Zinc phosphide (Zn3P2) is a promising photovoltaic absorber for thin-film and flexible solar cells due to its earth-abundant composition and favourable optoelectronic properties. Recent advances in epitaxy have enabled the growth of high-quality Zn3P2 thin films despite the challenges posed by its incompatible lattice parameter and thermal expansion coefficient. However, Zn3P2 remains prone to intrinsic extended defects, such as rotated domains, that can limit device performance. Here, using (scanning) transmission electron microscopy, we identify a previously unreported class of extended defects that appear as planar faults described by displacement vectors lying in the (001) plane. Within a pseudo-cubic description of Zn3P2, we establish a direct correspondence between planar faults and rotated domains, showing that both arise from the flexible ordering of vacant sites in the Zn sublattice. First-principles calculations reveal an extremely low planar-defect formation energy of 2.5 mJ m-2, demonstrating that these defects form at essentially negligible energetic cost, in excellent agreement with their high experimentally observed occurrence. Additional density functional theory (DFT) calculations show that intrinsic planar defects neither introduce mid-gap electronic states nor significantly perturb the local electrostatic potential, indicating that they are electronically benign. Instead, we propose that planar defects indirectly degrade device performance by acting as preferential segregation sites for optically active point defects.

In recent work, we have developed a model-agnostic framework for cosmological inference using the baryon acoustic oscillation (BAO) feature in redshift space. The framework, which we dub the `Zel'dovich smearing approximation', involves several ingredients, including an optimal basis for the linear theory correlation function in real space, a Gaussian kernel that describes the smearing of the BAO feature due to bulk flows, and a model for the impact of scale dependent bias and mode coupling in redshift space. Unlike traditional, template-based approaches, this framework does not assume any particular cosmological model. An important ingredient -- which impacts both the traditional as well as model-agnostic frameworks -- is the geometric distortion introduced by the inevitable choice of the fiducial cosmology used for converting observed angles and redshifts to comoving separations. In this work we show how this distortion, which was not yet included in our framework, affects the output of the Zel'dovich smearing approximation. We test our completed framework on two halo samples derived from the AbacusSummit simulation suite and designed to mimic galaxy samples from the ongoing DESI and Euclid surveys, respectively. We show that our framework produces unbiased cosmological constraints when applied to these semi-realistic samples and compare the organization of cosmological information in the model-agnostic and traditional approaches. We end with a roadmap to a detailed comparison of the performance of the traditional approach with the Zel'dovich smearing approximation, which is `data ready' as presented here.

In many settings one is often interested in determining whether two networks share some joint structural connectivity patterns such as communities. However, while communities may be shared across networks, edge probabilities may differ significantly. Therefore, in this paper we consider testing a general null hypothesis that two networks have the same underlying subspace, which in particular includes the setting that communities are the same for either stochastic blockmodels or mixed-membership stochastic blockmodels (even if edge probabilities are different). We propose a test statistic based on the Frobenius norm of the difference of the leading subspace projection matrices, and we prove that our test statistic, after appropriate centering and scaling, converges in distribution to a Gaussian random variable as long as the average expected degree grows at least logarithmically in the number of vertices. We then provide estimators for the asymptotic mean and variance and show consistency under a stronger signal condition, and we give the local power of our test when the networks are sufficiently dense. Our theoretical results are based on a limit theorem for the projection difference of empirical and true eigenvectors which can also be viewed as the one-sample version of our test statistic, and this result may be of independent interest. We demonstrate our results through numerical simulations and an application to US Flight data.

This work establishes a bipartite generalization of the Harer-Zagier formula using non-Hermitian Random Matrix Theory. More specifically, we use a decomposition of powers of Ginibre eigenvalues as a superposition of independent point processes to identify all coefficients of the generating function of the genus of a surface obtained by a random bipartite pairing of the sides of one polygon with $kM$ sides and $k$ polygons with $M$ sides.

In this paper, we study how the Frobenius--Perron dimension of finite-dimensional algebras behaves under tensor products and related constructions. We prove that Frobenius--Perron dimension is super-additive under tensor products and is additive whenever one tensor factor is local. In particular every non-negative integer occurs as a Frobenius--Perron dimension. We further show that the invariant equals $1$ for every representation-infinite cycle-finite algebra, such as a tame concealed or tubular algebra, and we determine it on the grids $\mathsf{k} A_m\otimes_{\mathsf{k}}\mathsf{k} A_n$, where it is $0$, $1$, or $\infty$ according to representation type. Finally we treat skew group algebras of local algebras, for which a McKay quiver computation gives a lower bound and shows that the dimension can jump from finite to infinite.

LLM agents increasingly write and maintain developer documentation, but usefulness and accuracy often rely on dependency chains that are not obvious to follow. Even with more files in context, the agent must still decide which cross-file dependencies to trace. We present Context-as-AI-Service (CAIS), a retrieval layer that LLM agents query to find evidence across the codebase as they review or generate documentation. CAIS indexes source code, API references, and upstream documentation, then enables agents to query the index through tool calls that combine keyword and semantic search. We evaluate CAIS in two case studies using Claude Sonnet 4.6 on a production SDK: improving API reference comments in a core source file and validating an LLM-generated tutorial. In both studies, the baseline already had ordinary repository tools such as file reads, keyword search, and symbol navigation. CAIS adds a retrieval layer on top, so the comparison isolates added retrieval rather than basic repository access. In the API-reference review, the CAIS-augmented agent produced the same 5 missing-documentation fixes as the baseline and surfaced 4 findings the baseline missed: 2 cross-file factual errors and 2 underspecified API comments. In the tutorial validation, it surfaced 1 executable bug, 1 API-usage improvement, and 2 missing prerequisites that the baseline pipeline did not catch. These findings required tracing non-obvious dependency chains across utility files, framework internals, usage examples, tests, and component-creation logic. Over five runs per condition, adding CAIS reduced wall-clock time by 22% to 34% across the two tasks and lowered input-token usage.

The Sure Independence Screening and Sparsifying Operator (SISSO) framework is a powerful symbolic-regression method for extracting compact and interpretable descriptors from large nonlinear feature spaces. However, standard SISSO is deterministic: it returns a single descriptor and point prediction, without quantifying uncertainty in descriptor selection, regression coefficients, or predictions. Here we introduce a probabilistic extension in which the sure independence screening (SIS) stage is kept deterministic to preserve scalability, while the sparsifying operator (SO) stage is reformulated as Bayesian inference over the SIS-screened support space. The resulting deterministic-SIS/Bayesian-SO framework yields posterior probabilities for competing descriptor supports, feature-inclusion probabilities, Bayesian-model-averaged predictions, and predictive credible intervals, while recovering the deterministic SO descriptor of standard SISSO in the maximum-a-posteriori limit. Applied to an $X_2YZ$ Heusler-alloy magnetic-moment dataset, the approach gives modest improvements in five-fold cross-validation RMSE and near-nominal empirical coverage of the 95$\%$ predictive intervals. More importantly, the posterior exposes competing, physically related symbolic descriptor families that would appear artificially unique in a deterministic analysis. These results suggest that deterministic-SIS/Bayesian-SO can be used as an uncertainty-aware diagnostic extension of SISSO: a tool for assessing descriptor confidence, stability, and non-uniqueness in small-data materials regression problems.

Motivated by recent developments in stochastic modeling of clock jitter in Analog-to-Digital Converters (ADCs) as autoregressive processes of order one (AR(1)), we study the density and stability properties of AR(1)-jittered sampling sets for Paley-Wiener signals. We show that, despite having the correct asymptotic density both on average and almost surely, such sets almost surely fail to be stable sampling sets. We complement this negative result with a finite-dimensional analysis, showing that the corresponding jittered sinc matrices are nonetheless well-conditioned with high probability.

We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of conforming reaction-diffusion and fitted-interface problems. On conforming simplicial meshes, an owner-selected Falk--Winther bubble transform gives $L^2$- and $H^1$-stable components with constants independent of the mesh size, the local polynomial degrees, and the degree distribution. Minimal-degree owners preserve arbitrary variable-degree spaces with $p_K\ge1$, while coefficient-adapted owners yield weighted estimates under local chain conditions. Combined with a weighted continuous piecewise affine extraction, this gives $hp$-uniform Schwarz preconditioners for conforming reaction-diffusion problems with locally comparable coefficients, and a coefficient-weighted conforming variant in the uniform-degree case. For three-dimensional fitted-interface problems, we use a symmetric Nitsche discretization on a tetrahedral mesh fitted to a piecewise planar interface. Surface jump components are lifted into the side selected by the penalty scaling using patch-level $p$-robust trace liftings. The conforming remainder is decomposed by the low-order extraction and a weighted one-sided bubble transform. Grouping the resulting components by vertices yields a practical vertex-patch Schwarz preconditioner whose condition number is independent of the mesh size, local polynomial degrees, diffusion contrast, and coefficient magnitudes under a common-degree condition on interface-touching tetrahedra. Numerical experiments for pure diffusion problems support the theory and suggest robustness beyond the common-degree assumption.

A spherical Penning trap has well-separated, clean microwave resonances, making it attractive for precision measurements of the electron magnetic moment and for dark-photon and axion searches with trapped electrons. We demonstrate single-electron trapping in a spherical Penning trap and characterize its microwave resonance structure. The design, single-electron detection, microwave mode characterization, and advantages of this geometry are presented.

Optimizing energy conversion in active matter remains a central challenge in nonequilibrium physics. Here, we develop a unified thermodynamic framework that characterizes the finite-time performance of interacting active machines. We show that cyclic work admits a geometric decomposition into an antisymmetric thermodynamic curvature, governing work extraction, and a symmetric metric, controlling dissipation. Minimal-dissipation protocols follow geodesics in parameter space, while optimal work extraction deviates from them due to a curvature-induced, Lorentz-like effect. This geometric structure directly determines the finite-time scaling of work and dissipation, enabling a mapping onto Onsager-type quasi-linear current--force relations. We show that both the maximal efficiency and the efficiency at maximum power are governed by an asymmetry parameter and a figure of merit, establishing a formal correspondence between active machines and thermoelectric devices with broken time-reversal symmetry. Our results reveal a fundamental geometric origin of energy-conversion performance and provide a general framework for optimizing active machines.

This paper investigates a class of Schrödinger-Poisson systems in $\mathbb R^3$ featuring the (p,q)-Laplacian operator and a combination of critical and subcritical nonlinearities in the Schrödinger equation while the m-Laplacian and a power type nonlinearity in the Poisson's one. We consider both the attractive and repulsive cases, which correspond to different signs in front of the nonlocal term. While most existing literature relies on auxiliary functionals or specialized techniques to overcome the lack of compactness and ensure the boundedness of Palais-Smale sequences, we employ a direct variational approach. By applying the Mountain Pass Theorem and concentration compactness principles, we establish the existence of positive solutions. A careful analysis is conducted to identify the parameter ranges for which the Mountain Pass level falls within the compactness threshold, despite the technical challenges posed by the unbalanced growth of the operator and the nonlocal interaction.

Accurate distances to molecular clouds are crucial for determining their physical properties, understanding star formation, and tracing Galactic spiral structure. A number of 103,517 molecular clouds has been identified by the DBSCAN algorithm in the MWISP Phase I CO survey (l = 9.75-229.75 deg, |b| <= 5.25 deg), most of which lack reliable distances. In this work, we propose three independent methods, all of which match the molecular cloud's velocity-integrated intensity maps of 12CO lines from the MWISP with the three-dimensional dust extinction maps derived from Gaia, Pan-STARRS 1, and 2MASS, to determine molecular cloud distances. We present a catalog of 1,573 molecular clouds with robust distances ranging from approximately 150 pc to 3000 pc, 90 percent of which are measured for the first time, with typical statistical and systematic uncertainties of approximately 20% and 10%, respectively. We also derive their physical properties, such as their mass and sizes. This publicly available catalog of molecular clouds with distances provides a foundation for testing molecular cloud scaling relations and probing how cloud conditions influence star formation across diverse Galactic environments.

In inventory market making, the running-penalty coefficient $ϕ$ of the Cartea-Jaimungal framework and the risk-aversion parameter $γ$ of the Avellaneda-Stoikov framework are typically treated as independent free parameters, calibrated separately. We show that they are in fact not independent. A small set of axioms on the market maker's dynamic preference functional, namely cash-additivity, normalization, concavity, strong dynamic consistency, and law-invariance, forces the preference functional to be the entropic certainty-equivalent on liquidation-adjusted terminal wealth, parametrized by a single positive scalar $γ$. The Avellaneda-Stoikov framework is the unique representative of this axiom class. The Cartea-Jaimungal framework is its second-order Taylor expansion in inventory magnitude, with the running coefficient forced to $ϕ= γσ^2/2$ and (under a mild regularity condition on the liquidation cost) the terminal coefficient forced to $α= \frac{1}{2}L''(0)$. The two frameworks, typically presented as competing alternatives with the choice between them driven by tractability, are different manifestations of a single underlying object. The forced relation is invertible, $γ= 2ϕ/σ^2$, giving a consistency cross-check on independently calibrated desk parameters.

We give a straightforward, self-contained, and natural construction of the Big Witt ring using the eñe product that is defined through the action on zeros of polynomials. This is in contrast with classical constructions of the Big Witt ring using formulas out of nowhere.

In this paper, we investigate the computational hardness of finding fractional allocations to unit-demand players using competitive equilibria from equal incomes (CEEI), where we allow a small constant error in players' response to market prices (also known as an approximate Hylland-Zeckhauser equilibrium). We show that assuming the $\mathbf{(\varepsilon,δ)}$-Generalized Circuits problem is PPAD-hard (the "PCP-for-PPAD" conjecture), finding an approximate HZ equilibrium is also PPAD-hard. This result provides additional motivation for trying to prove the PCP-for-PPAD conjecture as a tool for obtaining robust computational hardness results about markets. Further, we introduce a natural restriction on approximate HZ equilibria, where players' bundles may still only be approximately optimal given the prices, but may not contain positive-price items for which the player has zero utility. We show unconditionally that there exists a constant $ε$ such that finding a restricted $ε$-HZ equilibrium is PPAD-hard.

A semiflexible ring polymer on a motor-protein bed exhibits activity- and processivity-dependent rotational and conformational dynamics that are not captured by linear-chain behavior. Using coarse-grained Langevin simulations with bending elasticity, excluded-volume interactions, and stochastic motor attachment, stepping, and detachment, we vary activity (Peclet number), motor processivity, and chain stiffness to map the nonequilibrium response. The mean-squared displacement shows crossover dynamics, with semiflexible rings displaying subdiffusive-to-diffusive behavior at low activity and an intermediate ballistic regime at higher activity, while increasing flexibility shifts the short-time response toward a Rouse-like limit. Diameter autocorrelations exhibit damped oscillations associated with coherent rotation; the rotational frequency increases with activity and processivity, whereas the decorrelation time is non-monotonic at high processivity. Fourier mode analysis identifies competition between the radius (k=0) and elliptic (k=2) modes as the origin of the non-monotonic asphericity.

The Fourier Entropy-Influence (FEI) conjecture states that the Fourier entropy of Boolean functions is uniformly bounded by their total influence. It has been verified for canonical examples such as disjoint tribes and for some classes of Boolean functions such as symmetric functions and read-$k$ decision trees (with a constant that depends linearly on $k$). In this note we present new classes of Boolean functions that verify the FEI conjecture. The key element is an inequality controlling the difference between the entropy of a function $f$ and the average of the entropies of $f^{\pm}$, the sub-functions obtained by setting $x_m=\pm1$ for some $m$, by the $m$-influence of $f$. If this key inequality were to hold for Boolean functions, then the full FEI conjecture would follow by induction. We introduce the notion of a stopping binary tree and observe that functions that satisfy the key inequality at the branching nodes of the tree and the FEI conjecture at the stopping nodes will satisfy the FEI conjecture. We identify some classes of functions that fit this framework: the $δ$-tribes functions, the monotone Boolean functions with the tribe separation property, and the Boolean functions with the semi-separation property, and, and, along the way, demonstrate some results that we hope the experts in this fascinating field might find useful.

The Gaia Data Release 3 (GDR3) parallaxes are affected by a complex bias that depends on stellar magnitude, color, and celestial position, with amplitudes reaching tens of microarcseconds ($μ$as). Standard global parametric models (e.g., Lindegren et al. 2021, hereafter L21) effectively remove large-scale trends but struggle to resolve small-scale spatial systematics due to functional rigidity. We aim to construct a flexible, data-driven calibration map that eliminates these residual local systematics without imposing rigid functional forms. We propose a "Global Pre-correction + Local Refinement" hybrid strategy. First, we utilize the L21 model as a baseline to remove the dominant magnitude and color-dependent biases. Second, we model the residual zero-point using a Local Non-parametric method based on a Sliding Window technique. This approach fits local trends using k-nearest neighbors from quasars (for faint stars, G>18) and wide binaries combined with Large Magellanic Cloud (LMC) (for bright stars, G < 18). Our hybrid model demonstrates significant improvements over the standard L21 solution. Validation against different samples reveals a remarkably flat residual map with near-zero bias across the full sky. Our mathematical attempt at calibrating the parallax zero-point is expected to provide a useful reference for the zero-point correction in future Gaia DR4, and to help move towards a physical resolution of this issue.

Trapped neutral atoms are one of the leading platforms for quantum information technologies, in particular for quantum computing, but scaling them to array sizes needed for utility-scale quantum computing is a major engineering challenge. Here we review optical metasurfaces as an enabling technology that provides fine control over the phase, amplitude, and polarization of light, with pixel counts far exceeding what is available with spatial light modulators (SLMs) and other active devices. The large pixel counts have recently led to demonstrations of arrays of optical tweezers with hundreds of thousands of sites and arrays of optical bottle-beams with complex three-dimensional trapping profiles. The flexibility and scalability of optical metasurfaces provides a route towards miniaturized, integrated, and highly scalable atomic experiments and instruments.

Background: In the bottom layer of the inner crust of neutron stars, various crystalline structures are expected to emerge that are collectively called ``nuclear pasta.'' It is desirable to know properties of nuclear pasta in a wide variety of conditions for astrophysical applications. However, three-dimensional fully-microscopic calculations require huge computational effort that makes it still challenging to carry out systematic calculations. Purpose: In this paper, we propose an efficient method to calculate various nuclear pasta configurations in a non-empirical manner, based on three-dimensional orbital-free density functional theory (OF-DFT). We demonstrate the feasibility of the proposed approach by applying it to densities across the inner crust of neutron stars. Methods: As a first application of OF-DFT for nuclear pasta, we employ the second-order extended Thomas-Fermi (ETF) expansion of Skyrme energy density functional (EDF) to construct an EDF that depends only on neutron and proton number densities. Based on the variational principle, we derive Euler-Lagrange equations to determine optimal neutron and proton density distributions and solve them self-consistently. In this work, we call this approach the self-consistent ETF (SC-ETF) method. Results: We perform three-dimensional SC-ETF calculations with various box sizes. We successfully obtain various pasta structures, depending on given average nucleon number densities, consistent with earlier studies. Moreover, we find other exotic structures, such as bending and/or connected rods, slabs with a hole, etc., underlining the advantage of the self-consistent formalism. Conclusions: We demonstrate that the SC-ETF method proposed in this study, which can be regarded as a realization of OF-DFT, is a promising tool that can efficiently describe complex pasta structures without empirical assumptions on geometric shapes.

Our aim is to study matrix polynomials over max-algebras and their growth in terms of max-induced seminorms. In particular, we compare the set growth of a bounded family $Ψ$ of matrix polynomials, measured in terms of the seminorms $η_{\|\cdot\|}$ and $\hatη_{\|\cdot\|}$ with the induced joint spectral radius of the coefficient pool $Ψ_0$ of the matrix polynomials. Dynamics of max-linear maps and convergence to periodic points under a single joint spectral radius condition and the existence of common max-eigenvectors of the coefficient pool are also brought out.

We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a particular affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and composition. The same fixed functions can also be used to approximate multivariate continuous functions, provided that the coordinate functions are also available. We also show that the number of generators can be reduced from two to one. We construct a specific continuous function that generates a dense class in the univariate setting and, together with the coordinate functions, in the multivariate setting.

Coherent light-matter coupling via STIRAP can offer a versatile route to nucleate quantized vortices in Bose-Einstein condensates through the orbital angular momentum transfer from a vortex beam, yet its efficacy in dipolar condensates remains an open question. Can the orbital angular momentum of a Laguerre-Gaussian beam be coherently transferred to a dipolar BEC via STIRAP? We investigate this for a quasi-two-dimensional trapped dipolar condensate using co-propagating Gaussian and Laguerre-Gaussian laser beams. The interplay between long-range dipole-dipole interactions and short-range contact interactions enables access to three interaction-driven phases: superfluid, droplet, and supersolid. We find that the amount of angular momentum transferred from the optical field to the dipolar condensate, along with the nucleation and persistence of vortices, depends strongly on the underlying phases of the dipolar BEC. In the superfluid, STIRAP achieves a near-complete population transfer and nucleates a long-lived quantized vortex, reflecting efficient transfer of angular momentum to the condensate. In the droplet phase, although the vortex remains pinned within the density profile, the angular momentum is partially retained and oscillatory, accompanied by droplet fragmentation and recombination. In the supersolid phase, when the external magnetic field is oriented perpendicular to the LG beam's propagation direction, the emergence of a modulated density distribution along with a slight reduction in inter-droplet coherence leads to vortex delocalization and eventually exits from the condensate along the field direction, yielding a vanishing average angular momentum. However, reorienting the magnetic polarization along the beam propagation direction restores efficient angular momentum transfer and stabilizes the vortex within the supersolid phase.

It is shown how some deviations of ergodic averages can be structured. The deviations tend to zero almost everywhere. They are asymptotically almost invariant with respect to the action due to averaging. In this situation, the question of the distribution of the values of such deviations is meaningful. It turns out that for any free ergodic $Z^d$-action these distributions can be weakly close to any given distribution if we change the scale on the value line. This article shortly provides related proofs of the ergodic theorems of von Neumann, Birkhoff, Wiener, and Rokhlin's lemma for $Z^d$-actions with an invariant measure.

Accurate modeling of electric potential and current distribution in head tissues is crucial for the design and evaluation of neuro-sensing and neuro-stimulation systems operating in the sub-megahertz frequency range. Numerical methods are widely employed in electromagnetic simulations, however their computational cost can limit their applicability to rapid prototyping, real-time simulations, and circuit-level integration. In this work, we introduce a lumped RC equivalent circuit model that reproduces the electrical behavior of a canonical three-layer spherical head geometry over a frequency range up to 50 kHz. The model accounts for frequency-dependent tissue conductivity and permittivity to capture dispersive effects, employing complex conductivity in the electro-quasi-static (EQS) regime. The circuit topology uses a minimal set of impedance elements in order to represent the essential mechanisms of electric signal propagation. Validation was performed using a dipolar brain source configuration for scalp voltage peak estimation, showing close agreement with semi-analytical solutions across different skull thicknesses and dipole eccentricities. In addition, the impact of tissue dispersion and capacitive branches on the model predictions was quantitatively assessed, showing their contribution to the overall fidelity of the proposed approach.

Optical cycling refers to repeated excitation and spontaneous emission on an electronic transition in an atom or molecule. Optical cycling in molecules can enable a wide range of quantum control and readout techniques, but unfortunately it has only been demonstrated on a small class of alkali-like or alkaline-earth-like molecules. Thorium monoxide (ThO), a molecule used in one of the most precise permanent electron electric dipole moment (eEDM) searches (ACME [1]), does not fall into this category. In this work, we demonstrate the first optical cycling on this non-conventional class over a range of experimental parameter space, including laser intensity, polarization switching rate, and interaction time. We show that both the $J = 1, 2$ rotational levels of ThO molecule are capable of cycling $11(2)$ photons on average with a single laser, at $1.9(6) \times 10^{6}~\mathrm{s}^{-1}$ and $2.3(7)\times 10^6~\mathrm{s}^{-1}$ scattering rate, respectively, before population is lost to other vibronic levels. We outline a scheme to apply this demonstrated optical cycling in an ACME-style eEDM measurement, improving the detection efficiency by over fourfold compared to non-cycling fluorescence detection. This would lead to over a twofold enhancement in the statistical sensitivity of the eEDM search. This optical cycling scheme can be further extended to scatter about 100 photons, which would enable a wider range of quantum control and sensing using ThO molecules. [1] V. Andreev, D. G. Ang, D. DeMille, J. M. Doyle, G. Gabrielse, J. Haefner, N. R. Hutzler, Z. Lasner, C. Meisenhelder, B. R. O`Leary, C. D. Panda, A. D. West, E. P. West, and X. Wu, Nature 562, 355 (2018).

We prove that smooth quartic threefolds are symplectically irrational: they cannot be related to projective space by a sequence of symplectic blow-ups, blow-downs, and deformations. This recovers the classical irrationality theorem of Iskovskikh-Manin. The obstruction is constructed from big quantum cohomology, using the multiplicities of eigenvalues of quantum multiplication by the Euler vector field. To prove its invariance, we establish a decomposition theorem for quantum cohomology under symplectic blow-ups, following the work of Iritani.

The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is investigated from the perspective of parameter-dependent ordinary differential equations. Starting from the radial Schrödinger equation for a short-range central potential, a first-order differential system is derived for the coefficient functions associated with the Ricatti--Bessel and Ricatti--Neumann solutions. The multivalued dependence on the energy variable is shown to originate from the square-root relation between energy and momentum. By explicitly factorizing the momentum-dependent branching terms, the scattering problem is transformed into a differential system whose coefficients are single-valued analytic functions of the complex energy. Using the classical theory of analytic dependence of solutions of ordinary differential equations on parameters, it is shown that the transformed Jost functions are single-valued analytic functions of the energy variable for finite radial distance. The geometric interpretation of the factorization procedure is also discussed in terms of the topology of the associated Riemann surface.

The sliced Wasserstein distance $SW_2(μ,ν)$ compares high-dimensional probability measures by averaging one-dimensional optimal transport distances over linear projections. Although sliced Wasserstein distances are now standard computational tools in statistics, imaging, and machine learning, the rigidity behind the elementary comparison \[ SW_2^2(μ,ν)\leq \frac1d W_2^2(μ,ν) \] has not been systematically studied. Let $μ,ν\in\mathcal P_2(\mathbb R^d)$, $d\ge2$, with $μ\ll\mathcal L^d$, and define the sliced Wasserstein deficit by \[ {\mathrm D}(μ,ν):=\frac1d W_2^2(μ,ν)-SW_2^2(μ,ν)\geq 0. \] We prove that ${\mathrm D}(μ,ν)=0$ if and only if the Brenier map $T=\nablaφ$ from $μ$ to $ν$ is homothetic affine, \[ T(x)=λx+b \qquad μ\text{-a.e.}, \] for some $λ\ge0$ and $b\in \mathbb R^d$. For quantitative stability, we introduce the sliced Poincaré--Korn (SPK) constant $κ_{\mathrm{SPK}}(μ)$, defined as an new spectral gap of an averaged ridge-projection quadratic form on gradient fields modulo the family $\{λx+b\}$. Whenever this constant is positive, we prove a stability estimate for the sliced Wasserstein deficit, up to a one-dimensional Lipschitz scale for the projected monotone transports. We obtain the sharp SPK constant for the Gaussian measures as the most important example, and establish positive SPK bounds for bounded perturbations of the Gaussian and compact classes of gradient fields for fixed source measures. Finally, we show that anisotropic Gaussians give a sharp obstruction: neither a Bakry--Émery lower curvature bound nor a usual Poincaré inequality alone can imply a global sliced Poincaré--Korn inequality.