1,614 research outputs found
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 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
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
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
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