Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page

Searching for Low Mass Dark Portal at the LHC

Light dark matter with mass smaller than about 10 GeV is difficult to probe from direct detection experiments. In order to have the correct thermal relic abundance, the mediator of the interaction between dark matter and the Standard Model (SM) should also be relatively light, $\sim 10^2$ GeV. If such a light mediator couples to charged leptons, it would already be strongly constrained by direct searches at colliders. In this work, we consider the scenario of a leptophobic light $Z'$ vector boson as the mediator, and study the the prospect of searching for it at the 8 TeV Large Hadron Collider (LHC). To improve the reach in the low mass region, we perform a detailed study of the processes that the $Z'$ is produced in association with jet, photon, $W^\pm$ and $Z^0$. We show that in the region where the mass of $Z'$ is between 80 and 400 GeV, the constraint from associated production can be comparable or even stronger than the known monojet and dijet constraints. Searches in these channels can be complementary to the monojet search, in particular if the $Z'$ couplings to quarks ($g_{Z'}$) and dark matter ($g_D$) are different. For $g_D < g_{Z'}$, we show that there is a larger region of parameter space which has correct thermal relic abundance and a light $Z'$, $M_{Z'} \sim 100$ GeV. This region, which cannot be covered by the mono-jet search, can be covered by the resonance searches described in this paper.Comment: 16 pages, 5 figure

The Competing Risks of Prepayment and Default on the Single-Family Mortgage Market

This study contains three chapters. Since the subprime crisis, it has become increasingly important to understand the competing risks of prepayment and default on the single-family mortgage market. This research studies the economic factors that affect the competing risks of prepayment and default in locations where the aggregate of the prepayment risk and the default risk are simultaneously high. Chapter 1 outlines the analysis based on thirty-year, fixed-rate, single-family mortgages in five Metropolitan Statistical Areas (MSAs): Phoenix, Miami, Tampa, Detroit and Las Vegas. These MSAs are chosen from a sample Single-family Loan-Level Dataset constructed by Freddie Mac based on high simultaneous prepayment and default rates. The results are estimated by a discrete time competing risks model based on restricted multinomial logit. Two different combinations of dependent variables are used to make the analysis more comprehensive. The first combination is prepayment and default and the second is prepayment and 90-days-delinquency. The indicator for a prepayment penalty and the value of the call option are used to evaluate the prepayment risk and the best three combinations (using the Bayesian information criterion) of explanatory variables – the value of negative equity, a negative equity dummy, and original loan-to-value ratio – together with the unemployment rate are used to evaluate the default risk. Because of the ambiguous effect of the credit score on the prepayment decision discussed in the previous literature, two estimations to explain the effect of the credit score on the prepayment and default are run. One estimation considers how the credit score affects both termination risks and the other considers how the credit score affects only default. The effect of the debt-to-income ratio on the prepayment and default is also tested. By controlling other mortgage characteristics, such as loan size and loan age, the brief summary of results shows us the prepayment penalty has a negative effect on the prepayment decision. However, its effect in Detroit is insignificantly positive. The value of the call option has a significantly positive impact on the prepayment in each MSA and its effect is the strongest among all of the explanatory variables. The unemployment rate has a positive effect on default/90-days-delinquency. Moreover, negative equity, the negative equity dummy and original loan-to-value are all positively related to the default/90-days-delinquency decision. As expected, in most MSAs, the credit score has a strongly positive effect on the prepayment; comparatively, it has a strong negative impact on the default. When using the credit score only in the default risk and not in the prepayment risk, the effect of the credit score is still significantly negative, but the coefficients decrease slightly. Moreover, debt-to-income does not appear to affect prepayment; however, it has a positive relationship with the default/90-days-delinquency in most MSAs. A Wald test is constructed to test the equality of the coefficients among five MSAs and the results of this test support the argument that prepayment and default risks are heavily influenced by local characteristics. In earlier studies, the proportional hazards model becomes a popular method to analyze the single (prepayment or default) risk of mortgages. This model has been developed into a competing risks model and been widely used to analyze the prepayment and default risks simultaneously in later studies. However, the process of constructing the competing risks model is ambiguous. In Chapter 2, this study clearly presents the calculation process of this model based on the proportional hazards model using Sueyoshi’s method and then implements the model to analyze the termination risks of single-family mortgages in Phoenix. Ding, Tian, Yu and Guo (2012) construct a new model based on a class of transformation survival models to analyze the risk of bankruptcy and they argue that that the proportional hazards model is not the best model to analyze this risk. Therefore, a question is raised by this argument: whether the proportional hazards model is the best model to analyze the default/prepayment risk of single-family mortgages? A new competing risks model based on a class of discrete transformation survival models is constructed in Chapter 2 and it is used to analyze the termination risks of the single-family mortgages in Phoenix. The model is controlled by the transformation parameters (for the prepayment risk) and (for the default risk). When =0 and =0, it is the competing risks model based on proportional hazards, and when \u3e0and \u3e0, its framework is changed according to the value of and . The results show that the proportional hazards framework is the best model to estimate the prepayment risk, but it is not the best model to estimate the default/90-days-delinquency risk. The results of both models support the important arguments made in Chapter 1. Comparing the coefficients estimated by three competing risks models, the coefficients estimated by the model based on the Sueyoshi proportional hazards are insignificantly distinguishable from those estimated by the model based on the multinomial logit. Moreover, the coefficients estimated by the model based on a class of transformation survival models are significantly different from those estimated by the other two models. Unobserved heterogeneity is an important component that should be considered in the modeling process, even though it is not commonly involved in the analysis of the termination risks of the mortgages. In Chapter 3, this study uses latent classes to control unobserved heterogeneity of two different groups of borrowers and constructs three competing risks models based on the multinomial logit, the proportional hazards model and a class of transformation survival models. The models allow the coefficients of the explanatory variables to be different between two groups of borrowers by keeping the baseline the same (the coefficients of the loan age splines are the same between two groups of borrowers). The models are used to analyze the competing risks of prepayment and default/90-days-delinquency of the single-family mortgages in Phoenix and the estimated average conditional hazard for prepayment, default and 90-days-delinquency are compared with those estimated by models that do not control for unobserved heterogeneity. The results show that when the loan age is between 120 and 165 months, models that do not control for unobserved heterogeneity highly overpredict the prepayment hazard. In the average conditional default and 90-days-delinquency hazard, models that do not control for unobserved heterogeneity overpredict the average conditional hazard compared with models that control for unobserved heterogeneity when the loan age is between around 49 and 94 months. Another question answered in this study is that if housing prices did not boom and bust since 2004, what would the average conditional default hazard and the average conditional 90-days-delinquency hazard be? This paper constructs a simulation process by assuming that the housing price remains the same since September 2004 and compares the simulated conditional hazards with those estimated based on the real trend of the housing price. The results show that, in the case when the housing price changes across time, the average conditional hazard dramatically increases from around age month 11 and reaches the maximum hazard at around age month 54, and then sharply decreases until around age month 93. This dramatic change of the average conditional hazard disappears in the case when the housing price is assumed to be unchanged after September 2004. The simulated average conditional hazard slowly increases from age month 1 up to age month 169 with an average rate of increase of 3.72 percent for default hazard and 1.80 percent for 90-days-delinquency hazard. The average difference of the conditional hazard is approximately 0.21 percent between the two cases

ELECTROCHEMICAL PROCESSES IN MICROFLUIDICS SYSTEMS UNDER AC ELECTRIC FIELDS

Alternating current (AC) electric signal has been widely applied in microfluidic systems to induce AC electrokinetic behavior. AC electrokinetic phenomena including AC electrophoresis, AC dielectrophoresis, AC electroosmosis flow and AC electrothermal flow are widely applied in (bio)particle sorting, separation and concentration and micropumps. However, numbers of non-ideal AC electrokinetic behaviors have been reported: human erythrocyte deformation in AC dielectrophoresis system has been observed; flow reversal in AC electroosmosis flow pumps has also been reported. In this dissertation, a systematic study on human erythrocyte crenation in AC dielectrophoresis system was firstly conducted. Multiple possible physical mechanisms inducing cell crenation including temperature, temperature jump, pH, shear force and osmotic pressure was examined. pH change and osmotic pressure change induced by ionic concentration change was attributed as mechanisms induced cell crenation. Such pH change and ionic concentration gradient in AC non-uniform electric fields were then further studied. pH change was detected using Fluorescein sodium salt in sodium chloride solution at relative frequency ~5 to 25 times to electrode charging frequency. Time, spatial, frequency and peak-to-peak potential dependencies have been examined on such pH change and pH gradient. Ion concentration behavior was detected by using ionized FITC molecule as fluorescing ion dissolved in inert solvent methanol. Electrode surface is also coated with HfO2 dielectric layer to minimize effect from electrochemical reaction on FITC emission intensity. Time, spatial, frequency and peak-to-peak potential dependencies have also been examined on ion concentration change and ion concentration gradient. Both pH change and ion concentration change have been observed under high relative AC frequency

STUDIES ON REGULATION OF PQQ-DEPENDENT PHOSPHATE SOLUBILIZATION AMONG RHIZOSPHERE DWELLING BACTERIA

Plant growth promotion can be enhanced by soil- and rhizosphere-dwelling bacteria by a several different methods. One method is by promoting nutrient acquisition from soil. Phosphorus is an essential nutrient that plants obtain from soil, but in many cases it is immobilized in forms that are not available for plant uptake. Bacteria can solubilize insoluble soil phosphates by secreting gluconic acid. This chemical is produced from glucose by the activity of the bacterial enzyme glucose dehydrogenase, which requires a coenzyme called PQQ. In this dissertation, I studied the regulation of the glucose dehydrogenase enzyme and the PQQ coenzyme in the model rhizosphere-dwelling bacteria Pseudomonas putida KT2440 according to differences in bacterial growth conditions. I also extended this study to the bacteria in environmental samples. Broccoli rhizosphere soil samples were collected to study the diversity of the PQQ-producing phosphate solubilizing bacteria in rhizosphere soil and if PQQ was a universal phosphate-solubilizing factor among rhizosphere-dwelling bacteria. While GDH-dependent phosphate solubilization has been observed in numerous bacteria, little is known concerning the mechanism by which this process is regulated. This study indicated that GDH specific activity and PQQ levels vary according to growth condition, with the highest levels of both occurring when glucose is used as the sole carbon source and under conditions of low soluble phosphate. Under these conditions, however, PQQ levels limit in vitro phosphate solubilization. GDH specific activity data correlated well with gcd gene expression data, and the levels of expression of the pqqF and pqqB genes mirrored the levels of PQQ synthesized, suggesting that one or both of these genes may serve to modulate PQQ levels according to the growth conditions. The pqq gene cluster (pqqFABCDEG) encodes at least two independent transcripts, and expression of the pqqF gene appears to be under the control of an independent promoter and terminator. Due to the significance of PQQ in mineral phosphate solubilization, I isolated phosphate-solubilizing bacteria from broccoli rhizosphere soil using culture dependent methods and screened the PQQ-producing phosphate solubilizing bacteria to study how the phosphate-solubilizing ability and PQQ-producing capacity has correlated among the rhizosphere-dwelling bacteria. A positive correlation were observed between the two parameters, and a similar changing pattern was observed for them. Several new genera of PQQ-producing phosphate-solubilizing bacteria were isolated and identified by 16S rRNA gene sequencing analysis

Insulators: A “Safety Guard” for Genome Stability in \u3ci\u3eDrosophila melanogaster\u3c/i\u3e

Chromatin insulators are DNA-protein complexes that assist in the formation of chromatin loop structures by mediating long-range contacts between distant sites, which regulate proper organization of the chromatin fiber within the tridimensional space of the nucleus. It is considered that this function of insulators is required for the regulation of gene expression during development and in differentiated cells. This thesis focuses specifically in the Suppressor of Hairy wing [Su(Hw)] insulator of Drosophila and its associated proteins, and explores the possibility that chromatin insulators are not only significant for regulation of gene expression, but are also essential for DNA replication and for the maintenance of genome stability. Su(Hw) is one of the best characterized insulators in Drosophila and requires the insulator proteins Su(Hw), Modifier of mdg4 [Mod(mdg4)] and Centrosomal protein 190 (CP190) to accomplish its function. Traditionally, there are two well-known properties that are shared by chromatin insulators: they have the ability to block the communication between enhancers and promoters when located between them and they can function as heterochromatin barriers. However, previous studies have revealed that not all insulator sites in the genome share the enhancer-promoter blocking property, leaving open the possibility that, in addition to the establishment of chromatin loops and gene transcription regulation, insulators might play yet unexplored roles in the genome. Chapter one introduces a new role for the phosphorylation of H2Av (γH2Av), traditionally a marker for DNA damage, in insulator function. This work shows that γH2Av is required for the Su(Hw) enhancer-blocking function, and suggests that the ATM and ATR kinases modulate insulator function through phosphorylation of H2Av at insulator sites. Chapter two explores the possibility that Su(Hw) and HIPP1 (HP1-Insulator Protein Partner 1) may play a role in the regulation of DNA replication in the genome. Findings in this work suggest that insulators regulate activation of origins of replication by cooperation with other proteins such as HP1 and H4K20me1. Altogether these findings provide new insights into insulator function and suggest that Su(Hw) and likely other insulators are critical for DNA replication and for the maintenance of genome stability