The Trigonometric Polynomial Like Bernstein Polynomial

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given

Investigating drug translational research using PubMed articles

Drug research and development are embracing translational research for its potential to increase the number of drugs successfully brought to clinical applications. Using the publicly available PubMed database, we sought to describe the status of drug translational research, the distribution of translational lags for all drugs as well as the collaborations between basic science and clinical science in drug research. For each drug, an indicator called Translational Lag was proposed to quantify the interval time from its first PubMed article to its first clinical article. Meanwhile, the triangle of biomedicine was also used to visualize the status and multidisciplinary collaboration of drug translational research. The results showed that only 18.1% (24,410) of drugs/compounds had been successfully entering clinical research. It averagely took 14.38 years (interquartile range, 4 to 21 years) for a drug from the initial basic discovery to its first clinical research. In addition, the results also revealed that, in drug research, there was rare cooperation between basic science and clinical science, which were more inclined to cooperate within disciplines.Comment: 7pages, 1 figure

Multiscale sub-octave wavelet transform for de-noising and enhancement

This paper describes an approach for accomplishing sub- octave wavelet analysis and its discrete implementation for noise reduction and feature enhancement. Sub-octave wavelet transforms allow us to more closely characterize features within distinct frequency bands. By dividing each octave into sub-octave components, we demonstrate a superior ability to capture transient activities in a signal or image more reliably. De-noising and enhancement are accomplished through techniques of minimizing noise energy and nonlinear processing of transform coefficient energy by gain

In vivo delivery of transcription factors with multifunctional oligonucleotides.

Therapeutics based on transcription factors have the potential to revolutionize medicine but have had limited clinical success as a consequence of delivery problems. The delivery of transcription factors is challenging because it requires the development of a delivery vehicle that can complex transcription factors, target cells and stimulate endosomal disruption, with minimal toxicity. Here, we present a multifunctional oligonucleotide, termed DARTs (DNA assembled recombinant transcription factors), which can deliver transcription factors with high efficiency in vivo. DARTs are composed of an oligonucleotide that contains a transcription-factor-binding sequence and hydrophobic membrane-disruptive chains that are masked by acid-cleavable galactose residues. DARTs have a unique molecular architecture, which allows them to bind transcription factors, trigger endocytosis in hepatocytes, and stimulate endosomal disruption. The DARTs have enhanced uptake in hepatocytes as a result of their galactose residues and can disrupt endosomes efficiently with minimal toxicity, because unmasking of their hydrophobic domains selectively occurs in the acidic environment of the endosome. We show that DARTs can deliver the transcription factor nuclear erythroid 2-related factor 2 (Nrf2) to the liver, catalyse the transcription of Nrf2 downstream genes, and rescue mice from acetaminophen-induced liver injury

Speckle Reduction and Contrast Enhancement of Echocardiograms via Multiscale Nonlinear Processing

This paper presents an algorithm for speckle reduction and contrast enhancement of echocardiographic images. Within a framework of multiscale wavelet analysis, the authors apply wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features. In addition, nonlinear processing of feature energy is carried out to enhance contrast within local structures and along object boundaries. The authors show that the algorithm is capable of not only reducing speckle, but also enhancing features of diagnostic importance, such as myocardial walls in two-dimensional echocardiograms obtained from the parasternal short-axis view. Shrinkage of wavelet coefficients via soft thresholding within finer levels of scale is carried out on coefficients of logarithmically transformed echocardiograms. Enhancement of echocardiographic features is accomplished via nonlinear stretching followed by hard thresholding of wavelet coefficients within selected (midrange) spatial-frequency levels of analysis. The authors formulate the denoising and enhancement problem, introduce a class of dyadic wavelets, and describe their implementation of a dyadic wavelet transform. Their approach for speckle reduction and contrast enhancement was shown to be less affected by pseudo-Gibbs phenomena. The authors show experimentally that this technique produced superior results both qualitatively and quantitatively when compared to results obtained from existing denoising methods alone. A study using a database of clinical echocardiographic images suggests that such denoising and enhancement may improve the overall consistency of expert observers to manually defined borders

Training-free Diffusion Model Adaptation for Variable-Sized Text-to-Image Synthesis

Diffusion models (DMs) have recently gained attention with state-of-the-art performance in text-to-image synthesis. Abiding by the tradition in deep learning, DMs are trained and evaluated on the images with fixed sizes. However, users are demanding for various images with specific sizes and various aspect ratio. This paper focuses on adapting text-to-image diffusion models to handle such variety while maintaining visual fidelity. First we observe that, during the synthesis, lower resolution images suffer from incomplete object portrayal, while higher resolution images exhibit repetitively disordered presentation. Next, we establish a statistical relationship indicating that attention entropy changes with token quantity, suggesting that models aggregate spatial information in proportion to image resolution. The subsequent interpretation on our observations is that objects are incompletely depicted due to limited spatial information for low resolutions, while repetitively disorganized presentation arises from redundant spatial information for high resolutions. From this perspective, we propose a scaling factor to alleviate the change of attention entropy and mitigate the defective pattern observed. Extensive experimental results validate the efficacy of the proposed scaling factor, enabling models to achieve better visual effects, image quality, and text alignment. Notably, these improvements are achieved without additional training or fine-tuning techniques.Comment: Accepted by NeurIPS 2023. 23 pages, 13 figure