Rigidity controllable as-rigid-as-possible shape deformations

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method

The Intoxication Effects of Methanol and Formic Acid on Rat Retina Function

Objective. To explore the potential effects of methanol and its metabolite, formic acid, on rat retina function. Methods. Sprague-Dawley rats were divided into 3- and 7-day groups and a control. Experimental groups were given methanol and the control group were provided saline by gavage. Retinal function of each group was assessed by electroretinogram. Concentrations of methanol and formic acid were detected by GC/HS and HPLC, respectively. Results. The a and b amplitudes of methanol treated groups decreased and latent periods delayed in scotopic and photopic ERG recordings. The summed amplitudes of oscillatory potentials (OPs) of groups B and C decreased and the elapsed time delayed. The amplitudes of OS1, OS3, OS4, and OS5 of group B and OS3, OS4, and OS5 of group C decreased compared with the control group. The IPI1 of group B and IPI1-4 of group C were broader compared with the control group and the IPI1-4 and ET of group B were broader than group C. Conclusions. Both of scotopic and photopic retinal functions were impaired by methanol poisoning, and impairment was more serious in the 7-day than in the 3-day group. OPs, especially later OPs and IPI2, were more sensitive to methanol intoxication than other eletroretinogram subcomponents

Combating Unknown Bias with Effective Bias-Conflicting Scoring and Gradient Alignment

Models notoriously suffer from dataset biases which are detrimental to robustness and generalization. The identify-emphasize paradigm shows a promising effect in dealing with unknown biases. However, we find that it is still plagued by two challenges: A, the quality of the identified bias-conflicting samples is far from satisfactory; B, the emphasizing strategies just yield suboptimal performance. In this work, for challenge A, we propose an effective bias-conflicting scoring method to boost the identification accuracy with two practical strategies -- peer-picking and epoch-ensemble. For challenge B, we point out that the gradient contribution statistics can be a reliable indicator to inspect whether the optimization is dominated by bias-aligned samples. Then, we propose gradient alignment, which employs gradient statistics to balance the contributions of the mined bias-aligned and bias-conflicting samples dynamically throughout the learning process, forcing models to leverage intrinsic features to make fair decisions. Experiments are conducted on multiple datasets in various settings, demonstrating that the proposed solution can alleviate the impact of unknown biases and achieve state-of-the-art performance

Singleton-Optimal LRCs and Perfect LRCs via Cyclic and Constacyclic Codes

Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have been widely investigated. Optimal LRCs via cyclic and constacyclic codes provide significant benefit of elegant algebraic structure and efficient encoding procedure. In this paper, we continue to consider the constructions of optimal LRCs via cyclic and constacyclic codes with long code length. Specifically, we first obtain two classes of $q$-ary cyclic Singleton-optimal $(n, k, d=6;r=2)$-LRCs with length $n=3(q+1)$ when $3 \mid (q-1)$ and $q$ is even, and length $n=\frac{3}{2}(q+1)$ when $3 \mid (q-1)$ and $q \equiv 1(\bmod~4)$, respectively. To the best of our knowledge, this is the first construction of $q$-ary cyclic Singleton-optimal LRCs with length $n>q+1$ and minimum distance $d \geq 5$. On the other hand, an LRC acheiving the Hamming-type bound is called a perfect LRC. By using cyclic and constacyclic codes, we construct two new families of $q$-ary perfect LRCs with length $n=\frac{q^m-1}{q-1}$, minimum distance $d=5$ and locality $r=2$

Bounds and Constructions of Singleton-Optimal Locally Repairable Codes with Small Localities

Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum distance $d=6$, locality $r=3$ and minimum distance $d=7$ and locality $r=2$, respectively. Firstly, we establish equivalent connections between the existence of these two families of LRCs and the existence of some subsets of lines in the projective space with certain properties. Then, we employ the line-point incidence matrix and Johnson bounds for constant weight codes to derive new improved bounds on the code length, which are tighter than known results. Finally, by using some techniques of finite field and finite geometry, we give some new constructions of Singleton-optimal LRCs, which have larger length than previous ones