Query-Efficient Locally Decodable Codes of Subexponential Length

We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the ``algebraic niceness'' phenomenon in $\mathbb{Z}_m$. We show that every integer $m = pq = 2^t -1$, where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as $m=511$ that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki's composition method. More precisely, we construct a $3^{\lceil r/2\rceil}$-query LDC for every positive integer $r<104$ and a $\left\lfloor (3/4)^{51}\cdot 2^{r}\right\rfloor$-query LDC for every integer $r\geq 104$, both of length $N_{r}$, improving the $2^r$ queries used by Efremenko (2009) and $3\cdot 2^{r-2}$ queries used by Itoh and Suzuki (2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.Comment: to appear in Computational Complexit

Pyrolysis of Low-Rank Coal: From Research to Practice

Low-rank coal (LRC), as a conventional fossil fuel, has wealth of reserves and a wide range of distribution around the world, and pyrolysis is thought to be an easy way for clean and efficient conversion of LRC. In this chapter, the characteristics and world’s reservation of LRC are introduced. Then, the chemical reactions and product formation process during pyrolysis of LRC are described. Meanwhile, how the factors, such as temperature, minerals in coal, heating rate, particle size and atmosphere, influence the pyrolysis process are discussed. Finally, three LRC pyrolysis-based polygeneration systems are illustrated for recent developments on LRC industrial practice

Reconstruction of relativistic modified Newtonian dynamics for various cosmological scenarios

In this paper, we present several explicit reconstructions for a novel relativistic theory of modified Newtonian dynamics (RMOND) derived from the background of Friedmann-Lema$\hat{\text{\i}}$tre-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the $\Lambda$ cold dark matter ($\Lambda$CDM) universe filled solely with dust-like matter and the only way to achieve this expansion history for the RMOND theory is to introduce additional degrees of freedom to the matter sectors. Besides, we find that the $\Lambda$CDM-era also can be replicated without any real matter field within the framework of the RMOND theory and the cosmic evolution exhibited by both the power-law and de-Sitter solutions also can be obtained

Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters

Spontaneous imbibition is a crucial process for oil recovery from fractured and unconventional reservoirs. Herein, with the assumption of capillaries being independent, a new mathematical model for spontaneous imbibition is proposed and solved using a numerical method. The simulated results show that the wetting phase preferentially enters smaller capillaries where the advancement velocity is higher than that in larger ones, while the non-wetting phase can be displaced out in the larger capillaries. In addition, the effect of fluid viscosity ratio on counter-current imbibition is analyzed. The results show that imbibition velocity becomes higher with the increase in the viscosity ratio. When the viscosity of the non-wetting phase is larger than that of the wetting phase, the end pressure gradually increases as the imbibition front advances. In contrast, when the viscosity of the non-wetting phase is less than that of the wetting phase, the end pressure decreases with the infiltration. With a higher viscosity ratio of non-wetting and wetting phase, the heterogeneity of the interface advancement among different capillaries increases.Cited as: Chen, K., Xu, H., Zhang, Z., Meng, Q., Zhang, T. Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters. Capillarity, 2022, 5(6): 115-122. https://doi.org/10.46690/capi.2022.06.0

Is the status of gold threatened by Bitcoin?

This paper evinces the ability of gold to avoid risks during periods with great fluctuations in the Bitcoin market. We apply bootstrap full- and subsample rolling-window Granger causality tests to explore the causal relationship between Bitcoin price (BCP) and gold price (GP). The empirical results show that an increase in BCP can cause GP to decrease, indicating that the prosperity of the Bitcoin market undermines the hedging ability of gold. However, a decrease in BCP causes GP to increase, and it also emphasizes that the ability of gold to avoid risks persists. Hence, the status of gold will not be completely threatened by Bitcoin, and they are complementary to each other instead of in competition. In turn, both positive and negative influences of GP on BCP suggest that fluctuations in BCP can be predicted through the gold market. In situations of severe global uncertainty and complicated investment environments, investors can benefit from complementary markets to optimize their asset allocation. Additionally, countries can grasp the trends in Bitcoin and gold prices to prevent large fluctuations in both markets and to reduce the uncertainty of the financial system