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.)

What is the Decision-Making Process of Computer Service Technicians in Their Routine Work?

This study describes the computer service technicians' decision-making process. The investigator observed the decision-making process in computer service technicians' routine work and compared it to a general decision-making process model. Results show that the decision-making process of computer service technicians basically fits into the general decision-making process model, but does have some specific characteristics. The model includes understanding symptoms, reproducing symptoms, gathering information, diagnosing problems, setting goals, thinking of alternatives, consulting with customers, repairing and confirming solutions. Experience and group discussion play an important role in their decision-making process. Computer service technicians obtain experience from previous work, the Internet and colleagues

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

An operator-algebraic formulation of self-testing

We give a new definition of self-testing for correlations in terms of states on $C^*$-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Baptista, Chen, Kaniewski, Lolck, Man{\v{c}}inska, Gabelgaard Nielsen, and Schmidt. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.Comment: 35 pages. v2: Typos corrected and references added. See video abstract at https://youtu.be/Rli8yM_KkN