An extension of the generalized pascal matrix and its algebraic properties

AbstractThe extended generalized Pascal matrix can be represented in two different ways: as a lower triangular matrix Φn[x, y] or as a symmetric Ψn[x, y]. These matrices generalize Pn[x], Qn[x], and Rn[x], which are defined by Zhang and by Call and Velleman. A product formula for Φn[x, y] has been found which generalizes the result of Call and Velleman. It is shown that not only can Φn[x, y] be factorized by special summation, but also Ψn[x, y] as Qn[xy]ΦsT[y,1/x] or Φn[x, y]PnT[y/x]. Finally, the inverse of Ψn[x, y] and the values of det Φn[x, y], det Φn−1[x, y], det Ψn[x, y], and det Ψn−1[x, y] are given

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

AbstractIn this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series

Youla-Kucera parameterized adaptive tracking control for optical data storage systems

In the next generation optical data storage systems, the tolerance of the tracking error will become even smaller under various unknown working situations. However, the unknown external disturbances caused by vibrations make it difficult to maintain the desired tracking precision during normal disk operation. It is proposed in this paper to use an adaptive regulation approach to maintain the tracking error below its desired value despite these unknown disturbances. The design of the regulator is formulated by augmenting a base controller into a Youla-Kucera (Q) parameterized set of stabilizing controllers so that both the deterministic and the random disturbances can be deal with properly. The adaptive algorithm is developed to search the desired Q parameter which satisfies the Internal Model Principle and thus the exact regulation against the unknown deterministic disturbance can be achieved. The performance of the proposed control approach is evaluated with experimental results that illustrate the capability of the proposed adaptive regulator to attenuate the unknown disturbances and achieve the desired tracking precision

PIAVE: A Pose-Invariant Audio-Visual Speaker Extraction Network

It is common in everyday spoken communication that we look at the turning head of a talker to listen to his/her voice. Humans see the talker to listen better, so do machines. However, previous studies on audio-visual speaker extraction have not effectively handled the varying talking face. This paper studies how to take full advantage of the varying talking face. We propose a Pose-Invariant Audio-Visual Speaker Extraction Network (PIAVE) that incorporates an additional pose-invariant view to improve audio-visual speaker extraction. Specifically, we generate the pose-invariant view from each original pose orientation, which enables the model to receive a consistent frontal view of the talker regardless of his/her head pose, therefore, forming a multi-view visual input for the speaker. Experiments on the multi-view MEAD and in-the-wild LRS3 dataset demonstrate that PIAVE outperforms the state-of-the-art and is more robust to pose variations.Comment: Interspeech 202

MRVM-NeRF: Mask-Based Pretraining for Neural Radiance Fields

Most Neural Radiance Fields (NeRFs) have poor generalization ability, limiting their application when representing multiple scenes by a single model. To ameliorate this problem, existing methods simply condition NeRF models on image features, lacking the global understanding and modeling of the entire 3D scene. Inspired by the significant success of mask-based modeling in other research fields, we propose a masked ray and view modeling method for generalizable NeRF (MRVM-NeRF), the first attempt to incorporate mask-based pretraining into 3D implicit representations. Specifically, considering that the core of NeRFs lies in modeling 3D representations along the rays and across the views, we randomly mask a proportion of sampled points along the ray at fine stage by discarding partial information obtained from multi-viewpoints, targeting at predicting the corresponding features produced in the coarse branch. In this way, the learned prior knowledge of 3D scenes during pretraining helps the model generalize better to novel scenarios after finetuning. Extensive experiments demonstrate the superiority of our proposed MRVM-NeRF under various synthetic and real-world settings, both qualitatively and quantitatively. Our empirical studies reveal the effectiveness of our proposed innovative MRVM which is specifically designed for NeRF models

Rosavin exerts an antitumor role and inactivates the MAPK/ERK pathway in small-cell lung carcinoma in vitro

This study attempts to explore the function and mechanism of action of rosavin in small-cell lung cancer (SCLC) in vitro. The viability and clone formation of SCLC cells were assessed using cell counting kit-8 and colony formation assays, respectively. Apoptosis and cell cycle were detected using flow cytometry and cell cycle analysis, respectively. Wound healing and transwell assays were performed to evaluate the migration and invasion of SCLC cells. Besides, protein levels of p-ERK, ERK, p-MEK and MEK were determined using western blot analysis. Rosavin repressed the viability and clone formation of SCLC cells, and promoted apoptosis and G0/G1 arrest of SCLC cells. At the same time, rosavin suppressed migration and invasion of SCLC cells. Moreover, protein levels of p-ERK/ERK and p-MEK/MEK were decreased after rosavin addition in SCLC cells. Rosavin impaired malignant behaviors of SCLC cells, which may be associated with inhibition of the MAPK/ERK pathway in vitro

3D Textured Shape Recovery with Learned Geometric Priors

3D textured shape recovery from partial scans is crucial for many real-world applications. Existing approaches have demonstrated the efficacy of implicit function representation, but they suffer from partial inputs with severe occlusions and varying object types, which greatly hinders their application value in the real world. This technical report presents our approach to address these limitations by incorporating learned geometric priors. To this end, we generate a SMPL model from learned pose prediction and fuse it into the partial input to add prior knowledge of human bodies. We also propose a novel completeness-aware bounding box adaptation for handling different levels of scales and partialness of partial scans.Comment: 5 pages, 3 figures, 2 table

Unsupervised Continual Semantic Adaptation through Neural Rendering

An increasing amount of applications rely on data-driven models that are deployed for perception tasks across a sequence of scenes. Due to the mismatch between training and deployment data, adapting the model on the new scenes is often crucial to obtain good performance. In this work, we study continual multi-scene adaptation for the task of semantic segmentation, assuming that no ground-truth labels are available during deployment and that performance on the previous scenes should be maintained. We propose training a Semantic-NeRF network for each scene by fusing the predictions of a segmentation model and then using the view-consistent rendered semantic labels as pseudo-labels to adapt the model. Through joint training with the segmentation model, the Semantic-NeRF model effectively enables 2D-3D knowledge transfer. Furthermore, due to its compact size, it can be stored in a long-term memory and subsequently used to render data from arbitrary viewpoints to reduce forgetting. We evaluate our approach on ScanNet, where we outperform both a voxel-based baseline and a state-of-the-art unsupervised domain adaptation method.Comment: Zhizheng Liu and Francesco Milano share first authorship. Hermann Blum and Cesar Cadena share senior authorship. 18 pages, 7 figures, 10 table