The rapid development and wide application of unmanned aerial vehicles (UAVs) have made illegal and unauthorized flights a serious threat to public safety, making timely detection essential. However, existing UAV detection methods still struggle to accurately detect small UAVs because of low feature resolution, background clutter, and dense spatial distribution. Transformer-based detectors, such as Detection Transformer (DETR), have shown promising improvements in detection accuracy; however, they demand significant computation and exhibit high inference latency, limiting deployment on resource-constrained platforms. To address these challenges, we propose UDRT-DETR, a small UAV detection method based on infrared imaging and the Real-Time Detection Transformer (RT-DETR). To reduce the computational cost of conventional transformer backbones, we design a cascaded inverted residual backbone (CIRB) that combines cascaded inverted residual mobile blocks (CI-RMBs) with depthwise separable convolutions and structured reparameterization, thereby enhancing feature representation and reducing computation. To reduce the cost of multi-head self-attention, we propose a super token attention-based intra-scale feature interaction (STA-IFI) module that projects tokens into a compact super-token space, eliminating redundant interactions while preserving global context for detecting densely distributed small UAVs. For effective cross-scale integration, we design a slim-neck-ASF, which combines lightweight convolutional units with adaptive upsampling for a precise multi-scale fusion. We design the inner-MPDIoU loss to refine bounding-box regression using auxiliary constraints, thereby improving localization accuracy. Experiments on our self-built infrared UAV dataset demonstrate that UDRT-DETR achieves a precision of 90.71%, which is 4.66% higher than RT-DETR, while reducing GFLOPs by 17.84%, confirming state-of-the-art accuracy and enabling real-time UAVs surveillance.

The field of neural rendering has seen remarkable progress, driven by advancements in generative models and differentiable rendering techniques. While 2D diffusion has achieved notable success, the development of a unified 3D diffusion pipeline remains an open challenge. This paper presents a novel framework, LN3Diff++, designed to bridge this gap and facilitate fast, high-quality, and versatile conditional 3D generation. Our method leverages a 3D-aware architecture and a variational autoencoder (VAE) to encode input image(s) into a structured, compact 3D latent space. The latent representation is then decoded by a transformer-based decoder into a high-capacity 3D neural field. By training a diffusion model on this 3D-aware latent space, our method achieves superior performance for category-specific 3D generation on ShapeNet and FFHQ, as well as category-free image/text-conditioned 3D generation over Objaverse. Moreover, it surpasses existing 3D diffusion methods in inference speed, requiring no per-instance optimization.

Abstract In this work, we introduce a selective and scalable extension of
the multi-step Rayleigh–Schrödinger and Brillouin–Wigner (RSBW) perturbative
scheme (see Ref. [5]) , designed to efficiently access the low-energy spectrum
of molecular systems. The method proceeds by combining successive effective
Hamiltonian diagonalizations inspired by second-order Rayleigh–Schrödinger
perturbation theory, with a Brillouin–Wigner correction applied to individually
optimized states using an updated partitioning of the Hamiltonian. At each
step, a candidate zeroth-order state is identified and progressively decoupled
from the remaining higher-lying states, thereby enabling a well-conditioned
Brillouin–Wigner expansion for the energy correction. In contrast to previous
approaches, the method selectively targets a small number of low-lying
states, significantly reducing the numerical overhead while maintaining chemical
accuracy. The robustness of the method is demonstrated on the LiH and
H4 molecules, where accurate excitation energies are obtained for the lowest
singlet states using compact model spaces, confirming its potential for realistic
applications.

Abstract Let be a locally compact separable metric measure space satisfying the doubling and reverse doubling conditions. Assume that on the Green function exists and satisfies a two‐sided estimate. Given a nonnegative Radon measure on , the authors investigate restricting principles for Green–Morrey potentials on ‐weak‐Morrey and ‐Morrey spaces. With an additional assumption of the Hölder estimate of the Green function, the authors study not only restricting properties for Green–Morrey potentials on ‐Campanato spaces, but also restricting properties for Green–Hardy potentials on ‐Lebesgue spaces. As applications, if there is a regular Dirichlet form on which corresponds to a positive definite self‐adjoint operator in , then these restricting properties can be used to derive regularity properties of the duality solutions to the equation .

This paper presents a disc-type stepper motor based on PCB technology. Aiming to provide a solution for the difficulty of torque enhancement in multi-pole PCB stepper motors under the limited wiring space of the PCB stator, a novel spiral winding configuration is proposed. Without increasing the number of PCB stator layers or the overall dimensions, an axially offset layout is employed to enlarge the coil flux-linkage area, thereby increasing the electromagnetic torque. Theoretical analysis and finite element simulation results show that the proposed winding achieves approximately 30% higher torque than conventional spiral windings. Meanwhile, to address the current fluctuation problem caused by the low-inductance characteristic resulting from the coreless PCB stator, the influence of current ripple on the microstepping drive of the stepper motor is analyzed. A series-inductor approach is adopted to suppress current fluctuation, and the optimal inductor value is selected through theoretical calculation and simulation, which effectively reduces the current ripple and significantly improves the microstepping performance. Finally, a prototype is fabricated and tested experimentally. The results indicate that the motor output torque reaches 46.4 mN·m, and the step-angle error under 16-microstep drive is within 0.25°, providing a feasible solution for the design and control of PCB stepper motors in compact spaces.

Discovering novel molecules within the vast chemical space is a central scientific challenge, increasingly delegated to deep generative models. However, the prevailing "black box" paradigm, built on continuous latent spaces, faces a fundamental mismatch between smooth optimization landscapes and inherently discrete molecular structures, often limiting global exploration. To overcome these limitations, we introduce Janus, a framework that recasts molecular design as a transparent, physics-inspired combinatorial optimization problem. At its core, Janus employs a Transformer-based autoencoder with a regularized binary bottleneck to map molecules into a compact discrete latent space. This representation enables the reformulation of molecular generation and optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem. This approach unlocks synergistic capabilities. For molecular generation, Janus leverages classical and quantum annealers to efficiently traverse the structured energy landscape, enabling the global discovery of diverse chemical scaffolds. Crucially, for molecular optimization, it moves beyond blind search by utilizing quantifiable feature interactions as machine-discovered SAR rules. This allows for rational, interpretable optimization─selectively modifying latent bits to enhance properties. Benchmarking against state-of-the-art methods reveals that this approach achieves superior multiobjective performance while preserving scaffold integrity, avoiding the structural fragmentation common in heuristic baselines. We validate the feasibility of the workflow on a quantum annealer and demonstrate its efficacy in drug-like property optimization. By unifying powerful combinatorial exploration with deep model interpretability, Janus establishes a robust framework for rational, quantum-assisted molecular design.

Compactification of perception pairs and spaces of group equivariant non-expansive operators

3D tibial HU reconstruction from biplanar X-rays utilizing a hybrid PCA-CNN framework.

ABSTRACT Accurate prediction of excited states in battery electrolytes is crucial for understanding photostability, oxidative stability, and degradation. We employ hybrid quantum‐classical algorithms–the Variational Quantum Eigensolver (VQE) for ground states and the quantum equation of motion (qEOM) for vertical singlet excitations to study , , LiFSI, and NaFSI. Compact active spaces from frontier orbitals were mapped to qubits and reduced via symmetry tapering and commuting‐group measurements to lower sampling cost. Within 10‐qubit models, VQE‐qEOM agrees closely with exact diagonalization, while sample‐based quantum diagonalization (SQD) in larger spaces recovers near‐exact (subspace‐FCI) energies. Spectra show clear anion‐cation trends within the VQE‐qEOM framework: salts have higher first‐excitation energies ( 13.2 eV) and a compact three‐state cluster at 12–13 eV, whereas FSI salts exhibit lower onsets (8–9 eV) with nearly degenerate and states and a higher separated by 1.3 eV. Independent TDDFT calculations yield systematically lower absolute excitation energies but reproduce the same anion‐ and cation‐dependent trends, confirming that the relative ordering and physical interpretation of the quantum results are robust. Replacing with narrows the gap by 0.4–0.8 eV per anion family. Converting to wavelengths places onsets in the deep UV ( 94 nm; 100 nm; LiFSI 141 nm; NaFSI 148 nm). Results for isolated species or embedded clusters are NISQ‐feasible, with solvent shifts incorporable via classical ‐solvation. Current quantum algorithms capture excitation trends, advancing electrolyte design.

We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally compact Polish space where the underlying measure is Radon. We also investigate the distinction between spatial and boolean actions in the infinite measure-preserving setup. In particular, we extend Kwiatkowska and Solecki’s Point Realization Theorem to the infinite measure setup. We finally obtain a streamlined proof of a recent result of Avraham-Re’em and Roy: Lévy groups cannot admit non-trivial continuous measure-preserving actions on Polish spaces when the measure is locally finite.

We show that the vanishing of higher derived limits of the system A κ \mathbf {A}_{\kappa } implies the additivity of strong homology on the class of locally compact metric spaces of weight at most κ \kappa , thereby establishing a converse to a theorem of Mardešić and Prasolov [Trans. Amer. Math. Soc. 307 (1988), 725–744].

In this paper we have introduced the new concept of Compact spaces. We discussed about points, continuous and homeomorphism in dense connected spaces. We also discussed about the properties and characteristics of Compact spaces.

Abstract We present a systematic quantization scheme for bounded symplectic domains of the form D × G ⊂ T ∗ G , where D ⊂ g ∗ is a bounded region defined by algebraic inequalities and G is a compact Lie group with Lie algebra g . The finiteness of the symplectic volume implies that quantization yields a finite-dimensional Hilbert space, with observables represented by Hermitian matrices, for which we provide an explicit realization. Boundary effects necessitate modifications of the standard von Neumann and Dirac conditions, which usually underlie the correspondence principle. Physically, the compact group G plays the role of momentum space, while g ∗ corresponds to the (noncommutative) position space of a particle. The assumption of compact momentum space has profound physical consequences, including the supertunneling phenomenon and the emergence of a maximal fermion density.

The search for maximal elements of preference relations has been recently related to the optimization of one-way utilities on compact topological spaces. In this paper, we deepen this study by referring to upper semicontinuous finite Richter–Peleg multi-utility representations of preorders. We provide necessary and sufficient conditions for the existence of representations of this kind and then, under the assumption of near-completeness, we characterize the identification of all maximal elements by maximizing all functions in an appropriate representation under compactness.

In this work, we show that the set of invariant measures with packing dimension equal to infinity is a dense G δ subset of M ( T ) , the space of T-invariant measures endowed with the weak topology, where T is the full-shift system in a product space whose alphabet M is any infinite Polish metric space. We also show that the set of invariant measures with upper q-generalized fractal dimension (with q>1) equal to infinity is a dense G δ subset of M ( T ) , in case M is any countably infinite compact metric space. This improves the results obtained by Carvalho and Condori in [Generic properties of invariant measures of full-shift systems over perfect polish metric spaces, Stochast. Dyn. 21(07) (2021), p. 2150040] and [Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behaviour, Forum Math. 33(2) (2021), pp. 435–450], respectively. Furthermore, we obtain results regarding the upper recurrence rates and upper quantitative waiting time indicator for typical T-orbits, and how the fractal dimensions of invariant measures and such dynamical quantities behave under an α-Hölder conjugation.

Discovering the compactness properties in generalized-type metric spaces opens up a fascinating area of research. The present study tries to develop a theoretical framework for compactness with key properties in the recently developed interval metric space. This work begins with explaining the covers and open covers to define compact interval metric spaces and their main features. Next, a similar definition of compactness using the finite intersection property is introduced. Then, the famous Heine–Borel theorem for compactness is extended in the case of interval metric spaces. Also, the concepts of sequential-type compactness and Bolzano–Weierstrass (BW)-type compactness for interval metric spaces are introduced with their equivalency relationship. Finally, the notion of total boundedness in interval metric spaces and its connection with compactness is introduced, providing new insights into these mathematical concepts.

Well-posedness of Dirichlet boundary value problems for reflected fractional p-Laplace-type inhomogeneous equations in compact doubling metric measure spaces

We characterize the upper semicontinuous representability of a semiorder ≺ as an interval order (namely, by a pair (u,v) of upper semicontinuous real-valued functions) on a topological space with a countable basis of open sets, where one of the representing functions is a one-way utility for the characteristic weak order ≺0 associated with the semiorder. Such a description generalizes the upper semicontinuous threshold representation. To this end, we introduce a suitable upper semicontinuity condition concerning a semiorder, namely strict upper semicontinuity. We further characterize the mere existence of an upper semicontinuous one-way utility for this characteristic weak order, with a view to the identification of maximal elements on compact metric spaces.

While Neural Architecture Search (NAS) has revolutionized the automation of deep learning model design, gradient-based approaches like DARTS often suffer from high computational overheads, the collapse of skip-connections, and optimization instability. To address these limitations, we propose Efficient and Lightweight Differentiable Architecture Search (EL-DARTS). EL-DARTS constructs a compact and redundancy-reduced search space, integrates a partial channel strategy to lower memory usage, employs a Dynamic Coefficient Scheduling Strategy to balance edge importance, and introduces entropy regularization to sharpen operator selection. Experiments on CIFAR-10 and ImageNet demonstrate that EL-DARTS substantially improves both search efficiency and accuracy. Remarkably, it attains a 2.47% error rate on CIFAR-10, requiring merely 0.075 GPU-days for the search. On ImageNet, the discovered architecture achieves a 26.2% top-1 error while strictly adhering to the mobile setting (<600 M MACs). These findings confirm that EL-DARTS effectively stabilizes the search process and pushes the efficiency frontier of differentiable NAS.

A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each locally compact Nyikos inverse topological semigroup is compact. Also, we show that a topological semigroup S that contains a dense inverse subsemigroup is a topological inverse semigroup, provided (i) S is compact, or (ii) S is countably compact and sequential. The latter result solves a problem of Banakh and Pastukhova and provides the automatic continuity of inversion in certain compact-like inverse semigroups.