Analytical Solutions of Singular Isothermal Quadrupole Lens

Using analytical method, we study the Singular Isothermal Quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this paper, including deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. As have been found, naked cusps will appear when the relative intensity $k$ of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations that a point source infinitely approaches a cusp or a fold. The sum of magnifications of cusp image triplet is usually not equal to 0, and it is usually positive for major cusp while negative for minor cusp. Similarly, the sum of magnifications of fold image pair is usually neither equal to 0. Nevertheless, the cusp and fold relations are still equal to 0, in that the sum values are divided by infinite absolute magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ

The next-to-next-to-leading order soft function for top quark pair production

We present the first calculation of the next-to-next-to-leading order threshold soft function for top quark pair production at hadron colliders, with full velocity dependence of the massive top quarks. Our results are fully analytic, and can be entirely written in terms of generalized polylogarithms. The scale-dependence of our result coincides with the well-known two-loop anomalous dimension matrix including the three-parton correlations, which at the two-loop order only appear when more than one massive partons are involved in the scattering process. In the boosted limit, our result exhibits the expected factorization property of mass logarithms, which leads to a consistent extraction of the soft fragmentation function. The next-to-next-to-leading order soft function obtained in this paper is an important ingredient for threshold resummation at the next-to-next-to-next-to-leading logarithmic accuracy.Comment: 34 pages, 9 figures; v2: added references, matches the published versio

A contextual usage control model

Model praćenja uporabe (UCON) je najnovije veliko poboljšanje tradicionalnih modela za praćenje pristupa. On omogućava promjenljivost atributa subjekta i objekta i kontinuitet praćenja uporabe. Međutim, taj model može zabraniti pristup zbog promjena u okolini čak i ako su zadovoljeni zahtjevi autorizacije i obveze te tako korisnicima stvoriti prekide. Predložen je kontekstualni UCON (CUC) kako bi se prevladala ta osnovna slabost UCONa. U CUC-u se uvodi kontekst kao zamjena za komponentu uvjeta u UCON-u. Dodaje se modul upravljanja za manipuliranje atributima subjekta, objekta i konteksta. CUC izravno kombinira module praćenja i upravljanja i može dinamički prilagođavati promjene u kontekstu te je uistinu baziran na atributima. Primijenjen je algebarski pristup za opis sintakse i semantike CUCa.The usage control model (UCON) is the latest major enhancement of traditional access control models. It enables subject and object attributes mutability and usage control continuity. However, with the model access permission may be denied as a result of the environmental changes even though the authorization and obligation requirements are met, thus causing disruptions to users. Contextual UCON (CUC) was proposed to overcome this major weakness of UCON. In CUC context was introduced to replace the conditions component in UCON. And management module was added to manipulate the subject and object and context attributes. CUC seamlessly combines control and management modules and has the ability to dynamically adapt the changes in context, and is truly attribute-based. An algebra approach was employed to describe CUC syntax and semantics formally

Fault Identification of Rotor System Based on Classifying Time-Frequency Image Feature Tensor

In the field of rotor fault pattern recognition, most of classical pattern recognition methods generally operate in feature vector spaces where different feature values are stacked into one-dimensional (1D) vector and then processed by the classifiers. In this paper, time-frequency image of rotor vibration signal is represented as a texture feature tensor for the pattern recognition of rotor fault states with the linear support higher-tensor machine (SHTM). Firstly, the adaptive optimal-kernel time-frequency spectrogram visualizes the unique characteristics of rotor fault vibration signal; thus the rotor fault identification is converted into the corresponding time-frequency image (TFI) pattern recognition. Secondly, in order to highlight and preserve the TFI local features, the TFI is divided into some TFI subzones for extracting the hierarchical texture features. Afterwards, to avoid the information loss and distortion caused by stacking multidimensional features into vector, the multidimensional features from the subzones are transformed into a feature tensor which preserves the inherent structure characteristic of TFI. Finally, the feature tensor is input into the SHTM for rotor fault pattern recognition and the corresponding recognition performance is evaluated. The experimental results showed that the method of classifying time-frequency texture feature tensor can achieve higher recognition rate and better robustness compared to the conventional vector-based classifiers, especially in the case of small sample size

l-connectivity, l-edge-connectivity and spectral radius of graphs

Let G be a connected graph. The toughness of G is defined as t(G)=min{\frac{|S|}{c(G-S)}}, in which the minimum is taken over all proper subsets S\subset V(G) such that c(G-S)\geq 2 where c(G-S) denotes the number of components of G-S. Confirming a conjecture of Brouwer, Gu [SIAM J. Discrete Math. 35 (2021) 948--952] proved a tight lower bound on toughness of regular graphs in terms of the second largest absolute eigenvalue. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] then studied the toughness of simple graphs from the spectral radius perspective. While the toughness is an important concept in graph theory, it is also very interesting to study |S| for which c(G-S)\geq l for a given integer l\geq 2. This leads to the concept of the l-connectivity, which is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. Gu [European J. Combin. 92 (2021) 103255] discovered a lower bound on the l-connectivity of regular graphs via the second largest absolute eigenvalue. As a counterpart, we discover the connection between the l-connectivity of simple graphs and the spectral radius. We also study similar problems for digraphs and an edge version

A novel method to analysis strong dispersive overlapping lamb-wave signatures

Dispersive propagation and overlapping wave modes are two main obstacles for guided Lamb wave SHM applications. In an effort to overcome such obstacles, a new signal-processing technique taking advantage order tracking based on dispersion relation, is developed. In this approach, by referencing the wave number-frequency function of specified mode, the operations of resampling and interpolating are performed on the frequency-spectral series of raw signal. The orders referenced to wave number-frequency are calculated, according to which the individual wave-packet is identified and its corresponding propagating distance is estimated. In the order domain, the overlapping modes are readily separated by Gabor expansion on the frequency-spectral series of raw signal. Numerical and FEM simulations on strongly dispersive and multimode overlapping guided waves were carried out to evaluate the performance of the proposed approach. The results demonstrated that the proposed approach is effective in dispersion analysis, mode differentiation and overlapped wave-packets separation

FairGRAPE: Fairness-aware GRAdient Pruning mEthod for Face Attribute Classification

Existing pruning techniques preserve deep neural networks' overall ability to make correct predictions but may also amplify hidden biases during the compression process. We propose a novel pruning method, Fairness-aware GRAdient Pruning mEthod (FairGRAPE), that minimizes the disproportionate impacts of pruning on different sub-groups. Our method calculates the per-group importance of each model weight and selects a subset of weights that maintain the relative between-group total importance in pruning. The proposed method then prunes network edges with small importance values and repeats the procedure by updating importance values. We demonstrate the effectiveness of our method on four different datasets, FairFace, UTKFace, CelebA, and ImageNet, for the tasks of face attribute classification where our method reduces the disparity in performance degradation by up to 90% compared to the state-of-the-art pruning algorithms. Our method is substantially more effective in a setting with a high pruning rate (99%). The code and dataset used in the experiments are available at https://github.com/Bernardo1998/FairGRAPEComment: To appear in ECCV 202