On the Derivative Imbalance and Ambiguity of Functions

In 2007, Carlet and Ding introduced two parameters, denoted by $Nb_F$ and $NB_F$, quantifying respectively the balancedness of general functions $F$ between finite Abelian groups and the (global) balancedness of their derivatives $D_a F(x)=F(x+a)-F(x)$, $a\in G\setminus\{0\}$ (providing an indicator of the nonlinearity of the functions). These authors studied the properties and cryptographic significance of these two measures. They provided for S-boxes inequalities relating the nonlinearity $\mathcal{NL}(F)$ to $NB_F$, and obtained in particular an upper bound on the nonlinearity which unifies Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the Workshop WCC 2009 and in its postproceedings in 2011, a further study of these parameters was made; in particular, the first parameter was applied to the functions $F+L$ where $L$ is affine, providing more nonlinearity parameters. In 2010, motivated by the study of Costas arrays, two parameters called ambiguity and deficiency were introduced by Panario \emph{et al.} for permutations over finite Abelian groups to measure the injectivity and surjectivity of the derivatives respectively. These authors also studied some fundamental properties and cryptographic significance of these two measures. Further studies followed without that the second pair of parameters be compared to the first one. In the present paper, we observe that ambiguity is the same parameter as $NB_F$, up to additive and multiplicative constants (i.e. up to rescaling). We make the necessary work of comparison and unification of the results on $NB_F$, respectively on ambiguity, which have been obtained in the five papers devoted to these parameters. We generalize some known results to any Abelian groups and we more importantly derive many new results on these parameters

A Recursive Construction of Permutation Polynomials over Fq2\mathbb{F}_{q^2} with Odd Characteristic from R\'{e}dei Functions

In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These permutation polynomials can be generated recursively. As a consequence, we can generate recursively permutation polynomials with arbitrary number of terms. More importantly, the conditions of these polynomials being permutations are very easy to characterize. For wide applications in practice, several classes of permutation binomials and trinomials are given. With the help of a computer, we find that the number of permutation polynomials of these types is very large

Domain Adaptive Semantic Segmentation by Optimal Transport

Scene segmentation is widely used in the field of autonomous driving for environment perception, and semantic scene segmentation (3S) has received a great deal of attention due to the richness of the semantic information it contains. It aims to assign labels to pixels in an image, thus enabling automatic image labeling. Current approaches are mainly based on convolutional neural networks (CNN), but they rely on a large number of labels. Therefore, how to use a small size of labeled data to achieve semantic segmentation becomes more and more important. In this paper, we propose a domain adaptation (DA) framework based on optimal transport (OT) and attention mechanism to address this issue. Concretely, first we generate the output space via CNN due to its superiority of feature representation. Second, we utilize OT to achieve a more robust alignment of source and target domains in output space, where the OT plan defines a well attention mechanism to improve the adaptation of the model. In particular, with OT, the number of network parameters has been reduced and the network has been better interpretable. Third, to better describe the multi-scale property of features, we construct a multi-scale segmentation network to perform domain adaptation. Finally, in order to verify the performance of our proposed method, we conduct experimental comparison with three benchmark and four SOTA methods on three scene datasets, and the mean intersection-over-union (mIOU) has been significant improved, and visualization results under multiple domain adaptation scenarios also show that our proposed method has better performance than compared semantic segmentation methods

Spatial and Modal Optimal Transport for Fast Cross-Modal MRI Reconstruction

Multi-modal magnetic resonance imaging (MRI) plays a crucial role in comprehensive disease diagnosis in clinical medicine. However, acquiring certain modalities, such as T2-weighted images (T2WIs), is time-consuming and prone to be with motion artifacts. It negatively impacts subsequent multi-modal image analysis. To address this issue, we propose an end-to-end deep learning framework that utilizes T1-weighted images (T1WIs) as auxiliary modalities to expedite T2WIs' acquisitions. While image pre-processing is capable of mitigating misalignment, improper parameter selection leads to adverse pre-processing effects, requiring iterative experimentation and adjustment. To overcome this shortage, we employ Optimal Transport (OT) to synthesize T2WIs by aligning T1WIs and performing cross-modal synthesis, effectively mitigating spatial misalignment effects. Furthermore, we adopt an alternating iteration framework between the reconstruction task and the cross-modal synthesis task to optimize the final results. Then, we prove that the reconstructed T2WIs and the synthetic T2WIs become closer on the T2 image manifold with iterations increasing, and further illustrate that the improved reconstruction result enhances the synthesis process, whereas the enhanced synthesis result improves the reconstruction process. Finally, experimental results from FastMRI and internal datasets confirm the effectiveness of our method, demonstrating significant improvements in image reconstruction quality even at low sampling rates

Traditional Chinese Mind and Body Exercises for Promoting Balance Ability of Old Adults: A Systematic Review and Meta-Analysis

The purpose of this study was to provide a quantitative evaluation of the effectiveness of traditional Chinese mind and body exercises in promoting balance ability for old adults. The eligible studies were extensively searched from electronic databases (Medline, CINAHL, SportDicus, and Web of Science) until 10 May 2016. Reference lists of relevant publications were screened for future hits. The trials used randomized controlled approaches to compare the effects of traditional Chinese mind and body exercise (TCMBE) on balance ability of old adults that were included. The synthesized results of Berg Balance Scale (BBS), Timed Up and Go Test (TUG), and static balance with 95% confidence intervals were counted under a random-effects model. Ten studies were selected based on the inclusion criteria, and a total of 1,798 participants were involved in this review. The results of the meta-analysis showed that TCMBE had no significant improvement on BBS and TUG, but the BBS and TUG could be obviously improved by prolonging the intervention time. In addition, the results showed that TCMBE could significantly improve the static balance compared to control group. In conclusion, old adults who practiced TCMBE with the time not less than 150 minutes per week for more than 15 weeks could promote the balance ability

Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purposes, it has the attractive feature that random draws from an uncorrelated standard normal distribution yield model realizations with spatial characteristics that are in agreement with the training set. In comparison with the most commonly used parametric representations in probabilistic inversion, we find that our dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model. For the considered examples, important compression ratios (200 - 500) are achieved. Given that the construction of our parameterization requires a training set of several tens of thousands of prior model realizations, our DR approach is more suited for probabilistic (or deterministic) inversion than for unconditional (or point-conditioned) geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D transient hydraulic tomography data are used to demonstrate the DR-based inversion. For the 2D case study, the performance is superior compared to current state-of-the-art multiple-point statistics inversion by sequential geostatistical resampling (SGR). Inversion results for the 3D application are also encouraging

CoBigICP: Robust and Precise Point Set Registration using Correntropy Metrics and Bidirectional Correspondence

In this paper, we propose a novel probabilistic variant of iterative closest point (ICP) dubbed as CoBigICP. The method leverages both local geometrical information and global noise characteristics. Locally, the 3D structure of both target and source clouds are incorporated into the objective function through bidirectional correspondence. Globally, error metric of correntropy is introduced as noise model to resist outliers. Importantly, the close resemblance between normal-distributions transform (NDT) and correntropy is revealed. To ease the minimization step, an on-manifold parameterization of the special Euclidean group is proposed. Extensive experiments validate that CoBigICP outperforms several well-known and state-of-the-art methods.Comment: 6 pages, 4 figures. Accepted to IROS202

Numerical simulation of separation shock characteristics of a piston type explosive bolt

A piston type explosive bolt is modeled by using a hydrocodes AUTODYN. The influence of the charge amount on the separation shock is analyzed. The results show that the separation shock of the piston type explosive bolt mainly includes two aspects: the shock caused by explosive detonation and the impact of the piston at the end of stroke. As the charge amount increases, the collision speed of piston first increases and then decreases, and the separation shock first increases and then stabilizes