Approximation Algorithms for Interdiction Problem with Packing Constraints

We study a bilevel optimization problem which is a zero-sum Stackelberg game. In this problem, there are two players, a leader and a follower, who pick items from a common set. Both the leader and the follower have their own (multi-dimensional) budgets, respectively. Each item is associated with a profit, which is the same to the leader and the follower, and will consume the leader's (follower's) budget if it is selected by the leader (follower). The leader and the follower will select items in a sequential way: First, the leader selects items within the leader's budget. Then the follower selects items from the remaining items within the follower's budget. The goal of the leader is to minimize the maximum profit that the follower can obtain. Let $s_A$ and $s_B$ be the dimension of the leader's and follower's budget, respectively. A special case of our problem is the bilevel knapsack problem studied by Caprara et al. [SIAM Journal on Optimization, 2014], where $s_A=s_B=1$. We consider the general problem and obtain an $(s_B+\epsilon)$-approximation algorithm when $s_A$ and $s_B$ are both constant. In particular, if $s_B=1$, our algorithm implies a PTAS for the bilevel knapsack problem, which is the first O(1)-approximation algorithm. We also complement our result by showing that there does not exist any $(4/3-\epsilon)$-approximation algorithm even if $s_A=1$ and $s_B=2$. We also consider a variant of our problem with resource augmentation when $s_A$ and $s_B$ are both part of the input. We obtain an O(1)-approximation algorithm with O(1)-resource augmentation, that is, we give an algorithm that returns a solution which exceeds the given leader's budget by O(1) times, and the objective value achieved by the solution is O(1) times the optimal objective value that respects the leader's budget

Whither China?: Restarting the Reform Agenda

How has China been able to maintain high-speed economic growth during the last thirty-plus years and successfully transform itself from a poor, backward, and developing country to become the world's second-largest economy? What are the challenges that China faces today and how will she deal with them in order to continue moving toward a truly prosperous and modern society? Standing at a crossroads today, what future direction should China choose: a free market economy or state capitalism? In a series of penetrating dialogues, Wu Jinglian, China's most celebrated and influential economist, and Ma Guochuan, chief commentator of Caijing Magazine, attempt to address the following question: "Where is China going?" This volume offers critical insights into the historical evolution of China's ongoing economic and social transformation. Strongly reflecting Professor Wu's views on the future prospects of the economic reforms, the book provides readers with a deep and lucid understanding of the social and economic issues now confronting China, analyzes their underlying causes, and examines the serious challenges to implementing further reforms. Professor Wu argues that the only way to escape the various social ills in China today is to restart the economic and political reforms, which began thirty years ago but have slowed down during the recent decade, and to move China in the direction of a market economy, the rule of law, and democracy

Theoretical study on multi-range pulsewidth tuning in a dissipative soliton laser mode-locked by a Dirac semimetal

Ultrashort pulse fiber lasers with tunable pulsewidth have a wide range of applications in telecommunication, micro-fabrication, and nonlinear bioimaging. In this paper, we reported the simulation of multi-range pulsewidth-tunable ultrashort pulse laser generation in a mode-locked Er3+ doped fiber laser based on Cd3As2 as a saturable absorber (SA) for the first time. By changing the modulation depth (MD) of Cd3As2 SA from 35% to 75% at the different net normal dispersion, the pulsewidth of the fiber laser is tuned from 4.07 to 48.9 ps. In our simulation, the maximum single tunable range (20.3–48.9 ps) can be obtained when we use a long normal dispersion fiber to increase the net normal dispersion of the cavity, and the minimum tunable range of 1.68–2.45 ps is also achieved by further simultaneously decreasing the cavity length and the net normal dispersion. This model of a mode-locked fiber laser controlled by the MD of Cd3As2 SA provides a simple, reliable, and low-cost solution for a variety of applications that require width-tunable pulses

An enterovirus A71 virus-like particle with replaced loops confers partial cross-protection in mice

Enterovirus A71 (EV-A71), coxsackievirus A16 (CV-A16), and CV-A10 belong to the main prevailing types causing hand-foot-and-mouth disease. Since EV-A71 monovalent vaccine does not confer cross-protection, developing a multivalent vaccine is essential. In this study, a trivalent chimeric virus-like particle of EV-A71 (EV-A71-VLPCHI3) was constructed based on EV-A71-VLP backbone by replacing the corresponding surface loops with CV-A16 VP1 G-H, CV-A10 VP1 B-C and E-F loops, which are critical for immunogenic neutralization. The baculovirus-insect cell expression system was employed for EV-A71-VLPCHI3 production. EV-A71-VLPCHI3 was purified by sucrose density gradient and observed by transmission electron microscopy. The immunogenicity and protective efficacy of EV-A71-VLPCHI3 were evaluated in mice. Our results revealed that EV-A71-VLPCHI3 had a similar morphology to inactivated EV-A71 particles and could induce specific IgG antibodies against EV-A71, CV-A16 and CV-A10 in mice. More importantly, EV-A71-VLPCHI3 enhanced cross-reactive protection against CV-A16 and CV-A10, by 20 % and 40 %, compared to inactivated EV-A71 counterparts, respectively. In conclusion, the successful construction of EV-A71-VLPCHI3 suggested that loop-dependent heterologous protection could be transferred by loops replacement on the surface of viral capsid. This strategy may also supplement the development of multivalent vaccines against other infectious viral diseases

The epidemiological and clinical features of primary giant cell tumor around the knee: A report from the multicenter retrospective study in china

Objectives: We aimed to determine the demographic characteristics of giant cell tumor around the knee in China. Methods: Between March 2000 and June 2014, patients with primary giant cell tumor around the knee were recruited from 6 institutions located in different regions of China, and were reviewed retrospectively the clinical features according to gender and age. Results: 334 qualified patients were included in this study. The sex ratio was 1.14:1 (178/156), with mean ages of 36.9 years in men and 33.1 years in women, constituting a significant difference (P=0.007). The prevalence of pathological fracture was 32.9% overall (28.7% in men and 37.8% in women). The prevalence of simple fracture was significantly higher in women (26.3%) than in men (15.2%), P=0.042. Tumor location and staging did not differ significantly according to sex (P>0.05). However, comparing with >40 years old, those patients aged ≤40 were more likely to have a right knee tumor (56.7% vs. 44.7%, P=0.042), less likely to have Enneking stage 3 disease (18.6% vs. 35.0%, P=0.005), and less likely to have both soft-tissue extension and a mass (18.6% vs. 34.0%, P=0.009). Conclusions: Giant cell tumor around the knee was more common in men than in women, although female patients were younger on average. Further, cases among patients ≤40 years old were observed to be milder than cases among older patients. The results suggest that efficient treatment and preservation of function should both be valued for young patients with giant cell tumor around the knee

Adjunctive sarcosine plus benzoate improved cognitive function in chronic schizophrenia patients with constant clinical symptoms: A randomised, double-blind, placebo-controlled trial

<p><i>Objectives</i> Hypofunction of NMDA receptor is implicated in the pathophysiology, particularly cognitive impairment, of schizophrenia. Sarcosine, a glycine transporter I (GlyT-1) inhibitor, and sodium benzoate, a d-amino acid oxidase (DAAO) inhibitor, can both enhance NMDA receptor-mediated neurotransmission. We proposed simultaneously inhibiting DAAO and GlyT-1 may be more effective than inhibition of either in improving the cognitive and global functioning of schizophrenia patients. <i>Methods</i> This study compared add-on sarcosine (2 g/day) plus benzoate (1 g/day) vs. sarcosine (2 g/day) for the clinical symptoms, as well as the cognitive and global functioning, of chronic schizophrenia patients in a 12-week, double-blind, randomised, placebo-controlled trial. Participants were measured with the Positive and Negative Syndrome Scale and the Global Assessment of Functioning Scale every 3 weeks. Seven cognitive domains, recommended by the Measurement and Treatment Research to Improve Cognition in Schizophrenia Committee, were measured at weeks 0 and 12. <i>Results</i> Adjunctive sarcosine plus benzoate, but not sarcosine alone, improved the cognitive and global functioning of patients with schizophrenia, even when their clinical symptoms had not improved. <i>Conclusions</i> This finding suggests <i>N</i>-methyl-d-aspartate receptor-enhancement therapy can improve the cognitive function of patients with schizophrenia, further indicating this pro-cognitive effect can be primary without improvement in clinical symptoms.</p