Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions

To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known general theory for this task is much far from giving the exact dimension when applied to a specific linearized polynomial. The first contribution of this paper is to give a better general method to get more precise upper bound on the root number of any given linearized polynomial. We anticipate this result would be applied as a useful tool in many research branches of finite field and cryptography. Really we apply this result to get tighter estimations of the lower bounds on the second order nonlinearities of general cubic Boolean functions, which has been being an active research problem during the past decade, with many examples showing great improvements. Furthermore, this paper shows that by studying the distribution of radicals of derivatives of a given Boolean functions one can get a better lower bound of the second-order nonlinearity, through an example of the monomial Boolean function $g_{\mu}=Tr(\mu x^{2^{2r}+2^r+1})$ over any finite field \GF{n}

Carbonic anhydrase XII expression is associated with histologic grade of cervical cancer and superior radiotherapy outcome

BACKGROUND: To investigate whether expression of carbonic anhydrase XII (CA12) is associated with histologic grade of the tumors and radiotherapy outcomes of the patients with invasive cervical cancer. METHODS: CA12 expression was examined by immunohistochemical stains in cervical cancer tissues from 183 radiotherapy patients. Histological grading was classified as well (WD), moderately (MD) or poorly differentiated (PD). Oligonucleotide microarray experiment was performed using seven cervical cancer samples to examine differentially expressed genes between WD and PD cervical cancers. The association between CA12 and histological grade was analyzed by chi-square test. CA12 and histological grades were analyzed individually and as combined CA12 and histologic grade categories for effects on survival outcome. RESULTS: Immunohistochemical expression of CA12 was highly associated with the histologic grade of cervical cancer. Lack of CA12 expression was associated with PD histology, with an odds ratio of 3.9 (P = 0.01). Microarray analysis showed a fourfold reduction in CA12 gene expression in PD tumors. CA12 expression was marginally associated with superior disease-free survival. Application of the new combined categories resulted in further discrimination of the prognosis of patients with moderate and poorly differentiated tumor grade. CONCLUSIONS: Our study indicates that CA12 may be used as a novel prognostic marker in combination with histologic grade of the tumors

Exploring the pore fluid origin and methane-derived authigenic carbonate properties in response to changes in the methane flux at the southern Ulleung Basin, South Korea

We investigated the geochemistry of gas, pore fluid, and methane-derived authigenic carbonate (MDAC) from four sites in the southern Ulleung Basin, South Korea. In contrast to Sites 16GH-P1 and 16GH-P5, Sites 16GH-P3, and 16GH-P4 are characterized by acoustic chimney structures associated with gas flux. The composition of gas and isotopic signatures of methane (CH4) (C1/C2+ > 300, δ13CCH4 < -60‰, δDCH4 ≤ -190‰) indicate microbial source CH4 at all sites. The upward migration of CH4 can affect the chemical and isotopic properties of pore fluid and gas-related byproducts (e.g., gas hydrate (GH) and MDAC) within the shallow sediments including the current sulfate-methane transition (SMT) (< 5 meters below seafloor). Although no GH was found, elevated Cl- concentrations (maximum = 609 mM) with low δD and δ18O values in Site 16GH-P4 pore fluids delineate the influence of massive GH formation in deeper sediment. In contrast, relatively constant Cl-, δD, and δ18O values in fluids from Sites 16GH-P1, 16GH-P3, and 16GH-P5 indicate a predominant origin from seawater. Pore fluids also exhibit higher concentrations of H4SiO4, B, Mg2+, and K+, along with increasing alkalinity compared to seawater. These observations suggest that marine silicate weathering alters fluid chemistry within the sediment, affecting element and carbon cycles. High alkalinity (up to 60 mM) and Mg2+/Ca2+ ratios (> 6) alongside decreasing Ca2+ and Sr2+ concentrations imply carbonate precipitation. MDACs with diverse morphologies, mainly composed of aragonite and magnesian calcite, and characterized by low carbon isotopic values (δ13CMDAC < -31.3‰), were found at Sites 16GH-P3 and 16GH-P4. Interestingly, δ13CMDAC values at Site 16GH-P3 are clearly differentiated above and below the current SMT. High δ13CMDAC values above the SMT (> -34.3‰) suggest the combined influence of seawater and CH4 migrating upward on MDAC precipitation, whereas low δ13CMDAC values below it (< -41.6‰) indicate a predominant impact of CH4 on MDAC formation. Additionally, the vertical variation of δ18OMDAC values at Site 16GH-P4, compared to the theoretical values, reflects an association with GH dissociation and formation. Our findings improve the understanding of fluid, gas, and MDAC geochemistry in continental margin cold seeps, providing insights into global carbon and element cycles

Impact of High Methane Flux on the Properties of Pore Fluid and Methane-Derived Authigenic Carbonate in the ARAON Mounds, Chukchi Sea

We investigated the pore fluid and methane-derived authigenic carbonate (MDAC) chemistry from the ARAON Mounds in the Chukchi Sea to reveal how methane (CH4) seepage impacts their compositional and isotopic properties. During the ARA07C and ARA09C Expeditions, many in situ gas hydrates (GHs) and MDACs were found near the seafloor. The fluid chemistry has been considerably modified in association with the high CH4 flux and its related byproducts (GHs and MDACs). Compared to Site ARA09C-St 08 (reference site), which displays a linear SO42- downcore profile, the other sites (e.g., ARA07C-St 13, ARA07C-St 14, ARA09C-St 04, ARA09C-St 07, and ARA09C-St 12) that are found byproducts exhibit concave-up and/or kink type SO42- profiles. The physical properties and fluid pathways in sediment columns have been altered by these byproducts, which prevents the steady state condition of the dissolved species through them. Consequently, chemical zones are separated between bearing and non-bearing byproducts intervals under non-steady state condition from the seafloor to the sulfate-methane transition (SMT). GH dissociation also significantly impacts pore fluid properties (e.g., low Cl-, enriched delta D and delta O-18). The upward CH4 with depleted delta C-13 from the thermogenic origin affects the chemical signatures of MDACs. The enriched delta O-18 fluid from GH dissociation also influences the properties of MDACs. Thus, in the ARAON Mounds, the chemistry of the fluid and MDAC has significantly changed, most likely responding to the CH4 flux and GH dissociation through geological time. Overall, our findings will improve the understanding and prediction of the pore fluid and MDAC chemistry in the Arctic Ocean related to CH4 seepage by global climate change

On the number of the rational zeros of linearized polynomials and the second-order nonlinearity of cubic Boolean functions

International audienc

Effect of excess Re on the magnetic properties of Sr2FeReO6 double-perovskite

A solid solution Sr2FeReO6-xRe [SFRO-xRe] system with 0 wt% <= x <= 20 wt% was synthesized by conventional solid state method. With increasing the amount of Re, crystallinity of SFRO was confirmed to increase, but the addition of large amount of Re induced the formation of the second phase (Re and unknown), resulting in the solubility limit of Re into SFRO. Compared to a sample by a muffle furnace, relative density of SFRO by SPS was relatively high and increased with increasing the amount of Re. Besides, with increasing the Re content, it was found that the dense microstructure was formed with large grains, which is probably due to the liquid phase related to Re inside the sample during sintering. The magnetic property was found as a function of Re content that saturation magnetization was increased while remnant magnetization was not significant. In addition, coercive magnetic field was slightly decreased as well, reflecting the typical soft materials. Therefore, the addition of Re is strongly effective to improve microstructure and magnetic property of SFRO. (C) 2012 Elsevier B.V. All rights reserved.112sciescopu