Papers

In this paper, we propose and study $r$-minimal codes with respect to $\mathbf{P}$-support, where $\mathbf{P}=(\Omega,\preccurlyeq_{\mathbf{P}})$ is a poset defined on the coordinate set of the ambient space $\mathbf{H}$. $r$-Minimal $\mathbf{P}$-codes are natural extensions of Hamming metric minimal codes that have been extensively studied in the literature. We characterize $r$-minimal $\mathbf{P}$-codes in terms of the notion so called cutting $r$-blocking maps, which generalizes the well-known equivalence between minimal Hamming metric codes and cutting blocking sets. We also give a necessary and sufficient condition for $r$-minimality in terms of $(\mathbf{P},\omega)$-weight defined on $\mathbf{H}$, where $\omega:\Omega\longrightarrow\mathbb{R}^{+}$ is an arbitrary weight function. This leads to a generalization of the well-known Ashikhmin-Barg criterion for Hamming metric minimal codes. We then prove two existence results for $r$-minimal $\mathbf{P}$-codes, both for general $\mathbf{P}$ and for the special case that $\mathbf{P}$ is a disjoint union of chains. When $\mathbf{P}$ is hierarchical, we characterize $r$-minimal $\mathbf{P}$-codes in terms of $r$-minimal Hamming metric codes. Finally, we characterize cutting $r$-blocking sets induced by hierarchical posets with two levels, which further enables us to answer a question raised in Hyun, Kim, Wu and Yue \cite{28}.

This paper investigates the global dynamics and bifurcation structures of a two-dimensional piecewise linear map defined by four partitions, involving absolute value terms for both state variables. We analyze the stability of fixed points and demonstrate that the emergence of period-2 dynamics is initiated by a Flip bifurcation. A detailed analysis of these cycles reveals a unique branch manifesting in two topologically distinct configurations, connected via a Border Collision Bifurcation. Furthermore, we show that higher-period cycles (period 3 and 4) emerge in stable-saddle pairs through Fold Border Collision Bifurcations, leading to regions of multistability organized by the stable manifolds of saddle orbits. Finally, we examine the degenerate parameter regime where the system reduces to a one-dimensional discontinuous map. In this case, we prove the existence of an absorbing invariant interval and identify parameter regions exhibiting robust chaotic dynamics.

In this note, we establish essentially optimal bounds for certain spectral moments of automorphic forms for $\mathrm{GL}(2)$. More precisely, we consider the family of Hecke–Maaß cusp forms with spectral parameter in a dyadic interval and study the fourth moment of these forms evaluated at a Heegner point. We additionally present applications of our main result to the shifted convolution problem involving the sum of two squares function $r(n)$ as well as to pointwise Diophantine exponents.

Vertex splitting replaces a vertex (v) by two nonadjacent vertices whose neighborhoods together equal (N(v)). A split is exclusive if these neighborhoods are disjoint and shallow if no newly created vertex is split again. For a graph property (\Pi), (\Pi)-Vertex Splitting asks whether at most (k) splits can transform a graph (G) into one satisfying (\Pi). We continue the systematic study of this operation and settle several open problems. First, we prove that Cograph Vertex Splitting is NP-complete, even on graphs of girth at least 5, resolving a question of Firbas and Sorge (ISAAC 2024). More generally, (P_t)-free Vertex Splitting is NP-complete for every fixed (t\geq 4). We also prove that Chordal Vertex Splitting and Unit-Interval Vertex Splitting are NP-complete, resolving two questions of Abu-Khzam, Chakraborty, Isenmann, and Oijid (IWOCA 2026). Our hardness results extend to the exclusive and shallow variants. Assuming the Exponential Time Hypothesis, none of these problems admits an algorithm running in (2^{o(k)}n^{O(1)}) time; moreover, except for the unit-interval cases, none admits an algorithm running in (2^{o(n)}) time.

Let $E$ be a rational elliptic curve. We generalize a theorem due to Avc{\i}\cite{AVCI2026153}, which asserts that for any quadratic field $K$ and prime $p>5$, the equality $E(K)_{\mathrm{tors}} = E(L)_{\mathrm{tors}}$ holds for every $\mathbb{Z}_p$-extension $L/K$. In this paper, we consider the setting where the $\mathbb{Z}_p$-extension $L$ is replaced by the compositum $K_{\infty}$ of all $\mathbb{Z}_p$-extensions of $K$. Under this new setting, we prove the analogous statement for $p=5$, and further provide some results for the remaining primes $p=3$ and $p=2$, where we also try to study the growth pattern of torsion groups. Moreover, we completely classify all triples $(E,K,p)$ for which $E(K_\infty)_{\mathrm{tors}}$ is infinite.

In this paper, we develop a novel multi-frequency factorization method to reconstruct the spatial support of the ambient noise source. The proposed method only requires sparse correlation data and has low computational cost. Numerical experiments in two and three dimensions are presented to demonstrate the effectiveness of the proposed method.

In an abstract functional framework, we investigate the equivalence between two fundamental properties: weak observability and energy decay associated with certain classes of dissipative operators. This analysis is motivated by the study of evolution equations and their long-time behavior. Our main result establishes that under appropriate assumptions, these two notions are not only closely related but in fact equivalent. The proof relies on recent advances in the theory of weak observability, particularly those presented in \cite{AT1}, where new techniques have been developed to quantify the weak observability inequalities. These tools allow us to bridge the gap between qualitative decay properties and spectral estimates, offering a unified perspective on stability and control in abstract dynamical systems.

We develop a norm-cone conjugation framework, generated by translated norm-cones \[ x\mapsto r-\alpha\|x-x_0\|, \qquad \alpha\geq 0. \] We show that this family generates the same abstract-convex class as the family of Lipschitz continuous concave functions, and exploit its explicit metric structure to obtain a concrete support geometry, a Fenchel–Moreau-type biconjugation theorem, and an associated norm-cone subdifferential. The main optimization consequence is a perturbation-duality theory based on partial norm-cone conjugation. Although the partial conjugate depends on a slope and a centre, the centre can be fixed at the nominal perturbation in the complete biconjugate expression without changing its value. Consequently, the effective dual problem is a scalar program whose only dual variable is the real slope $\alpha\geq0$, even when the primal and perturbation spaces are vector-valued or infinite-dimensional. The resulting dual value is the norm-cone biconjugate of the value function at the nominal perturbation, so that strong duality is characterized by exact pointwise biconjugation. For nonconvex conic inequality problems, exact distance penalization is characterized by norm-cone supportability of the natural value function: the exact penalty parameters form its norm-cone subdifferential, and the least exact parameter is the minimal support slope. Global error bounds, equivalently global metric subregularity, provide a variational-analytic sufficient condition for exactness and hence for strong norm-cone duality. An infinite-dimensional example shows that the results remain applicable with a nonconvex objective and a nonsolid ordering cone.

The development of smart transportation systems and the introduction of 6G wireless communication technologies have significantly changed vehicle network topologies. Future connected autonomous vehicle (CAV) networks require bandwidth-efficient, reliable, and low-latency communication for safety-critical applications such as traffic sign recognition and decision-making. Conventional communication systems transmit raw data regardless of task relevance, which is inefficient in resource-constrained satellite channels where uplink bandwidth is scarce and propagation losses are large. Semantic communication addresses this limitation by transmitting task-relevant information instead of full signal representations. It extracts and conveys essential semantic features and leverages deep learning to optimize task performance at the receiver. Therefore, we present a Variational Autoencoder (VAE)-based multi-task semantic communication framework for satellite-assisted autonomous driving. Unlike deterministic autoencoder-based methods, the proposed model uses probabilistic latent representations for more robust and efficient encoding. The learned features are transmitted over noisy wireless channels to perform traffic sign reconstruction and classification. The framework is trained end-to-end to jointly optimize both tasks. Results show that the proposed approach achieves significant bandwidth reduction of up to 87.23% to 98.17% while maintaining stable performance across varying signal-to-noise ratio conditions.

Let $\mathbf{F}$ be a real quadratic field. Let $f $ traverse a Hecke orthonormal basis of Hilbert cusp forms over $ \mathbf{F} $ of full level and parallel weight $(k,k)$. As $k \rightarrow \infty$, we prove an asymptotic formula for the second moment of central Asai $L$-values $L (1/2, \mathrm{As} (f))$: \begin{equation*} {\sum}_{f } \, \omega_f L(1/2,\mathrm{As}(f))^2 = P_3 ( \log {k } ) k^2 + O_{\mathbf{F},\varepsilon} (k^{3/2 + \varepsilon} ), \end{equation*} where $\omega_f$ are the harmonic weights and $P_3 (X)$ is an explicit polynomial of degree $3$. This refines the mean Lindelöf bound $ O_{\mathbf{F},\varepsilon} (k^{2 + \varepsilon} ) $ proved by Wenzhi Luo.

This paper bridges the domains of degenerate special polynomials, the Euler-Seidel matrix method, and Morgan-Voyce polynomials. We introduce two new families of Morgan-Voyce type polynomials and establish their structural properties, including explicit formulas and recurrence relations. Additionally, we define three polynomial variants and prove that three distinct binomial-type sums for Bell polynomials can be expressed as finite sums involving these new families, and derive their exponential generating functions. We then construct Euler-Seidel matrices using the initial sequences associated with Morgan-type polynomials. Our results yield novel algebraic identities and expand the application of matrix methods in combinatorial analysis.

In this paper, we determine the Wiener index and the Harary index for the $(p,q)$-generalized splitting graph $S_{p,q}(G)$ and the $(c,k)$-shadow-splitting graph $H_{c,k}(G)$ for a connected graph $G$.

We introduce the concept of a golden Finsler structure on a finite-dimensional smooth manifold $M$ and investigate it from both local (coordinate-based) and global (coordinate-free) perspectives. Locally, we explicitly compute the fundamental metric tensor, establish the positive definiteness condition, and derive the geodesic spray coefficients. Furthermore, we investigate the projective flatness of the golden $(\alpha, \beta)$-metric and prove the non-existence of almost rational golden $(\alpha, \beta)$-metrics. Globally, we define the golden Finsler change $\widetilde{F}$ of a base Finsler metric $F$ and examine its geometric properties utilizing a special concurrent $\pi$-vector field. We explicitly determine how fundamental non-linear structures, including the Barthel and Berwald connections, transform under this change. Finally, we prove that $\widetilde{F}$ and $F$ cannot be projectively related.

Let M_3 be the coarse moduli space of smooth complex projective curves of genus 3. Through a general point of M_3, we construct a smooth complete curve of genus 21 and gonality 7, and a singular complete curve whose normalization has genus 19 and gonality 6. We also construct a Hodge-generic complete trigonal curve of geometric genus 5 in M_3.

Let $\mathbf{F} = \mathbf{Q}(\sqrt D)$ be a real quadratic field. In this paper, we establish a large sieve inequality for the Asai lifts $ \mathrm{As} (f) $ with $f$ in a Hecke orthonormal basis of the space of Hilbert modular cusp forms of parallel weight $(k, k)$ over $ \mathbf{F} $. As an application, for a fixed Hecke–Maass cusp form $\phi $ over $\mathbf{Q}$, we prove a non-trivial bound for the second moment of the convoluted central $L$-values $ L (1/2, \mathrm{As}(f) \times \phi) $ in the $k$-aspect.

Quantum process tomography, the task of learning an unknown quantum channel from black-box access, is a central problem in quantum information. In this setting, protocols with quantum memory can coherently store and jointly process quantum information obtained from multiple channel uses, whereas protocols without quantum memory must measure after each use and retain only a classical transcript of the measurement outcomes. A fundamental open question is whether quantum memory provides a query-complexity advantage even when protocols without quantum memory may adapt their experiments based on all previous outcomes with unbounded classical computational power. In this work, we show that it does. We determine the optimal query complexity of quantum process tomography without quantum memory up to a constant factor to be $\Theta(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$, where $d_{\mathrm{in}}$ and $d_{\mathrm{out}}$ are the channel input and output dimensions, respectively, and $\varepsilon$ is the target diamond-norm accuracy. More precisely, we prove that any incoherent protocol for this task, including adaptive protocols, requires $\Omega(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$ queries, even when each channel use may be assisted by arbitrary fresh ancilla, and we present a non-adaptive, ancilla-free incoherent protocol achieving the matching upper bound $O(d_{\mathrm{in}}^3 d_{\mathrm{out}}^3/\varepsilon^2)$. Our results thereby generalize the optimal sample-complexity bounds for single-copy state tomography, recovered as the special case $d_{\mathrm{in}}=1$. By contrast, coherent protocols with quantum memory achieve query complexity $\Theta(d_{\mathrm{in}}^2 d_{\mathrm{out}}^2/\varepsilon^2)$. Hence, our results establish a rigorous learning separation between quantum process tomography with and without quantum memory.

In many practical scenarios the shapes of scatterers exhibit uncertain geometric variations arising from diverse physical or environmental factors. For inverse scattering problems which are inherently ill-posed, the presence of such geometric uncertainties may have a non-negligible impact on the recovery process. With the aim of recovering both obstacle geometry and statistics of the shape uncertainties, in this paper we study an inverse acoustic scattering problem for three-dimensional smooth star-shaped obstacles with random isotropic fluctuations. We propose an efficient Monte Carlo-based multi-frequency recursive linearization algorithm in which the far-field operator is linearized with respect to the geometry parameters and frequency continuation is employed to recover the unknown geometry from coarse to fine scales. Based on the reconstructed samples, we further estimate the reference geometry and key statistics of the shape fluctuation field including Karhunen–Loève eigenvalues, covariance hyper-parameters for Gaussian perturbations and covariance structure, representative marginal distributions for non-Gaussian perturbations. We also prove that the probability law of the far-field data uniquely determines the radial function in distribution which implies uniqueness of the reference shape and related statistics. Numerical experiments demonstrate the effectiveness of the proposed method in recovering both the scatterer shapes and the associated statistical information under Gaussian and non-Gaussian random variations.

We establish a nonlinear Bochner-Kodaira-Nakano identity for sections of complex fiber bundles. As applications, we obtain a nonlinear Bochner-type vanishing theorem for holomorphic sections and a generalization of Yau's Schwarz lemma. After incorporating a nonlinear Higgs field, we derive the $D'$-$D''$ and $D^c$-$D$ identities. Under natural Hamiltonian and compactness assumptions, these identities imply that a section of a nonlinear harmonic bundle is flat if and only if it is a Higgs section with vanishing degree. We extend this correspondence first to sub-fibrations and then, via the graph construction, to morphisms.

We classify the involutions of all of the most well-studied diagram monoids – namely the partition, planar partition, partial Brauer, Motzkin, Brauer and Temperley–Lieb monoids – and characterise those that give rise to star-regular or regular star-monoid structures. We then complete the same program for the associated twisted diagram monoids, with respect to both the canonical float-counting twisting, and the recently-discovered rank-based twisting. This necessitates developing a general theory of involutions of twisted products. Some of our results were quite unexpected. For example, a Brauer monoid is star-regular with respect to many of its involutions, but only a regular star-monoid for one of them. We will also see that twisted diagram monoids over the integers are always star-regular, thereby providing new and very natural examples of star-regular monoids. Along the way, we also obtain (by necessity) a number of results of independent interest; specifically, we classify the automorphisms of the Motzkin and Temperley–Lieb monoids (and hence also of the planar partition monoids), and we show that all of our diagram monoids generically have trivial centre.

We study periodicity properties of the 2-D $\bigl(p_1(t)/p_2(t),\, tp_3(t)\bigr)$ and 3-D $\bigl(p_1(t)/p_2(t),\, tp_3(t),\, p_4(t)\bigr)$ Riordan arrays over a finite field ${\mathbb F}_q$, where each $p_i(t)$ is a polynomial with $p_i(0)\neq 0$. We show that the columns of the 2-D Riordan array are eventually periodic sequences, where a circulant matrix generated by the coefficients of $p_3(t)$ determines the behavior of this periodicity as the column index grows indefinitely. Furthermore, we prove that the preperiodic column partial sums of the 2-D array are periodic, and present a family of the Riordan arrays for which such sequences of partial sums are identically zero. We also show that the layers of the 3-D Riordan array contain periodic orbits related to each other via powers of a circulant matrix generated by the coefficients of $p_4(t)$.

The domination number $\gamma(G)$ of a graph $G$ is the smallest possible size of a vertex set that intersects every radius-$1$ ball of $G$, and the packing number $\rho(G)$ is the maximum number of pairwise vertex-disjoint radius-$1$ balls. We prove that $\frac{\gamma(G)}{\rho(G)}\le 5$ for every planar graph and $\frac{\gamma(G)}{\rho(G)} \le \frac{18\sqrt3}{\pi}\approx 9.924$ for every unit disk graph, thus yielding Erdős-Pósa-type bounds for the hypergraph of radius-$1$ balls in the two graph classes. This improves upon results of Gutiérrez and Paul, and Dúcz and Gujgiczer, who in turn lowered bounds of Bonamy, Csikós, Gujgiczer and Yuditsky, and Böhme and Mohar. For both graph classes, the best known lower bound on the optimal constant remains $3$.

This paper proposes a rigorous framework for sensing of environmental objects using diffraction mechanisms prevalent at wireless communication frequencies. Specifically, we develop a physics-consistent parameterized diffraction channel model, derive maximum likelihood (ML) approaches for estimating the blockage shape, range, and source directions of arrival (DoAs), and quantify fundamental performance limits via the Cramér–Rao bound (CRB). In our physics-based modeling, we integrate various approximations for the wave propagation (far-field, paraxial Fresnel, and exact near-field regimes), enabling a wide range of applicability. The underlying model is frequency-agnostic, and we derive Fresnel-number scaling laws that map the diffraction pattern, and hence the estimation problem, across carrier frequency, object size, and range. We quantify the maximum likelihood estimation performance and its relationship to the CRB, and we study the impact of the modeling approximations developed in this work. Numerical results demonstrate that ML estimators closely approach the CRB at moderate to high signal-to-noise ratio (SNR), and highlight the utility of diffraction-based modeling for high-fidelity blockage characterization.

We prove cutoff in total variation distance for the discrete-time Kac walk on $S^{n-1}$ started from a coordinate vector. The cutoff occurs at $ C_{\mathrm{BRW}}n\log n$, where $C_{\mathrm{BRW}} \approx 3.8916$ is an explicit constant determined by the speed of the leftmost particle in a branching random walk. In particular, the cutoff location is not at the conjectured time $ 2n\log n$.

Let $G(z)$ be the Green function on the flat torus $E_{\tau}=\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau)$ with the singularity at $0$. Lin and Wang (Ann. Math. 2010) proved that $G(z)$ has at most one pair of nontrivial critical points. This is the third of a series of papers to study the sum of two Green functions which can be reduced to $G_p(z):=\frac12(G(z+p)+G(z-p))$. We study how the geometry of the torus and the location of singularities $\pm p$ affect the structure of critical points of $G_p(z)$. In Part I \cite{CFL}, we proved that $G_p(z)$ has at most three pairs of nontrivial critical points for all tori. In Part II \cite{CFL-II} (Proc. Lond. Math. Soc. 2026), we studied the important case that $E_{\tau}$ is a rectangular torus. In this paper, first we prove that if $G_p(z)$ has three pairs of nontrivial critical points, then critical points are all non-degenerate. Secondly, we study the other important but more challenging case that $E_{\tau}$ is a rhombus torus, by developing different approaches from \cite{CFL, CFL-II}. As applications, we show that the curvature equation $\Delta u+e^{u}=4\pi(\delta_p+\delta_{-p})$ on $E_{\tau}$ has exactly either $0$, $1$ or $2$ even axisymmetric solutions and each number really occurs.

We consider coupled stochastic systems decomposed into exterior, boundary, and interior variables, with the boundary variables sometimes carrying the directed structure of a sensor and actuator. The central question is when the conditional law of histories factorises, and how this path space statement is detected by log likelihoods, by Girsanov changes of measure, and by information theoretic quantities used in nonequilibrium statistical physics. The basic object is a regular conditional probability on a path space. Under domination by clamped reference laws, the boundary property becomes multiplicative separation of a Radon–Nikodym derivative, or equivalently additive separation of a path log likelihood. For Itō diffusions this log likelihood is computed by Girsanov's theorem; its expectation is the quadratic control energy appearing in the Föllmer entropy identity and in the stochastic control formulation of Schrödinger bridge problems. When exact factorisation fails, the remaining coupling is measured by conditional mutual information, namely the relative entropy between the true boundary-conditioned path law and the product of its conditional marginals. This gives a common language for boundary screening, path likelihood inference, controlled changes of path law, and the thermodynamic value of mutual information.

We recall the concept of the dimension of a finite poset $P$, and the longstanding conjecture that for all finite nonempty posets $P$ and $Q$, $\dim(P\times Q)\geq\dim(P)+\dim(Q)-2.$ We then note two other plausible inequalities, either of which would imply that one. In the final section, writing $P\preccurlyeq P'$ if, for all $Q,$ $\dim(P\times Q)\leq\dim(P'\times Q),$ and writing $P\approx P'$ if $P\preccurlyeq P'$ and $P'\preccurlyeq P,$ we note some results and questions concerning these relations.

In this study, the formal derivation of a one-dimensional nonlinear generalized Langevin equation is demonstrated using a decomposition method based on the conformal transformation governed by the chordal Loewner equation. Here, we used a modified Mori-Zwanzig method whose operator is substituted by that is derived from the discrete Loewner evolution. By this approach, the different types of fluctuation-dissipation relation (FDR) were reformulated using mathematical terms affected by the conformal maps. Dealing with a memory kernel that models the cell migration experiment, the numerical simulation was performed to obtain the specific scaling law of energy dissipation that is common among the two obtained types of FDRs. In addition, the concept of Loewner entropy is used for the estimation of the canonical ensemble in the colored noise environment throughout the theoretical analyses.

This work introduces a nonlinear Hager-Zhang conjugate gradient method for solving set optimization problems. The objective function under consideration is defined by a finite collection of continuously differentiable functions. Notably, the proposed approach imposes restrictions neither on the existence of a finite generator of the ordering cone nor on any regularity condition at the optimal solution. As a result, the proposed method holds considerable significance for both set optimization and vector optimization problems, with the latter serving as a special case of the former. The study begins by discussing Wolfe line search conditions using Drummond-Svaiter scalarization function. Thereafter, we establish the existence of a step length satisfying the Wolfe line search conditions along a descent direction. The Hager-Zhang scalar conjugate parameter is introduced to derive the search direction for the proposed method. It is established that the direction generated by the proposed method is a descent direction. The well-definedness of the proposed method is given. Furthermore, we discuss some important results and a Zoutendijk-like condition to ensure global convergence. Subsequently, the global convergence of the proposed method is established in an asymptotic manner. Finally, numerical experiments on various test problems validate the practical performance and effectiveness of the proposed technique.

Random feature collocation fixes a randomly generated trial space and determines its coefficients from a linear least-squares system. Stability then depends on whether the sampled residual equations represent the geometry induced by the differential operator. We construct an operator-aware discretization in which the operator-applied features determine both the collocation measure and a coefficient whitening map. The randomized scheme combines a residual-Christoffel density with inverse-density weights, while a deterministic scalar-row alternative maximizes successive regularized log-determinant increments. Conditional on the realized trial space, the sampled whitened interior Gram is a spectral approximation to the reference Gram on the retained residual space, with sample complexity linear in the retained dimension up to a logarithmic factor. For uniformly analytic residual kernels, the associated operator has stretched-exponentially decaying eigenvalues and ridge effective dimension that is polylogarithmic in the inverse ridge scale. Experiments on scalar and vector equations, varied geometries, and one to three spatial dimensions show that residual-space sampling and whitening produce numerically full-rank transformed systems with substantially smaller condition numbers and iteration counts. The deterministic construction attains the lowest errors at the smallest scalar sample sizes. Residual-space geometry therefore yields a principled design for stable strong-form random feature collocation.

X ray Computed Tomography (CT) is a widely used imaging modality in medical, industrial, and scientific applications. In practical CT implementations, forward, A, and back projection, B, operators are often constructed using different discretization schemes to improve computational efficiency on available software and hardware platforms. Consequently, the resulting projector pair is generally unmatched, meaning that the back projector is not the exact adjoint of the forward projector. This mismatch alters the mathematical properties of the reconstruction problem and can affect the convergence behavior of iterative reconstruction methods. Previous studies have proposed AB and BA Golub Kahan bidiagonalization (GKB) methods, as well as GMRES and hybrid GMRES methods, for solving CT reconstruction problems with unmatched projector pairs, demonstrating reduced semiconvergence effects compared with conventional approaches. In this work, we develop hybrid variants of the AB- and BA-GKB algorithms by incorporating regularization within the projection process. The singular value decomposition for the operator on the projected space is used to efficiently reconstruct the solution, and to automatically select the regularization parameter using either the L-curve or generalized cross-validation. Numerical experiments on several CT reconstruction problems demonstrate the effectiveness of the proposed hybrid methods in improving robustness against semiconvergence.