We observe microwave nonreciprocal one-way transparency via ultrastrongly-coupled magnetochiral polaritons (MChPs) in a metamolecule at room temperature. The experimental results using MCh metamolecules with simultaneous breaking of time-reversal and space-inversion symmetries are reproduced by numerical simulations. Based on effective polarizability tensor analyses, we verify massive synthetic motion of MChPs as an origin of the one-way transparency. This study paves a way to hybrid quantum systems and synthetic gauge fields using metamaterials.

Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume fault-tolerant quantum computers, so they cannot yet be benchmarked on real hardware. Because an algorithm with better asymptotic scaling can underperform on instances of practical interest, the question of which of these algorithms is the most promising remains open. In this work, we implement a method to partially address this question. We consider four well-known QLS algorithms which directly implement an approximate matrix inversion function: the Harrow-Hassidim-Lloyd algorithm, two algorithms utilizing a linear combination of unitaries, and one utilizing the quantum singular value transformation (QSVT). These methods, known as functional QLS, share nearly identical assumptions about the problem setup and oracle access. Their computational cost is dominated by query calls to a matrix oracle encoding the problem one wants to solve. We provide formulas to count the number of queries needed to solve specific problem instances; these can be used to benchmark the algorithms on real-life instances without access to quantum hardware. We select three data sets: random generated instances that obey the assumptions of functional QLS, linear systems from simplex iterations on MIPLIB, and Poisson equations. Our methods can be easily extended to other data sets and provide a high-level guide to evaluate the performance of a QLS algorithm. In particular, our work shows that HHL underperforms in comparison to the other methods across all data sets, often by orders of magnitude, while the QSVT-based method shows the best performance.

To address the computational challenges of Model Predictive Control (MPC), recent research has studied using imitation learning to approximate MPC with a computationally efficient Deep Neural Network (DNN). However, this introduces a common issue in learning-based control, the simulation-to-reality (sim-to-real) gap. Inspired by Robust Tube MPC, this study proposes a new control framework that addresses this issue from a control perspective. The framework ensures the DNN operates in the same environment as the source domain, addressing the sim-to-real gap with great data collection efficiency. Moreover, an input refinement governor is introduced to address the DNN's inability to adapt to variations in model parameters, enabling the system to satisfy MPC constraints more robustly under parameter-changing conditions. The proposed framework was validated through two case studies: cart-pole control and vehicle collision avoidance control, which analyzed the principles of the proposed framework in detail and demonstrated its application to a vehicle control case.

Defects and interfaces are essential to understand the properties of matter. However, studying their dynamics in the quantum regime remains a challenge in particular concerning the regime of two spatial dimensions. Recently, it has been shown that a quantum counterpart of the hard-disk problem on a lattice yields defects and interfaces, which are stable just due to quantum effects while they delocalize and dissolve in an analogous classical stochastic process. Here, we study in more detail the properties of defects and interfaces in this quantum hard-disk problem with a particular emphasis on the stability of these quantum effects upon including perturbations. Specifically, we introduce short-range soft-core interactions between the hard disks. From both analytical arguments and numerical simulations we find that large classes of defects and interfaces remain stable even under such perturbations suggesting that the quantum nature of the dynamics exhibits a large range of robustness. Our findings demonstrate the stability and non-classical behavior of quantum interface dynamics, offering insights into the dynamics of two-dimensional quantum matter and establishing the quantum hard-disk model as a platform for studying unconventional constrained quantum dynamics.

Rhythmic phenomena, which are ubiquitous in biological systems, are typically modelled as systems of coupled limit cycle oscillators. Recently, there has been an increased interest in understanding the impact of higher-order interactions on the population dynamics of coupled oscillators. Meanwhile, the estimation of a mathematical model from experimental data is an essential step in understanding the dynamics of real-world complex systems. In coupled oscillator systems, identifying the type of interaction (e.g. pairwise or three-body) is challenging, because different interactions can exhibit similar dynamical states in experimental conditions. In this study, we have developed a method based on the adaptive LASSO (Least Absolute Shrinkage and Selection Operator) to infer the interactions among oscillators from time series data. The proposed method successfully identifies the type of interaction and estimates the probabilities of pairwise and three-body couplings. Through systematic analysis of synthetic datasets, we have demonstrated that our method outperforms two baseline methods, LASSO and OLS (Ordinary Least Squares), in accurately inferring the topology and strength of couplings between oscillators. Furthermore, the proposed method is applied to human brain network data, demonstrating its practical utility. Finally, we extend the method to more general oscillatory systems, including those exhibiting the deformation of limit cycles and those with four-body interactions. These results suggest that our method is a promising tool for identifying interaction mechanisms in oscillatory systems.

In this article, we present two new characterizations of circular-arc bigraphs based on their vertex ordering. Also, we provide a characterization of circular-arc bigraphs in terms of forbidden patterns with respect to a particular ordering of their vertices.

We compute the magnetoelectric conductivity for ideal nodal-line semimetals (NLSMs), with a finite but tiny mass-gap, in distinct planar-Hall set-ups. Each differing configuration results from the relative orientation of the nodal-ring's plane with respect to the plane spanned by the electric ($\mathbf E $) and magnetic ($\mathbf B$) fields. The net conductivity tensor has components comprising the Drude, anomalous-Hall, in-plane (with $\mathbf E$ and $\mathbf B$) longitudinal and transverse, and Lorentz-force-operator-induced parts. Our results feature the signatures of the inherent topology of a gapped NLSM, revealed through nonzero values of the Berry curvature and the orbital magnetic moment. In particular, we show that both of these vector fields, arising in the momentum space, give rise to terms of comparable magnitudes in the resulting response. Our explicit theoretical expressions will help identify unique signatures of NLSMs in contemporary experiments.

We prove a quasi-linear upper bound on the size of $K_{t,t}$-free polygon visibility graphs. For visibility graphs of star-shaped and monotone polygons we show a linear bound. In the more general setting of $n$ points on a simple closed curve and visibility pseudo-segments, we provide an $O(n \log n)$ upper bound and an $Ω(nα(n))$ lower bound.

The search for light scalar and pseudoscalar particles provides a promising avenue for probing physics beyond the Standard Model (SM). In this study, we investigated the exotic decay channels of the 125 GeV SM-like Higgs boson into pairs of light CP-odd ($a_s$) or CP-even ($h_s$) Higgs bosons within the framework of the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM). A comprehensive parameter space scan is performed using the MultiNest algorithm, incorporating constraints from $ \textsf{HiggsSignals-2.6.2} $, $ \textsf{HiggsBounds-5.10.2} $, and ATLAS experimental searches, under two distinct scenarios where either the lightest ($h_1$) or next-to-lightest ($h_2$) CP-even state is the observed Higgs boson ($h$). Our results demonstrate that $ \textsf{HiggsBounds} $ imposes the most stringent exclusion limits due to its sensitivity to direct searches for non-SM Higgs bosons. In the $h_2$ scenario, $ \textsf{HiggsSignals} $ can additionally exclude regions with suppressed exotic branching ratios (e.g., $ Br(h \to a_sa_s \to ττbb) \leq 2.5\%$), due to its sensitivity to indirect deviations caused by the kinematically enhanced decay \( h \to h_sh_s \). Under combined constraints from \( \textsf{HiggsTools} \), $h$ must retain at least 93\% SM-like component (\( V_h^\text{SM} \geq 0.93 \)) with no more than 32\% singlet admixture (\( V_h^\text{S} \leq 0.32 \)); in the $ h_2 $ case, the lightest scalar $ h_s $ exhibits high singlet purity ($ V_{h_s}^\text{S} \geq 0.94 $). Furthermore, dark matter (DM) phenomenology indicates that singlino- or higgsino-dominated DM is viable in the $ h_1 $ scenario, with dominant annihilation channels including $ \tildeχ_1^0\tildeχ_1^0 \to h_sa_s $ for singlino-like DM and chargino co-annihilation for higgsino-like DM, whereas the $ h_2 $ scenario favors higgsino-dominated DM.

Entangled photon pairs are key elements in quantum communication and quantum cryptography. State-of-the-art sources of entangled photons are mainly based on parametric down-conversion from nonlinear crystals, which is probabilistic in nature, and on cascade emission from biexciton quantum dots, which finds difficulties in generating entangled photons in the visible regime. Here, we use the Wigner-Weisskopf theory to provide a demonstration that polarization-entangled photon pairs can be emitted from two interacting quantum emitters with two-level-system behavior and perpendicular transition dipole moments. These emitters can represent a large variety of systems (e.g., organic molecules, quantum dots, and diamond color centers) offering a large technological versatility, for example, in the spectral regime of the emission. We show that a highly entangled photon pair can be postselected from this system by including optical filters. Additionally, we verify that the photon entanglement is not significantly affected by small changes in the detection directions and in the orientation between the dipole moments.

In South Korea, power grid is currently operated based on the static line rating (SLR) method, where the transmission line capacity is determined based on extreme weather conditions. However, with global warming, there is a concern that the temperatures during summer may exceed the SLR criteria, posing safety risks. On the other hand, the conservative estimates used for winter conditions limit the utilization of renewable energy. Proposals to install new lines face significant financial and environmental hurdles, complicating efforts to adapt to these changing conditions. Dynamic Line Rating (DLR) offers a real-time solution but requires extensive weather monitoring and complex integration. This paper proposes a novel method that improves on SLR by analyzing historical data to refine line rating criteria on a monthly, seasonal, and semi-annual basis. Through simulations, we show our approach significantly enhances cost effectiveness and reliability of the power system, achieving efficiencies close to DLR with existing infrastructure. This method offers a practical alternative to overcome the limitations of SLR and the implementation challenges of DLR.

In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local interaction terms in the space of nonnegative Radon measures equipped with the flat metric. The solutions, given by families of Radon measures, are approximated by linear combinations of Dirac measures. For this purpose, we introduce a finite-range approximation of the measure-valued model functions, provided that they are linear. By applying an operator splitting technique, we are able to separate the effects of the transport from those of growth and the non-local interaction. We derive the order of convergence of the numerical scheme, which is linear in the spatial discretization parameters and polynomial of order $α$ in the time step size, assuming that the model functions are $α$ Hölder regular in time. In a second step, we show that our proposed algorithm can approximate the posterior measure of Bayesian inverse models, which will allow us to link model parameters to measured data in the future.

We prove that the quadratically enriched count of rational curves in a smooth toric del Pezzo surface passing through $k$-rational points and pairs of conjugate points in quadratic field extensions $k\subset k(\sqrt{d_i})$ can be determined by counting certain tropical stable maps through vertically stretched point conditions with a suitable multiplicity. Building on the floor diagram technique in tropical geometry, we provide an algorithm to compute these numbers. Our tropical algorithm computes not only these new quadratically enriched enumerative invariants, but simultaneously also the complex Gromov-Witten invariant, the real Welschinger invariant counting curves satisfying real point conditions only, the real Welschinger invariant of curves satisfying pairs of complex conjugate and real point conditions, and the quadratically enriched count of curves satisfying $k$-rational point conditions.

In resonance fluorescence excitation experiments, light emitted from solid-state quantum emitters is typically filtered to eliminate the laser photons, ensuring that only red-shifted Stokes photons are detected. However, theoretical analyses of the fluorescence intensity correlation often model emitters as two-level systems, focusing on light emitted exclusively from the purely electronic transition (the zero-phonon line), or they rely on statistical approaches based on conditional probabilities that neglect the quantum coherence between the emitters and the coherence between the electric fields they generate. Here, we propose a model to characterize the correlation of either zero-phonon line photons or Stokes-shifted photons. This model successfully reproduces the experimental correlation of Stokes-shifted photons emitted from two interacting molecules and predicts that this correlation is affected by quantum coherence. Besides, we analyze the role of quantum coherence in the Stokes-shifted emission from two distant emitters, showing a sharp peak at zero time delay due to the Hanbury Brown--Twiss effect.

We propose a scalable trapped-ion quantum-computing architecture that efficiently incorporates quantum error correction. The chip design exploits orthogonal qubit connectivity by assigning horizontal trap regions to transversal logical gates and vertical regions to nontransversal gates and syndrome extraction, thereby enabling universal gate operations with minimal ion shuttling and reduced hardware complexity. Using a dedicated software tool, we evaluate the architecture on several benchmark algorithms and scheduling policies for two-dimensional color code of varying code distance. Our results demonstrate that increasing the code distance by two reduces the effective logical two-qubit gate error probability by approximately two orders of magnitude, reaching values as low as $10^{-8}$ with the $[[31, 1, 7]]$ color code. This improvement substantially expands the range of algorithms that can be executed reliably, up to scales of a few thousand logical qubits, depending on the algorithmic structure. Overall, these findings validate the practicality and scalability of the proposed architecture and its control strategies, highlighting a viable route toward fault-tolerant, trapped-ion quantum computing.

Comparing information structures in between deep neural networks (DNNs) and the human brain has become a key method for exploring their similarities and differences. Recent research has shown better alignment of vision-language DNN models, such as CLIP, with the activity of the human ventral occipitotemporal cortex (VOTC) than earlier vision models, supporting the idea that language modulates human visual perception. However, interpreting the results from such comparisons is inherently limited due to the "black box" nature of DNNs. To address this, we combined model-brain fitness analyses with human brain lesion data to examine how disrupting the communication pathway between the visual and language systems causally affects the ability of vision-language DNNs to explain the activity of the VOTC. Across four diverse datasets, CLIP consistently captured unique variance in VOTC neural representations, relative to both label-supervised (ResNet) and unsupervised (MoCo) models. This advantage tended to be left-lateralized at the group level, aligning with the human language network. Analyses of 33 stroke patients revealed that reduced white matter integrity between the VOTC and the language region in the left angular gyrus was correlated with decreased CLIP-brain correspondence and increased MoCo-brain correspondence, indicating a dynamic influence of language processing on the activity of the VOTC. These findings support the integration of language modulation in neurocognitive models of human vision, reinforcing concepts from vision-language DNN models. The sensitivity of model-brain similarity to specific brain lesions demonstrates that leveraging manipulation of the human brain is a promising framework for evaluating and developing brain-like computer models.

Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive, and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.

We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP incorporates several enhancements to PDHG, including diagonal preconditioning, presolving, adaptive step sizes, adaptive restarting, and feasibility polishing. Our algorithm is implemented in C++, available in Google's open-source OR-Tools library, and supports multithreading. To evaluate our method, we introduce a new collection of eleven large-scale LP problems with sizes ranging from 125 million to 6.3 billion nonzeros. PDLP solves eight of these instances to optimality gaps of 1% (with primal and dual feasibility errors of less than $10^{-8}$) within six days on a single machine. We also compare PDLP with Gurobi barrier, primal simplex, and dual simplex implementations. These traditional methods are designed to solve linear programs to much tighter optimality gaps but struggle to solve these instances. Gurobi barrier solves only three instances, exceeding our 1TB RAM limit on the other eight. While primal and dual simplex are more memory-efficient than the barrier method, they are slower and solve only three instances within six days. Compared with the conference version of this work (in: Advances in Neural Information Processing Systems 34 (NeurIPS 2021)), the key new contributions are: (i) feasibility polishing, a technique that quickly finds solutions that are approximately optimal but almost exactly feasible (without which only two of the eleven problems can be solved); (ii) a multithreaded C++ implementation available in Google OR-Tools; and (iii) a new collection of large-scale LP problems. Note that the conference version should be referred to for comparisons with SCS and ablation studies, which we do not repeat in this paper.

In light of increasing observational evidence supporting the existence of ultra-compact objects, we adopt the term astrophysical black hole to refer to any object having a huge mass confined within a sufficiently small region of spacetime. This terminology encompasses both the classical black hole solutions predicted by general relativity, as well as alternative compact objects that may not possess an event horizon. We propose models of Astrophysical Black holes (ABHs) without event horizons (EHs), as a more viable explanation for the long-term quenching phenomenon in galaxies. At the same time, the short-term quenching is explained here in terms of an efficient feedback expected in the models of stellar-mass astrophysical black holes (StMABHs). We have calculated the radiative flux from the disk in a general spherically symmetric metric background and used it to contrast the distinctive features of the BHs and ABHs scenarios. We demonstrate the relative ease of wind generation from the accretion disk surrounding an ABH without an event horizon, compared to a BH, and highlight the significant strength of these winds. The nature of the feedbacks arising from accretion onto a BH and an ABH in the `quasar' and `radio' modes are compared and some possible observational signatures of the StMABHs are pointed out.

Background: In the mass regions with an abnormal shell structure, the so-called ``island of inversion," the spin-parity of odd-mass nuclei provides quantitative insights into the shell evolution. However, the experimental determination of the spin-parity is often challenging, leaving it undetermined in many nuclei. Purpose: We discuss how the shell structure affects the density profiles of nuclei in the island of inversion and investigate whether these can be probed from the total reaction and elastic scattering cross sections. Method: The antisymmetrized molecular dynamics (AMD) is employed to generate various particle-hole configurations and predict the energy levels of these nuclei. The obtained density distributions are used as inputs to the Glauber model, which is employed to calculate the total reaction and elastic scattering cross sections for revealing their relationship to the particle-hole configurations. Results: In addition to the well-known correlation between nuclear deformation and radius, we show the correlations between the particle-hole configurations and both central density and diffuseness. We show that different particle-hole configurations are well reflected in the total reaction and elastic scattering cross sections. Conclusion: The total reaction and elastic scattering cross sections are useful probes to identify the spin-parity of nuclei when different particle-hole configurations coexist.

Understanding the mechanism of single photon emission (SPE) in two-dimensional (2D) material is an unsolved problem important for quantum optical materials and the development of quantum information applications. In 2D transition metal dichalcogenides (TMDs) such as tungsten diselenide (WSe2), quantum emission has been broadly attributed to exciton localization from atomic point defects, yet the precise microscopic origins are not fully understood. This work introduces an empirically grounded computational framework that explains both the origins of facile SPE in WSe2 and its relative scarcity in related TMD, tungsten disulfide. High resolution microscopy identifies native defect geometries existing in monolayer WSe2 lattices providing the ingredients necessary to build a realistic model. The qualitative effects of chalcogen type, defect geometry, and mechanical strain on the electronic structure are then individually assessed using density functional theory, from which a specific divacancy configuration emerges as the candidate for localized single-electron transitions that match observed spectral energies. Spectroscopy and photon correlation measurements further validate this model, establishing a self-consistent link between defect geometry, electronic structure, and quantum emission. By isolating the distinct roles of chalcogen type, defect configuration, and mechanical strain, this work provides a thorough investigation of exciton localization and optical behavior, contributing to a clearer picture of the physical drivers of single photon emission in tungsten-based TMDs.

Nonrelativistic spin splitting (NRSS) challenges conventional wisdom about antiferromagnets by allowing spin-split electronic bands even in collinear orders with zero net magnetization. This sub-class of antiferromagnets, recently dubbed "altermagnets," enforces distinctive spin textures via spin-group symmetries in the crystal. However, direct experimental evidence for such symmetry-driven magnetism remains scarce, and distinguishing it from relativistic spin splitting presents additional challenges. Here, we combine first-principles calculations, symmetry analysis, and two spin-resolved spectroscopies--angle-resolved photoemission (spin-ARPES) and our newly developed spin- and angle-resolved electron reflection spectroscopy (spin-ARRES)--to achieve the first complete momentum-resolved mapping of relativistic (RSS) and nonrelastivistic (NRSS) spin splitting in CoNb$_4$Se$_8$. By probing both the occupied (spin-ARPES) and unoccupied (spin-ARRES) electronic states in a single experiment, we uncover a series of momentum-dependent spin splitting phenomena each of which switch sign under sixfold rotations and persists far above and below the Fermi level. Crucially, distinct nodal planes in momentum space distinguish NRSS from RSS features. Additionally, the observed collapse of NRSS and the persistence of RSS above the Néel temperature, distinguishes a genuine magnetic phase transition from inversion symmetry breaking. Our work demonstrates, for the first time, the combined power of spin-ARPES and spin-ARRES in capturing the full spin texture across an extended energy range, positioning CoNb$_4$Se$_8$ as a prototype for exploring spin-group-based phenomena. These findings open new routes for engineering spin-based functionalities ranging from neuromorphic computing to unconventional superconductivity in layered antiferromagnets.

In experimental and observational data settings, researchers often have limited knowledge of the reasons for missing outcomes. To address this uncertainty, we propose bounds on causal effects for missing outcomes, accommodating the scenario where missingness is an unobserved mixture of informative and non-informative components. Within this mixed missingness framework, we explore several assumptions to derive bounds on causal effects, including bounds expressed as a function of user-specified sensitivity parameters. We develop influence-function based estimators of these bounds to enable flexible, non-parametric, and machine learning based estimation, achieving root-n convergence rates and asymptotic normality under relatively mild conditions. We further consider the identification and estimation of bounds for other causal quantities that remain meaningful when informative missingness reflects a competing outcome, such as death. We conduct simulation studies and illustrate our methodology with a study on the causal effect of antipsychotic drugs on diabetes risk using a health insurance dataset.

Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of $\sim 94\%$ of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44\,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73\% and a SPAM-corrected Bell state fidelity of 98.61\%. When subtracting erasure errors, this fidelity becomes 99.16\%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.

Interest on the possible future scenarios the universe could have has grew substantially with breakthroughs on late-time acceleration. Holographic dark energy (HDE) presents a very interesting approach towards addressing late-time acceleration, presenting an intriguing interface of ideas from quantum gravity and cosmology. In this work we present an extensive discussion of possible late-time scenarios, focusing on rips and similar events, in a universe with holographic dark energy. We discuss these events in the realm of the generalized Nojiri-Odintsov cutoff and also for the more primitive holographic cutoffs like Hubble, particle and event horizon cutoffs. We also discuss the validity of the generalized second law of thermodynamics and various energy conditions in these regimes. Our work points towards the idea that it is not possible to have alternatives of the big rip consistently in the simpler HDE cutoffs, and shows the flexibility of the generalized HDE cutoff as well.

Let $\mathcal{H}$ be a hyperplane arrangement in $\mathbb{CP}^n$. We define a quadratic form $Q$ on $\mathbb{R}^{\mathcal{H}}$ that is entirely determined by the intersection poset of $\mathcal{H}$. Using the Bogomolov-Gieseker inequality for parabolic bundles, we show that if $\mathbf{a} \in \mathbb{R}^{\mathcal{H}}$ is such that the weighted arrangement $(\mathcal{H}, \mathbf{a})$ is stable, then $Q(\mathbf{a}) \leq 0$. As an application, we consider the symmetric case where all the weights are equal. The inequality $Q(a, \ldots, a) \leq 0$ gives a lower bound for the total sum of multiplicities of codimension $2$ intersection subspaces of $\mathcal{H}$. The lower bound is attained when every $H \in \mathcal{H}$ intersects all the other members of $\mathcal{H} \setminus \{H\}$ along $(1-2/(n+1))|\mathcal{H}| + 1$ codimension $2$ subspaces; extending from $n=2$ to higher dimensions a condition found by Hirzebruch for line arrangements in the complex projective plane.

We investigate the constraints on the Inert Doublet Model (IDM), a minimal extension of the Standard Model of Particle Physics featuring a scalar dark matter candidate, using data from recent and future gamma-ray observatories. The relevance of the model for indirect searches of dark matter stems from two key features: first, in the high-mass regime, IDM can achieve the correct dark matter relic abundance for masses between approximately 500 GeV and 25 TeV, aligning perfectly with the energy sensitivity of Imaging Atmospheric Cherenkov Telescopes. Second, this regime is dominated by co-annihilation processes, which elevate the thermal-relic velocity-weighted annihilation cross-section to the range of 0.5 $-$ 1.0$\times 10^{-25}$ cm$^3$ s$^{-1}$, thereby enhancing the potential gamma-ray signal from dark matter annihilation. Analyzing recent H.E.S.S. observations of the Galactic Center region, we find that dark matter particle masses within the 1 to 8 TeV range are excluded by current data. Furthermore, we project that the Cherenkov Telescope Array Observatory (CTAO) will comprehensively probe the remaining viable parameter space of the IDM. Our findings are further examined in the context of the most recent theoretical constraints, collider searches, and direct detection results from the LUX-ZEPLIN experiment.

We introduce a new class of $U(1)_X$ symmetries where all Standard Model fermions are ``chiral," i.e., the left- and right-handed components have different charges under the $U(1)_X$ symmetry. Gauge anomaly cancellation is achieved by introducing three Standard Model gauge singlet dark fermions ($f^i$; $i=1,2,3$) charged under this symmetry. We systematically present chiral solutions for cases in which (a) one, (b) two, or (c) all three generations of Standard Model fermions are charged under the $U(1)_X$ symmetry. The $U(1)_X$ charges of these dark fermions are uniquely determined by anomaly cancellation conditions. These new fermions belong to the dark sector, with the lightest of them being a good dark matter candidate. Additionally, the $Z'$ gauge boson mediates interactions between the dark and visible sectors, and we call this $U(1)_X$ symmetry as the ``dark hyperCharge" symmetry. Using a benchmark model, we explore phenomenological implications in the heavy $Z'$ case ($M_{Z'} > M_Z$), analyzing collider constraints and examining the lightest dark fermion's viability as dark matter. Our analysis shows that it satisfies all current dark matter constraints over a wide range of dark matter mass.

Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as sparsity in the regression model. The performance of such procedures can be poor under either misspecified nonlinear models or a violation of the sparsity assumption. In this paper, we propose a sufficient dimension association (SDA) technique that measures the association between each predictor and the response variable conditioning on other predictors in the high-dimensional setting. Our proposed SDA method requires neither a specific form of regression model nor sparsity in the regression. Alternatively, our method assumes normalized or Gaussian-distributed predictors with a Markov blanket property. We propose an estimator for the SDA and prove asymptotic properties for the estimator. We construct three types of test statistics for the SDA and propose a multiple testing procedure to control the false discovery rate. Extensive simulation studies have been conducted to show the validity and superiority of our SDA method. Gene expression data from the Alzheimer Disease Neuroimaging Initiative are used to demonstrate a real application.

We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional $p$-Laplace non-homogeneous equation $(-Δ_p)^su =f$, with $0<s<1$, $1<p<\infty$, for data $f$ satisfying a weighted $L^{p'}$ condition in a doubling metric measure space $(Z,d_Z,ν)$ that is possibly unbounded. Our approach is inspired by the work of Caffarelli and Silvestre \cite{CS} (see also Mol{č}anov and Ostrovski{ĭ} \cite{MO}), and extends the techniques developed in \cite{CKKSS}, where the bounded case is studied. Unlike in \cite{EbGKSS}, we do not assume that $Z$ supports a Poincaré inequality. The proof is based on the well-posedness of the Neumann problem on a Gromov hyperbolic space $(X,d_X, μ)$ that arises as an hyperbolic filling of $Z$.