Commercial fusion energy requires frameworks to assess both the scientific and economic viability of a wide variety of fusion concepts. Inspired by the Lawson criterion's ability to universally describe fusion energy gain, a generalized framework is developed to determine the economic gain of fusion power plants. The model exploits temporal equilibrium, and engineering and cost parameters normalized to the energy capture surface. The derived criteria for economic gain are therefore independent of the power plant's absolute power, impartial to the particulars of its fusion technology, and can be applied to any fusion confinement concept. The derivation of the economic gain factor, $Q_{econ}$, results in nonlinear equations with ten controlling normalized design parameters ranging from fusion power density and surface component lifetime to energy fluence, price of energy, and component efficiency and cost. These ten controlling parameters are varied over a wide range to provide high-level insights in design, finance and operational tradeoffs that improve the prospects for economically viable fusion energy.

The rapid growth of software vulnerabilities has turned cyber threat intelligence analysis into a challenging data mining problem over heterogeneous and continuously changing sources. Public repositories such as the National Vulnerability Database (NVD), Common Vulnerabilities and Exposures (CVE), Common Weakness Enumeration (CWE), Exploit Database (EDB), and CVE Details provide valuable information, but their record-centric schemas make it difficult to capture cross-source relationships among vulnerabilities, weaknesses, exploits, affected products, vendors, and references. Existing graph-based vulnerability resources highlight the value of relational threat modelling, yet many remain static, offline, or difficult to access for downstream graph mining. This paper presents VulLink, a deployed, dynamic, and open-access vulnerability graph database for cybersecurity data mining. VulLink integrates multiple public repositories through an automated Extract-Transform-Load (ETL) pipeline that converts isolated, record-centric vulnerability data into a continuously updated graph database with typed entities and explicit cross-source relationships. It provides an interactive Web interface and public API for exploring, querying, and exporting mining-ready vulnerability subgraphs. It also provides pre-computed embeddings of vulnerability descriptions generated by pretrained language models, which users can query and download by model and embedding dimension as semantic features for downstream mining tasks such as exploitability prediction. To demonstrate the practical utility of VulLink, we implement a downstream exploitability prediction use case that leverages heterogeneous graph context and semantic vulnerability features. The VulLink platform, including the Web interface, public API, source code, and deployment resources, is publicly available online.

We present a framework to compute non-Gaussian likelihoods for two-point correlation functions. The non-Gaussianity is most pronounced on large scales that will be well-measured by stage-IV weak-lensing surveys. We show how such a multivariate likelihood can be constructed and efficiently evaluated using a copula approach by incorporating exact one-dimensional marginals and a dependence structure derived from the exact multivariate likelihood. The copula likelihood is found to be in better agreement with simulated sampling distributions of correlation functions than Gaussian likelihoods, particularly on large scales. We furthermore investigate the effect of the non-Gaussian copula likelihood on posterior inference, including sampling the full parameter space of contemporary weak-lensing analyses. We find potential parameter shifts in $S_8$ on the order of one standard deviation for $1 \ 000 \ \mathrm{deg}^2$ surveys but negligible shifts for areas of $10 \ 000 \ \mathrm{deg}^2$, suggesting Gaussian likelihoods are sufficient for stage-IV surveys, though results depend on the detailed mask geometry and data-vector structure.

Deterministic Fock-state generation and inter-mode SWAP are foundational primitives for bosonic quantum computing, yet most implementations rely on numerically optimized pulses, per-state calibration, strong dispersive coupling, or higher transmon levels, each adding control overhead that grows with system size. We present an analytical, calibration-light protocol operating entirely within the two-level g-e manifold of a weakly dispersively coupled transmon. A Rabi drive on the qubit, combined with a single sideband tone per mode, synthesizes an on-demand Jaynes-Cummings interaction whose entire family of pulse times follows the closed-form scaling $τ_n=τ_1/\sqrt{n}$. Once the single base time $τ_1$ is set, every higher-$n$ operation is fixed analytically, with no per-state retuning, shelving, or numerical optimization. On a superconducting flute cavity with two high-Q modes, we deterministically prepare Fock states through $|n{=}5\rangle$, realize an inter-mode SWAP characterized on vacuum, single-photon, and coherent-state inputs, and generate and coherently swap the dual-rail Bell state $(|1,0\rangle+|0,1\rangle)/\sqrt{2}$, confirming that the operation preserves inter-mode coherence. Because the pulses are constant-amplitude and free of per-state optimization, the achievable fidelity is set directly by ancilla coherence and drive-ramp duration; a master-equation analysis isolates these hardware factors and shows that the analytical scaling itself imposes no obstacle to high-fidelity operation at high $n$. Requiring only one sideband line per mode and a single Rabi drive, the protocol is well suited to weakly coupled, high-$Q$ 3D architectures where calibration economy and analytical pulse design are at a premium.

The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent work based on the Koopman-von Neumann-Sudarshan (KvNS) Hilbert space formulation of classical mechanics suggests the Wigner function arises as a quantum probability amplitude projected onto classical phase space, rather than a quasiprobability density (Bondar et al., 2013; McCaul et al., 2023). In the classical limit, this amplitude reduces to the classical Koopman wavefunction. In this work, we extend this perspective to relativistic QCD by constructing a Koopman description of the quark Wigner operator. We show that the Wigner operator is naturally isomorphic to a phase space spinor, providing a unified framework in which both classical and quantum dynamics are expressed. Within this formulation, the Wigner function retains its interpretation as an amplitude even in the relativistic regime. This viewpoint clarifies the origin of negativity and other nonclassical features, and provides a more transparent foundation for parton distribution functions in QCD. Remarkably, the relativistic Koopman framework reproduces the classical limit of QCD.

We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy--Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{α_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(β_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $α_k$ and~$β_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-τ}$. We find that the critical exponents vary continuously with $τ$, recovering Kardar--Parisi--Zhang behavior only for $τ\ge 3$. For $τ<3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $ζ$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $ξ$. The coexistence of these two relevant scales signals the breakdown of the usual Family--Vicsek scaling. These results point to a new phenomenology of surface growth beyond the standard scale-invariant paradigm.

Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape wave dynamics, especially near resonances in highly dispersive platforms such as epsilon-near-zero materials. Here, we develop a general frequency transition theory for electromagnetic scattering at moving interfaces between dispersive media. From phase continuity, we derive nonlinear frequency transition relations and show that dispersion fundamentally reshapes the space-time scattering landscape, enabling additional propagating solutions with no counterpart in nondispersive systems. Applied to Drude, Lorentz and double-Drude media, the theory reveals how resonant dispersion, material loss and negative-index branches reorganize the scattering channels. For the two-wave scattering class, we further introduce a mixed-domain formulation that combines time-domain interface kinematics with frequency-domain constitutive relations, yielding closed-form scattering coefficients. These results establish a unified framework for dispersive space-time scattering and open opportunities for dispersion-based transition engineering in realistic materials.

We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems, where the computational domain does not coincide exactly with the physical one. We quantify geometric errors in terms of boundary location and normal perturbations and carry out the analysis in an abstract CutFEM framework under standard stability assumptions. In the energy norm, we obtain an estimate exhibiting an $h^{-1/2}$ amplification of the boundary location error. We then prove a refined $H^1$-seminorm estimate that removes this amplification, yielding a sharper bound with additive contributions from boundary location and normal errors. Finally, we establish an optimal order $L^2$-error estimate based on a refined duality argument, where the geometry contribution appears as a separate additive term, decoupled from the mesh size $h$. The results reveal a fundamental distinction between the norms: the energy norm amplifies boundary location errors while remaining insensitive to normal perturbations, the $H^1$-seminorm separates location and normal errors, and the $L^2$-norm is insensitive to normal perturbations. This provides a clear characterization of how geometric approximation affects convergence in Nitsche-based finite element methods, with particular relevance for unfitted discretizations.

Duality is a foundational tool in robust and distributionally robust optimization (RO/DRO), underpinning both analytical insights and tractable reformulations. While most RO/DRO duality results are derived through saddle-point, Lagrangian, or conic arguments, this paper leverages perturbation duality. We show that this perspective provides a natural and unifying framework for deriving RO/DRO dual formulations, proving the associated duality results, and diagnosing the regularity assumptions on which they depend. First, guided by perturbation duality, we establish new duality theorems for a recent DRO framework that unifies several canonical models, including $ϕ$-divergence and Wasserstein models, through optimal transport subject to conditional moment constraints. Our results resolve an open conjecture on this DRO duality by clarifying the role of compactness: compactness itself is not necessary, but can be replaced by perturbation-based regularity conditions. Second, we revisit \emph{robust duality}, commonly described as \emph{primal-worst equals dual-best.} Using bifunctions, we unify dual-best formulations appearing in the literature and derive concise perturbation-based proofs that streamline recent results. Overall, the paper positions perturbation duality as a versatile and underutilized tool for RO and DRO, offering both conceptual unification and technical generality across a broad class of models.

Galaxy scaling relations encode key information about the structural, dynamical, and mass assembly histories of galaxies, and provide constraints on galaxy formation models as well as the onset of galaxy assembly. While these relations are well characterized out to intermediate redshifts, their existence during the first billion years of cosmic history remains largely unconstrained due to observational limitations. In this work, we investigate the Kormendy relation (KR) for spheroidal systems at $z~\ge~6$ using rest-frame $B$-band structural parameters derived from publicly available deep \textit{JWST} imaging of the GOODS, CEERS, PRIMER-UDS, and PRIMER-COSMOS fields. We find that spheroidal galaxies at these epochs already occupy a well-defined locus in the mean effective surface brightness $(\langle~μ_{\rm e}~\rangle)$ and effective radius ($\rm~R_{\rm e}$) plane, demonstrating that a KR is already in place when the universe was less a gigayear old. The best-fit relation has a slope of $β~=~4.25^{+0.40}_{-0.39}$ and a zero-point of $α~=~15.89^{+0.17}_{-0.17}$, indicating a steeper relation and systematically higher surface brightness compared to the local relation. This steepness reflects the compact sizes and high central stellar-mass densities of these systems, consistent with rapid, dissipative assembly in environments with high gas fractions, likely driven by efficient gas inflows, and gas-rich mergers. The presence of dense bulges embedded in some of these galaxies at similar redshifts further supports a common formation pathway for both bulges and spheroids. Altogether, these findings indicate a predominantly dissipative mode of assembly for the first spheroidal systems which may evolve into the compact quiescent galaxies observed at later cosmic epochs.

We present a systematic analysis of the statistical properties of cosmic voids using galaxies from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and subhaloes from the ELUCID constrained simulation. By comparing voids identified in redshift space, real space, and reconstructed volumes, we assess the impact of redshift-space distortions (RSD) and tracer bias. Using the \texttt{VAST} toolkit, we apply both the geometry-based \texttt{VoidFinder} algorithm and watershed-based methods. We find that void properties are not equally robust. The three-dimensional morphology of voids, quantified by their sphericity and triaxiality, remains stable across different reconstructions and tracer selections. In contrast, void size distributions and radial density profiles depend strongly on the identification algorithm, with watershed-based methods systematically producing larger voids and higher compensation walls than \texttt{VoidFinder}. Using the full ELUCID simulation box, we show that tracer bias mainly affects void density profiles, with noticeable changes only for the most massive subhaloes ($>10^{11.5}\,h^{-1}{\rm M}_\odot$). The agreement between SDSS observations, the ELUCID reconstruction, and the full simulation box demonstrates the high fidelity of constrained simulations and reveals a clear hierarchy in the robustness of void statistics.

A novel semiclassical gravity model proposed by Oppenheim et al., that consistently describes interactions between quantum systems and a classical gravitational field, has recently attracted considerable attention. However, the limitations and phenomenological viability of this model have not yet been thoroughly investigated. In this work, based on the model, we study quantum fluctuations of geodesic deviation coupled with a classical gravitational field. We analytically derive the strain spectrum expected from the fluctuations and show that the original Oppenheim et al. model can be tested with the current observational sensitivity of gravitational-wave experiments. Furthermore, motivated by the novel semiclassical model, we construct two additional models: a modified Oppenheim et al. model that is manifestly consistent with Einstein equation, and a classical-quantum model with environment-induced noise. We analyze the strain spectra predicted by these two models through comparison with those of the original Oppenheim et al. model and perturbative quantum gravity.

We present a discrete Helmholtz--Hodge decomposition for H(div)-conforming Brezzi--Douglas--Marini (BDM) finite elements on triangulated surfaces of arbitrary topology. The divergence-free BDM subspace is split L2-orthogonally into rotated gradients of a continuous streamfunction space and a finite-dimensional space of discrete harmonic fields whose dimension equals the first Betti number of the surface. Consequently, any incompressible flow discretized on this subspace can be reformulated with a scalar streamfunction and finitely many harmonic coefficients as the only unknowns. This eliminates the pressure and the saddle-point structure while ensuring exact tangentiality, pointwise divergence-freeness, and pressure-robustness. We present a randomized algorithm for constructing the harmonic basis and discuss implementation aspects including hybridization, efficient treatment of the harmonic unknowns, and pressure reconstruction. Numerical experiments for unsteady surface Navier--Stokes equations on a trefoil knot and a multiply-connected sculpture surface demonstrate the method and illustrate the physical role of the harmonic velocity component.

Foundation models trained on DNA sequences have achieved strong performance across biological tasks including variant effect prediction and genome design. These models rely on massive public genomic datasets comprising trillions of nucleotide tokens. Unlike natural language, DNA sequences lack semantic transparency, making corrupted or adversarially crafted entries difficult to detect during data curation. We present the first systematic study of training data poisoning in genomic language models, targeting both pre-training and fine-tuning stages. At pre-training, using Evo 2 and GENERator architectures, we show that less than 1% adversarially crafted sequences in the training corpus can selectively degrade generative performance on targeted genomic contexts while leaving unrelated sequences unaffected. We evaluate three scenarios: corruption of TATA-box promoter motifs, disruption of CTCF binding sites, and insertion of synthetic sequences absent from all training genomes. At fine-tuning, we demonstrate two additional attacks. First, poisoning a subset of CTCF sites in a ClinVar-derived corpus installs a conditional backdoor in a LoRA-adapted model that activates almost exclusively when the trigger sequence is present. Second, using frozen Evo 2 7B embeddings, targeted label corruption of downstream training data selectively compromises a clinically relevant variant classification task, demonstrated on BRCA1 variant effect prediction. These results show genomic foundation models are susceptible to targeted data poisoning with minimal footprint. We urge the field to adopt data provenance tracking, integrity verification, and adversarial robustness evaluation as standard components of the genomic model development pipeline.

Surfactants are amphiphilic molecules that are generally anisotropic rather than spherical. Their orientation is therefore governed by the interplay between shear-induced reorientation, thermal rotational diffusion, and energetic alignment with the interface. The relative importance of these processes is characterized by the rotational Peclet number, $Pe_r$. We show that this microscopic coupling between flow and surfactant orientation can give rise to new macroscopic interfacial phenomena, including a shear-dependent effective surface tension and non-trivial droplet deformation. To investigate this mechanism, we develop a phase-field model that incorporates both the surfactant concentration and its local average orientation (polarization field). Using perturbation theory, we derive an analytical expression for the effective surface tension, which depends not only on the surfactant concentration but also on the local shear rate. We then employ a hybrid numerical method to study the deformation of a surfactant-covered droplet under imposed shear flow. For small $Pe_r$, droplet deformation can be accurately captured by a modified Taylor and Maffettone-Minale theories. For large $Pe_r$, shear-induced reorientation strongly distorts the surfactant polarization, and the droplet deformation progressively approaches that of a pure (surfactant-free) droplet.

Three-dimensional supersymmetric gauge theories with eight supercharges possess a unique duality known as 3D mirror symmetry. Under this correspondence, the Coulomb branch of one theory is equivalent to the Higgs branch of its mirror dual, and vice versa. Over the past decades, extensive effort has been devoted to charting the landscape of 3D mirror pairs, though progress has often been constrained by the need to identify suitable brane configurations. In this first installment, we introduce a new quiver-based algorithm, termed growth and fusion, which completes a quartet of Higgsing algorithms alongside decay and fission, quiver subtraction, and quiver addition. Together, these four algorithms provide a systematic framework that circumvents the limitations of brane constructions, enabling us to determine the mirror dual of a given quiver and to systematically bootstrap new 3D mirror pairs. We demonstrate the power of this approach on a new class of circular 3D mirror pairs.

Recently, binary pulsar timing has been proposed as a viable probe of dark matter subhalos with masses of $\sim 10^7\,M_{\odot}$ in the solar neighborhood. We present a comprehensive analytical framework that incorporates the subhalo mass function, projection effects of line-of-sight acceleration, and the spatiotemporal geometric requirements for joint detection by binary systems, enabling a quantitative evaluation of the detectability of nearby subhalos. Applying this framework to the current binary pulsar sample, we find a probability $\leq 1.7 \times 10^{-4}$ of detecting at least one subhalo within the effective volume. An independent timing residual analysis shows no statistically significant excess in line-of-sight accelerations beyond predictions from data-driven Galactic gravitational potential models. These results place stringent constraints on detecting $<10^8~M_{\odot}$ dark matter subhalos with existing pulsar timing data, aligning with the theoretical expectation that such subhalos have a low survival probability in the solar neighborhood. A low detection prospect still holds even for future Square Kilometre Array observations.

Households represent a key unit of interest in infectious disease epidemiology, in both empirical studies and mathematical modelling. The within-household transmission potential of a disease is often summarised by a secondary attack ratio (SAR). Despite its widespread use, the SAR depends on the household size distribution (HHSD) seen during the study period, making it difficult to generalise to new contexts. Extending estimates of transmission potential to new populations instead requires estimates of person-to-person transmission rates which can be convoluted with data on population structure to parametrise mechanistic transmission models. In this study we present a new Bayesian inference method which uses an MCMC algorithm to infer the transmission intensity by imputing the unreported household structure underlying the epidemic. This method can be run on household epidemiological data reported at varying levels of resolution. For synthetic data from a realistic underlying HHSD, we were able to achieve over 90% coverage in our estimates of transmission rate consistently. We were also able to consistently achieve over 90% coverage for data generated with a pathological underlying HHSD, given strong information about the HHSD. Using an existing dataset which recorded micro-scale household epidemiological outcomes during the COVID-19 pandemic, we show that stratifying observed SARs by household size substantially reduces the uncertainty in estimates. Our findings suggest that researchers conducting household epidemiological studies can improve the utility of results for infectious disease modellers by reporting household-stratified estimates. These results aim to encourage the reporting of higher resolution outputs in epidemiological field work as, in the absence of strong priors, transmission parameters were not easily identifiable from low resolution datasets, which are often reported.

We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems that involves taking powers of reduced density matrices in a particular geometric configuration. This quantity, which we denote by $ω_{α,β}$, is parameterized by two positive real numbers $α, β$, and can be seen as a ``Rényi-like" generalization of the modular commutator -- another entanglement probe proposed as a way to compute the chiral central charge from a bulk wave function. We obtain analytic expressions for $ω_{α,β}$ for gapped ground states of non-interacting fermion Hamiltonians as well as ground states of string-net models. In both cases, we find that $ω_{α,β}$ takes a universal value related to the chiral central charge. For integer values of $α$ and $β$, our quantity $ω_{α,β}$ can be expressed as an expectation value of permutation operators acting on an appropriate replica system, providing a natural route to measuring $ω_{α,β}$ in numerical simulations and potentially, experiments.

The JWST provides exoplanet transit observations with unprecedented spectral coverage, enabling detailed atmospheric characterisation. However, systematics introduced during data reduction can lead to small but significant uncertainties that propagate into atmospheric retrievals, making it essential to assess their impact on inferred properties. We aim to quantify the impact of different JWST/NIRSpec PRISM data-reduction processes as well as the relevance of saturation on the retrieved atmospheric properties of WASP-39b. We also assess whether or not these biases are comparable to those introduced by assumptions made in atmospheric modelling, particularly in the treatment of aerosol extinction. We perform nested-sampling Bayesian retrievals using MultiNest and forward models generated with the Planetary Spectrum Generator. Six independently reduced spectra are analysed, considering both the full wavelength range and versions excluding the saturated region. We further test the effect of including three different cloud-opacity parameterisations. Differences among JWST/NIRSpec data-reduction pipelines lead to substantial variations in retrieved atmospheric properties of WASP-39b, often exceeding one order of magnitude, comparable to uncertainties from modelling assumptions. Excluding the saturated region reduces inter-pipeline dispersion but increases parameter degeneracies. This highlights the need for robust and homogeneous calibration strategies. The results also confirm that JWST data possess the sensitivity required to probe aerosol spectral behaviour, although such constraints remain strongly dependent on the adopted data-reduction strategy.

This is the second part of a two--part series investigating bifurcation phenomena in autonomous Lagrangian systems and geodesic flows on Finsler and Riemannian manifolds. Building upon the abstract bifurcation theorems established in earlier work and the results of Part I, this study makes contributions in two main directions. In Part A, we focus on bifurcations of generalized periodic solutions in autonomous Lagrangian systems. By employing Morse index and nullity techniques within the normal space to the $\mathbb{R}$-orbits of solutions, we derive necessary and sufficient conditions for bifurcation, encompassing scenarios of both Fadell--Rabinowitz and Rabinowitz type. In Part B, we extend these results to the geometric setting of geodesic bifurcations in Finsler and Riemannian manifolds. A principal achievement is the significant refinement of the classical Gauss lemma and its generalizations by Morse-Littauer and Savage, providing a precise description of geodesic behavior near critical points of the exponential map. The sharpness of these theoretical results is rigorously tested and confirmed through explicit counterexamples, such as the round sphere. The work is technically rigorous, leveraging a specialized technique developed by the author to establish novel bifurcation theorems. These findings have profound theoretical implications and potential applications in related fields such as the Zermelo navigation problem and the study of stationary spacetimes.

Exploring novel magnetoelectric coupling mechanisms to achieve control of ferroelectric polarization and magnetism is highly significant for both fundamental science and electronic device applications. Although extensive studies have been conducted on electrical switching of magnetism in multiferroic materials, simultaneous ultrafast laser switching of ferroelectric polarization and altermagnetism remains unexplored. In this letter, we propose that the ultrafast laser can be used to switch ferroelectric polarization and altermagnetism concurrently in charge-order-induced altermagnetic ferroelectrics. Building on this idea, we further demonstrate that such dual switching can be realized in charge-order-induced altermagnetic ferroelectric LiV$_2$F$_6$ by symmetry analysis and time-dependent density functional theory (TDDFT) calculation. Given that LiV$_2$F$_6$ has already been experimentally synthesized, our work not only provides an ideal material platform for experimentally realizing simultaneous switching of ferroelectric polarization and altermagnetism but also holds potential application value in future ultrafast spintronic devices.

We propose a finite-sample risk-optimal selection criterion for Cressie-Read power divergence (CRPD) estimation in overidentified moment-based models. The CRPD family, dual to generalized empirical likelihood, is indexed by the power parameter $γ$. Although $γ$ is conventionally fixed at a researcher-chosen value, we argue that it should be interpreted as a data-tunable curvature parameter governing the finite-sample behavior of the CRPD objective. Through implied probability weights and associated Lagrange multipliers, $γ$ affects how the empirical distribution is reweighted to enforce the moment restrictions, even when population identification is unchanged. The proposed criterion selects $γ$ by minimizing an estimation- and system-oriented risk measure. It combines a structural component, which measures finite-sample distortion in the estimate of the structural parameter relative to a first-order GMM benchmark, with a multiplier-stability component, which measures the cost of moment enforcement in the full estimator-multiplier system. A researcher-specified weight determines the relative importance of the two components, allowing the selection rule to prioritize structural accuracy, multiplier stability, or a balance between them. The resulting selector is designed to reduce second-order finite-sample distortion while discouraging unstable multipliers, concentrated implied weights, and proximity to the feasible-probability boundary. Simulations show that the selected CRPD estimator remains approximately centered around the structural parameter while improving finite-sample stability. An empirical illustration using Owen's dairy-cow data shows that similar point estimates can correspond to different implied weighting schemes, highlighting the practical role of $γ$ as a curvature parameter in moment-based estimation.

We prove that for any real number $ξ\neq 0$ and any coprime integers $p>q\ge1$ such that $ξ$ is irrational or $q>1$, the image in $\mathbb{R}/\mathbb{Z}$ of the sequence $(ξ(-p/q)^n)_{n\ge 0}$ is not contained in any interval of length less than $(1+q/p-q^2/p^2)/p$.

Semidefinite programming (SDP) provides a fundamental framework for studying properties of sum-of-squares (sos) representations of nonnegative polynomials. In this paper we study the quartic forms GF = (|x|^4 + F(x))/2 associated with isoparametric polynomials F of OT-FKM type with g = 4. We characterize the sos property of GF in terms of the feasibility of an explicit SDP determined by the underlying Clifford system, and in the sos cases we obtain quantitative rank bounds for sos representations, with rigidity when m >= 3.

We propose a frequency-division multiplexed (FDM) continuous-variable quantum key distribution (CV-QKD) system with enhanced spectral efficiency through optimized channel spacing of low-symbol-rate signals. A four-channel 10-Mbaud FDM-CV-QKD system was experimentally demonstrated using Gaussian modulation, a transmitted local oscillator, and homodyne detection. Despite the inter-channel interference, under a finite-size scenario (m=1.25x10^6), the system achieved a 3.6-fold back-to-back secret key rate gain and outperformed the single-channel frequency-upconverted signal up to 26.8 km.

Water-based Liquid Scintillator (WbLS) was proposed over a decade ago as a novel detector medium that might allow the separation and tuning of the relative ratio of the Cherenkov and Scintillation signals. A detector deploying this technology could combine GeV-scale and MeV-scale neutrino detection at scale. Furthermore, the metal-loading capability of such a material enables neutron tagging and allows the effective particle containment to be tuned. WbLS is attractive both for the potential to use it in large detectors and the ability to modify the configuration in situ. At Brookhaven National Laboratory (BNL), two prototypes have been built for understanding WbLS properties and stability, with masses of 1-ton and 30-ton, respectively. We present here the 30-ton prototype detector design, installation, and operation. Results from the analysis of data collected in the two detectors will follow in future publications.

We study a class of maps having the Collatz function (famously related to the Collatz Conjecture) as an example, under topological and ergodic perspectives, including an approach with thermodynamic formalism. By introducing a key topology and its Borel sigma-algebra we show that recurrence implies periodicity. Moreover, we establish that if every continuous potential with finite pressure possesses some equilibrium state then we have either finiteness of cycles or infinitely many cycles sharing the same period. The existence of some continuous potential with no equilibrium state is equivalent to the unboundedness of periods of cycles. The uniqueness of periodic orbits is equivalent to the uniqueness of equilibrium state for every bounded and continuous potential. We also prove that we have either infinitely many cycles or no divergent orbits. Finally, we apply our technique to the Baker and Syracuse maps, obtaining a similar result for this general class of important maps.

We take two approaches to classifying the complexity of Presburger models: Scott analysis and degree spectra. In particular, we investigate the possible Scott sentence complexities and possible degree spectra of models of Presburger arithmetic. Many of our results will be achieved by showing how given a linear order $\mathcal{L}$, we can construct a Presburger group $P_\mathcal{L}$ that maintains much of the structure of $\mathcal{L}$.