When is Eaton's Markov chain irreducible?

Consider a parametric statistical model $P(\mathrm{d}x|\theta)$ and an improper prior distribution $\nu(\mathrm{d}\theta)$ that together yield a (proper) formal posterior distribution $Q(\mathrm{d}\theta|x)$. The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of $\theta$ is admissible under squared error loss. Eaton [Ann. Statist. 20 (1992) 1147--1179] has shown that a sufficient condition for strong admissibility of $\nu$ is the local recurrence of the Markov chain whose transition function is $R(\theta,\mathrm{d}\eta)=\int Q(\mathrm{d}\eta|x)P(\mathrm {d}x|\theta)$. Applications of this result and its extensions are often greatly simplified when the Markov chain associated with $R$ is irreducible. However, establishing irreducibility can be difficult. In this paper, we provide a characterization of irreducibility for general state space Markov chains and use this characterization to develop an easily checked, necessary and sufficient condition for irreducibility of Eaton's Markov chain. All that is required to check this condition is a simple examination of $P$ and $\nu$. Application of the main result is illustrated using two examples.Comment: Published at http://dx.doi.org/10.3150/07-BEJ6191 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Characterization of plant carbonic anhydrases involvement in nitric oxide production from nitrite and NO-regulated genes during hypersensitive cell death

Since the discovery that Nitric oxide (NO) plays a crucial role in mediating plant defense response in the late nineties, extensive research over the past 20 years revealed that NO is acting as a mediator in plant growth and development, as well as coping with biotic and abiotic stresses. However, both NO biosynthesis and NO downstream signaling during the hypersensitive response triggered by an avirulent pathogen still need further clarification. Two routes for NO production in plants are known, the oxidative pathway and the reductive pathway. To date, the reductive route from nitrite is the most firmly described. Nitrate reductase (NR) can produce NO from nitrite but the physiological relevance of this activity is unclear. Furthermore, exogenous nitrite supply to an NR deficient mutant demonstrates that other routes for NO production from nitrite should exist in plants. Interestingly, it was reported that bovine carbonic anhydrase II, an alpha type carbonic anhydrase (CA), can convert nitrite to NO. Moreover, additional literature reports suggested the involvement of carbonic anhydrases belonging to the beta family of plant CAs in immunity. Therefore, the first aim of this work was to explore the possible involvement of plant carbonic anhydrase enzymes in nitric oxide synthesis during the hypersensitive response (HR). Firstly, we tried to explore the NO producing activity of At\u3b1CA2, an Arabidopsis enzyme belonging to the same family as the bovine CA, which expression was induced by pathogen. We found that this protein requires glycosylation for its activity and localizes to plant thylakoids. Unfortunately, the transient expression in plant system, which yielded a properly glycosylated protein, led to low protein expression not enough to verify its NO production activity. Alternative production system should be eventually considered. Two representatives of \u3b2 and\u3b3type carbonic anhydrases were also cloned, expressed and purified. As expected, tobacco \u3b2CA1 showed high carbonic anhydrase activity, and Arabidopsis \u3b3CA2 showed no detectable carbonic anhydrase activity. However, these proteins were not able to catalyze the nitrite conversion to NO. In the second part of this work, we enquired the NO downstream signaling, focusing on transcriptomic changes associated to NO induced cell death. A massive transcriptomic rearrangement was found to be associated to the NO induced plant cell death. The functional class response to stimuli was strongly enriched in the differentially expressed genes modulated by NO. Moreover, we found a large modulation in signaling and transcription factors. Genes encoding for proteins involved in protein degradation or metabolism of nucleic acids were induced, while genes involved in anabolic processes were down-regulated. Importantly, we confirmed that NO treatment leads to a massive metabolic reprogramming, which specially affects lipid metabolism. Finally, among induced genes the enrichment in genes previously found to be involved/associated to cell death confirmed that chosen conditions were adequate to select for genes involved in cell death activation and execution during the HR

Numerical investigation on rock fragmentation under decoupled charge blasting

Blasting using decoupled charge is extensively applied in rock excavation and rock fragmentation. In this study, the rock fragmentation induced by blasting using decoupled charge is investigated by combined finite element modelling and image-processing. After calibrating the numerical model developed in LS-DYNA against the fragment morphology and fragmentation size distribution (FSD) in three air-coupling blasts and three water-coupling blasts, a series of cubic single-hole models are constructed to simulate rock cracking induced by decoupled charge blasting with various decoupling ratios, distinct coupling mediums and different decoupled charge modes. The simulated fracture networks are obtained by blanking the damaged elements whose damage level is over the threshold of crack formation, and the resulting crack patterns are image-processed using ImageJ to identify fragment size. Then, the blast-created FSDs are characterized by a three-parameter generalized extreme value function, and the FSDs with decoupling ratios, coupling mediums and different decoupled charge modes are quantitatively analyzed and compared. The results show that rock fragmentation becomes finer and the FSD range gets narrower with the decrease in decoupling ratio. Meanwhile, smaller fragment sizes and narrower FSD spans are obtained when changing coupling material from air to water and altering radial decoupling to axial decoupling.acceptedVersio

Preparation of α-Fe2O3 hollow spheres, nanotubes, nanoplates and nanorings as high efficient Cr(VI) adsorbents

This work was financially supported by the National Nature Science Foundation of China (No: 51302280, 51574286), Natural Science Foundation in Qinghai province (No: 2014-ZJ- 936Q). CAS "Light of West China" Program and Youth Innovation Promotion Association (2016377), CAS.α-Fe2O3 nanoparticle with different morphologies, such as hollow spheres, nanotubes with limited {0001} plane exposed, nanoplates and nanorings with the {0001} plane predominantly exposed, have been synthesised by using NaH2PO4 and urea in a facile hydrothermal method. The mechanism of the morphology evolution from hollow sphere to nanoring has been investigated. It is proposed that the polymerisation of Fe3+/H2PO4− plays an important role in the formation of these morphologies. The adsorption of Cr (VI) from aqueous solution onto these α-Fe2O3 nanoparticles showed that the α-Fe2O3 with nanoring morphology has the highest removal efficiency, and the adsorption capacity reached to 16.9 mg/g. These results indicate that the adsorption mechanism of Cr (VI) onto hematite nanoparticles is a chemisorption process through doubly and triply coordinated hydroxyl groups on the outer surface of α-Fe2O3.PostprintPeer reviewe

Modeling Haplotype-Haplotype Interactions in Case-Control Genetic Association Studies

Haplotype analysis has been increasingly used to study the genetic basis of human diseases, but models for characterizing genetic interactions between haplotypes from different chromosomal regions have not been well developed in the current literature. In this article, we describe a statistical model for testing haplotype-haplotype interactions for human diseases with a case-control genetic association design. The model is formulated on a contingency table in which cases and controls are typed for the same set of molecular markers. By integrating well-established quantitative genetic principles, the model is equipped with a capacity to characterize physiologically meaningful epistasis arising from interactions between haplotypes from different chromosomal regions. The model allows the partition of epistasis into different components due to additive × additive, additive × dominance, dominance × additive, and dominance × dominance interactions. We derive the EM algorithm to estimate and test the effects of each of these components on differences in the pattern of genetic variation between cases and controls and, therefore, examine their role in the pathogenesis of human diseases. The method was further extended to investigate gene-environment interactions expressed at the haplotype level. The statistical properties of the models were investigated through simulation studies and its usefulness and utilization validated by analyzing the genetic association of sarcoidosis from a human genetics project

TransRepair: Context-aware Program Repair for Compilation Errors

Automatically fixing compilation errors can greatly raise the productivity of software development, by guiding the novice or AI programmers to write and debug code. Recently, learning-based program repair has gained extensive attention and became the state-of-the-art in practice. But it still leaves plenty of space for improvement. In this paper, we propose an end-to-end solution TransRepair to locate the error lines and create the correct substitute for a C program simultaneously. Superior to the counterpart, our approach takes into account the context of erroneous code and diagnostic compilation feedback. Then we devise a Transformer-based neural network to learn the ways of repair from the erroneous code as well as its context and the diagnostic feedback. To increase the effectiveness of TransRepair, we summarize 5 types and 74 fine-grained sub-types of compilations errors from two real-world program datasets and the Internet. Then a program corruption technique is developed to synthesize a large dataset with 1,821,275 erroneous C programs. Through the extensive experiments, we demonstrate that TransRepair outperforms the state-of-the-art in both single repair accuracy and full repair accuracy. Further analysis sheds light on the strengths and weaknesses in the contemporary solutions for future improvement.Comment: 11 pages, accepted to ASE '2

Vulnerability Disclosure Consultation Paper response

Submission by invitation in response to Vulnerability Disclosure Consultation Paper

Real3D-AD: A Dataset of Point Cloud Anomaly Detection

High-precision point cloud anomaly detection is the gold standard for identifying the defects of advancing machining and precision manufacturing. Despite some methodological advances in this area, the scarcity of datasets and the lack of a systematic benchmark hinder its development. We introduce Real3D-AD, a challenging high-precision point cloud anomaly detection dataset, addressing the limitations in the field. With 1,254 high-resolution 3D items from forty thousand to millions of points for each item, Real3D-AD is the largest dataset for high-precision 3D industrial anomaly detection to date. Real3D-AD surpasses existing 3D anomaly detection datasets available regarding point cloud resolution (0.0010mm-0.0015mm), 360 degree coverage and perfect prototype. Additionally, we present a comprehensive benchmark for Real3D-AD, revealing the absence of baseline methods for high-precision point cloud anomaly detection. To address this, we propose Reg3D-AD, a registration-based 3D anomaly detection method incorporating a novel feature memory bank that preserves local and global representations. Extensive experiments on the Real3D-AD dataset highlight the effectiveness of Reg3D-AD. For reproducibility and accessibility, we provide the Real3D-AD dataset, benchmark source code, and Reg3D-AD on our website:https://github.com/M-3LAB/Real3D-AD