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Surface-enhanced Raman spectroscopy of serum exosomes coupled with support vector machine for diagnosis of Parkinson's disease.

Semi-supervised classification and projection with adaptive flexible structure optimal graph.

Linear maps preserving matrices annihilated by a fixed polynomial, II

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning-physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

We introduce a notion of quasiconvexity for continuous functions f defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold (M,g) and \mathbb{R}^{m} , naturally generalizing the classical Euclidean definition. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functional F(u,\Omega) = \int_{\Omega}f(du)\,d\mu with respect to the weak ^{*} topology of W^{1,\infty}(\Omega,\mathbb{R}^{m}) , for every bounded open subset \Omega\subseteq M .

Abstract Lorentzian polynomials are a fascinating class of real polynomials with many applications. Their definition is specific to the nonnegative orthant. Following recent work, we examine Lorentzian polynomials on proper convex cones. For a self-dual cone $${\mathcal {K}}$$ K we find a connection between $${\mathcal {K}}$$ K -Lorentzian polynomials and $${\mathcal {K}}$$ K -positive linear maps, which were studied in the context of the generalized Perron-Frobenius theorem. We find that as the cone $${\mathcal {K}}$$ K varies, even the set of quadratic $${\mathcal {K}}$$ K -Lorentzian polynomials can be difficult to understand algorithmically. We also show that, just as in the case of the nonnegative orthant, $${\mathcal {K}}$$ K -Lorentzian and $${\mathcal {K}}$$ K -completely log-concave polynomials coincide.

This paper proposes a three-dimensional image hierarchical encryption method based on structured light holography and chained iris keys, aiming to address issues in the existing 3D image encryption techniques, such as low decryption quality, insufficient key security, inconvenient key management, and lack of hierarchical access control. The method first divides the 3D image into equidistant slices along the depth direction, generates encrypted structured light using a custom-designed structured light phase mask, and computes the structured light hologram for each slice layer via an iterative angular spectrum algorithm. Subsequently, user iris images are captured, and after preprocessing and feature extraction, user-specific chaotic phase masks are generated through a piecewise linear chaotic map, serving as keys for the hierarchical encryption. On this basis, a chained hierarchical encryption strategy is adopted, where the hologram of each level is coupled with the corresponding user's chaotic mask and the hologram from the previous level for the encryption, forming a dependent ciphertext sequence. During decryption, users must undergo iris authentication to obtain the chaotic key corresponding to their access level, followed by sequential chained decryption and optical reconstruction, thereby achieving identity- and authority-based hierarchical information access. Simulation experiments demonstrate that the method ensures high-quality 3D reconstruction while exhibiting high key sensitivity and robustness against noise, occlusion, and statistical attacks. Furthermore, the multi-parameter design in the structured light phase mask further expands the key space and enhances system security. This study provides a secure, practical, and manageable solution for the confidential transmission and hierarchical management of sensitive 3D visual data, with potential applications in fields such as medical imaging, military simulation, and virtual reality.

Physical reservoir computing (RC) extracts temporal features by utilizing the inherent physical characteristics of materials. Although memristor-based RC systems process time series effectively, they have issues with explainability and compatibility for edge intelligence. In order to go beyond single-mode current/conductance sampling in conventional physical RC, this work makes use of the coexistence of nonlinear event detection and linear exact mapping in phase-change materials to construct a novel spiking RC system. Device-mapped features are processed using an innovatively proposed sliding-window spike sampling architecture and a parameter optimization approach that creates a high-dimensional mapping reservoir by combining a simulated annealing algorithm with a generative adversarial network. This system achieves a low error rate of 0.075 in Mackey-Glass time series prediction and 96.67% accuracy in Iris data set classification. Additionally, this work not only introduces a novel material system into physical RC but also establishes a three-dimensional collaborative mapping mechanism to improve explainability by including a weight-quantification-based explainability analysis method. This method is adaptable to broader material platforms for advancing physical RC development.

Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact transformations arise whenever the adjoint action of a unitary's generator defines a linear map within a finite-dimensional operator space. In this regime, there exists a finite-degree polynomial that annihilates the adjoint map, rendering the Baker-Campbell-Hausdorff (BCH) expansion finite. We identify the role of Lie algebras and their modules in producing finite BCH expansions in all known cases. This perspective brings together previously disparate examples of exact transformations under a single unifying principle and clarifies how algebraic relations between generators and transformed operators determine the polynomial degree of the transformation. We illustrate this framework for previously known cases of efficient unitary transformations including unitary coupled-cluster and Pauli product generators. Using this framework, we propose a new class of Fermionic generators that can be used for efficient transformations. The result establishes sufficient algebraic conditions for when exact unitary transformations are possible and provides new strategies for reducing their computational cost in quantum simulation and constructing feasible unitary transformations.

Despite the widespread clinical adoption of volumetric modulated arc therapy (VMAT), advances in its fundamental optimization methodology have remained relatively limited, particularly with respect to open and researcher-accessible optimization frameworks. This study introduces a novel machine learning (ML) inspired approach for VMAT optimization, reformulating the problem as a multilayer neural network solvable with modern ML toolkits. In this framework, multileaf collimator (MLC) leaf positions and control-point weights are optimized. They are represented as trainable parameters embedded within parameterized activation functions and the final weighting layer, respectively. The dose-deposition matrix provides a fixed linear mapping. Optimization was performed using PyTorch's built-in L-BFGS optimizer with GPU acceleration. Machine-specific constraints, including maximum dose rate, gantry speed, MLC motion limits, and trajectory smoothness, were incorporated as regularization terms. The framework was evaluated using prostate cases with two arcs and head-and-neck (HN) cases with two and four arcs, with results compared against corresponding benchmark IMRT plans. All VMAT optimizations converged successfully, with stable reduction of total objective values and reasonable trends in machine-related regularization terms. The optimized plans were successfully imported into Eclipse TPS and delivered on a TrueBeam linac without interlocks, confirming deliverability. For prostate cases, two-arc VMAT plans achieved planning target volume (PTV) coverage and organ-at-risk (OAR) sparing comparable to benchmark IMRT plans with similar DVH characteristics. For HN cases, four-arc VMAT plans provided plan quality comparable to benchmark IMRT, and consistently improved target dose conformity and OAR sparing compared with two-arc plans, particularly in regions adjacent to complex target geometries. All observations and comparisons are consistent with established clinical experience on VMAT optimization. The proposed ML based VMAT optimization framework bridges modern machine learning optimization with treatment plan optimization and demonstrates strong potential as a flexible and extensible platform for future algorithmic development and research-driven innovations.

The paper addresses the problem of phase synthesis of apertures with assigned amplitude. Applying the method of stationary phase it will be shown that the asymptotic solution satisfies a Monge–Ampère partial differential equation (PDE) with appropriate boundary value conditions. In agreement Chu’s energy mapping principle for reflector shaping, the Monge–Ampère PDE can solved identifying an irrotational transport map from the source aperture to the target beam. After a description of the general theory, the paper focuses on irrotational linear maps associated to quadratic phase solutions demonstrating the possibility of obtaining beams of the same shape of the source aperture, a result only observed for circular and square apertures. Exploiting a polar decomposition of the affine transformation matrix, it will be also demonstrated the possibility of rotating the beam, a result reported (to the best knowledge of the authors) for the first time. In a companion paper, the general problem of finding a solution to the Monge–Ampère PDE via irrotational transport maps will be addressed by mean of the theory of “optimal transport”.

Novel strings of letters (i.e., pseudowords) lack established meaning(s), yet they may still evoke systematic, distributional signals that influence human behavior. Here, we tested whether distributional determinants of word memorability generalize to these novel strings. To do so, we leveraged a word-embedding model that was able to represent in a vector space not only attested words but also unmapped strings as bags of character n-grams. A ridge model trained on item-level word memorability norms learned a linear mapping from 300-dimensional embeddings to recognition memorability and achieved strong out-of-fold performance. We then applied this model zero-shot to predict memorability for 2,100 phonotactically legal pseudowords, whose baseline predictability was captured by orthographic and frequency features. Adding the zero-shot distributional score significantly improved the baseline model. These findings show that distributional representations derived from subword statistics carry mnemonic information that is not reducible to orthographic familiarity, and that novel strings are interpreted within a shared representational space learned from language experience. More broadly, they support the view that memorability is an intrinsic attribute predictable from representational information, even in the absence of learned meanings.

Abstract Criteria for piecewise linear (PWL) circle homeomorphisms to be conjugate to a rigid rotation, x → x + ω ( mod 1 ) , with rational rotation number ω are given. The consequences of the existence of such maps in families of maps is considered and the results are illustrated using two examples: Herman’s classic family of PWL maps with two linear components, and a map derived from geometric optics which has four components. These results show how results for piecewise smooth circle homeomorphisms with irrational rotation numbers have natural correspondences with the case of rational rotation numbers for PWL maps. In natural families of maps the existence of a parameter value at which the map is conjugate to a rigid rotation implies linear scaling of the rotation number in a neighbourhood of the critical parameter value and no mode-locked intervals, in contrast to the behaviour of generic families of circle maps.

For the problem of fuzzy model predictive control (FMPC), this paper tackles two fundamental challenges: handling the nonconvexity inherent in the optimisation problem and designing reliable algorithms to enlarge the feasible region. To this end, nonlinear systems are first exactly represented by Takagi-Sugeno (T-S) fuzzy models. By exploiting the representational properties of fuzzy models and applying a convex envelope approach to the membership functions (MFs), the original nonlinear constraints are reformulated into linear ones. Subsequently, building on a dual-mode FMPC framework, two algorithms – iterative FMPC (IFMPC) and hierarchical FMPC (HFMPC) – are proposed. IFMPC decouples fuzzy subsystems by reformulating the optimisation as a quadratic programme, eliminating dependencies on linear mappings between premise variables and MFs. HFMPC employs a hierarchical structure: its upper layer coordinates submodels to approximate the original problem, while the lower layer solves submodel optimisations sequentially. Crucially, HFMPC incorporates free fuzzy control variables into online optimisation, enhancing feasible regions and robustness against parametric disturbances. Both algorithms are rigorously validated through numerical examples encompassing stabilisation, reference tracking, and partial tracking scenarios.

With the omnipresence of digital interaction, the need to secure sensitive information has increased tremendously. Hence, crypto-steganography has become an integral part of secret communication in various applications, ranging from image confidentiality in medical informatics to secured data transfer in sensor-based wireless networks. The challenge for researchers in IoT and embedded systems is to work under resource-constrained environments while preserving image quality and achieving computational efficiency. However, most of the current approaches consider cryptography and steganography as independent techniques, which often leads to higher computation overhead, reduced imperceptibility with increased payload, and low cryptographic security. Addressing these limitations, this work proposes a lightweight and unified crypto-steganographic approach whereby encryption is integrated into the embedding operation. A dual Piecewise Linear Chaotic Map (PWLCM) randomizes the reading order of payload and pixel embedding positions, while an in-place XOR transformation combines each payload bit with selected bits of pixels prior to embedding. The integration of Huffman compression effectively increases payload capacity, and multi-format support for lossless cover images (PNG, BMP, TIFF) and input file formats (.txt, .json, .csv) extends practical applicability. Experimental evaluation with both grayscale and color images shows very high imperceptibility, with peak PSNR values reaching $$\varvec{77.42dB}$$ and SSIM of approximately $$\varvec{1.0}$$ for smaller payloads, while sustaining the PSNR above $$\varvec{51dB}$$ even for a full capacity of $$\varvec{166,336}$$ characters. Also, embedding and extraction remain less than $$\varvec{1.6}$$ seconds. Further, the robust statistical undetectability allows RS Analysis, Sample Pairs Analysis, and Chi-Square tests to be evaded even at high payload capacities. A key space of more than $$\varvec{1.2483 \times 2}^{\varvec{199}}$$ ensures high cryptographic strength. All these observations together establish that the proposed approach is a lightweight embedding technique that can be used for big data, provides high cryptographic security and maintains image quality, hence is appropriate for low-resource situations.

An acoustic framework for quantifying hydrogen leakage flow rates in next-generation liquid-hydrogen-cooled superconducting cables

Abstract We consider a 2-homogeneous bipartite distance-regular graph $$\Gamma $$ Γ with diameter $$D \ge 3$$ D ≥ 3 . We assume that $$\Gamma $$ Γ is not a hypercube nor a cycle. We fix a Q -polynomial ordering of the primitive idempotents of $$\Gamma $$ Γ . This Q -polynomial ordering is described using a nonzero parameter $$q \in \mathbb {C}$$ q ∈ C that is not a root of unity. We investigate $$\Gamma $$ Γ using an $$S_3$$ S 3 -symmetric approach. In this approach one considers $$V^{\otimes 3} = V \otimes V \otimes V$$ V ⊗ 3 = V ⊗ V ⊗ V where V is the standard module of $$\Gamma $$ Γ . We construct a subspace $$\Lambda $$ Λ of $$V^{\otimes 3}$$ V ⊗ 3 that has dimension $$\left( {\begin{array}{c}D+3\\ 3\end{array}}\right) $$ D + 3 3 , together with six linear maps from $$\Lambda $$ Λ to $$\Lambda $$ Λ . Using these maps we turn $$\Lambda $$ Λ into an irreducible module for the nonstandard quantum group $$U^\prime _q(\mathfrak {so}_6)$$ U q ′ ( so 6 ) introduced by Gavrilik and Klimyk in 1991.

The primary focus of this paper is to extend the concept of pseudospectrum from operators and matrices to elements of a unital complex Banach Jordan algebra, thereby moving from the associative to the non-associative setting. We introduce the notion of ε-invertibility in a Banach Jordan algebra J and establish the invariance of pseudospectra with respect to full subalgebras of J. We further investigate fundamental properties of the pseudospectrum of an element in a Banach Jordan algebra, including its relationship with level sets of analytic functions and pseudospectral bounds. The paper also examines linear maps that preserve pseudospectra in Banach Jordan algebras, as well as decomposition results for certain elements into simpler components within suitable localized subalgebras. Finally, we study an extension of the Roch–Silberman theorem in the setting of JB-algebras.

Let B ( H ) be the algebra of all bounded linear operators acting on a complex Hilbert space H . The polar decomposition theorem asserts that every operator T ∈ B ( H ) can be uniquely written as T = V T | T | , the product of a partial isometry V T ∈ B ( H ) that has the same kernel as that of T and the modulus | T | := ( T ∗ T ) 1 / 2 of T. In this paper, we obtain the form of all bijective linear maps Φ on B ( H ) for which V Φ ( T ) and V Φ ( S ) are unitary similar whenever T , S ∈ B ( H ) are two operators unitary similar. We also obtain the form of all bijective linear maps Φ on B ( H ) for which Φ ( V T ) = V Φ ( T ) for all T ∈ B ( H ) . Furthermore, a number of related results and consequences is obtained.