter content of such theories is discussed. Also, the 1-loop partition function of this theory around thermal Euclidean AdS space-time, with different matter fields, is calculated by heat-kernel method.

Studies of kinematics and geometry of outflowing gas rely on modeling features in integrated spectra using empirical quantiles or fitting multiple Gaussian or Voigt profiles. Such methods can miss key underlying physics and even lead to spurious interpretations of observations. To address this problem, we present the public python code OutLines, which predicts spectral emission and absorption line profiles produced by winds, bubbles, and outflows. By design, OutLines is phenomenologically and scale agnostic to bridge the gap between observations and simulations across a broad swath of astrophysics. The OutLines code accounts for differences in velocity field, density profile, and outflow geometries, making OutLines versatile for a wide variety of astrophysical phenomena. We demonstrate the wide applicability of OutLines by using the code to model line profiles in an H II region knot, super star clusters, a starburst galaxy, and an AGN. In each of these contexts, we illustrate how OutLines can illuminate key underlying physics in ways that improve scientific understanding and address important open questions in astronomy, including the key mechanisms in the baryon cycle, the evolution of H II regions and galaxies, and even Lyman continuum escape. OutLines will be a critical resource as massively multiplexed spectroscopic surveys with facilities like WEAVE and 4MOST come online, providing the means to probe feedback with deeper, higher resolution spectroscopy for unprecedented large samples of objects.

Based on the eigenvector continuation, which is mathematically an instance of the reduced basis method (RBM), we construct an emulator for coupled-channels calculations for heavy-ion fusion reactions at energies around the Coulomb barrier. We apply this to the $^{16}$O+$^{144,154}$Sm, $^{186}$W reactions and examine whether the emulator can be used to extract the deformation parameters of the target nuclei. We show that the emulator not only accelerates the calculations but also has an ability to accurately extract the nuclear shapes. This indicates that the emulator provides a powerful tool to systematically explore intrinsic shapes of atomic nuclei, enhancing our understanding of the fundamental properties of nuclear systems.

This paper investigates the interaction between scalar field dark matter and stepped dark radiation as an extension of the Wess-Zumino dark radiation (WZDR) model. The WZDR framework, based on supersymmetry, shows promise in alleviating the Hubble tension. Previous studies have explored the interaction between stepped dark radiation and cold dark matter to address both the Hubble and $S_8$ tensions. In this work, we replace cold dark matter with scalar field dark matter, introducing its interaction with stepped dark radiation via pure momentum coupling, creating a novel model. We constrain the model parameters using a range of cosmological datasets, including the Cosmic Microwave Background, Baryon Acoustic Oscillations, Type Ia Supernovae, $H_0$ measurement from SH0ES, $S_8$ data from the Dark Energy Survey Year 3, and Atacama Cosmology Telescope data. Our analysis shows that the new model performs similarly to the original WZDR model, with only a marginal improvement. The best-fit $H_0$ values for the coupled model and WZDR model are $70.89$ km/s/Mpc and $70.68$ km/s/Mpc, respectively. The $S_8$ parameter decreases from $0.8136$ in the original model to $0.8113$ in the new model. Compared to the $Λ$CDM model, the new model improves the $χ^2_{\min}$ statistic by $-8.34$, while the WZDR model improves it by $-7.49$. The coupling signal remains weak, with the coupling parameter constrained to $\log_{10}(ξ)<4.56$. Although the coupling model provides some improvement, it does not fully resolve the cosmological tensions, suggesting the need for further investigation.

The electromagnetic calorimeter (ECAL) is a key detector component for precise electron and photon measurements in electron-ion collision experiments. At the Electron-Ion Collider in China (EicC), high-performance calorimetry is essential for exploring the internal structure of nucleons and studying the dynamics of quarks and gluons within quantum chromodynamics (QCD). This paper presents the optimized design and performance simulation of the EicC ECAL system. The ECAL consists of three specialized sections tailored to distinct detection environments: (1) an electron-Endcap employing high-resolution pure Cesium Iodide (pCsI) crystals, (2) a central barrel, and (3) an ion-Endcap, both adopting a cost-effective Shashlik-style sampling calorimeter with improved light yield. Each segment's geometry and material composition have been systematically optimized through Geant4 simulations to achieve excellent energy and position resolutions as well as strong electron-pion discrimination. The simulated performance indicates that the ECAL can achieve energy resolutions of 2 percent divided by sqrt(E) for pCsI crystals and 5 percent divided by sqrt(E) for Shashlik modules, meeting the design goals of the EicC detector.

The higher rank numerical range is a concept that generalizes the classical numerical range, and it has application in quantum error correction. We investigate these sets for $2$-by-$2$ block matrices with associated Kippenhahn curves consisting of ellipses (and eventually points). As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky {\it et al}.

We report the discovery of two broad-line X-ray AGNs (cid_414 and cid_947) at z ~ 3 identified in the JWST Cycle 3 COSMOS-3D program using NIRCam F444W grism spectroscopy. Both exhibit prominent HeI+Pa$γ$ emission and absorption, indicative of circumnuclear dense gas that is traced in these systems. Complementary UV and optical spectroscopy in the COSMOS field provides Ly$α$, Si IV, and C IV measurements. Both sources are detected in MIRI F1000W, and cid_414 is also detected in F2100W, indicating hot dust emission. The two AGNs show distinct black hole and obscuration properties. The source cid_414 displays little red dots (LRD)-like V-shape spectra energy distribution (SED) shape with a turnover near the Balmer 4000 Å break, and a narrow Ly$α$ line with $\log L_{\rm Lyα}=42.49\pm0.01~\mathrm{erg\ s^{-1}}$, with no additional metal lines detected. In contrast, cid_947 exhibits a higher HeI absorption column density, larger X-ray--inferred $N_{\rm H}$, lower intrinsic 2--10 keV luminosity, and strong blueshifted features in He I, Si IV, and C IV absorption with velocity offsets exceeding $5000~\mathrm{km\ s^{-1}}$. Photoionization modeling implies gas densities of $\sim10^{9-10} \mathrm{cm^{-3}}$ and sizes comparable to the broad-line region, consistent with dense gas envelopes predicted for LRDs. Together with previous detections of HeI absorption in compact little red dots, these results suggest that dense circumnuclear gas is likely prevalent at high redshift and may regulate obscuration and black hole--host co-evolution across AGN types.

In this work, we use neutrino masses as a probe of the neutrino-light-quark effective scalar interactions. It is found that neutrinos can acquire masses not only from the usual light quark loop corrections but also from the light quark condensates. The latter contribution has been overlooked in the literature. We show that both contributions are comparable for operators involving $u$ and $d$ quarks, while quark loop corrections dominate for operators involving the $s$ quark. Using the low-energy effective field theory extended with light right-handed neutrinos and matching to chiral perturbation theory, we systematically analyze these contributions, deriving constraints on the corresponding Wilson coefficients from neutrino mass bounds, coherent elastic neutrino-nucleus scattering, and light pseudoscalar meson invisible decays. Our analysis shows that electron neutrino mass measurements provide the most stringent constraints on these scalar couplings, significantly improving upon limits from other observables. The results highlight the importance of including both perturbative and nonperturbative contributions in complete phenomenological analyses of neutrino mass generation mechanisms.

We present a Matlab code for modelling and topology optimization of hyperelastic structures, including contact modelled by the Third Medium Contact (TMC) approach. By using the so-called HuHu-regularization we penalize the skew distortion of the bilinear finite elements discretizing void regions, thus promoting convergence of the nonlinear solver. First, we show how this method is implemented in a compact code, allowing to simulate contact and force transfer in hyperelastic structures. We then solve two topology optimization problems for minimum end-compliance of structures exhibiting contact. In the first example, contact happens at the supported boundary, while the second features self-contact. The Matlab scripts that replicate the results are included, and we discuss some possible extensions to more general problems.

This review provides an introduction to the essential physics of soft adhesion, including the thermodynamics of adhesion and wetting, the mechanics of contact with deformable materials, and the material properties that most affect interfacial interactions with soft solid gels and elastomers. Throughout, we emphasize both foundational physics and current experimental and theoretical research in these areas. We conclude with a practical overview of standard experimental test methods for characterizing soft adhesion. The physical understanding developed herein provides the basis for understanding the mechanics of contact with soft materials.

We analyze JWST observations of the central region of the globular cluster $ω$ Centauri (NGC 5139, $ω$ Cen hereafter), around the position of the candidate IMBH inferred by \cite{haberle_fast-moving_2024} from the motion of fast-moving stars in multi-epoch HST observations. We performed PSF-fitting photometry for sources in NIRCam (F200W and F444W) and MIRI (F770W and F1500W) and constructed UV to IR SEDs for sources within the central region of the cluster by using HST photometry from oMEGACat \citep{haberle_omegacat_2024}. None of the SEDs of reliably measured sources within this region resembles the SEDs computed from models of \cite{pesce_toward_2021} for IMBHs accreting from intracluster medium at low rates. Our JWST limits place constraints on combinations of IMBH mass and accretion rate, either due to the amount of material available to be accreted, or due to the fraction of accreting matter that actually falls into the IMBH. Our non-detection then does not necessarily contradict the mass range of the IMBH inferred from the fast moving stars. We discuss these constraints in the context of the model of \cite{pesce_toward_2021}. We find that JWST limits are more restrictive than the existing radio limits for IMBH masses $\lesssim 6000 M_{\odot}$. It is also possible that the faint IMBH emission is dominated by the light of a nearby star. Tighter limits on accretion onto the candidate IMBH can be placed with deeper observations, a more precise localization of the IMBH, and better measurements of the local intracluster medium density and temperature at the center of the cluster.

Caustic-crossing stars observed in giant arcs behind galaxy clusters provide a powerful probe of dark matter substructure. While previous work has focused on point-like lenses such as primordial black holes, we extend this framework to extended dark objects (EDOs), including ultracompact minihalos formed from the collapse of primordial overdensities. We develop an analytic model of microlensing by EDOs embedded in a macrolensing cluster potential and derive the resulting caustics and light curves. Depending on the EDO size relative to the effective Einstein radius, we show that they may generate additional narrow caustics, leading to novel features in the light curve. Applying our framework to the MACS J1149 LS1 ``Icarus'' event, we constrain EDOs with radii up to $10^7 R_\odot$. Our results demonstrate that caustic-crossing events complement galactic microlensing searches, as they can probe EDOs with larger physical size. We discuss the implications for current and future observations, which promise to deliver a statistical sample of caustic transients and correspondingly sharper constraints on dark objects.

We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational letters or a rational argument. It complements the previous implementation, HyperInt, in MAPLE by Erik Panzer, utilizing the advantages of FORM in the efficient handling of large symbolic expressions. Among a wide range of applications, this approach enables the computation of many Feynman integrals.

Nanofluidic transport is ubiquitous in natural systems from extra-cellular communication in biology to geological phenomena, and promotes the emergence of new technologies such as energy harvesting and water desalination. While experimental access to ultraconfined fluids has advanced rapidly, their behavior challenges conventional theoretical descriptions based on Poisson-Boltzmann theory or the Stokes equation whose possible extension remains an open question. In this work, we use molecular dynamics simulations to investigate ionic transport within wetting films of water confined on silica surfaces down to the sub-nanometer scale. We then analyze these results using a simple one-dimensional theoretical framework. Remarkably, we show that this model remains valid even at confinement close to the molecular scale. Our results reveal that the dynamic of ion plays a key role in ionic transport, through ion adsorption at the water-silica interface. Adsorbed cations do not participate in ionic conduction, but instead generate molecular-scale roughness and transmit additional frictional forces to the substrate. This mechanism produces an apparent viscosity increase in electrostatically driven flows, reaching up to four times the bulk value in the case of potassium. Our findings highlight the critical role of interfacial ion adsorption in nanoscale hydrodynamics and provide new insights for interpreting experiments and designing nanofluidic systems.

Entanglement between remote quantum mechanical systems enables a range of quantum information tasks in communication, computation and distributed sensing. Large numbers of entangled subsystems also require experimentally accessible and practically feasible methods of verifying the genuine, i.e., simultaneous, entanglement of all subsystems. We have derived a class of entanglement witnesses suitable for $W$-states, which are states where a single excitation is coherently distributed across subsystems initially in their ground state or a state with low thermal occupation, e.g., via detection of a Raman-scattered photon. The entanglement is witnessed through violation of an inequality involving number statistics, which can be measured via detection of subsequent Raman-scattered photons. Unlike conventional, partially tomographic, witnesses, our method is experimentally accessible for both multipartite and continuous variable systems. The thermal robustness of the method is quantified by the initial thermal occupations for which violation occurs. As an alternative approach, we have derived an inequality which tests the nonlocal, or quantum coherent, nature of the photon measurement backaction which produces the $W$-state. Violation of this alternative inequality implies the entanglement of the resulting state given the assumption of a separable initial state, under less stringent thermal constraints than the general entanglement witness. Our results are applicable to all Raman-scattering systems which can exhibit sufficient degrees of quantum indistinguishability.

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $α\in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $α$-stable coherent systems of type $(n; c_{1}, c_{2}, k)$ with $k < n$ on $X$, for sufficiently large values of $α$. We prove that, for $α$ sufficiently large, the moduli space admits a description as a Grassmann bundle over a moduli space of $H$-stable torsion free sheaves. As a consequence, we obtain results on irreducibility, dimension. Our approach relies on establishing a correspondence between $α$-stable coherent systems and extensions of $H$-stable torsion free sheaves by trivial bundles.

In this paper, we study transfer learning for high-dimensional factor-augmented sparse linear models, motivated by applications in economics and finance where strongly correlated predictors and latent factor structures pose major challenges for reliable estimation. Our framework simultaneously mitigates the impact of high correlation and removes the additional contributions of latent factors, thereby reducing potential model misspecification in conventional linear modeling. In such settings, the target dataset is often limited, but multiple heterogeneous auxiliary sources may provide additional information. We develop transfer learning procedures that effectively leverage these auxiliary datasets to improve estimation accuracy, and establish non-asymptotic $\ell_1$- and $\ell_2$-error bounds for the proposed estimators. To prevent negative transfer, we introduce a data-driven source detection algorithm capable of identifying informative auxiliary datasets and prove its consistency. In addition, we provide a hypothesis testing framework for assessing the adequacy of the factor model, together with a procedure for constructing simultaneous confidence intervals for the regression coefficients of interest. Numerical studies demonstrate that our methods achieve substantial gains in estimation accuracy and remain robust under heterogeneity across datasets. Overall, our framework offers a theoretical foundation and a practically scalable solution for incorporating heterogeneous auxiliary information in settings with highly correlated features and latent factor structures.

In this paper, we study (noisy) linear systems, and their $\ell_0$-regularized optimization problems, coupled with general data fidelity terms. Recent approaches for solving this class of problems have proposed to consider non-convex exact continuous relaxations that preserve global minimizers while reducing the number of local minimizers. Within this framework, we consider the class of $\ell_0$-Bregman relaxations, and establish sufficient conditions under which a critical point is isolated in terms of sparsity, in the sense that any other critical point has a strictly larger cardinality. In this way, we ensure a form of uniqueness in the solution structure. Furthermore, we analyze the exact recovery properties of such exact relaxations. To that end, we derive conditions under which the oracle solution (i.e., the one sharing the same support as the ground-truth) is the unique global minimizer of the relaxed problem, and is isolated in terms of sparsity. Our analysis is primarily built upon a novel property we introduce, termed the Bregman Restricted Strong Convexity. Finally, we specialize our general results to both sparse Gaussian (least-squares) and Poisson ((generalized) Kullback-Leibler divergence) regression problems. In particular, we show that our general analysis sharpens existing bounds for the LS setting, while providing an entirely new result for the KL case.

Hypergraph product (HGP) codes are one of the most popular family of quantum low-density parity-check (LDPC) codes. Circuit-level simulations show that they can achieve the same logical error rate as surface codes with a reduced qubit overhead. They have been extensively optimized by importing classical techniques such as the progressive edge growth, or through random search, simulated annealing or reinforcement learning techniques. In this work, instead of machine learning (ML) algorithms that improve the code performance through local transformations, we impose additional global symmetries, that are hard to discover through ML, and we perform an exhaustive search. Precisely, we focus on the hypergraph product of two cyclic codes, which we call CxC codes and we study C2 codes which are the product a cyclic code with itself and CxR codes which are the product of a cyclic codes with a repetition code. We discover C2 codes and CxR codes that significantly outperform previously optimized HGP codes, achieving better parameters and a logical error rate per logical qubit that is up to three orders of magnitude better. Moreover, some C2 codes achieve simultaneously a lower logical error rate and a smaller qubit overhead than state-of-the-art LDPC codes such as the bivariate bicycle codes, at the price of a larger block length. Finally, leveraging the cyclic symmetry imposed on the codes, we design an efficient planar layout for the QCCD architecture, allowing for a trapped ion implementation of the syndrome extraction circuit in constant depth.

Here we introduce the SEEDZ simulations, a suite of cosmological hydrodynamic simulations exploring the formation and growth of the first massive black holes in the Universe. SEEDZ includes models for Population III star formation, supernovae explosions and the resulting formation of light seed black holes, metal enrichment and subsequent Population II star formation, heavy seed black hole formation, Eddington and super-Eddington accretion schemes as well as black hole feedback. In this paper, we cover the overall methodologies employed and present our current results at $z=15$. Our main result so far is that black holes initially grow faster than their host galaxy, and hence over-massive black holes are a feature of the high-redshift Universe. The fundamental black hole-galaxy relationships we observe at $z = 0$ (especially the M$_{\rm BH}$ - M$_*$ relationship) likely only emerge in more mature galaxies. At high-redshift, that relationship has not yet been established. We find that even at these high redshifts, MBHs can grow from their initial heavy seed mass of $\sim$10$^4$ M$_\odot$ up to 10$^6$ M$_\odot$. At the high end of our MBH masses, our simulated galaxy M$_{\rm BH}$ - M$_*$ relations match the observed high redshift trends i.e. over-massive BHs with M$_{\rm BH}$/M$_{\rm star} \sim 10^{-2}$. This initial set of simulations will continue to run down to $z=10$, where we will perform a comprehensive comparison of simulated MBH number densities and M$_{\rm BH}$ - M$_*$ relations with JWST observations. Further simulations with higher resolution will then follow.

The value alignment of sociotechnical systems has become a central debate, but progress depends on how human values are perceived in the content these systems surface and how such perceptions can be measured at scale. Social media platforms are a prominent class of sociotechnical systems where algorithmic curation shapes exposure to value-laden content at scale. Large-language models offer new opportunities for measuring expressions of human values (e.g., humility or equality) in social media data, but value expressions can be subjective: different people will annotate the same post with different values. In this paper, we draw on the Schwartz value system as a broadly encompassing and theoretically grounded set of basic human values, and introduce a framework to personalize the measurement of expressions of Schwartz values in social media posts at scale. We collect 32,370 ground truth value expression annotations from N=1,079 people on 5,211 social media posts representative of real users' feeds. Due to the subjectivity of the task, we observe low levels of inter-rater agreement between people, and low agreement between human raters and LLM-based methods. In response, we construct a personalization architecture for classifying value expressions by learning from a small number of highly informative calibration annotations per user. In evaluation, we find that modeling these differences successfully yields value expression predictions that people agree with more than they agree with other people. These results contribute new methods and understanding for the measurement of human values in social media data.

Glassy dynamics in active biological cells remain a subject of debate, as cellular activity rarely slows enough for true glassy features to emerge. In this study, we address this paradox of glassy dynamics in epithelial cells by integrating experimental observations with an active vertex model. We demonstrate that while crowding is essential, it is not sufficient for glassy dynamics to emerge. A mechanochemical feedback loop (MCFL), mediated by cell shape changes through the contractile actomyosin network, is required to drive glass transition in dense epithelial tissues, as revealed via a crosstalk between actin-based cell clustering and dynamic heterogeneity in experiments. Incorporating MCFL into the vertex model reveals contrasting results from those previously predicted by theories -- we show that the MCFL can counteract cell division-induced fluidisation and enable glassy dynamics to emerge through active cell-to-cell communication. Furthermore, our analysis reveals, for the first time, the existence of novel collective mechanochemical oscillations that arise from the crosstalk of two MCFLs. Together, we demonstrate that an interplay between crowding and active mechanochemical feedback enables the emergence of glass-like traits and collective biochemical oscillations in epithelial tissues with active cell-cell contacts.

The deep connection between black hole thermodynamics and spacetime geometry remains a central focus of general relativity. While recent studies have revealed a precise correspondence for null orbits, given by $K = -λ^2$ between the Gaussian curvature $K$ and the Lyapunov exponent $λ$, its validity for timelike orbits had remained unknown. Our work introduces the massive particle surface (MPS) framework and constructs a new geometric quantity $\mathcal{G}$. We demonstrate that $\mathcal{G} \propto -λ^2$ on unstable timelike orbits, thus establishing the geometry-dynamics correspondence for massive particles. Crucially, near the first-order phase transition of a black hole, $\mathcal{G}$ displays synchronized multivalued behavior with the Lyapunov exponent $λ$ and yields a critical exponent $δ=1.0244$. Our results demonstrate that spacetime geometry encodes thermodynamic information, opening a new pathway for studying black hole phase transitions from a geometric perspective.

As demand for quantum technologies increases, so does the need to generate and classify non-classical correlations in complex many-body systems. We introduce a simple and versatile method for creating and certifying entanglement and many-body Bell correlations. This method relies on a single qubit interacting with an $N$-qubit system. We demonstrate that: (i) such pairwise interaction is sufficient to induce many-body quantum correlations, and (ii) the qubit can serve as a probe to extract all information about these correlations. Thus, single-qubit measurements reveal multi-partite entanglement and $N$-body Bell correlations, enabling the rapid and efficient certification of non-classicality in complex systems.

Optical periodic structures exhibiting a degenerate band edge (DBE) are of significant interest for various applications such as switching, sensing, high-power amplification, and lasing. At the edge of the bandgap in such structures, a fourth-order exceptional point degeneracy arises, leading to an extremely flat dispersion band. We propose and study a Silicon-on-Insulator-compatible structure composed of two coupled waveguides with asymmetric gratings. The dispersion relations and the field profiles are obtained using three-dimensional finite-difference time-domain simulations, and we provide a set of practical guidelines for the design and optimization of such structures, in order to obtain a DBE. We analyze the transmission and reflection spectra of finite-size devices, and investigate their spectral properties near the stationary points. The scaling of the resonance quality factor with the number of unit cells is studied, revealing a performance that surpasses that of conventional periodic structures. Finally, we examine the robustness of the DBE with respect to fabrication tolerances and structural imperfections.

Particle therapy relies on up-to-date knowledge of the stopping power of the patient tissues to deliver the prescribed dose distribution. The stopping power describes the average particle motion, which is encoded in the distribution of prompt-gamma photon emissions in time and space. We reconstruct the spatiotemporal emission distribution from multi-detector Prompt Gamma Timing (PGT) data. Solving this inverse problem relies on an accurate model of the prompt-gamma transport and detection including explicitly the dependencies on the time of emission and detection. Our previous work relied on Monte-Carlo (MC) based system models. The tradeoff between computational resources and statistical noise in the system model prohibits studies of new detector arrangements and beam scanning scenarios. Therefore, we propose here an analytical system model to speed up recalculations for new beam positions and to avoid statistical noise in the model. We evaluated the model for the MERLINO multi-detector-PGT prototype. Comparisons between the analytical model and a MC-based reference showed excellent agreement for single-detector setups. When several detectors were placed close together and partially obstructed each other, intercrystal scatter led to differences of up to 10 % between the analytical and MC-based model. Nevertheless, when evaluating the performance in reconstructing the spatiotemporal distribution and estimating the stopping power, no significant difference between the models was observed. Hence, the procedure proved robust against the small inaccuracies of the model for the tested scenarios. The model calculation time was reduced by 1500 times, now enabling many new studies for PGT-based systems.

We consider cohomological stable envelopes for a natural torus action $\mathsf{T}$ on $X=T^*Gr(k,n)$, introduced by Maulik-Okounkov. We define the $\mathbb{C}^*_\hbar$-equivariant integral of the stable envelope using equivariant localization over the subtorus $\mathbb{C}^*_\hbar\subset\mathsf{T}$, and compute the integral as a non-equivariant limit of the localization over the full torus, $\mathsf{T}$. The integral of such a class is an integer times a power of $\hbar$, and the main result of this paper is a combinatorial formula for these integers. In 3d mirror symmetry, these non-equivariant limits are expected to reflect some curve counting phenomena on the 3d mirror dual, $X^\vee$. When $k=1$, we obtain the binomial coefficients, and we study some of the combinatorics of the integers for higher $k$, which haven't appeared in the literature before. We give some conjectures and interpretations on extending this phenomena to type A quiver and bow varieties.

Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as a given threshold, a standard decision version of the problem, is NP-complete. However, this decision problem becomes tractable when either the number of lower-level variables or the number of lower-level constraints is fixed, which prompts the question: What if restrictions are placed on the upper-level problem? In this paper, we address this gap by showing that the decision version of bilevel LP remains NP-complete even when there is only a single upper-level variable, no upper-level constraints (apart from the constraint enforcing optimality of the lower-level decision) and all variables are bounded between 0 and 1. This result implies that fixing the number of variables or constraints in the upper-level problem alone does not lead to tractability in general. On the positive side, we show that there is a polynomial-time algorithm that finds a local optimal solution of such a rational bilevel LP instance. We also demonstrate that many combinatorial optimization problems, such as the knapsack problem and the traveling salesman problem, can be written as such a bilevel LP instance.

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we prove a well-posedness result in Gelfand-Shilov spaces.