Search Results (308)

We consider the problem of privately updating a message out of K messages from N replicated and non-colluding databases where a user has an outdated version of the message ${\hat{W}}_{\theta }$ of length L bits that differ from the current version $W_{\theta }$ in at most f bits. The user also has a cache containing coded combinations of the K messages (with a pre-specified structure), which are unknown to the N databases (unknown prefetching). The cache Z contains ℓ linear combinations from all K messages in the databases with $r=\frac{\mathcal{l}}{L}$ being the caching ratio. The user needs to retrieve $W_{\theta }$ correctly using a private information retrieval (PIR) scheme without leaking information about the message index $\theta$ to any individual database. Our objective is to jointly design the prefetching (i.e., the structure of said linear combinations) and the PIR strategies to achieve the least download cost. We propose a novel achievable scheme based on syndrome decoding where the cached linear combinations in Z are designed to be bits pertaining to the syndrome of $W_{\theta }$ according to a specific linear block code. We derive a general lower bound on the optimal download cost for $0\le r\le 1$, in addition to achievable upper bounds. The upper and lower bounds match for the cases when r is exceptionally low or high, or when $K=3$ messages for arbitrary r. Such bounds are derived by developing novel cache-aided arbitrary message length PIR schemes. Our results show a significant reduction in the download cost if $f<{\displaystyle \frac{L}{2}}$ when compared with downloading $W_{\theta }$ directly using typical cached-aided PIR approaches. Full article

In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient use of unlabeled data, low pseudo-label accuracy, and inefficient label propagation. To address these issues, this paper proposes dual label propagation-driven least squares regression with feature selection, named DLPLSR, which is a pseudo-label-free SSL framework. DLPLSR employs a fuzzy-graph-based clustering strategy to capture global relationships among all samples, and manifold regularization preserves local geometric consistency, so that it implements the dual label propagation mechanism for comprehensive utilization of unlabeled data. Meanwhile, a dual-feature selection mechanism is established by integrating orthogonal projection for maximizing feature information with an ℓ_2,1-norm regularization for eliminating redundancy, thereby jointly enhancing the discriminative power. Benefiting from these two designs, DLPLSR boosts learning performance without pseudo-labeling. Finally, the objective function admits an efficient closed-form solution solvable via an alternating optimization strategy. Extensive experiments on multiple benchmark datasets show the superiority of DLPLSR compared to state-of-the-art LSR-based SSL methods. Full article

Background: Current cosmological fits typically assume a direct relation between cosmic time (t) and the scale factor ($a\left(t\right)$), yet this ansatz remains largely untested across diverse observations. Objectives: We (i) test whether a single power-law scaling ($a\left(t\right)\propto t^{\alpha }$) can reproduce late- and early-time cosmological data and (ii) explore whether a dynamically evolving ($\alpha \left(t\right)$), modeled as a scalar–tensor field, naturally induces directional asymmetry in cosmic evolution. Methods: We fit a constant-$\alpha$ model to four independent datasets: 1701 Pantheon+SH0ES supernovae, 162 gamma-ray bursts, 32 cosmic chronometers, and the Planck 2018 TT spectrum (2507 points). The CMB angular spectrum is mapped onto a logarithmic distance-like scale ($\mu ={log}_{10}{D}_{\ell }$), allowing for unified likelihood analysis. Each dataset yields slightly different preferred values for $H_0$ and $\alpha$; therefore, we also perform a global combined fit. For scalar–tensor dynamics, we integrate $\alpha \left(t\right)$ under three potentials—quadratic, cosine, and parity breaking (${\alpha }^{3}sin\alpha$)—and quantify directionality via forward/backward evolution and Lyapunov exponents. Results: (1) The constant-$\alpha$ model achieves good fits across all datasets. In combined analysis, it yields $H_0\simeq 70\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and $\alpha \simeq 1.06$, outperforming $\Lambda$CDM globally ($\Delta \mathrm{AIC}\simeq 401254$), though $\Lambda$CDM remains favored for some low-redshift chronometer data. High-redshift GRB and CMB data drive the improved fit. Numerical likelihood evaluations are approximately three times faster than for $\Lambda$CDM. (2) Dynamical $\alpha \left(t\right)$ models exhibit time-directional behavior: under asymmetric potentials, forward evolution displays finite Lyapunov exponents (${\lambda }_L\sim {10}^{-3}$), while backward trajectories remain confined (${\lambda }_L<0$), realizing classical arrow-of-time emergence without entropy or quantum input. Limitations: This study addresses only homogeneous background evolution; perturbations and physical derivations of potentials remain open questions. Conclusions: The time-scaling approach offers a computationally efficient control scenario in cosmological model testing. Scalar–tensor extensions naturally introduce classical time asymmetry that is numerically accessible and observationally testable within current datasets. Code and full data are available. Full article

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data $p\left(M|D\right)$, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates $p\left(D|M\right)$, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

Some properties on Banach spaces, such as the Radon–Riesz, Dunford–Pettis and approximation properties, allow us to better understand the naive details about the structure of space and the robust inhomogeneities and symmetries in space. In this work we try to examine such properties of vector-valued Schröder sequence spaces. Further, we show that these sequence spaces have a kind of Schauder basis. We also prove that ${\ell }_1\left(\mathcal{S},V\right)$ possesses the Dunford–Pettis property and demonstrate that ${\ell }_p\left(\mathcal{S},V\right)$ satisfies the approximation property for $1\le p<\infty$ under certain conditions and ${\ell }_{\infty }\left(\mathcal{S},V\right)$ has the Hahn–Banach extension property. Finally, we show that ${\ell }_2\left(\mathcal{S},V\right)$ has the Radon–Riesz property whenever V has it. Full article

The study of various subclasses of univalent functions involving the solutions to various differential equations is not totally new, but studies of analytic functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points are rarely conducted. Here, using a differential operator which was defined using the Hadamard product of Mittag–Leffler function and general analytic function, we introduce a new class of starlike functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points associated with the vertical domain. To define the function class, we use a Carathéodory function which was recently introduced to study the impact of various conic regions on the vertical domain. We obtain several results concerned with integral representations and coefficient inequalities for functions belonging to this class. The results obtained by us here not only unify the recent studies associated with the vertical domain but also provide essential improvements of the corresponding results. Full article

We numerically construct compact stars in the scalar–tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature and nonzero cosmological constant. There are two free parameters in this model of gravity: the non-minimal derivative coupling parameter ℓ and the cosmological constant parameter $\xi$. We study the relationship between the model parameters and characteristic of the neutron star, which allowed us to limit the permissible range of $\xi$ and ℓ. In particular, in the case $\xi =-1$, the external geometry of the neutron star coincides with the Schwarzschild–anti-de Sitter geometry, while the internal geometry of the star differs from the case of the standard gravity theory. Many realistic equations of the state of neutron star matter were considered. In general, the neutron star model in the theory of gravity with a non-minimal derivative coupling does not contradict astronomical data and is viable. Full article

This study addresses the problem of simultaneous variable selection and model estimation in multivariate failure time data, a common challenge in clinical trials with multiple correlated time-to-event endpoints. We propose a unified framework that identifies predictors shared across outcomes, applicable to both low- and high-dimensional settings. For linear marginal hazard models, we develop a penalized pseudo-partial likelihood approach with a group LASSO-type penalty applied to the ${\mathsf{\ell }}_2$ norms of coefficients corresponding to the same covariates across marginal hazard functions. To capture potential nonlinear effects, we further extend the approach to a sparse-input neural network model with structured group penalties on input-layer weights. Both methods are optimized using a composite gradient descent algorithm combining standard gradient steps with proximal updates. Simulation studies demonstrate that the proposed methods yield superior variable selection and predictive performance compared to traditional and outcome-specific approaches, while remaining robust to violations of the common predictor assumption. In an application to advanced prostate cancer data, the framework identifies both established clinical factors and potentially novel prognostic single-nucleotide polymorphisms for overall and progression-free survival. This work provides a flexible and robust tool for analyzing complex multivariate survival data, with potential utility in prognostic modeling and personalized medicine. Full article

As a knowledge-intensive activity, the Kansei engineering (KE) process encounters numerous challenges in the design knowledge flow, primarily due to issues related to information reliability, uncertainty, and subjectivity. Bridging this gap, this study introduces an advanced KE framework integrating a cloud model with Z-numbers (CMZ) and Bayesian elastic net regression (BENR). In stage-I of this KE, data mining techniques are employed to process online user reviews, coupled with a similarity analysis of affective word clusters to identify representative emotional descriptors. During stage-II, the CMZ algorithm refines K-means clustering outcomes for market-representative product forms, enabling precise feature characterization and experimental prototype development. Stage-III addresses linguistic uncertainties in affective modeling through CMZ-augmented semantic differential questionnaires, achieving a multi-granular representation of subjective evaluations. Subsequently, stage-IV employs BENR for automated hyperparameter optimization in design knowledge inference, eliminating manual intervention. The framework’s efficacy is empirically validated through a domestic cleaning robot case study, demonstrating superior performance in resolving multiple information processing challenges via comparative experiments. Results confirm that this KE framework significantly improves uncertainty management in design knowledge flow compared to conventional implementations. Furthermore, by leveraging the intrinsic symmetry of the normal cloud model with Z-numbers distributions and the balanced ℓ₁/ℓ₂ regularization of BENR, CMZ–BENR framework embodies the principle of structural harmony. Full article

We discuss an extension of the Single-Active-Electron (SAE) approximation in atoms by allowing the model potential to depend on the angular-momentum quantum number ℓ. We refer to this extension as the ℓ-SAE approximation. The main ideas behind ℓ-SAE are illustrated using the helium atom as a benchmark system. We show that introducing ℓ-dependent potentials improves the accuracy of key quantities in atomic structure computed from the Time-Independent Schrödinger Equation (TISE), including energies, oscillator strengths, and static and dynamic polarizabilities, compared to the standard SAE approach. Additionally, we demonstrate that the ℓ-SAE approximation is suitable for quantum simulations of light−atom interactions described by the Time-Dependent Schrödinger Equation (TDSE). As an illustration, we simulate High-order Harmonic Generation (HHG) and the three-sideband (3SB) version of the Reconstruction of Attosecond Beating by Interference of Two-photon Transitions (RABBITT) technique, achieving enhanced accuracy comparable to that obtained in all-electron calculations. One of the main advantages of the ℓ-SAE approach is that existing SAE codes can be easily adapted to handle ℓ-dependent potentials without any additional computational cost. Full article

In the development of digital twin (DT) workshops, constructing accurate DT models has become a key step toward enabling intelligent manufacturing. To address challenges such as incomplete data acquisition, noise sensitivity, and the heavy reliance on manual annotations in traditional modeling methods, this paper proposes a self-supervised deep learning approach for point cloud completion. The proposed model integrates self-supervised learning strategies for inferring missing regions, a Feature Pyramid Network (FPN), and cross-attention mechanisms to extract critical geometric and structural features from incomplete point clouds, thereby reducing dependence on labeled data and improving robustness to noise and incompleteness. Building on this foundation, a point cloud-based DT workshop modeling framework is introduced, incorporating transfer learning techniques to enable domain adaptation from synthetic to real-world industrial datasets, which significantly reduces the reliance on high-quality industrial point cloud data. Experimental results demonstrate that the proposed method achieves superior completion and reconstruction performance on both public benchmarks and real-world workshop scenarios, achieving an average CD-${\ell }_2$ score of 15.96 on the 3D-EPN dataset. Furthermore, the method produces high-fidelity models in practical applications, providing a solid foundation for the precise construction and deployment of virtual scenes in DT workshops. Full article

This paper concerns a class of robust factorization models of low-rank matrix recovery, which have been widely applied in various fields such as machine learning and imaging sciences. An ${\ell }_1$-loss robust factorized model incorporating the ${\ell }_{2,0}$-norm regularization term is proposed to address the presence of outliers. Since the resulting problem is nonconvex, nonsmooth, and discontinuous, an approximation problem that shares the same set of stationary points as the original formulation is constructed. Subsequently, a proximal alternating minimization method is proposed to solve the approximation problem. The global convergence of its iterate sequence is also established. Numerical experiments on matrix completion with outliers and image restoration tasks demonstrate that the proposed algorithm achieves low relative errors in shorter computational time, especially for large-scale datasets. Full article

In recent years, face recognition under occluded or corrupted conditions has emerged as a prominent research topic. The advancement in sparse sampling techniques based on regression analysis has provided a novel solution to this challenge. Currently, numerous regression-based sparse sampling models have been investigated by researchers to address this problem. However, the recognition accuracy of most existing models deteriorates significantly when handling heavily occluded or severely corrupted facial images. To overcome this limitation, this paper proposes a wing-constrained sparse coding (WCSC) model and its weighted variant (weighted wing-constrained sparse coding, WWCSC) for robust face recognition in complex scenarios. The corresponding minimization problems are solved using the alternating direction method of multipliers (ADMM) algorithm. Extensive experiments are conducted on four benchmark face databases: the Olivetti Research Laboratory (ORL) database, the Yale database, the AR database and the Face Recognition Technology (FERET) database, to evaluate the proposed method’s performance. Comparative results demonstrate that the WWCSC model maintains superior recognition rates even under challenging conditions involving significant occlusion or corruption, highlighting its remarkable robustness in face recognition tasks. This study provides both theoretical and empirical validation for the effectiveness of the proposed approach. Full article

We study the $g_E$-approximation property for the Banach space $E={\mathcal{\ell }}_q({\mathcal{\ell }}_p)$, which is an extension of Saphar’s p-approximation property. We establish some characterizations of the $g_E$-approximation property using the space of E-summing operators, which is an extension of the space of p-summing operators. Full article

In this study, the generalized $(p,q)$-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to $|{\ell }_5|$. The functions are analyzed using a suitable operational method, which enables us to derive new bounds for the Fekete–Szegö functional, as well as explicit estimates for important coefficients like $|{\ell }_2|$ and $|{\ell }_3|$. In addition, we establish the upper bounds of the second and third Hankel determinants, providing insights into the geometrical and analytical properties of this class of functions. Full article