arXiv subjects
Publications and source records attributed to Xiaodong Zhuang.
The solution of the Diophantine equation ay^2=b(x^k-c^k) is studied in different cases of k. Methods are proposed for different cases of k, which are convenient for computer algorithm implementation. The original equation is reduced to lower-degree equations, which can improve the efficiency in searching possible integer solutions. A sufficient condition of the unsolvability of ay^2=b(x^2n-c^2n) is presented.
As a valuable theoretical and application problem, the integer points on two types of elliptic curve y^2=(x-a)(x-b)(x-c) and y^2 = (x-a)(x^2+ax+b) are studied. By using elementary number theory method, the solution of the original equations is reduced to the solution of simultaneous Pell equations or generalized Pell equation, which can improve the efficiency in searching integer solutions by computer. Effective methods are proposed to find the integer solutions of the equations, which are convenient for algorithm programming implementation. At the same time, the derivation of the methods leads to two sufficient conditions, which can determine the unsolvability of these two types of equation respectively. The methods proposed are for equations with undetermined coefficients, which are more general than the solutions of the equations with specific known coefficients, and more suitable for computer programming implementation.
The quadratic sieve method is a core tool in number theory. In this paper, we present two optimization methods for the Quadratic Sieve algorithm. In the sieving process, the original polynomial root value accumulation step is changed from the original di to the mdi (m is a small integer), which can change the complexity from O(n) to O(n/m). Another optimization method is that for all parameter lookup steps, the original traversal lookup can be changed to an efficient binary search, which can change the complexity of the loop from O(n) to O(logn). This enhancement reduces the computational complexity of RSA modulus factorization in practical settings.
Quantum manipulation of molecular radical spins provides a crucial platform for exploring emergent phenomena in many-body systems. Here, we combine surface-confined synthesis with scanning tunneling microscopy(STM)tip-induced dehydrogenation to achieve atom-precise engineering of quasi-one-dimensional porphyrin-based Kondo chains (1-7 units) on Au(111). High-resolution STS measurements and low-energy effective modeling collectively demonstrate that π-radicals at each fused-porphyrin unit form Kondo singlets screened by conduction electrons. Adjacent singlets develop direct coherent coupling via quantum-state-overlap-enabled electron tunneling. Crucially, chiral symmetry in the effective model governs zero-mode distribution-present in odd-length chains yet absent in even-length chains-which dictates pronounced odd-even quantum effects in STS spectra of finite chains. Furthermore, the number of parallel porphyrin chains non-monotonically tunes the competition between the Kondo effect and spin exchange, showing opposing trends in strength and demonstrating that both wave-function overlap and the SOMO-LUMO gap collectively govern these interactions. This work simultaneously resolves the dimensional dependence of many-body correlations in confined quantum systems and pioneers approaches for quantum-critical manipulation in molecular spin architectures.
A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data points. The flattening of data manifold is achieved as an emergent behavior under the elastic and repelling interactions between data points, meanwhile the topological structure of the manifold is preserved. To overcome the uneven sampling (or "short-cut edge") problem, the soft neighborhood is proposed, in which the neighbor degree is defined and adaptive interactions between neighbor points is implemented. The proposed method provides a novel geometric viewpoint on dimension reduction. Experimental results prove the effectiveness of the proposed method in dimension reduction, and implicit feature of data sets may also be revealed.
In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have clear physical meanings. The proposed model is a modification of the general differential dynamic model, with constraints of spatial and temporal continuity on the deforming field. The deformation integral and derivative are presented as compact expressions of manifold deforming process. Moreover, a specific autonomous deforming field with flattening effect is defined, which provides a novel geometric viewpoint on data dimension reduction. The effectiveness of this autonomous deforming field is proved by numerical computation simulations, which indicate the promising potential of the proposed model in practical dimension reduction tasks.
A novel WS2-graphite dual-ion battery (DIB) is developed by combining together a conventional graphite cathode and high-capacity few-layer WS2 flakes anode. The WS2 flakes are produced by exploiting wet-jet milling (WJM) exfoliation, which allows mass production of few-layer WS2 flakes in dispersion, with an exfoliation yield of 100%. The WS2-anodes enable DIBs, based on hexafluorophosphate (PF6-) and lithium (Li+) ions, to achieve charge specific capacities of 457, 438, 421, 403, 295 and 169 mAh g-1 at current rates of 0.1, 0.2, 0.3, 0.4, 0.8 and 1.0 A g-1, respectively, outperforming conventional DIBs. The WS2-based DIBs operate in the 0 to 4 V cell voltage range, thus extending the operating voltage window of conventional WS2-based Li-ion batteries (LIBs). These results demonstrate a new route towards the exploitation of WS2, and possibly other transition metal dichalcogenides (TMDs), for the development of next-generation energy storage devices.
In this paper, a new statistic feature of the discrete short-time amplitude spectrum is discovered by experiments for the signals of unvoiced pronunciation. For the random-varying short-time spectrum, this feature reveals the relationship between the amplitude's average and its standard for every frequency component. On the other hand, the association between the amplitude distributions for different frequency components is also studied. A new model representing such association is inspired by the normalized histogram of amplitude. By mathematical analysis, the new statistic feature discovered is proved to be necessary evidence which supports the proposed model, and also can be direct evidence for the widely used hypothesis of "identical distribution of amplitude for all frequencies".
In order to analyze the moving and deforming of the objects in image sequence, a novel way is presented to analyze the local changes of object edges between two related images (such as two adjacent frames in a video sequence), which is inspired by the physical electromagnetic interaction. The changes of edge between adjacent frames in sequences are analyzed by simulation of virtual current interaction, which can reflect the change of the object's position or shape. The virtual current along the main edge line is proposed based on the significant edge extraction. Then the virtual interaction between the current elements in the two related images is studied by imitating the interaction between physical current-carrying wires. The experimental results prove that the distribution of magnetic forces on the current elements in one image applied by the other can reflect the local change of edge lines from one image to the other, which is important in further analysis.
A novel model for image segmentation is proposed, which is inspired by the carrier immigration mechanism in physical P-N junction. The carrier diffusing and drifting are simulated in the proposed model, which imitates the physical self-balancing mechanism in P-N junction. The effect of virtual carrier immigration in digital images is analyzed and studied by experiments on test images and real world images. The sign distribution of net carrier at the model's balance state is exploited for region segmentation. The experimental results for both test images and real-world images demonstrate self-adaptive and meaningful gathering of pixels to suitable regions, which prove the effectiveness of the proposed method for image region segmentation.
A novel way of matching two images with shifting transformation is studied. The approach is based on the presentation of the virtual edge current in images, and also the study of virtual electromagnetic interaction between two related images inspired by electromagnetism. The edge current in images is proposed as a discrete simulation of the physical current, which is based on the significant edge line extracted by Canny-like edge detection. Then the virtual interaction of the edge currents between related images is studied by imitating the electro-magnetic interaction between current-carrying wires. Based on the virtual interaction force between two related images, a novel method is presented and applied in image matching for shifting transformation. The preliminary experimental results indicate the effectiveness of the proposed method.
In this paper, a novel model of 3D elastic mesh is presented for image segmentation. The model is inspired by stress and strain in physical elastic objects, while the repulsive force and elastic force in the model are defined slightly different from the physical force to suit the segmentation problem well. The self-balancing mechanism in the model guarantees the stability of the method in segmentation. The shape of the elastic mesh at balance state is used for region segmentation, in which the sign distribution of the points'z coordinate values is taken as the basis for segmentation. The effectiveness of the proposed method is proved by analysis and experimental results for both test images and real world images.
A novel approach of image matching for rotating transformation is presented and studied. The approach is inspired by electromagnetic interaction force between physical currents. The virtual current in images is proposed based on the significant edge lines extracted as the fundamental structural feature of images. The virtual electromagnetic force and the corresponding moment is studied between two images after the extraction of the virtual currents in the images. Then image matching for rotating transformation is implemented by exploiting the interaction between the virtual currents in the two images to be matched. The experimental results prove the effectiveness of the novel idea, which indicates the promising application of the proposed method in image registration.