Quantum batteries provide a useful setting for exploring nonequilibrium many-body effects in energy storage. Here we investigate the optimization of a quantum battery based on the central-spin model. We identify two complementary structural indicators associated with the effective charging dynamics: one yields an upper bound on the average charging power, while the other characterizes the buildup of stored energy. We show that these two indicators are jointly optimized at a distinguished initial charger excitation number, which selects a particular Dicke sector of the model. At this common optimal point, the effective charging Hamiltonian becomes exactly mirror symmetric, suggesting mirror symmetry as a useful structural indicator for optimizing quantum batteries. We further show that the corresponding optimal dynamics can be closely approximated by product initial states, in particular by spin coherent states whose excitation-number distribution is centered at the symmetry-selected point. Our results establish a direct connection between charging performance, optimal-state structure, and emergent symmetry in the central-spin quantum battery, and suggest symmetry as a useful organizing principle for efficient charging in interacting many-body quantum systems.

This paper investigates an inverse problem for the simultaneous reconstruction of two spatially varying reaction coefficients, the local proliferation rate and the competition (saturation) coefficient, together with the unknown initial condition, in a nonlinear, density-dependent reaction-diffusion model motivated by cell invasion and tumor growth dynamics. Using Carleman estimates, we establish a global uniqueness result together with a Lipschitz-type stability estimate for the reaction coefficients and a weaker, logarithmic stability estimate for the initial condition. For the numerical reconstructions, we develop a two-stage algorithm employing a time-shift strategy to decouple the coefficient and the initial condition. Numerical experiments are presented to illustrate the feasibility, accuracy, and robustness of the proposed inversion method.

In this paper we develop a combinatorial algorithm to compute the Gelfand--Kirillov (GK) dimension of simple highest weight modules for basic classical Lie superalgebras. Building upon the results for classical Lie algebras via Lusztig's {\bf a}-function and the Robinson--Schensted (RS) insertion algorithm, we extend these techniques to the super setting, providing explicit formulas for types $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(2|2n)$. Our results show that the GK dimension of a simple highest weight module is determined entirely by the even part of the Lie superalgebras.

By forming hybrid light-matter states, optical cavities offer a route for engineering material properties, however, unambiguously probing the effects of light-matter coupling remains difficult. Here, we show that the polarization-resolved statistics of photons transmitted through a cavity, measurable via $g^{(2)}$, provide one such diagnostic. By relating $g^{(2)}$ to matter correlation functions such as the Raman structure factor, we link photon bunching and antibunching to material properties. By applying this method to the stripy-to-antiferromagnetic transition in the Kitaev-Heisenberg spin model, we find that polarization-dependent patterns of bunching and antibunching encode the magnetic point-group symmetries of each phase and characterize the behavior at the phase boundary. Finally, we predict measuring $g^{(2)}$ for output photon pairs polarized orthogonal to the input field will isolate higher-order light-matter scattering processes that probe higher-order material correlations.

Let $q$ be a prime power and write $Ω$ for the bigraded algebra of regular differential forms over $\mathbb{F}_q^n$. The general linear group $GL_n(\mathbb{F}_q)$ acts on $Ω$; write $SI \subseteq Ω$ for the ideal generated by $GL_n(\mathbb{F}_q)$-invariants with vanishing constant term. The {\em $GL_n(\mathbb{F}_q)$-superspace coinvariant ring} is the quotient $SR := Ω/SI$. We calculate the bigraded Hilbert series of $SR$ and give an operator-theoretic characterization of the inverse system $SI^\perp$. Our results extend to subgroups $G$ of $GL_n(\mathbb{F}_q)$ which contain $SL_n(\mathbb{F}_q)$.

This paper is concerned with estimating the local false discovery rate (lfdr) in a two-groups model where the only assumption regarding the null distribution is symmetry about zero. Our motivation comes from the contemporary framework for multiple hypothesis testing, particularly relevant in variable selection problems, which transforms any user-specified scores into statistics whose null distributions are symmetric about zero, whereas enrichment to the right of zero is generally expected for the non-nulls. While modern methods such as the knockoff filter (Barber and Candes; 2015) are able to exploit the null property for controlling the false discovery rate (FDR), an arguably more appropriate goal is to target control of the local false discovery rate for the rejected hypotheses, as proposed in Soloff et al. (2024) where the standard two-groups model (known $f_0$ and independence) is analyzed. Here, we take a step in this direction and propose to estimate the lfdr by targeting the surrogate density ratio $f(-w)/f(w)$, for $w>0$, where $f$ is the marginal density in the aforementioned ``stripped-down'' two-groups model. We study several estimators and propose a logistic regression based method with natural cubic spline basis. We also show that any consistent estimator of this surrogate yields asymptotic lfdr control of the multiple testing procedure that thresholds the estimate at the nominal level.

Let $G$ be a graph with $p(G)$ pendant vertices and $q(G)$ quasi-pendant vertices. Denote by $m_{L(G)}(λ)$ the multiplicity of $λ$ as a Laplacian eigenvalue of $G$. A graph $G$ is called reduced, if $p(G)=q(G)$. It is known that deleting a pendant path $P_3$ from a graph $G$ cannot change $m_{L(G)}(1)$. By the reduction operation for a graph (defined by Tian and Wong, 2026), we could turn to the reduced graphs with each quasi-pendant vertex of degree 2 to investigate $m_{L(G)}(1)$. Then let $T$ be a reduced tree on $n(\geq 7)$ vertices with each quasi-pendant vertex of degree 2 and without pendant path $P_3$. We first prove that \begin{equation*} m_{L(T)}(1)\leq \frac{n-5}{6} \end{equation*} and the extremal trees attaining the upper bound are determined completely. In addition, let $G$ be an arbitrary connected reduced graph with order $n\geq 6$ and size $m$. Denote by $c=m-n+1$ the first Betti number of $G$, then we obtain \begin{equation*} m_{L(G)}(1)\leq c+\frac{n-2}{4}, \end{equation*} and the extremal graphs attaining the upper bound are characterized completely.

We investigate stationary halo-like solutions of the Gross-Pitaevskii-Poisson (GPP) system, which describes self-gravitating Bose-Einstein condensates with repulsive self-interactions, as a dark matter model. The boson mass $m_ϕ$, scattering length $a_s$, and total particle number $N$ are kept explicit, with $N$ treated as an independent macroscopic control parameter. Solving the stationary GPP equations over a broad parameter space, we identify ground-state, excited-state, and unbound solution branches according to their binding properties and nodal structure. The ground-state branch occupies a well-defined region of the $(m_ϕ,N)$ plane whose location depends strongly on the self-interaction strength, whereas the excited-state and unbound regions are largely insensitive to the initial ansatz. From the converged solutions, we derive empirical scaling relations connecting the characteristic halo radius $R_{99}$ to $m_ϕ$, $a_s$, and $N$. In the weakly interacting regime, the results reproduce the standard Schrodinger-Poisson mass-radius relation, while finite self-interactions reveal an intermediate regime in which gravity, quantum pressure, and repulsive interactions jointly determine the equilibrium structure. As an astrophysical application, we show that ground-state solutions can reproduce representative dwarf-galaxy rotation curves using only the solitonic component. We also examine the implications of current Lyman-$α$ forest constraints and find that, although increasing $a_s$ shifts equilibrium solutions toward larger boson masses compatible with existing bounds, the resulting configurations do not reproduce the observed dwarf-galaxy kinematics. These results provide a systematic characterization of stationary GPP halos and establish a direct connection between microscopic particle properties and observable galactic quantities.

We report on NICER and MAXI observations of a long-duration thermonuclear X-ray burst and a subsequent outburst-like X-ray flare from the neutron star low-mass X-ray binary MAXI J0911--655. Prior to the burst, the source was in a persistent low/hard state with a power-law-dominated spectrum ($Γ\sim 1.7$) and a mass accretion rate of $\sim 1\%$ of the Eddington limit. The long burst, detected by MAXI on 2020 May 22 (MJD 58991.7101), was rapidly followed up by NICER. From time-resolved spectroscopy of the cooling tail, we estimate an exponential decay time of $\approx43$ minutes, the ignition column depth of $\approx0.1\times 10^{12}~{\rm g ~cm^{-2}}$, the burst fluence of $\approx 1.1\times 10^{-4}~{\rm erg~cm^{-2}}$, and the total energy release of $\approx1.2\times10^{42}$ erg. Approximately one day after the burst onset, the 0.5-10 keV light curve unexpectedly re-brightened, initiating an outburst-like flare. During the peak of this flare, the persistent power-law flux increased from its pre-burst level of $\sim0.27\times10^{-9}~{\rm erg~cm^{-2}~s^{-1}}$ to $1.4\times10^{-9}~{\rm erg~cm^{-2}~s^{-1}}$. This flux enhancement was accompanied by significant spectral softening, with the photon index increasing to $Γ\sim 2.2$. Subsequently, the flux decayed and the source returned to its baseline low/hard state. The observed timescales and energetics suggest that intense irradiation from the long burst amplified the ongoing thermal-viscous accretion process. This heating drove an inside-out heating front that temporarily enhanced the mass accretion rate, providing compelling observational evidence of a thermonuclear burst directly modulating the accretion dynamics of its surrounding disk.

Fully homomorphic encryption (FHE) enables computations on encrypted data without decryption, offering strong data privacy at the expense of substantial computational and memory overheads. Prior efforts have steadily improved FHE performance through cryptographic and algorithmic enhancements or hardware acceleration, yet these two directions have progressed largely in isolation, hindering the full exploitation of available hardware capabilities. This work presents WHET, which introduces memory-centric, architecture-aware optimizations to better align cryptographic and algorithmic constructions with FHE accelerator architectures. We identify conventional FHE constructions as major sources of excessive working sets and heavy off-chip memory traffic. We propose accelerator-specific techniques, including fine-grained coefficient-to-slot transformation, plaintext compression, and intermediate modulus raising, to reduce the on-chip data footprint by minimizing temporary ciphertexts and plaintext loads. With these techniques applied, we observe additional opportunities to improve on-chip memory efficiency; hence, we introduce lightweight architectural refinements, including a special-purpose buffer and functional unit extensions. With these optimizations, WHET achieves 1.38-8.74$\times$ per-area performance improvements over state-of-the-art FHE accelerators and the first-ever sub-millisecond CKKS bootstrapping.

An $n$-partite graph is a graph such that every vertex has a color in $\{1,\ldots,n\}$ and every two vertices of the same color are not adjacent. We study the model comparisons of the theories of $n$-partite graph and $K_{\overline{m}}$-free $n$-partite graph, where $K_{\overline{m}}$ is a complete graph of a given size. The model companion of the theory of $n$-partite graph is simple and has IP. The model companion of the theory of $K_{\overline{m}}$-free $n$-partite graph has $\operatorname{TP}_2$, $\operatorname{SOP}_3$ and $\operatorname{NSOP}_4$ if $n > 2$. Forking independence coincides with dividing independence in this theory.

Bilateral attribute-based access control for data trading must hide policies, provide cryptographic fairness, and avoid trusted third parties. Existing solutions either leak policy information, incur super-linear costs, or rely on trusted dispute resolution. We present PriME-Deal, a non-interactive protocol that simultaneously achieves policy-hiding bilateral matching, efficient threshold access control, and auditable fair exchange on public blockchains. The seller embeds a secret token under the buyer policy into an oblivious key-value store with pseudorandom masking; the buyer reconstructs the token locally via tag-based probing, eliminating combinatorial enumeration, and proves correctness in zero-knowledge. Fair exchange is enforced through a collateralized on-chain reveal with a cryptographic audit that penalizes misbehaviour without trusted parties. We prove security in the Universal Composability framework under standard assumptions. Compared with the state-of-the-art threshold fuzzy IB-ME scheme, the seller's publishing time is reduced by two orders of magnitude (e.g., 8.76s vs. 690s for a policy of 500 attributes). For a typical configuration of (200,20,5), the buyer completes token reconstruction and proof generation in 8.9s, with the zero-knowledge proof taking under 0.6s and remaining constant across all parameter scales. The on-chain cost is approximately 28.6M gas, well within Ethereum's block limit. PriME-Deal thus delivers the first practical privacy-preserving data trading protocol that combines linear seller overhead, bilateral policy hiding, and auditable fairness.

In this paper, we develop a generalized differentiation theory at infinity for convex sets and functions. In particular, we study several fundamental notions of convex analysis at infinity, including tangent cones, normal cones, and subdifferentials. Our work complements the recently developed theories of nonsmooth analysis at infinity by focusing on the convex setting, where these constructions preserve convexity and admit natural connections with recession analysis, polarity, and epigraphical geometry. We show that, in the convex case, many results can be established under weaker assumptions and admit simpler and more explicit representations than those available in the general nonsmooth framework. In addition, we develop calculus rules and geometric characterizations for these constructions and apply them to optimality conditions and attainment criteria for convex optimization problems over unbounded feasible sets. The results obtained in this paper provide new tools for the study of convex sets and functions at infinity and further strengthen the connections between convex analysis, variational analysis, and optimization.

While private information retrieval (PIR) enables private database services by fully concealing access patterns, it simultaneously requires high computational throughput, large memory capacity, and substantial memory bandwidth. We introduce VIPIR, a versatile GPU framework that co-designs PIR protocols with GPU acceleration. We develop a unified analytic model showing that state-of-the-art PIR protocols fall into two categories with complementary limitations, and propose two protocols that flexibly combine techniques across these categories, overcoming the limitations of both classes. These protocols incorporate a GPU-friendly data compression method called expansion-based ring packing (ExpPack), which offers a high degree of parallelism and minimal communication cost. VIPIR applies further optimizations to core operations, including number-theoretic transforms (NTTs) and various matrix-matrix multiplications (GEMMs). Notably, we develop a tensor-core-based execution method for database multiplication by interpreting it as a mixed-integer-type GEMM. We also design memory-efficient scheduling methods that minimize intermediate buffers and enable multi-GPU scaling under memory capacity constraints. Overall, VIPIR achieves orders-of-magnitude higher throughput than prior PIR systems while reducing communication and memory overheads, making large-scale PIR practical.

As an effective anti-censorship mechanism, network covert channels can provide data privacy protection and ensure communication security. However, the covertness of existing network covert channels primarily depends on the secrecy of their covert algorithms. With the increasing depth of research in this field, the difficulty of breaking such algorithms has gradually decreased. Once the algorithm is exposed, the network covert channel can be easily detected by adversaries. To address this issue, this paper proposes a covert carrier filtering strategy based on the hash. In this strategy, a key-dependent filtering rule is introduced during the construction of the network covert channel, enabling the communicating parties to randomly and dynamically filter a sparse subset from the carrier set as the covert carrier set. This strategy not only enhances the randomness of carrier selection but also tightly couples the covertness of the network covert channel with the security of the key. We employ machine learning-based traffic analysis methods to experimentally validate the strategy in two types of network covert channels: network storage and timing covert channels. The experimental results demonstrate that the proposed strategy significantly improves the detection resistance of network covert channels. When the filter key size exceeds six bits, the impact on the detection effect of the classifier becomes quite significant. Furthermore, the processing delay for a single packet is less than 8 $μs$, indicating the feasibility of deploying the proposed strategy in high-speed network environments.

The Grover mixer quantum alternating operator ansatz (GM-QAOA) employs the Grover mixer to confine the quantum evolution to the feasible subspace defined by the problem. Its mixing unitary, however, requires a global multi-controlled phase-shift gate acting on all qubits, resulting in substantial circuit overhead on near-term quantum devices. In this work, we propose locally acting Grover mixers tailored to initial states that admit a product structure over disjoint qubit subsystems, which may be obtained by encoding only a subset of problem constraints into the initial state preparation. The proposed method preserves the search space defined by the initial state while significantly lowering implementation cost, as the global multi-controlled phase-shift gate is replaced with local operations on disjoint subsystems. Numerical simulations on the exact-cover problem and the traveling salesman problem (TSP) demonstrate that the proposed method achieves convergence behavior comparable to that of the original GM-QAOA, while using shallower circuits with fewer gates. We further compare two constraint encoding strategies for the TSP, encoding only a subset of constraints versus all constraints into the initial state preparation, and show that the former combined with the proposed mixer yields markedly more compact circuits at the point where comparable solution quality is achieved.

We give a dynamical proof of Benoist's non-arithmeticity theorem for Jordan spectra of Zariski dense subgroups of connected semisimple real algebraic groups. After passing to a Zariski dense Schottky subgroup, we use the coding of the limit set to realize Jordan projections as periods of a vector-valued Busemann return map for an expanding map on the Furstenberg boundary. The key step is to prove that a suitable two-branch asymptotic discrepancy is not locally constant on the limit set. We also show that the same criterion applies beyond Lie groups; in particular, it yields a direct density result for multiplier spectra of hyperbolic rational maps whose Julia set is not contained in a circle.

We describe Chronos LTV, a system to measure the long-term impact of delays and other service defects on key business metrics. We use Markov decision processes to model customer interactions over time, and formalize our target estimand as the marginal policy effect with respect to moving the average delay rate. Given this setup, we show that we can identify long-term effects under a sequential unconfoundedness assumption where delays are as good as random given observed order characteristics; and can estimate these effects using a simple covariate-balancing algorithm.

Unraveling the mechanism that binds electrons into Cooper pairs in cuprate high-temperature superconductors remains one of the most fundamental challenges in condensed-matter physics. While both magnetic interactions and lattice vibrations are known to govern key electronic properties, their possible cooperation has never been directly observed. We investigate HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ (Hg1223) - the cuprate with the highest $T_{\mathrm{c}}$ at ambient pressure - as a magnifying glass to probe the possible entwining of the excitations at the core of the pairing. Using resonant inelastic X-ray scattering, we find that the charge response is dominated by dynamic charge density fluctuations (CDF) extending up to several hundred meV, where magnetic excitations reside. At the same momentum where CDF are most intense, the paramagnon energy exhibits a pronounced softening, revealing a strong interplay among charge, lattice, and spin excitations. Our results point to a cooperative mechanism in which dynamic charge fluctuations mediate the coupling between lattice, charge and spin degrees of freedom-shedding new light on the fundamental origin of high-$T_{\mathrm{c}}$ superconductivity.

In this paper, we present a new approach for unmanned aerial vehicle (UAV) positioning and reconfigurable intelligent surface (RIS) partitioning to enhance connectivity of uplink RIS-assisted UAV networks. To achieve this, our approach optimizes RIS-aided link selection, RIS partitioning, and UAV positions to maximize network connectivity characterized by its Fiedler value. Meanwhile, it maintains a specific signal-to-interference plus noise ratio (SINR) constraint for user equipment (UE), which is influenced by RIS partitioning and UAV reliability. The network connectivity optimization problem is formulated using the Fiedler value subject to RIS elements allocation and SINR constraints. This problem is a computationally expensive combinatorial optimization, necessitating an efficient iterative approach. In particular, we propose a perturbation method for RIS-aided link selection, and derive a closed-form solution for RIS partitioning, with each partition tailored to optimize SINR for individual UAV. For the given RIS-aided links and RIS partitioning, we then show that the problem of UAV positioning can be formulated as a low complexity semi-definite programming (SDP) optimization problem, which can be solved using off-the-shelf CVX solvers. Our simulations show the potential gain of UAV positioning and RIS partitioning compared to the benchmark schemes from the literature.

This paper investigates the utility of the movable antenna (MA) and reconfigurable intelligent surface (RIS) framework for downlink wireless communications. In the considered scenario, a base station (BS) is equipped with two sub-arrays of MAs transmits signals to the users via the RIS. By jointly exploiting the antenna-positioning flexibility of MAs and the RIS element selection capability, the proposed joint MA-RIS framework introduces additional design degrees of freedom to enhance desired signals and mitigate inter-user interference, thereby maximizing the network sum-rate. To this end, we formulate a joint optimization problem involving MA positioning, sub-array beamforming, and RIS element selection, subject to the minimum antenna separation and transmit power constraints. The resulting problem is highly non-convex and challenging to solve directly. To address this issue, an alternating optimization framework is developed that decomposes the problem into three tractable subproblems. Specifically, zero-forcing beamforming is employed for transmit beamformer design, a low-complexity one-dimensional search is derived for RIS element selection, and the MA positioning problem is solved using block coordinate descent (BCD) and convex optimization techniques implemented via CVX. Simulation results demonstrate that the proposed joint MA-RIS framework significantly improves the achievable sum-rate compared with conventional fixed MAs and benchmark schemes with random configurations.

We investigate a predictive and testable framework in which dark matter (DM), heavy-neutrino dynamics, and the BAU originate from correlated interactions within a local $U(1)_{B-L}$ extension of the SM. Unlike conventional $B-L$ constructions based on the type-I seesaw, we employ an inverse-seesaw mechanism realized through a sterile fermion $S_{1}$ and a complex scalar field $ϕ$, whose vacuum expectation value simultaneously generates the masses of the heavy neutrinos $N_{1,2}$ and the Majorana DM fermion $χ$ via Yukawa couplings. The small lepton-number-violating parameter induced by a higher-dimensional operator leads to naturally light active neutrinos together with TeV-scale heavy neutrinos and sizable active-sterile mixing, yielding distinctive collider signatures unavailable in minimal $B-L$ models. The relic abundance of $χ$ is governed by annihilation channels mediated by the same scalar and gauge interactions, producing a direct and model-specific correlation between successful leptogenesis and the observed DM relic density. A combined parameter-space analysis incorporating neutrino oscillation data, lepton-flavor-violating processes, direct-detection limits, and collider bounds on $N_{1,2}$ and $Z^\prime$ reveals a narrow yet robust region consistent with all these constraints. Representative benchmark points in this region are examined at a future multi-TeV muon collider. Heavy-neutrino production through electroweak processes yields striking signatures in the dilepton plus missing energy ($2\ell + E\!\!\!/_T$) and single-lepton plus di-jet plus missing energy ($1\ell + 2j + E\!\!\!/_T$) final states. These channels demonstrate that next-generation muon colliders offer a powerful and complementary probe of the inverse-seesaw origin of neutrino masses, the DM relic density, and the TeV-scale leptogenesis within such an extended $U(1)_{B-L}$ framework.

Single-photon optical nonlinearities face a fundamental trade-off: maximum nonlinearity requires both spectral resonance (narrow bandwidth) and high peak intensity (short duration), constraints that are incompatible due to the time-energy uncertainty relation. We demonstrate experimentally that this limitation does not need to exist in cases involving post-selection. We measure a cross-phase shift (XPS) produced by a resonant photon from a narrow-band source that is first transmitted through a cold atomic cloud and then localized in time through detection. The peak size of this XPS is greatly enhanced compared to that of Gaussian single-photon-level pulses without post-selection, benefiting from the narrow bandwidth of the resonant prepared state and the high intensity of the post-selected state simultaneously. We measure enhancements in the peak XPS of 6$\pm$1 at an optical depth (OD) of 2.4$\pm$0.1, and our results are in qualitative agreement across a range of optical depths with the recently developed weak value theory of atomic excitation [Thompson et al., APL Quantum 2, 036108 (2025)] for such post-selected photons. This work uncovers new consequences of having simultaneous knowledge of frequency and time, raising new foundational questions about how a particle behaves, and interacts with other systems, when its preparation and post-selection are non-commuting.

We present a novel method for solving conditional value-at-risk (CVaR) optimization problems based on the dual representation of CVaR, which is defined as the worst-case expectation over a risk envelope. The method is based on the Bregman proximal point algorithm and alternates between stochastic primal and dual stages. Every (inner) primal stage involves a subproblem solved by sampling from a probability distribution updated at each dual stage (outer iteration). The likelihood ratio of the dual probability distributions relative to the distribution underlying the original problem converges to the risk identifier of the solution's CVaR. Thus, the dual distribution provides the algorithm with a built-in importance sampling mechanism that draws from the tail of the underlying distribution. Because only samples in the tail influence the CVaR, and samples outside the tail are drawn with decreasing probability, the algorithm delivers exceptional performance over other stochastic approximation methods. We prove the convergence of the algorithm for convex objective functions. Our numerical experiments target representative problems in financial mathematics and machine learning, focusing on portfolio optimization and support-vector machines, respectively.

We study a critical multitype Bellman--Harris branching particle system in $\mathbb R^N$ with a finite type space $\mathbb K=\{1,\dots,K\}$. Particles of type $i$ move according to a symmetric $α_i$-stable process and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The lifetime distribution of type $1$ is assumed to have infinite mean with regularly varying tail $$ 1-F_1(t)\sim c_1t^{-γ},\, 0<γ<1, $$ whereas the remaining lifetime distributions satisfy polynomial upper-tail bounds $$ \overline F_i(t)\le C t^{-η_i},\, i=2,\dots,K, \, η_i>1, \, η:=\min_{2\le i\le K}η_i. $$ The branching mechanism is assumed to be in the domain of attraction of a $(1+β)$-stable law, with $β\in(0,1]$. Under the space--lifetime condition $$ ρ:=\left(η-1\right)\wedge\frac{N}{α_1} > \fracγβ, $$ and a local increment condition on the heavy lifetime distribution, we prove convergence of the system to a Poisson random measure concentrated on the infinite-mean type.

Biotic communities vary continuously across space, yet biome maps impose categorical boundaries that compress this variation, particularly at ecotones where transitional communities are ecologically distinct. Could Earth observation (EO) foundation models, which encode spectral, spatial, and temporal information with dense embeddings, convert discrete biome maps into continuous representations that better capture ecological variation? Here, we fit a linear classifier on Clay v1.5 satellite image embeddings to predict biome labels from a categorical map. The softmax output yields a continuous probability vector whose dimensions correspond to named biome classes. We evaluate this approach using six Brazilian biomes, 1.3 million embeddings, and 10,015 withheld forest inventory plots spanning 4,672 plant species. The continuous biome representation outperforms discrete biome labels for predicting species occurrence (mean per-species AUC 0.618 vs. 0.570 across 10 spatial cross-validation folds). Decomposing this gain shows that continuity in the graded probability output, rather than label reassignment, accounts for the improvement; the pattern holds across all distances from biome boundaries. The raw 1024-dimensional embedding remains the strongest predictor we tested (mean AUC 0.646 vs. 0.618), but the continuous representation recovers most of the embedding's gain over discrete labels. This simple approach provides a probabilistic replacement for categorical map labels, preserving their meaning while encoding graded variation that discrete maps suppress.

We consider the classical $N$-body problem with the $\frac{1}{|x|^p}$-type potential, where $p>0$. We construct hyperbolic, parabolic and hyperbolic-parabolic solutions with prescribed asymptotic data as $t \to+\infty$.

Ultraviolet spectroscopy with the Hubble Space Telescope (HST) provides the most direct and sensitive probe of the disk-circumgalactic medium (CGM) interface at radii of 20 kpc, where galaxies exchange gas, metals, and energy with their surroundings. Many of the key diagnostics of the multiphase circumgalactic medium -- including H I, O VI, C II-IV, Si II-IV, N V, Ne VIII, and other metal transitions -- lie in the ultraviolet and are inaccessible from the ground, making HST the only observatory capable of making the required observations. By measuring the physical (column density, density), chemical (metallicity, ionization structure), and kinematical properties of the gas at the disk-CGM interface, UV absorption-line spectroscopy reveals how galaxies acquire fresh fuel, recycle enriched material, and drive feedback into their halos. When combined with spectroscopic characterization of the host galaxy's stellar populations and the feedback they generate (outflow velocity, mass loading), we will establish a direct understanding of how stellar populations enable circulation of gas and metals through the galactic ecosystem. HST's ultraviolet (UV) spectroscopic capability provides the only comprehensive observational pathways for uncovering the physical drivers that regulate galaxy growth and evolution in the low-redshift Universe.

Accurate calibration of the gravitational-wave strain h(t) is essential for both detection and astrophysical inference. In operating detectors, slow temporal variations in the sensing response are tracked using calibration lines, but practical constraints can prevent those lines from being injected at frequencies that are favorable for precise estimation of sensing-side parameters. We present a statistical framework for preselecting evaluation frequencies under such constraints. We apply this framework to KAGRA data from the first part of the fourth LIGO-Virgo-KAGRA Observing Run, for which the nominal cavity-pole frequency was about 18 Hz, while the sensing-side calibration line used in practice was injected at 32.7 Hz. For each candidate evaluation frequency, we construct the sensing function, quantify its segment-wise statistical uncertainty from empirical percentiles of the sample distribution, and rank the candidates using a score that combines the interval widths of the amplitude and phase. When a 1% amplitude interval width and a 1 degree phase interval width are weighted equally, 244 Hz is selected in all 4096 s analysis segments throughout the analyzed period. Relative to the reference frequency of 32.7 Hz, the amplitude interval width is reduced to about one quarter over a broad frequency range, while the phase interval width remains broadly comparable. We also assess the discrepancy introduced by frequency translation separately. These results suggest that the proposed method provides a useful statistical preselection framework for evaluation frequencies under practical operational constraints.

We consider independent Bernoulli percolation on top of sequences of hierarchical graphs. Given a graph $G_{1}$ with two distinguished vertices $a_{1}$ and $b_{1}$, the hierarchical graph with seed $G_{1}$ is the sequence $\big( G_{k} \big)_{k \geq 1}$ resulting from the inductive procedure, where the graph $G_{k+1}$ is obtained from $G_{k}$ by replacing each of its edges with a copy of $G_{1}$, attached by the vertices $a_{1}$ and $b_{1}$. We prove that, under sharp hypotheses, percolation on these graphs presents a unique phase transition. Second, we establish the existence of several critical exponents in this context, such as the critical exponents for the correlation length $ν$, the surface tension $μ$, the one-arm exponent $α_{1}$. Several results are also obtained for their infinite counterpart $G_\infty$, which is the Benjamini-Schramm limit of $G_k$: uniqueness of the infinite cluster, continuity of $θ(p)$, existence of the percolation-probability exponent $β$ and scaling relations for the critical exponents $α_1$, $ν$ and $β$. Furthermore, we analyze noise sensitivity for crossing functions in $G_{k}$ and establish sharp noise sensitivity in this setting. Finally, we propose a setup where it is possible to verify the locality hypothesis, stating that the critical threshold for percolation is a local property, while critical exponents are determined by the global geometry of the graph. As a consequence of the techniques developed here, we also provide a necessary and sufficient condition for the existence of a unique fixed point for the map $p \mapsto \mathbb{E}_p[g]$ in $(0,1)$, where $g:\{0,1\}^n \to \{0,1\}$ is a nontrivial monotone Boolean function.