MANIPULATING SINGLE POLYMER MOLECULES FOR APPLICATIONS IN NANOMATERIALS

Polymeric nanoparticles have been utilized in an increasing number of fields over the past two decades due to their unique properties such as design flexibility and good biocompatibility. Despite various techniques available to produce polymer nanoparticles, the preparation of small nanoparticles with customized functions in the sub 20 nm dimension remains challenging. Inspired by the self-organizing behavior of natural biomacromolecules, a class of single-chain nanoparticles (SCNP) are synthesized featuring biomimicry and ultrafine size. These nanoparticles are prepared from self-folding of polymer precursors bearing reactive pendant groups by intramolecular cross-linking reactions. A variety of cross-linking chemistries are available including covalent, dynamic covalent and non-covalent chemistries. Among these methods intramolecular polymerization is of particular importance as it allows for easy control of an SCNP’s degree of cross-linking, and lead to SCNP with tunable level of compaction. The aim of this dissertation is to 1) provide a comprehensive overview of recent advances in the field of single-chain folding; 2) investigate the synthesis of SCNP by intramolecular polymerizations, and 3) study the synthetic variations relating to the efficiency of a polymer’s self-folding by intramolecular polymerization. Chapter 2 of this work discusses the synthesis of poly(oxanorbornene imide) single-chain nanoparticles by intrachain radical polymerization of pendant methacryloyl units. Structure/ property relationships related to methacryloyl pendant length and percent incorporation were studied. Chapter 3 investigates the synthesis of an epoxide-maleimide bifunctional monomer, and its ring-opening polymerization to afford polyethyleneglycol based polymer precursor. The polymer precursor could undergo intramolecular radical polymerization to afford SCNP, and the cross-linked moiety could potentially be isolated for the study of degree of intrachain polymerization. Chapter 4 expands the scope of intrachain polymerization and explores the synthesis of SCNP by intramolecular ring-opening metathesis polymerization (ROMP). A series of poly(pentafluoro-methacrylate)s containing pendant norbornene imide groups was synthesized and subjected to intrachain ROMP. The efficiency of chain folding was explored relating to norbornene content on the polymer precursor, species and feed ratio of Grubbs catalysts, as well as doping effects of fluorinated aromatic comonomer

An average-case lower bound against ACC0

In a seminal work, Williams [22] showed that NEXP (nondeterministic exponential time) does not have polynomial-size ACC0 circuits. Williams’ technique inherently gives a worst-case lower bound, and until now, no average-case version of his result was known. We show that there is a language L in NEXP and a function ε(n)=1/ log(n) ω(1) such that no sequence of polynomial size ACC0 circuits solves L on more than a 1/2+ε(n) fraction of inputs of length n for all large enough n. Complementing this result, we give a nontrivial pseudo-random generator against polynomial-size AC0[6] circuits. We also show that learning algorithms for quasi-polynomial size ACC0 circuits running in time 2n/nω(1) imply lower bounds for the randomised exponential time classes RE (randomized time 2O(n) with one-sided error) and ZPE/1 (zero-error randomized time 2O(n) with 1 bit of advice) against polynomial size ACC0 circuits. This strengthens results of Oliveira and Santhanam [15]

Covid-19 Diagnosis Based on CT Images Through Deep Learning and Data Augmentation

Coronavirus disease 2019(Covid-19) has made people around the world suffer. And there are many researchers make efforts on deep learning methods based on CT imgaes, but the limitation of  this work is the lackage of the dataset, which is not easy to obtain. In this study, we try to use data augmentation to compensate this weakness. In the first part, we use traditional DenseNet-169, and the result shows that data augmentation can help improve the calculating speed and the accuracy. In the second part, we combine Self-trans and DenseNet-169, and the result shows that when doing data augmentation, many model performance metrics have been improved. In the third part, we use UNet++, which reaches accuracy of 0.8645. Apart from this, we think GAN and CNN may also make difference

Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits

We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer d > 1, there is epsilon_d > 0 such that Parity has correlation at most 1/n^{Omega(1)} with depth-d threshold circuits which have at most n^{1+epsilon_d} wires, and the Generalized Andreev Function has correlation at most 1/2^{n^{Omega(1)}} with depth-d threshold circuits which have at most n^{1+epsilon_d} wires. Previously, only worst-case lower bounds in this setting were known [Impagliazzo/Paturi/Saks, SIAM J. Comp., 1997]. We use our ideas to make progress on several related questions. We give satisfiability algorithms beating brute force search for depth-$d$ threshold circuits with a superlinear number of wires. These are the first such algorithms for depth greater than 2. We also show that Parity cannot be computed by polynomial-size AC^0 circuits with n^{o(1)} general threshold gates. Previously no lower bound for Parity in this setting could handle more than log(n) gates. This result also implies subexponential-time learning algorithms for AC^0 with n^{o(1)} threshold gates under the uniform distribution. In addition, we give almost optimal bounds for the number of gates in a depth-d threshold circuit computing Parity on average, and show average-case lower bounds for threshold formulas ofany depth. Our techniques include adaptive random restrictions, anti-concentration and the structural theory of linear threshold functions, and bounded-read Chernoff bounds