Approximate Set Union Via Approximate Randomization

We develop an randomized approximation algorithm for the size of set union problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in \left((1-\beta_L)|A_i|, (1+\beta_R)|A_i|\right)$, and biased random generators with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over |A_i|}\right] for each input set $A_i$ and element $x\in A_i,$ where $i=1, 2, ..., m$. The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert is in the range $[(1-\epsilon)(1-\alpha_L)(1-\beta_L), (1+\epsilon)(1+\alpha_R)(1+\beta_R)]$ for any $\epsilon\in (0,1)$, where $\alpha_L, \alpha_R, \beta_L,\beta_R\in (0,1)$. The complexity of the algorithm is measured by both time complexity, and round complexity. The algorithm is allowed to make multiple membership queries and get random elements from the input sets in one round. Our algorithm makes adaptive accesses to input sets with multiple rounds. Our algorithm gives an approximation scheme with O(\setCount\cdot(\log \setCount)^{O(1)}) running time and $O(\log m)$ rounds, where $m$ is the number of sets. Our algorithm can handle input sets that can generate random elements with bias, and its approximation ratio depends on the bias. Our algorithm gives a flexible tradeoff with time complexity O\left(\setCount^{1+\xi}\right) and round complexity $O\left({1\over \xi}\right)$ for any $\xi\in(0,1)$

Functionalization of Carbon Nanotubes with Stimuli- Responsive Molecules and Polymers

“Smartly” functionalized carbon nanotubes (CNTs) constitute an actively pursued research topic in the fields of nanomaterials and nanotechnology. The development of highly efficient and selective methodologies for dispersing CNTs in the liquid phase has not only made efficient separation and purification of CNTs possible, but also opened the doors to many fascinating material and biological applications. Very recently, the development of CNT hybrid systems with controlled stimuli-responsiveness has achieved significant breakthroughs. This chapter outlines the state of the art within this vibrant research area, and examples from the most recent literature are selected to demonstrate progress in the preparation of CNT composites, the physical properties of which can be readily switched by various external stimuli (e.g., pH, photoirradiation, solvent, temperature, etc.)

Allocating Limited Resources to Protect a Massive Number of Targets using a Game Theoretic Model

Resource allocation is the process of optimizing the rare resources. In the area of security, how to allocate limited resources to protect a massive number of targets is especially challenging. This paper addresses this resource allocation issue by constructing a game theoretic model. A defender and an attacker are players and the interaction is formulated as a trade-off between protecting targets and consuming resources. The action cost which is a necessary role of consuming resource, is considered in the proposed model. Additionally, a bounded rational behavior model (Quantal Response, QR), which simulates a human attacker of the adversarial nature, is introduced to improve the proposed model. To validate the proposed model, we compare the different utility functions and resource allocation strategies. The comparison results suggest that the proposed resource allocation strategy performs better than others in the perspective of utility and resource effectiveness.Comment: 14 pages, 12 figures, 41 reference

PhysFormer: Facial Video-based Physiological Measurement with Temporal Difference Transformer

Remote photoplethysmography (rPPG), which aims at measuring heart activities and physiological signals from facial video without any contact, has great potential in many applications (e.g., remote healthcare and affective computing). Recent deep learning approaches focus on mining subtle rPPG clues using convolutional neural networks with limited spatio-temporal receptive fields, which neglect the long-range spatio-temporal perception and interaction for rPPG modeling. In this paper, we propose the PhysFormer, an end-to-end video transformer based architecture, to adaptively aggregate both local and global spatio-temporal features for rPPG representation enhancement. As key modules in PhysFormer, the temporal difference transformers first enhance the quasi-periodic rPPG features with temporal difference guided global attention, and then refine the local spatio-temporal representation against interference. Furthermore, we also propose the label distribution learning and a curriculum learning inspired dynamic constraint in frequency domain, which provide elaborate supervisions for PhysFormer and alleviate overfitting. Comprehensive experiments are performed on four benchmark datasets to show our superior performance on both intra- and cross-dataset testings. One highlight is that, unlike most transformer networks needed pretraining from large-scale datasets, the proposed PhysFormer can be easily trained from scratch on rPPG datasets, which makes it promising as a novel transformer baseline for the rPPG community. The codes will be released at https://github.com/ZitongYu/PhysFormer.Comment: Accepted by CVPR202