Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein--Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated innovations, with Wiener processes being replaced by fractional Brownian motions. It is also shown that limit theorems for the functionals involve nonstandard scaling and nonstandard limiting distributions. Results of this paper shed light on the asymptotic behavior of nearly unstable long-memory processes.Comment: Published in at http://dx.doi.org/10.1214/009053607000000136 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Moduli stacks of Serre stable representations in tilting theory

We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived equivalence between most concealed-canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the Serre stable moduli stack. We explain why the method works by showing that the Serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves. As a result, this new stack should be of interest in both representation theory and algebraic geometry

Formin isoforms are differentially expressed in the mouse embryo and are required for normal expression of fgf-4 and shh in the limb bud

Mice homozygous for the recessive limb deformity (ld) mutation display both limb and renal defects. The limb defects, oligodactyly and syndactyly, have been traced to improper differentiation of the apical ectodermal ridge (AER) and shortening of the anteroposterior limb axis. The renal defects, usually aplasia, are thought to result from failure of ureteric bud outgrowth. Since the ld locus gives rise to multiple RNA isoforms encoding several different proteins (termed formins), we wished to understand their role in the formation of these organs. Therefore, we first examined the embryonic expression patterns of the four major ld mRNA isoforms. Isoforms I, II and III (all containing a basic amino terminus) are expressed in dorsal root ganglia, cranial ganglia and the developing kidney including the ureteric bud. Isoform IV (containing an acidic amino terminus) is expressed in the notochord, the somites, the apical ectodermal ridge (AER) of the limb bud and the developing kidney including the ureteric bud. Using a lacZ reporter assay in transgenic mice, we show that this differential expression of isoform IV results from distinct regulatory sequences upstream of its first exon. These expression patterns suggest that all four isoforms may be involved in ureteric bud outgrowth, while isoform IV may be involved in AER differentiation. To define further the developmental consequences of the ld limb defect, we analyzed the expression of a number of genes thought to play a role in limb development. Most significantly, we find that although the AERs of ld limb buds express several AER markers, they do not express detectable levels of fibroblast growth factor 4 (fgf-4), which has been proposed to be the AER signal to the mesoderm. Thus we conclude that one or more formins are necessary to initiate and/or maintain fgf-4 production in the distal limb. Since ld limbs form distal structures such as digits, we further conclude that while fgf-4 is capable of supporting distal limb outgrowth in manipulated limbs, it is not essential for distal outgrowth in normal limb development. In addition, ld limbs show a severe decrease in the expression of several mesodermal markers, including sonic hedgehog (shh), a marker for the polarizing region and Hoxd-12, a marker for posterior mesoderm. We propose that incomplete differentiation of the AER in ld limb buds leads to reduction of polarizing activity and defects along the anteroposterior axis

Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution

This paper presents a Bayesian approach using Markov chain Monte Carlo methods and the generalized-t (GT) distribution to predict loss reserves for the insurance companies. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserves. To develop a more robust model for irregular claims, this paper extends the conventional normal error distribution to the GT distribution which nests several heavytailed distributions including the Student-t and exponential power distributions. It is shown that the GT distribution can be expressed as a scale mixture of uniforms (SMU) distribution which facilitates model implementation and detection of outliers by using mixing parameters. Different models for the mean function, including the log-ANOVA, log-ANCOVA, state space and threshold models, are adopted to analyze real loss reserves data. Finally, the best model is selected according to the deviance information criterion (DIC).Bayesian approach; state space model; threshold model; scale mixtures of uniform distribution; device information criterion

Non-uniqueness of weak solutions for the fractal Burgers equation

The notion of Kruzhkov entropy solution was extended by the first author in 2007 to conservation laws with a fractional laplacian diffusion term; this notion led to well-posedness for the Cauchy problem in the $L^\infty$-framework. In the present paper, we further motivate the introduction of entropy solutions, showing that in the case of fractional diffusion of order strictly less than one, uniqueness of a weak solution may fail.Comment: 23 page

Doping-Dependent Raman Resonance in the Model High-Temperature Superconductor HgBa2CuO4+d

We study the model high-temperature superconductor HgBa2CuO4+d with electronic Raman scattering and optical ellipsometry over a wide doping range. The resonant Raman condition which enhances the scattering cross section of "two-magnon" excitations is found to change strongly with doping, and it corresponds to a rearrangement of inter-band optical transitions in the 1-3 eV range seen by ellipsometry. This unexpected change of the resonance condition allows us to reconcile the apparent discrepancy between Raman and x-ray detection of magnetic fluctuations in superconducting cuprates. Intriguingly, the strongest variation occurs across the doping level where the antinodal superconducting gap reaches its maximum.Comment: 4 pages, 4 figures, contact authors for Supplemental Materia

The management of municipal solid waste in Hong Kong : a study of civic engagement strategies

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

TGLI1 transcription factor mediates breast cancer brain metastasis via activating metastasis-initiating cancer stem cells and astrocytes in the tumor microenvironment

Mechanisms for breast cancer metastasis remain unclear. Whether truncated glioma-associated oncogene homolog 1 (TGLI1), a transcription factor known to promote angiogenesis, migration and invasion, plays any role in metastasis of any tumor type has never been investigated. In this study, results of two mouse models of breast cancer metastasis showed that ectopic expression of TGLI1, but not GLI1, promoted preferential metastasis to the brain. Conversely, selective TGLI1 knockdown using antisense oligonucleotides led to decreased breast cancer brain metastasis (BCBM) in vivo. Immunohistochemical staining showed that TGLI1, but not GLI1, was increased in lymph node metastases compared to matched primary tumors, and that TGLI1 was expressed at higher levels in BCBM specimens compared to primary tumors. TGLI1 activation is associated with a shortened time to develop BCBM and enriched in HER2-enriched and triple-negative breast cancers. Radioresistant BCBM cell lines and specimens expressed higher levels of TGLI1, but not GLI1, than radiosensitive counterparts. Since cancer stem cells (CSCs) are radioresistant and metastasis-initiating cells, we examined TGLI1 for its involvement in breast CSCs and found TGLI1 to transcriptionally activate stemness genes CD44, Nanog, Sox2, and OCT4 leading to CSC renewal, and TGLI1 outcompetes with GLI1 for binding to target promoters. We next examined whether astrocyte-priming underlies TGLI1-mediated brain tropism and found that TGLI1-positive CSCs strongly activated and interacted with astrocytes in vitro and in vivo. These findings demonstrate, for the first time, that TGLI1 mediates breast cancer metastasis to the brain, in part, through promoting metastasis-initiating CSCs and activating astrocytes in BCBM microenvironment

Stable sulforaphane protects against gait anomalies and modifies bone microarchitecture in the spontaneous STR/Ort model of osteoarthritis

Osteoarthritis (OA), affecting joints and bone, causes physical gait disability with huge socio-economic burden; treatment remains palliative. Roles for antioxidants in protecting against such chronic disorders have been examined previously. Sulforaphane is a naturally occurring antioxidant. Herein, we explore whether SFX-01®, a stable synthetic form of sulforaphane, modifies gait, bone architecture and slows/reverses articular cartilage destruction in a spontaneous OA model in STR/Ort mice. Sixteen mice (n = 8/group) were orally treated for 3 months with either 100 mg/kg SFX-01® or vehicle. Gait was recorded, tibiae were microCT scanned and analysed. OA lesion severity was graded histologically. The effect of SFX-01® on bone turnover markers in vivo was complemented by in vitro bone formation and resorption assays. Analysis revealed development of OA-related gait asymmetry in vehicle-treated STR/Ort mice, which did not emerge in SFX-01®-treated mice. We found significant improvements in trabecular and cortical bone. Despite these marked improvements, we found that histologically-graded OA severity in articular cartilage was unmodified in treated mice. These changes are also reflected in anabolic and anti-catabolic actions of SFX-01® treatment as reflected by alteration in serum markers as well as changes in primary osteoblast and osteoclast-like cells in vitro. We report that SFX-01® improves bone microarchitecture in vivo, produces corresponding changes in bone cell behaviour in vitro and leads to greater symmetry in gait, without marked effects on cartilage lesion severity in STR/Ort osteoarthritic mice. Our findings support both osteotrophic roles and novel beneficial gait effects for SFX-01® in this model of spontaneous OA