Papers

We consider the estimation of linear functionals of the mixing distribution in a nonparametric empirical Bayes framework. Our main interest is in situations in which the mixing distribution is only partially identifiable, as may arise in complex sampling situations with nonresponse. We argue that estimating the functional by applying it to the semiparametric maximum likelihood estimator of the mixing distribution is an efficient tool, even when the maximum likelihood estimator is not unique.

Given a quasi-norm on $\mathbb{R}^d$ induced by a one-parameter dilation group, we consider matrix weights $W$ in an adapted Muckenhoupt class $\mathbf{A}_p$, $0 < p < \infty$, and use these weights to introduce and study anisotropic matrix-weighted smoothness spaces in both continuous and discrete settings. The spaces are constructed by means of a decomposition method in the frequency domain. We prove the equivalence of the continuous and discrete spaces using suitably adapted tight frames. Compatible notions of molecules and almost diagonal matrices are also introduced, and applications to the study of Fourier multipliers and pseudo-differential operators on vector-valued smoothness spaces are given.

Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation. We provide one. Data augmentation induces a similarity graph on the unlabeled data, so downstream learning on that graph is graph-Laplacian-regularized learning. We prove a fast transductive rate, $O(1/n_L)$ in the number of labels, in place of the supervised $O(1/\sqrt{n_L})$, by carrying the leave-one-out stability apparatus of Johnson and Zhang (JMLR 2007) over to the augmentation graph, and without the unrealistic assumptions of limit-based analyses (exact kernel, generalizing features). The bound makes augmentation quality explicit: the expected error is at most $C/n_L + R_{\mathrm{DA}}(y)$, where the data-augmentation alignment error $R_{\mathrm{DA}}(y)$ is proportional to the graph-cut mass of augmentations that cross a label boundary, so good augmentations let few labels suffice. The analysis uses a streamlined loss that drops the projector, negative-sample, and orthogonality overhead of standard objectives yet still recovers the top-$K$ ideal features in the infinite-data limit, the augmentation-kernel eigenspace studied by Zhai et al. The bound gives a mechanistic account of the accuracy-versus-label-count curve through augmentation quality, verified in a controlled model where the constants are known.

Let $F$ be a non-archimedean local field of characteristic 0, and let $G$ be either $\mathrm{Sp}_{2n}(F)$ or $\mathrm{SO}_{2n+1}(F)$. We introduce a new algorithm to compute the Aubert dual at the level of Langlands data. This algorithm acts as the dual to the recent Lanard-Mínguez algorithm. It fundamentally differs in two ways: it follows a bottom-up approach rather than a top-down one, and its internal computations strictly preserve the temperedness of the representations. Consequently, this approach naturally yields a new constructive characterization of co-tempered representations. By operating exclusively within the realm of tempered data, this algorithm enables inductive proofs of new properties for co-tempered representations. In particular, we provide a precise description of their tempered components and establish an explicit duality formula for a large class of tempered representations.

The least-squares neural network (LSNN) method introduced in [5] for linear advection-reaction equations is capable of accurately approximating discontinuous solutions without a priori knowledge of the interface location. However, the resulting discretization is a non-convex optimization problem that is computationally intensive and complex. In this paper, we propose a structure-guided Gauss-Newton (SgGN) method that alternates between the linear (output) and the nonlinear (hidden layer) parameters. At each outer iteration, the linear parameters are computed by a linear solver, and the nonlinear parameters are updated by a modified Gauss-Newton (GN) method that explicitly removes the singularities of the GN matrix. Numerical experiments for all test problems presented in [5] show that the SgGN method is superior to the Adam optimizer [13], the commonly used first-order optimization algorithm, not only in computational cost but, more importantly, in accuracy

We study the dimer model on two families of non-bipartite graphs on a torus. The first family is obtained by replacing degree $3$ vertices in a bipartite torus graph with triangles, while the second consists of corner graphs associated with bipartite torus graphs. We determine the relationship between the Newton polygons of these graphs and those of the underlying bipartite graphs. We also identify the primitive edge vectors of the Newton polygons with the homology classes of the zig-zag paths. We further consider the marginal polynomials obtained by restricting to monomials corresponding to a boundary side of the Newton polygon. For the triangular lattice and the Fisher graph of the hexagonal lattice, we prove that these polynomials are real-rooted and obtain an explicit factorization of their roots. Finally, we introduce new local moves, including a move on non-planar graphs, that preserve the dimer partition functions up to a scale.

Implicit methods are a natural approach for the integration of stiff differential equations, to avoid time-step restrictions faced by standard explicit integrators. Explicit stabilised integrators are an alternative to implicit methods, which can be particularly efficient in high-dimensional applications with diffusive terms. Towards the best of both worlds, we introduce a new explicit stabilised implementation of a class of diagonally implicit Runge-Kutta methods. This allows us to implement high-order singly-diagonally-implicit Runge-Kutta methods for advection-diffusion-reaction PDEs with a provable computational cost analogous to that of standard explicit stabilised methods. The main ingredient is to recast the implicit Runge-Kutta update as the steady state of a modified auxiliary system, which is then computed using a partitioned Runge-Kutta-Chebyshev method inspired by optimisation techniques.

We prove that any finite graph of finitely generated free groups admits a finite complete rewriting system after possibly taking a free product with a free group of rank two. As a corollary we obtain that any HNN-extension of a finitely generated free group over a finitely generated subgroup admits a finite complete rewriting system. We then use this result, and other tools, to give partial solutions to several fundamental open problems about finite complete rewriting systems for hyperbolic, one-relator, fully residually free, and three-manifold groups. In particular we prove that if $G = \langle \mathbb{F} , t \mid t^{-1}ft = \psi(f), \, \forall f\in \mathbb{F} \rangle$ is the mapping torus of an injective endomorphism $\psi$ of a free group $\mathbb{F} $ (of possibly infinite rank) then every finitely generated subgroup of $G$ admits a finite complete rewriting system. It follows that any finitely generated virtually free-by-cyclic group, and any finitely generated subgroup of such a group, admits a finite complete rewriting system. We apply this to show that every finitely generated subgroup of a locally quasi-convex hyperbolic and virtually compact special group admits a finite complete rewriting system. This includes all one-relator groups with torsion (and all their finitely generated subgroups) and all hyperbolic fully residually free groups. Moreover, we show there is an algorithm that computes a finite complete rewriting system for any such group, given a presentation for its containing group and a finite list of generators for the subgroup. We also prove that for every compact three-manifold $M$, the group $\pi_1(M) \ast \mathbb{Z}$ admits a finite complete rewriting system. Furthermore, we show that the fundamental group of any compact three-manifold is autostackable and thus has a rational cross section and admits a bounded regular convergent prefix-rewriting system.

Reaction–diffusion systems can produce spatial patterns such as stripes and spots by diffusion-driven instability. In synthetic developmental biology, such patterns are engineered in cell populations, and steering them toward a prescribed target pattern can be formulated as an optimal control problem. When the control acts on the entire spatial domain, the existence of optimal controls and the first-order optimality conditions are well established. In experiments, the control is applied with light by optogenetic tools, and the light illuminates a chosen region of the tissue, so the control acts on a subdomain. We consider the setting where the control is restricted to a subdomain fixed in advance, for a synthetic circuit in which the slowly diffusing activator Nodal and the fast-diffusing inhibitor Lefty form the pattern. We study the optimality loss, the difference between the optimal costs of the subdomain problem and of the full-domain problem, and we ask how much coverage keeps it within a desired precision. In simulations with one parameter set and two target patterns, nine squares give a smaller terminal error than one square at the same coverage. Moreover, the error depends on the average distance from the uncontrolled points to the control region. In particular, small errors occur when this distance is comparable to the length scale set by Nodal diffusion and degradation.

An analytic Hilbert module $\mathcal{H}$ over the polynomial ring, consisting of holomorphic functions over the bidisc, is said to be Möb-homogeneous if the corresponding pair of multiplication operators is homogeneous with respect to the diagonal action of the group $\{(\varphi,\varphi): \varphi \in \mbox{M\"ob}\} \cong \mbox{M\"ob}$. In this article, we construct three families of mutually unitarily inequivalent Möb-homogeneous analytic Hilbert modules, distinct from the family of weighted Bergman modules over the bidisc. We further show that none of the reproducing kernels in one of these families induces a Kähler–Einstein metric on the bidisc.

Recently we introduced the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) method as a multilevel, algebraic preconditioner for sparse symmetric positive definite (SPD) matrices that admit a Gram representation \(A=G^{\top}G\) \cite{southworth2026lsamgdd}. The factor \(G\) induces a local symmetric positive semidefinite (SPSD) splitting of \(A\) used to define local spectral problems from which an interpolation $P$ is built, and a coarse-level Gram operator induced under Galerkin coarsening, \(A_c=G_c^\top G_c\), for \(G_c:=GP\). This paper clarifies when this Gram structure arises, showing that, on a prescribed degree-of-freedom cover \({\cal C}\), a \({\cal C}\)-local Gram representation of $A$ exists if and only if \(A\) admits a \({\cal C}\)-local SPSD splitting. We then connect this viewpoint to conforming finite-element discretizations, where bilinear forms are naturally assembled from elementwise SPSD energies and therefore admit element-local Gram representations after choosing local factors (e.g., via algebraic factorizations of element blocks). Taken together, these observations provide an essentially black-box route for applying LS-AMG-DD to conforming finite-element problems. Numerical tests illustrate the robustness of the method on several problems for which classical AMG methods require more than $10^5$ iterations to converge, including high-order discretizations of grad–div in \(\hdiv\), anisotropic hyperdiffusion in $H^2$, and linear elasticity in vector \(H^1\). Moreover, in some comparisons with existing AMG methods, LS-AMG-DD produces errors that are 2–5 orders of magnitude smaller, even when all methods are stopped at the same relative residual tolerance.

Bombieri's inequality for polynomials requires that at least one of them be homogeneous. In this note an AI provides a natural example showing that, as stated in the title, there is no degree independent Bombieri type inequality for non-homogeneous polynomials.

We study Schubert subspace codes, which are constant-dimension subspace codes with prescribed intersection conditions with a fixed subspace. Our goal is to construct codes of maximum possible size in the extremal distance cases where a natural counting upper bound applies. We give two families of constructions. The first one uses a direct-sum decomposition of the ambient space, together with partial spreads and colorings of powers of $q$-Johnson graphs. For this construction, we also prove necessary conditions, which show how chromatic and clique obstructions arise. The second family is obtained by field reduction from evasive and scattered subspaces over extension fields. This gives codes whose size can be computed exactly in the scattered case and recovers the only previously known construction as a special case.

For a finitely generated commutative monoid $\Pi$, we present a constructive description of all (total) preorders on $\Pi$ that are compatible with the monoid structure. Equipped with a natural topology, these preorders form an irreducible spectral space, which we show can be covered by a countable union of admissible sets: subsets of $\mathbb{R}^N$ of the form $A \setminus H$ where $A$ is semialgebraic and $H$ is a countable union of hyperplanes, both defined over the rational numbers. As a consequence of this description, we show that the universal theory of commutative monoids with a total order is decidable. Our proofs use a divide-and-conquer technique that requires establishing all of our results in the greater generality of sets on which $\Pi$ acts with finitely many orbits. As a by-product, we find a new description of all monomoial orders on free modules over a polynomial ring.

We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\ell^1$, and observations are generated through a possibly nonlinear forward operator $A:\ell^1\to H$, where $H$ is a vector-valued reproducing kernel Hilbert space. We propose an $\ell^1$-regularized empirical risk minimizer and develop a theoretical analysis of its statistical properties. Under mild assumptions, we establish almost-sure consistency and derive non-asymptotic high-probability convergence rates in both the prediction and $\ell^1$ reconstruction norms. The rates depend on the source smoothness parameter $r$, characterized by a variational source condition, and the effective dimension exponent $b$, describing the polynomial spectral decay of the covariance operator. We further prove matching minimax lower bounds, showing that the obtained convergence rates are optimal. To relate the theory to practical sparsity models, we consider finitely smoothing operators of the form $A=G\circ S$, where $S$ is a synthesis operator, and show that approximation-space assumptions imply the required variational source conditions. In particular, we prove that membership in the approximation space $k_t$ is equivalent to polynomial decay of the best $n$-term approximation error. Finally, we verify the assumptions for two representative inverse problems: reaction coefficient identification in elliptic PDEs and sparse computed tomography. For filtered Radon transforms, we derive explicit effective-dimension asymptotics, yielding concrete convergence rates for standard image models and sparsifying systems.

We give a systematic analysis of the analytic spread of the determinantal ideal $J_{G,H}$ arising from a pair of graphs $(G, H)$. We give sharp bounds for this analytic spread, and combinatorial conditions and obstructions for its maximality via a linear matroid. When $H$ is a single edge, $J_{G,H}$ is isomorphic to the binomial edge ideal $J_G$ and its analytic spread is shown to equal the rank of $G$ in Kalai's $2$-hyperconnectivity matroid.

This paper presents a construction of a projector from an infinite-dimensional Hilbert complex of differential $k$-forms onto a finite-dimensional piecewise polynomial sub-complex. We demonstrate that, on contractable domains, the proposed projector attains the three properties of the Bounded Cochain Projector, namely that the projector is idempotent, uniformly bounded in the Sobolev norm, and it commutes with the exterior derivative. On non-contractible domains, the projector remains idempotent and uniformly bounded, while the commuting property is satisfied up to arbitrary accuracy.

We investigate pattern formation in a finite chain of bosonic modes whose dynamics is governed by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. The model combines local parametric driving and nonlinear damping with nonlocal dissipative couplings between modes that work on different discrete spatial scales. In the classical limit, these mechanisms generate a reaction-diffusion-like dynamics, allowing the emergence of Turing-type instabilities. The key aspect of the analysis is the coexistence and competition of different unstable spatial modes. Depending on the range of parameters, the system may select different stationary nonuniform configurations, oscillatory wave-like states, or regimes in which multiple modes interact before a dominant pattern is established, thus providing a mechanism for pattern selection. We compare the deterministic bifurcation scenario, generated by a reaction-diffusion-like system derived from semiclassical drift dynamics, with the quantum dynamics, derived via the GKSL master equation, using phase-space methods and reduced Wigner functions. The results show how Turing instabilities, mode competition, and pattern selection can be extended to multimode open quantum systems, providing a bridge between nonlinear dynamical systems, dissipative quantum mechanics, and spatial self-organization.

The Graham-Pollak theorem says that one needs at least $n - 1$ complete bipartite graphs to cover each edge of a complete graph $K_{n}$ on $n$ vertices exactly once. The odd cover problem is a parity analogue which seeks the minimum number of complete bipartite graphs, denoted by $b_2(n)$, such that each edge of $ K_n $ is covered an odd number of times. An odd cover of a complte 3-graph $K_n^{(3)}$ on $n$ vertices is a family of complete $3$-partite $3$-graphs such that every triple is covered an odd number of times. Let $b_3(n)$ be the minimum size of such a family. The values of $b_2(n)$ and $b_3(n)$ are determined for some $n$ in several previous works. In this paper, we first determine the value of $b_2(n)$ for all $n$, which confirms a conjecture due to Buchanan et al. (JGT, 2026), and then show $b_3(n+1)=b_2(n)$ by which the value of $b_3(n)$ is determined for all $n$, that resolves a question posed by Leader and Tan (EJC, 2026).

In parametrized linear systems $\mathsf{P}(\mu)\mathsf{x}=\mathsf{b}$ the system matrix $\mathsf{P}$ depends nonlinearly on a parameter $\mu$ and solutions are sought for many values of this parameter. We show that the compact rational Krylov (CORK) framework, originally introduced to solve nonlinear eigenvalue problems, can be used to efficiently produce approximate solutions to such a system for many values of the parameter at once. In this approach, the parametrized system is first linearized, resulting in a large shifted linear system $(\boldsymbol{\mathsf{A}}-\mu\boldsymbol{\mathsf{B}})\boldsymbol{\mathsf{y}}=\boldsymbol{\mathsf{d}}$. We formulate a left- and right-preconditioned rational Krylov GMRES method for shifted linear systems. In the setting of parametrized linear systems, these can exploit the structure in the linearization, and in combination with the CORK framework, computational and memory complexity mainly depend on the problem size, less the degree of the linearization. Additionally, we show how to incorporate a right-hand side $\mathsf{b}(\mu)$ that also depends on the parameter, how to choose the shifts to steer convergence and how to allow for inexact solves at these shifts throughout the iterations. As an application we consider the 'frequency sweeping' of Helmholtz scattering problems through the Boundary Element Method (BEM), enabled via an efficient representation of the dense but data-sparse wavenumber-dependent system matrix.

We introduce and develop the theory of semiadditive characters in the higher semiadditive setting, generalizing both the $T(n)$-local monoidal character and the $K(t)$-local transchromatic character. These are natural transformations compatible with restriction and transfer maps along $\pi$-finite spaces, with an $(n-t)$-fold $p$-typical free loop space correction built into the target. We show that every $\infty$-commutative monoid admits a universal $(n-t)$-fold character. This universal character has several strong structural properties: it exhibits blue shift, satisfies higher cyclotomic descent, and is compatible with the semiadditive Fourier transform. We compute it for an arbitrary $K(n)$-local object and show that, for Morava $E$-theory, it recovers the $K(t)$-local transchromatic character. By functoriality, the universal character carries a natural action of the profinite group $\mathrm{GL}_{n-t}(\mathbb{Z}_p)$. When $t=0$, the fixed points of this action recover rationalization. As a consequence, we derive an explicit description of $L_{\mathbb{Q}}(S^A_{K(n)})$ for every $\pi$-finite space $A$ and compute the ring of rational $K(n)$-local power operations.

For Shimura varieties of Hodge type, we optimally extend algebraic Maass–Shimura differential operators on $p$-integral nearly holomorphic automorphic forms to differential operators on $\mu$-ordinary Mantovan Igusa varieties. We then show that the rank one operators can be integrated to an action of an explicit formal group. Via $p$-adic Fourier theory, this provides a $p$-adic interpolation by extending the action of a symmetric algebra of differential operators to the algebra of functions on the Tate module of the dual $p$-divisible group. Passing to the generic fiber, we obtain an action of an explicit algebra of $p$-adic locally analytic functions, and we show that the action of the subalgebra of locally constant functions is equivalent to a natural Hecke action and thus preserves classical forms. In the ordinary case, we further show that the locally analytic action extends to nearly overconvergent automorphic forms. Our results extend, clarify, and recover prior constructions.

The free group of rank $2$ is the fundamental group of the genus $2$ handlebody $\mathcal{H}$. We study discrete representations of this group into $ \mathsf{PSL}(2,\mathbb{C}) $ so that three disjoint simple closed curves on the conformal boundary $\partial_\infty \mathcal{H} $ are sent to parabolic elements. We show that the only infinite covolume groups of this form are maximal cusp groups on the boundary of genus $2$ Schottky space. We also exhibit hitherto unexpected finite covolume groups which do not arise from Heegaard splitting presentations of tunnel number $1$ links.

The unit commitment (UC) problem is paramount for optimal operation of power systems, but it faces computational limitations in large-scale settings, especially in investment or stochastic models, because of the binary variables that it contains. A lot of research has attempted to improve the computational performance of UC models, either by reducing model size, resulting in lower fidelity and accuracy, or by improving the tightness of the formulation. Tightness and model size are the best a priori indicators of the computational performance of UC models, but there is no clear overview of what the best formulation is for different generators. In this research, we define models with different levels of detail, and present a formulation for each level that is based on the convex hull. We show new proofs on the tightness of well-known formulations for ramping, for start-up and shut-down costs and capabilities, and for UC with investment. These models, with a different level of detail, can be incorporated into large-scale problems to reduce the computational burden, as demonstrated in Part II.

We extend the theory of spherical embeddings to actions of connected non-reductive groups. This generalization is formally very similar to the usual reductive case: equivariant embeddings are described essentially by collections of convex cones in a rational vector space. We also show some new relationship between the combinatorics emerging in this case and the properties of the unipotent radical of the acting group. Finally, we apply our techniques to prove a characterization of log homogeneous varieties.

This paper investigates the essential spectrum and compactness property of Markov semigroups generated by multi-dimensional Brox diffusion processes under two types of random media: stationary Gaussian random fields and semi-selfsimilar Lévy random fields. For Gaussian environments satisfying general stationary covariance growth conditions, we prove that the associated semigroup is almost surely noncompact; if the covariance function grows sublinearly at infinity, then the bottom of the essential spectrum vanishes almost surely, with fractional Brownian fields as a concrete example. For multi-dimensional semi-selfsimilar Lévy environments with scaling index $\alpha\in(1,2)$, we show that the essential spectral bottom equals zero almost surely for arbitrary space dimension $d\ge1$, and the same conclusion holds for one-dimensional symmetric $\alpha$-stable Lévy processes with any $\alpha\in(0,2)$. Furthermore, we study one-dimensional diffusion operators perturbed by random Lévy drift. When $0<\delta\le 1/\alpha$, random environmental fluctuations can destroy the compactness of semigroups induced by deterministic power-law potentials $\pm|x|^\delta$, even if the unperturbed semigroup is compact. The analysis relies on almost sure volume growth estimates for the random reference measure induced by environmental potentials, sample path asymptotics of random fields, ergodic theory of scaling transforms, and spectral criteria for regular Dirichlet forms. A unified framework linking sample path behaviors of random potentials to spectral characteristics of diffusion semigroups is established, and several open problems for large potential exponents are stated.

In this paper, we introduce the multiset partition dimension of graphs. This parameter extends the classical partition dimension to the multiset setting by considering multiset distances from vertices to parts of a vertex partition. We establish some fundamental properties of this parameter and determine its exact values for several important classes of graphs.

Network realignment complexes were introduced by Kozlov. We generalise their definition to arbitrary connected base graphs. For a connected graph $G$, we characterise the connected components of the associated network realignment complex $X_G$ and show that $X_G$ admits an $\operatorname{Aut}(G)$-equivariant strong deformation retraction onto the disjoint union of a complete graph and a discrete $\operatorname{Aut}(G)$-space. For the complete base graph $K_n$, we study the metric structure of the network realignment graph $\mathcal{G}_n$ and obtain explicit upper and lower bounds for its diameter. Finally, we prove that $X_n$ is a cubical flag complex and that every automorphism of $X_n$ is induced by a relabelling of the underlying vertex set. In particular, $\operatorname{Aut}(X_n)\cong S_n$ for all $n\geq 5$.

We study inverse scattering from conformal infinity for impenetrable topological defects whose interaction surfaces are totally geodesic in hyperbolic space \(\mathbb H^n\), \(n \geq 2\). For a fixed spectral parameter \(\lambda_0 > 0\), the prescribed inputs are boundary labels \(\xi \in \partial_\infty \mathbb H^n\). Each label selects an incoming Helgason mode in the hyperbolic interior. Given a defect \(\mathcal P \Subset \mathbb H^n\), this mode generally fails to satisfy the homogeneous trace condition on the interaction surface and hence generates an outgoing correction. The leading coefficient of this correction at conformal infinity defines the measured far-field pattern. The central question is whether \(\mathcal P\) can be recovered from the far-field patterns corresponding to one or finitely many prescribed boundary labels. This gives a formally determined inverse problem at one fixed spectral parameter. Our first main result establishes the unique determination of totally geodesic defects, an admissible class that includes both bulk components and hypersurface-supported ones. For Dirichlet-type defects, a single boundary label suffices. For Neumann-type defects, \(n+1\) boundary labels are sufficient and in general necessary. These labels are required to satisfy the natural affine-independence condition at conformal infinity. Our second main result provides quantitative stability estimates within the same framework. The hyperbolic Hausdorff distance between two defects is controlled by the discrepancy of their far-field patterns at conformal infinity. The proof combines continuation from conformal infinity with quantitative geodesic reflection across totally geodesic hypersurfaces. Taken together, these results yield a qualitative and quantitative far-field inverse scattering theory at conformal infinity, based on formally determined data.

The Erdős Matching Conjecture concerns the maximum number of hyperedges in an $r$-uniform hypergraph with bounded matching number. In this paper, we study a spectral counterpart of this conjecture. For sufficiently large $n$, we determine the maximum spectral radius over all $n$-vertex $r$-uniform hypergraphs whose matching number is less than $s$, and characterize the unique extremal hypergraph. To establish the main theorem, we first apply the shifting method to reduce the problem to shifted hypergraphs. We then derive several spectral upper bounds through hypergraph decomposition and related variational estimates for tensor spectral radii. With these estimates, we analyze the structural properties of shifted-saturated hypergraphs and prove the spectral extremal theorem for shifted hypergraphs with bounded matching numbers. Finally, we drop the shifted condition and extend our spectral bound to general $r$-uniform hypergraphs. Our main theorem states that for any $n$-vertex $r$-uniform hypergraph $H$ with matching number $\nu(H)<s$, the inequality $\rho(H)\leq \rho(\mathcal{F}_{s-1}(n))$ holds whenever $n$ is sufficiently large. Here $\mathcal{F}_{a}(n)$ denotes the family of all $r$-subsets of $[n]$ intersecting the vertex set $[a]$, and equality is attained if and only if $H$ is isomorphic to $\mathcal{F}_{s-1}(n)$. As an immediate corollary, we derive a spectral counterpart of the classical Erdős-Ko-Rado theorem for intersecting hypergraph families.