Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in \omega(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $\mu_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=\mu\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $\mu>\mu_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $\mu<\mu_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur

Developing a dataset for the expected anthropogenic mercury release in China in response to the Minamata convention on mercury

This paper contains supplementary data in support of a research paper published [1] regarding the expected anthropogenic mercury release in China in response to the Minamata Convention on Mercury (MCM). The dataset provided within this article contains a set of excel spreadsheets. Each spreadsheet contains filtered (collected) and analysed data, i.e., parameters, collected data, calculated and summarized results for mercury distribution by the category of mineral production, intentional uses, secondary metal production, extraction and combustion, and waste treatment in a specific year. The collected (filtered) data in this article consist of the input factor (IF), activity rate data (ARD), output scenario (OS), initial distribution factor (iDF), and redistribution factor (rDF). IF was from the default IF in the United Nations Environment Programme (UNEP) Toolkit Level 2 and published scientific papers. ARD was obtained from the U.S. Geological Survey database, China Statistical Yearbooks, and published scientific papers. The OS content was from the default OS in the UNEP Toolkit Level 2 and published scientific papers. iDF was from the default distribution factor (DF) in the UNEP Toolkit Level 2 and published scientific papers. rDF was from published scientific paper. The mercury input was calculated using IF and ARD. The mercury release to different media in the initial distribution step was calculated using the mercury input and iDF. The release of mercury to the final sinks in the redistribution step was calculated using the amount of sector-specific treatment/disposal, product or by-product, and rDF. The dataset with combination of the collected (filtered) and analyzed data can contribute to an understanding of differences in anthropogenic mercury release before and after implementation of the MCM, especially considering technology transformation in China. Government policymakers involved in hazardous waste management, especially those working on MCM, and engineers and scientists interested in hazardous waste management may benefit from these data. The data can be used for identifying the environmental impact of anthropogenic mercury release before and after the MCM in China. The data can facilitate the creation of strategic management policies for mercury as the MCM is implemented in China

Anthropogenic Mercury Release Flow in China

China is the largest emitter of anthropogenic mercury worldwide. Implementation of the Minamata Convention on Mercury will significantly impact the development, use, and management of mercury resources. Chinese mercury management policies require significant adjustment. There is an urgent need to develop a current national mercury inventory to estimate mercury inputs and outputs by source category, and to clarify the distributions to various environmental scenarios. Here, the mercury releases are quantitatively analysed to facilitate the implementation of strategic mercury management policies in China. First, the mercury inputs and outputs by source categories in 2016 are quantified and then the mercury distributions to various environmental and intermediate sinks are estimated. The total mercury input was 5,116 t in 2016, of which 77% was attributable to mineral production. In total, 3,083 t were released into various environmental and intermediate reservoirs. Of this total, 53.8 % was intentional uses, followed by extraction and combustion (26.5%), and mineral production (19.6 %); 1,501 t were released into air, water, and land, of which extraction and combustion accounted for 48.6 % followed by mineral production (25.7 %) and intentional uses (25.6 %)

Non-Abelian Half-Quantum Vortices in 3P2{}^{3}P_{2} Topological Superfluids

The existence and stability of non-Abelian half-quantum vortices (HQVs) are established in ${}^{3}P_{2}$ superfluids in neutron stars with strong magnetic fields, the largest topological quantum matter in our Universe. Using a self-consistent microscopic framework, we find that one integer vortex is energetically destabilized into a pair of two non-Abelian HQVs due to the strong spin-orbit coupled gap functions. We find a topologically protected Majorana fermion on each HQV, thereby providing two-fold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.Comment: 6 pages, 4 figure

Application of PLD-Fabricated Thick-Film Permanent Magnets

Isotropic Nd-Fe-B thick-film magnets have been prepared using a pulsed laser deposition (PLD) method with the control of laser energy density (LED) followed by post-annealing. The characteristics of the method are a high deposition rate up to several tens of microns per hour together with a reliability of magnetic properties due to the good transfer of composition from an Nd-Fe-B target to a film. Several micro-machines comprising the isotropic Nd-Fe-B films such as a miniaturized DC motor and a swimming machine in liquid were demonstrated. Furthermore, the deposition of isotropic Nd (or Pr)-Fe-B thick-film magnets on a Si or glass substrate was carried out to apply the films to various micro-electro-mechanical-systems (MEMS). We also introduced the preparation of isotropic Sm-Co, Fe-Pt, and nano-composite Nd-Fe-B+α-Fe film magnets synthesized using the PLD

Effect of Different Dielectric Fluids on Micro EDM of Low Conductivity Ceramic Material RB-SiC

The machining characteristics of reaction bonded silicon carbide (RB-SiC) in micro electrical discharge machining process were studied by using EDM oil, deionized water, and graphite fiber mixed EDM oil as the dielectric fluids. The process performances were measured in terms of material removal rate, surface roughness and surface topography. The effect of deionized water on SUS 304 also was tried and compared with that on RB-SiC. It was found that when graphite fiber mixed EDM oil was used, higher material removal rate, better surface finish and smoother surface topography were obtained compared to that pure EDM oil and deionized water on RB-SiC. Deionized water could produce better form accuracy, however, electrolytic corrosion occurred and small pits were formed around the machining area of RB-SiC. In contrast, electrolytic corrosion was insignificant for SUS 304