Right unimodal and bimodal singularities in positive characteristic

The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple singularities positive characteristic was achieved by Greuel and the author in 2014. In the present paper we classify right unimodal and bimodal singularities in positive characteristic by giving explicit normal forms. It is surprising that in positive characteristic, there are no infinite series of unimodal and bimodal singularities. Moreover, the Milnor number of simple, unimodal and bimodal singularity satisfies $\mu(f)\leq 4p$. As an application we prove that, for singularities of right modality at most 2, the $\mu$-constant stratum is smooth and its dimension is equal to the right modality.IJCI-2016-2989

Equivariant motivic integration and proof of the integral identity conjecture for regular functions

We develop Denef-Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ring defined in this article is more elementary and it yields the application to the conjecture

Euler reflexion formulas for motivic multiple zeta functions

We introduce a new notion of \boxast-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational series. In the same context, we define a motivic multiple zeta function with respect to an ordered family of regular functions, which is integrable and connects closely to Denef-Loeser's motivic zeta functions. We also show that the \boxast -product is associative in the class of motivic multiple zeta functions. Furthermore, a version of the Euler reflexion formula for motivic zeta functions is nicely formulated to deal with the \boxast -product and motivic multiple zeta functions, and it is proved for both univariate and multivariate cases by using the theory of arc spaces. As an application, taking the limit for the motivic Euler reflexion formula we recover the well-known motivic Thom-Sebastiani theorem

Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents

In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a topological invariant. We next prove that the Łojasiewicz gradient exponent can be computed in terms of the polar quotients, and so it is also a topological invariant. For real plane curve singularities, we also give a formula computing the Łojasiewicz gradient exponent via real polar branches. As an application, we give effective estimates of the Łojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables

Development of Fuzzy Hybrid Approaches to Project Delivery Method Selection in Highway Construction

Selection of project delivery methods is a success factor in delivering highway construction projects because it has a substantial impact on the project performance, such as cost, time, and quality. Project delivery decision-making processes have been heavily relied on experts’ opinions and subjective judgements of professionals to evaluate quantitative and qualitative decision variables. Although current quantitative and probabilistic methods provide a robust means to analyze quantitative variables, they are not ideally suited for treating uncertainties encountered in qualitative variables. Fuzzy set theory is a mathematical approach that can accommodate a combination of quantitative and qualitative variables. This dissertation aimed at investigating the applications of fuzzy set theory and fuzzy logic to support decision-making processes in project delivery method selections. Using an empirical dataset of 254 completed highway construction projects, three fuzzy-based applications, including fuzzy cluster analysis, fuzzy pattern recognition, and fuzzy Bayesian inference system were developed, trained, and tested. As a result, fuzzy cluster analysis was used to establish seven common project clusters that share high similarities in project characteristics, project complexity, delivery risks, cost growth, and project delivery methods. Fuzzy pattern recognition was used to develop a fuzzy rule-based inference system based on the seven identified project clusters to help recognize an appropriate project delivery method associated with potential cost growth for new highway projects. Fuzzy Bayesian networks were used to develop the theoretical framework of fuzzy Bayesian inference system which is able to depict the causal relationships between project characteristics, project complexity, delivery risks, and project delivery methods. The flexibility of fuzzy membership functions in the developed applications helps leverage the evaluation of a combination of quantitative and qualitative variables in highway project delivery method selection. In addition, these data-driven fuzzy applications also allow for multiple decision scenarios based on the decision maker’s judgements of delivery risks and project complexity. This dissertation contributes to the body of knowledge by demonstrating quantitative approaches derived from fuzzy set theory and fuzzy logic to support the selection of project delivery methods in highway construction. Additionally, the results from the developed fuzzy-based applications also provide insights regarding cost performance comparisons between project delivery methods. This study may assist highway agencies in making project delivery decisions based on project attributes, historical data and their relevant experience

Progression of striped jack nervous necrosis virus (SJNNV) infection in naturally and experimentally infected striped jack Pseudocaranx dentex larvae.

The progress of infection with SJNNV (nodavirus), the causative agent of viral nervous necrosis (VNN), was investigated by using naturally infected (acute and subacute groups) and experimentally infected striped jack larvae at different stages of infection. Although there were slight differences in the progress of infection among the 3 groups of fish examined, the general features of infection were quite similar. Necrosis and vacuolation of the nerve cells were first observed in the spinal cord, particularly in the area just above the swimbladder, later in the brain, and then in the retina. Mortalities occurred 1 to 2 d after the commencement of lytic degeneration of the cells, which resulted in heavy vacuolation in these nervous tissues. Virus antigens were detectable in the nervous tissues by the fluorescent antibody technique (FAT) when conspicuous vacuolation appeared in the cytoplasm. Virus particles were detectable by electron microscopy in concurrence with the appearance of heavy tissue vacuolation. These results indicate that SJNNV exhibits a tropism for nerve cells and its initial multiplication site is the spinal cord, from which the virus spreads to the brain and finally to the retina. Hyperplasia was observed in the skin of 1 naturally infected larval group (acute infection) and virus multiplication was observed in these affected epithelial cells. However, the role of skin as a portal of entry for SJNNV remains unclear

Efficient and precise CRISPR/Cas9-mediated MECP2 modifications in human-induced pluripotent stem cells

Patients with Rett syndrome (RTT) have severe mental and physical disabilities. The majority of RTT patients carry a heterozygous mutation in methyl-CpG binding protein 2 (MECP2), an X-linked gene encoding an epigenetic factor crucial for normal nerve cell function. No curative therapy for RTT syndrome exists, and cellular mechanisms are incompletely understood. Here, we developed a CRISPR/Cas9-mediated system that targets and corrects the disease relevant regions of the MECP2 exon 4 coding sequence. We achieved homologous recombination (HR) efficiencies of 20% to 30% in human cell lines and iPSCs. Furthermore, we successfully introduced a MECP2(R270X) mutation into the MECP2 gene in human induced pluripotent stem cells (iPSCs). Consequently, using CRISPR/Cas9, we were able to repair such mutations with high efficiency in human mutant iPSCs. In summary, we provide a new strategy for MECP2 gene targeting that can be potentially translated into gene therapy or for iPSCs-based disease modeling of RTT syndrome

Tissue distribution of striped jack nervous necrosis virus (SJNNV) in adult striped jack.

Fluorescent antibody technique (FAT) and polymerase chain reaction (PCR) method were used to localize striped jack nervous necrosis virus (SJNNV, a nodavirus) in adult striped jack Pseudocaranx dentex. One group of brood stocks (N = 4) consisted of 13-yr-old spawners whose reproductive fluids were SJNNV-positive by the PCR test. The other group (N = 4) consisted of 4-yr-old fish which had not previously spawned whose reproductive fluids were negative by the PCR test. Positive FAT reactions using an anti-SJNNV rabbit serum were observed in the gonad, intestine, stomach, kidney, and liver of the 13-yr-old fish but not in the corresponding organs of the 4-yr-old fish. In neither group were the viral antigens detected in the spinal cord, brain, or retina tissues, the target organs of the virus in striped jack larvae. The FAT results were consistent with PCR results for the detection of the SJNNV coat protein gene. The present results suggest that SJNNV originates in various organs of striped jack spawners and is shed from the intestine and gonad, which results in contamination of eggs

Study on N-NH4+ removal from underground water by MBBR case study in Bach Khoa Ward, Hanoi, Vietnam

Moving bed biofilm reactor (MBBR) using porous carrier plastic material, Polyurethane (DHY-1) which has high porosity 92% -96%, has been researched and applied in many water treatment systems. The advantage of the material is that it has high surface area of about 6,000-12,000m2/m3 thereby increasing the density of biomass. In this research, they were tried to treat ammonium nitrogen (N-NH4+) in the ground water. It was found that the treatment efficiency was more than 90% with N-NH4+ concentration of 10-12mg/l. Different densities of carrier materials as well as different influent flow rates have significant impacts on the removal efficiency. The study showed that treatment capacity decreased with high influent flow rate while increased with high density of carrier materials