Papers

In this paper, we propose a model-free feature screening framework tailored for high-dimensional and heterogeneous datasets, based on a novel distributionally robust dependence measure termed Copula Divergence. The proposed screening method, named CD-Screen, addresses critical limitations of existing feature screening methods, such as restrictive modeling assumptions and sensitivity to heterogeneous feature distributions. CD-Screen ranks features according to their Copula Divergence without relying on a specific regression model or distributional assumptions. Additionally, we introduce CD-FDR, a data-driven procedure to control false discoveries, ensuring accurate and efficient feature selection. Theoretical analyses establish the sure screening and rank consistency properties of CD-Screen, along with asymptotic control of the false discovery rate by CD-FDR. Extensive simulation studies demonstrate the superior performance of our methods compared to traditional screening approaches across diverse scenarios. Furthermore, a real data analysis of the relationship between stock returns and inflation in the United States {illustrates the practical use of our method and provides descriptive evidence on} sector-specific responses to economic changes.

Motivated by Mader's conjecture on connectivity keeping trees, we study trees obtained from paths by adding one pendant vertex, as well as related problems in triangle-free graphs. For an integer $m$ and $1\leq i\leq m-1$, let $P_m^+(i)$ denote the tree obtained from a path of order $m-1$ by adding one pendant vertex adjacent to its $i$th vertex. We prove that, for positive integers $k,m,1\leq i\leq m-1$, every $k$-connected graph $G$ with $\delta(G)\geq \lfloor \frac{3k}{2}\rfloor+m-1$ contains a subgraph $T\cong P_m^+(i)$ such that $\kappa(G-V(T))\geq k$. This confirms Mader's conjecture for all pendant extensions of paths. For highly connected triangle-free graphs, a connectivity keeping result for paths was obtained in [J. Combin. Theory Ser. B, 174 (2025), 190-206]. Let $(X,Y)$ be the bipartition of $P_m^+(i)$. We further prove that every $k$-connected triangle-free graph $G$ with $\delta(G)\geq k+\max\{|X|,|Y|\}+[P_m^+(i)\text{ is bad}]$ contains a subgraph $T\cong P_m^+(i)$ such that $\kappa(G-V(T))\geq k$, where we use Iverson's convention for $[P_m^+(i)\text{ is bad}]$. This extends the corresponding result for paths to pendant extensions of paths.

We study the minimum time for perfect state transfer under polynomial Hamiltonians with bounded degree and spectral width. For a strongly cospectral pair and width bound $W$, the optimum, when finite, is an integer multiple of $\pi/W$, determined by integer interpolation with prescribed parities. For equally spaced supported eigenvalues with alternating signs, we give degree bounds under which every minimizer is affine, and sharp asymptotics for each fixed exact degree. Near-minimizing phase polynomials satisfy a quantitative Chebyshev stability estimate. We determine the optimal transfer time for every degree bound on hypercubes of odd prime dimension. For complementary vertices of $J(2m,m)$, the optimal time at fixed spectral width grows exponentially in $m$ throughout an interval of feasible degrees. We also construct polynomial Hamiltonians showing that every feasible degree $m-t$ with $t=o(m)$ admits subexponential transfer time.

Diatomic molecules consisting of one spin-1/2 ($\sigma$) and one spin-1 ($S$) atoms are put at each site of the Bethe lattice (BL) of the coordination number $q=3, 4$, or 6. Alongside the ferromagnetic (FM) interactions of individual atoms within a molecule, the molecules are permitted to engage in ferromagnetic interactions with their nearest neighbors (NN) through diverse bilinear interaction parameters $J$. The spin-1 sites are also under the influence of crystal field $D$. The phase diagrams on the ($D, T$) planes for a given $q$ are obtained by investigating the thermal variations of magnetizations for the case with zero external magnetic field $(H)$. It is discovered that the phase diagrams rely on $q$ both qualitatively and quantitatively. The crystal field is also included which operates only on the spin-1 sites. Three separate FM phases are observed with ($\sigma,S$) being $(1/2,1), (1/2,0)$ at the ground state level and a phase region with small magnetization (SM) values at a higher temperature range. In addition to the reentrant behavior in the transition zone from one phase to the other, the model produces first- and second-order phase transitions. Additionally, the impact of $H$ on the magnetization curves is examined, yielding quite intriguing findings.

We use deep observations from the Einstein Probe Follow-up X-ray Telescope (EP-FXT) to investigate the gas distribution and thermodynamic properties of the cool-core galaxy cluster Abell 478 (A478) from the center out to $R_{200}$, and to examine its azimuthal asymmetry and the influence of local dynamical disturbances on hydrostatic mass estimates. We derive the surface-brightness, temperature, electron-density, pressure, entropy, and total mass profiles. The surface-brightness distribution is well described by a double-$\beta$ model, while the temperature profile shows the characteristic cool-core behavior, with a cool center, a rise toward intermediate radii, and a gradual decline in the outskirts. The hydrostatic mass profile is well fitted by a Navarro-Frenk-White model, yielding $R_{200}=2082\pm95$ kpc and $M_{200}=(1.12\pm0.15)\times10^{15}\,M_\odot$, indicating that the cluster is close to quasi-static equilibrium on global scales. Despite the globally regular structure, clear azimuthal asymmetry is present. The SW sector shows lower temperatures, higher densities, and lower entropies at intermediate and large radii, together with signatures consistent with a cold-front candidate. Combined with the two-dimensional temperature distribution, these features suggest local dynamical disturbance, likely associated with gas sloshing. A478 is therefore globally relaxed but locally disturbed, demonstrating that nonequilibrium structures can still affect thermodynamic measurements and hydrostatic mass estimates even in an apparently regular cool-core cluster.

We prove that every extremal Kähler–Ricci soliton on a Fano manifold is Kähler–Einstein. This solves the problem of Calamai and Petrecca in full generality.

We prove the face-number conjecture of Hibi and Li: for every finite poset, the order polytope has no more faces of any given dimension than the chain polytope. More generally, the face numbers increase weakly along the admissible family of chain–order polytopes when one order coordinate is replaced by a chain coordinate. We also prove that, unless the order and chain polytopes are unimodularly equivalent, all face-number inequalities in dimensions $2,\ldots,|P|-1$ are strict.

The inverse scattering problem for the one-dimensional nonlinear Dirac equation \begin{align*} \begin{cases} i(u_t+u_x)+v=\mathcal{N}_1(u,v),\\ i(v_t-v_x)+u=\mathcal{N}_2(u,v) \end{cases} \end{align*} is studied. We assume that the unknown nonlinearities $\mathcal{N}_j(u,v)$ ($j=1,2$) of the equation belong to $C^\infty(\mathbb{C}^2;\mathbb{C})$ and satisfy $(\partial_\mathbf{z}^\alpha \mathcal{N}_j)(\mathbf{z})=O(|\mathbf{z}|^{\max\{ 5-|\alpha|,0 \}})$ ($|\mathbf{z}|\to 0$) for any multi-index $\alpha \in (\mathbb{N} \cup \{ 0 \})^4$. Here, $\mathbf{z}=(z_1,z_2)\in \mathbb{C}^2$, $ \partial_\mathbf{z}^\alpha= (\partial_{z_1},\partial_{\overline{z_1}},\partial_{z_2},\partial_{\overline{z_2}})^\alpha, $ and $\partial_{z_1},\partial_{\overline{z_1}},\partial_{z_2},\partial_{\overline{z_2}}$ are the Wirtinger differential operators. Under some additional assumptions on $\mathcal{N}_j$, we establish a reconstruction formula for $(\partial_\mathbf{z}^\alpha \mathcal{N}_j)(0)$ ($|\alpha|\ge 5$) using the knowledge of the scattering operator for the equation. Although such results were established for the nonlinear Schrödinger equation [Sasaki 2024] and the nonlinear Klein-Gordon equation [Sasaki 2025], the methods in [Sasaki 2024, 2025] are not directly applicable to the nonlinear Dirac equation due to its system nature. Specifically, it is quite difficult to prove the invertibility of a matrix associated with the input data. To overcome this difficulty, we introduce a new method based on the massless limit for the free solutions.

We prove that Lagrangian mean curvature flow starting from a closed, embedded, cohomogeneity-one Lagrangian in a closed, positive Kähler–Einstein manifold exists for all time, remains embedded, and converges smoothly and graphically to a minimal Lagrangian, under natural exactness and regularity assumptions. We also study the generalised Lagrangian mean curvature flow of Behrndt in Kähler manifolds which are almost-Einstein in the sense that the Ricci form satisfies $\rho = C\omega + ndd^cf$, and which satisfy $C>0$. With analogous assumptions on the flow, we obtain subconvergence to an $f$-minimal Lagrangian submanifold, with an upgrade to smooth graphical convergence in the case that $(M,g,f)$ is analytic. The proof proceeds by first reducing the flow to a weighted curve shortening flow on a compact two-dimensional orbifold. We then establish both a Grayson-type description of finite-time singularities and a long-time subconvergence theorem for weighted curve shortening flow in the orbifold setting. Finally, we use a Łojasiewicz–Simon inequality argument to upgrade to smooth convergence of the full flow.

The effect of B homopolymer adding on the aggregation behavior of amphiphilic coil/rod/coil BAB triblock copolymers was studied using lattice self-consistent field theory. It depends on the length of the hydrophobic rod block and copolymer concentration. Compared with the solutions, at low concentrations, homopolymer addition is favorable to the emergence of cubic and large lamellar micelles. Although it enriches the structural behavior, the rearrangement is suppressed. As rod blocks increase, the rearrangement is related to the orientation-dependent diffusion and inverse diffusion processes. At relatively high concentrations, adding homopolymers promotes rearrangement. For long rod block case, the arrangements related to inverse laminarization and the cooperative growth emerges. At high concentrations, for short rod block system, homopolymer addition is advantageous to micelle rearrangement concerned with order/disorder transition, and the rearrangements in the system of intermediate length and long rod blocks are suppressed. This work aids in understanding of the growth mechanism of micelles with rigid block cores.

We establish the complete integrability of the defocusing Calogero–Sutherland derivative nonlinear Schrödinger equation \begin{equation}\label{CS-abstract}\tag{CS} i\partial_t u +\partial_x^2 u + 2i u \partial_x\,\Pi\!\left(|u|^2\right)=0,\qquad x\in\mathbb T, \end{equation} by constructing a nonlinear Fourier transform \begin{equation*} \Phi : u\in L^2_+(\mathbb T)\mapsto\ (\zeta_n(u))_{n\geq 0}\in \ell^2(\mathbb N_0),\qquad \zeta_n(u)=\sqrt{\gamma_n(u)}\;e^{\,i\arg\langle u\mid f_n\rangle}, \end{equation*} built from the eigenvalues $(\lambda_n)$, the spectral gaps $\gamma_n:=\lambda_n-\lambda_{n-1}-1\geq 0$ and the eigenfunctions $(f_n)$ of the Lax operator $L_u$. We prove that $\Phi$ is a norm-preserving homeomorphism. In these coordinates, the flow becomes the explicit rotation $\zeta_n(t)=e^{-i\omega_n t}\zeta_n(0)$ for all $n$, whose frequencies $\omega_n$ depend only on the conserved spectrum $(\lambda_n)$. As consequences, every orbit of \eqref{CS-abstract} is precompact in $L^2_+(\mathbb T)$, and $t\mapsto u(t)$ is Bohr almost periodic. For finite-gap data, we obtain quasi-periodicity in time and a sharp criterion for genuine periodicity.

Genomic epidemiology has several methods for identifying which sampled individuals are linked by close proximity in the transmission chain, whether by grouping them into clusters under a genetic distance threshold or by identifying probable direct transmission pairs. Individuals found to have no sampled neighbours—singletons—are usually set aside. We argue that they are informative. Whether any two sampled individuals prove to be linked depends on the size of the sampling frame and the number of independent lineage introductions into it, and thus the balance of linked and unlinked individuals is itself data about these quantities. We formalise this by treating the intersection of a transmission tree with a sampling frame as a labelled rooted forest, from which a fixed number of nodes are sampled uniformly at random. Using the all-minors matrix-tree theorem, we derive a closed-form expression for the number of labelled rooted $k$-forests on $N$ nodes in which a specified set of nodes is independent. From this we obtain, again in closed form, the probability that a sample of a given size contains no linked individuals at all, and the likelihood of an arbitrary observed configuration of clusters, both when the transmission structure within each is known, and when only the cluster sizes are. The approach is closer to a survey, or to mark-recapture, than to conventional phylodynamic model fitting: the information comes from the linkage structure of a single sample alone with no assumptions regarding pathogen dynamics. We outline three applications: power calculations for prospective studies, a test of the uniform sampling assumption that underlies the reading of clusters as transmission hotspots, and demographic inference itself. We finally set out the assumptions that a more flexible implementation would need to relax.

In this work we study peculiarities of spatial rearrangement of solute and vacancy concentrations in Zr-Sn alloy at stages of both thermal treatment of solid solution and irradiation of annealed alloy under reactor conditions. To this end, we exploit phase field modelling including reaction rate theory and CALPHAD method combined in one generalized approach. Simulations were done in 3D in order to get a detailed information about rearrangement of solutes and defects in a bulk. We discuss the emergence of the secondary phase at the stage of thermal treatment and its stability under neutron irradiation. We analyze an influence of the irradiation dose onto statistical properties of the secondary phase particles.

The microscopic approach of the triaxial projected shell model (TPSM) is employed to investigate the properties of the $8^-$ isomer in the six isotones of $^{128}$Xe, $^{130}$Ba, $^{132}$Ce, $^{134}$Nd, $^{136}$Sm, and $^{138}$Gd. The observed decay pattern of the isomer for these isotones is unexpected with the hindrance factor decreasing with atomic number. It is shown in the present work that multi-quasiparticle mixing into the ground-state configuration is responsible for the observed decreasing trend of the hindrance factor. We have also calculated the excitation energies and in-band $B(E2)$ transition probabilities of the yrast and the band built on the $8^-$ isomer for the six isotones, and it is shown that TPSM approach reproduces the measured quantities quite satisfactorily.

Exponential potentials were used since Kramers, Hellman, Glauberman, Yukhnovskii and Kelbg for solving problems of quantum chemistry, ionic solutions and plasmas. Here we develop the theory further and add new results, in particular with respect to the quantum-statistical theory. In particular, we derive the Kelbg quantum potential for the exponential interactions and discuss screening as well as the problem of thermodynamic stability. Further we give new applications to a qualitative theory of alkali plasmas and fusion plasmas. We show that the exponential potential and the early analytical results of Yukhnovskii and Kelbg allow a qualtative analytical treatment of such difficult problems as the phase transitions in electrolytes and alkali plasmas.

We explore composition dependence of the principal properties of liquid dimethylsulfoxide (DMSO)-methanol (MeOH) liquid mixtures by using molecular dynamics computer simulations. A set of non-polarizable semi-flexible models for the DMSO molecule combined with methanol models is investigated. Composition trends of density, excess mixing volume and excess mixing enthalpy are evaluated. Besides, we study the composition dependence of self-diffusion of species and shear viscosity ofthe static dielectric constant and the surface tension.Certain aspects of the microscopic structure are analyzedin terms of radial distribution functions and of the average number of hydrogen-bonded molecules. The quality of several combinations of the models is illustrated and critically evaluated by comparisons with experimental data.

Snapshot hyperspectral imaging avoids sequential scanning, but systems that jointly achieve stable reconstruction, low cost, and compact optics remain limited. We present a snapshot hyperspectral imaging system based on angular-to-spectral diversity conversion. A tapered kaleidoscope creates replicated views with distinct incidence directions, and a directly attached birefringent filter converts them into view-channel-dependent spectral transmittances, yielding complementary measurements that better condition the inverse problem for more stable single-shot spectral reconstruction. The system preserves a simple pixel-wise linear model for fast non-learning-based reconstruction and uses only off-the-shelf components without relay optics or cascaded modules. We select the birefringent filter configuration using a condition-number-based criterion and validate the system on both synthetic and real data.

We investigate spin-dependent transport in a non-collinear helical antiferromagnet in the presence of spin-orbit coupling within a tight-binding framework. Using the Landauer-Büttiker formalism, we analyze the generation of spin polarization arising from the combined effects of the helical magnetic texture and spin-orbit interaction. We find that finite spin polarization can be generated simultaneously along the $\hat{x}$, $\hat{y}$, and $\hat{z}$-directions, in contrast to the predominantly single-axis spin polarization commonly observed in conventional spin-filtering systems. The multidirectional spin polarization originates from the symmetry breaking introduced by the non-collinear magnetic order. We further show that the spin polarization is modified significantly in the presence of spin-orbit coupling and it has strong dependence on the parameters associated with the helical system. In particular, long-range hopping significantly enhances the spin-filtering effect, leading to large spin polarization components along all three spatial directions.

We consider sparsely observed functional data generated by a latent Gauss-Markov process modeled through a linear stochastic differential equation (SDE). Motivated by an application to tumor growth data, we allow for outcome-dependent dropout, where sampling terminates once the most recent observation exceeds a prescribed threshold. Such observation schemes arise naturally in longitudinal studies and violate the fundamental missing completely at random assumption commonly imposed in the analysis of partially observed functional data. We develop a likelihood-based estimation framework that, in contrast to existing moment-based methods, avoids the bias induced by outcome-dependent dropout. We establish convergence rates for the proposed estimators and show that they are mini-max optimal up to logarithmic factors, with the diffusion coefficient admitting a faster rate than the drift coefficients under a random initial condition for the SDE. An application to tumor growth data further demonstrates the advantages of a fully probabilistic functional data model for tasks beyond second-order inference, including prediction bands, first-passage times, and tumor-age estimation.

In this paper, we study modulated $(C,\alpha)$-ergodic averages with operator-valued weights and their subsequential versions in the setting of semifinite von Neumann algebras. Our framework combines $(C,\alpha)$-type modulation with operator-valued weights and extends both scalar-weighted and operator-valued weighted ergodic theories. We establish mean ergodic theorems and maximal inequalities for these averages on noncommutative $L_p$-spaces. We then study bilateral almost uniform and almost uniform convergence in noncommutative Orlicz spaces, including convergence along subsequences of density one when $\alpha\geq 1$. A key ingredient in our approach is the introduction of the $p$-convexity condition on the underlying Orlicz function. This condition allows us to transfer appropriate maximal estimates from noncommutative $L_p$-spaces to establish bilateral uniform equicontinuity in measure at zero on the corresponding noncommutative $p$-convex Orlicz spaces. Together with the noncommutative Banach principle, this yields the desired pointwise convergence results. As an additional consequence of our $p$-convexity argument, we extend Rota theorem to a larger class of noncommutative Orlicz spaces associated with the $p$-convex Orlicz functions considered in this article.

Attosecond charge migration (CM) is an ultrafast process occurring when a molecule is irradiated by ultrashort laser pulses, creating a localized hole. The hole propagates rapidly through the molecule, generating electric currents and transferring charge across the molecular backbone. CM is a key ingredient in solar energy conversion, photosynthesis, and radiation damage. Despite its importance and intensive research, the fundamental physical and chemical mechanisms of CM remain not fully understood. Especially, a deeper insight into the role correlations play in the dynamics, and which chemical attributes determine CM timescales, is needed. Here we study with ab-initio time-dependent density functional theory CM in the benchmark molecule, BrC$_4$H. We thoroughly explore CM under different initial conditions at the electronic and structural levels, including with theories of varying degrees of electronic correlations. We uncover a universal behavior where the hole moment (connecting to experimental observables) dominant frequency is roughly independent of all of these characteristics. In contrast, the timescales of the hole density evolution do vary with the chemical conditions and level of correlations. Employing a semi-analytical theory that reconstructs the hole moments in the cationic reference frame, we show that the attosecond timescale of CM is determined by molecular dipoles that filter out specific frequency responses with an analogy to optical selection rules. Our results provide essential insight into CM physics, which should be useful for interpreting attosecond experiments and engineering CM timescales by tailoring transition dipoles.

Contact-rich manipulation, requiring robots to regulate not only motion but also how they yield to external forces, has emerged as the next frontier for Vision-Language-Action (VLA) models. However, existing VLAs output purely kinematic commands, degrading performance on real-world contact-rich tasks. In this paper, we introduce CompVLA, a unified VLA framework that jointly predicts motion and a stiffness matrix from RGB and language inputs. Our approach augments the conventional architecture with a dedicated Compliance Expert, which outputs time-varying stiffness and virtual displacement profiles executed via geometric impedance control. We demonstrate that CompVLA achieves the highest average success rate across diverse contact-rich tasks, outperforming both vanilla and compliance-aware VLA baselines, with ablations confirming each component is essential.

We study the functional equation $ f \circ p = g \circ q,$ where $ f,$ $g,$ $p,$ $q$ are branched covering maps between closed surfaces. In particular, we extend results on semiconjugate holomorphic maps between compact Riemann surfaces to this broader setting. As an application, we present an alternative proof of the fact that every quotient of a torus endomorphism has a parabolic orbifold, along with some extensions of this result.

We consider a Whitham-Boussinesq type system with surface tension arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water, which is characterized by a nonlinearity parameter $0<\epsilon\le 1$, a shallow water parameter $0<\mu\le 1$ and a nonnegative surface tension parameter $\beta$. In this paper, we establish well-posedness of the associated Cauchy problem for $\beta>1/3$ on a time scale of order $ ( \beta_\ast^{ 1/4} \mu^{ 1/4} h_0 \epsilon^{-1} )^{4/3}$ in one dimension and of order $( \beta_\ast^{ 1/4} \mu^{ 1/4} h_0 \epsilon^{-1})^{2-}$ in two dimensions, where $\beta_\ast= \min(|3\beta-1|, 1/2)$, assuming a non-cavitation condition with a parameter $h_0>0$. In addition, we established well-posedness for the classical Whitham equation with either $\beta=0$ or $\beta>1/3$ on the timescale of order $ ( \beta_\ast^{ 1/4} \mu^{ 1/4} \epsilon^{-1} )^{4/3}$. These results explicitly capture how the existence time depends on all the parameters involved. Our proofs rely on dispersive and Strichartz estimates combined with energy estimates.

Polymer properties emerge from interactions across scales, yet existing polymer models typically preserve either detailed monomer chemistry without an explicit polymer graph or polymer connectivity with simplified monomer representations, due to computational constraints, as polymers typically contain tens of thousands of atoms. We present Uni-Macro-FRPN (FRPN), a Full-Resolution Polymer Network that retains both detailed atom-level and monomer-level features and explicit polymer structure information within a unified framework. Two Transformers jointly learn atom-informed monomer semantics, sequence order, and chain topology from BigSMILES-derived representations. On the Block Copolymer Database (BCDB) lamellar-versus-non-lamellar classification task, FRPN achieves 86.4% accuracy and 90.6% ROC-AUC, establishing state-of-the-art performance. Ablation results indicate that the gain is not explained solely by increased parameter count. On a linear homopolymer benchmark, monomer-centric learning remains competitive, highlighting a boundary case where polymer-scale organization is simple. To test generalization beyond linear polymers, we further construct an all-atom molecular-dynamics benchmark of 1640 datapoints spanning diverse monomer chemistries, sequence orderings, chain topologies, and physical properties. FRPN achieves the strongest overall performance on this topology-rich benchmark, with diagnostics supporting the benefit of jointly modeling monomer chemistry and polymer structure. Taken together, FRPN provides a practical route for moving polymer representation learning beyond monomer-centric representations. The leading performance of FRPN also suggests a promising direction for polymer informatics: future polymer prediction models should treat polymers not only as collections of monomer descriptors, but as complete multiscale chemical and topological objects.

Simulation-trained humanoid proprioceptive odometry faces two transfer challenges: training trajectories generated by specific robot control policies intended for deployment cover only a limited range of motions, while sim-to-real mismatch can make unconstrained predictions unreliable. We address both with Prior-Informed Odometry from Human-Motion Tracking (PRIMO). On the data side, we generate odometry supervision by having the humanoid track diverse retargeted human motions in simulation, decoupling supervision from the deployment policies and broadening the training motion distribution. On the model side, a Prior-Informed estimator uses physics- and symmetry-informed priors to structure velocity and rotation prediction and a coarse raw-context pathway to preserve sensor context alongside encoded features, thereby strengthening sim-to-real generalization. Under a unified real-robot protocol, PRIMO reduces mean error by 31.6%-61.7% relative to the strongest evaluated external baseline in each domain-metric comparison. Across two locomotion-policy revisions, policy specialists exhibit symmetric crossover, whereas Tracking-Locomotion training reduces mean opposite-policy simulation error by 86.8%-94.6%. On real dynamic motion, Tracking-Locomotion training reduces mean error by 69.2%-81.7% relative to training on the union of both deployment policies. Across the tested motion compositions, the Prior-Informed estimator consistently lowers mean trajectory errors relative to its Unconstrained counterpart in both simulation and real-robot evaluation. Code is available at https://github.com/Agibot-Spatial-Intelligence/PRIMO.

Casimir forces, arising from quantum and thermal fluctuations, depend strongly on the electromagnetic susceptibilities of the interacting materials. Here, we theoretically investigate the Casimir force between two graphene sheets separated by a nanometer-thin layer of liquid water. We find that deviations from the bulk case can be as large as 24 %, mostly due to the static susceptibility components. This effect does not decrease monotonically as a function of the layer thickness: it increases up to a maximum at 70 nm and it slowly declines to the bulk limit only at 1 micron. This is due to two competing effects: on one hand, the anisotropy decreases with the layer thickness; on the other hand, the relative contribution of the most anisotropic, static susceptibility components increases.

We study complex geodesic actions and heat-kernel resurgence on isotropic Heisenberg groups. For real endpoints with $r>0,y\ne0$, the nonzero finite singularities reached by analytic continuation of the minimizing-saddle Borel germ are exactly the finite complex action differences. For nonresonant endpoints, we construct row-finite directional Stokes operators and compute the positive-ray Stokes matrix and its logarithm explicitly; the primitive alien support can be strictly smaller than the full Borel singular support. Near the vertical axis, we obtain uniform two-term large-order asymptotics from the nearest Borel singularity. Cubic resonances admit uniform $A_2$ confluence formulas. We also identify the combination of resurgent sectors selected by the original Fourier contour. Positive Borel summation is exact at horizontal endpoints. At nonzero isotropic complex endpoints, no finite normal trajectories exist, but the signed vertical action lattice is the complete limiting spectrum. The action and Stokes structures are independent of the dimension on isotropic $H^n$.

We study a circular variant of the $s$-choice parking model: $n$ cars park on $m=n+1$ spots arranged on a circle, each car carrying an anchor and $s-1$ clockwise increments at least $d$ apart with return gap at least $d$; a car tries its choices in order and then sweeps clockwise from its last choice. On the circle every car parks and exactly one spot remains empty. Exploiting rotational symmetry in the spirit of Pollak's proof of the count $(n+1)^{n-1}$, we prove that the empty spot is exactly equidistributed, which yields the closed formula $m^{n-1}\binom{m-sd+s-1}{s-1}^{n}$ for the number of preferences leaving any prescribed spot empty. This appears to be the first closed product formula in the multi-choice parking landscape. We further prove a refinement: within every class of preferences with prescribed increments, the empty spot is still exactly equidistributed, which explains the product structure of the formula and, for $s=2$, $d=1$, the appearance of the classical count $(n+1)^{n-1}$ as a factor of $(n+1)^{n-1}n^{n}$. The admissible tuples are enumerated through Kaplansky's lemma on circular selections, and all results are verified by exhaustive computer enumeration.

Mesh texture compression typically relies on 2D UV atlases, whose chart discontinuities and mapping overhead can limit coding efficiency. To tackle this challenge, we introduce TexF, a surface-aligned texture field that organizes texture attributes in sparse voxels derived from the mesh surface. This representation supports high-resolution textures while preserving local 3D correlations for compression and enabling direct surface queries. For bitstream compression, TexF reuses established 3D attribute codecs, with voxel locations reconstructed from the decoded mesh without separate transmission. For GPU-resident compression, we develop 3DNTC, which combines quantized hash features with a lightweight decoder for random-access reconstruction at surface positions. Differentiable rendering enables image-space refinement of both voxel attributes and compressed neural fields. Experiments on the MPEG and AOM mesh compression benchmarks demonstrate improved average rate-distortion performance over representative UV-based methods for both bitstream and GPU-resident compression. 3DNTC also supports real-time rendering.