A mathematical framework for inverse wave problems in heterogeneous media

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical properties of materials. Rocks, manufactured materials, and other wave propagation environments often exhibit spatial heterogeneity in mechanical properties at a wide variety of scales, and coefficient functions representing these properties must mimic this heterogeneity. We show how to choose domains (classes of nonsmooth coefficient functions) and data definitions (traces of weak solutions) so that optimization formulations of inverse wave problems satisfy some of the prerequisites for application of Newton's method and its relatives. These results follow from the properties of a class of abstract first-order evolution systems, of which various physical wave systems appear as concrete instances. Finite speed of propagation for linear waves with bounded, measurable mechanical parameter fields is one of the by-products of this theory

MOLECULAR MECHANISMS ALTERING SKELETAL DEVELOPMENT AND HOMEOSTASIS IN TS65NDN DOWN SYNDROME MICE

poster abstractDown syndrome (DS) is caused by three copies of human chromosome 21 (HSA21) and results in abnormal craniofacial and appendicular bone phe-notypes. The Ts65Dn mouse model of DS contains three copies of nearly half of the genes found on HSA21, and exhibits craniofacial skeletal phenotypes similar to those observed in humans with DS. We recently demonstrated ab-normalities in the development and homeostasis of the appendicular skele-ton of Ts65Dn mice. Femurs from trisomic mice exhibit alterations in trabec-ular bone architecture and overall bone strength. Furthermore, bone for-mation rates were found to be significantly reduced, suggesting trisomy im-pacts bone development and maintenance in Ts65Dn mice, and by extension humans with DS. DYRK1A is triplicated in both humans with DS and Ts65Dn mice and its protein acts as a kinase critical during development. Dyrk1A negatively regulates the nuclear localization and activation of Nfatc, a tran-scription factor critical to signaling pathways associated with cell proliferation and bone development, and is overexpressed in the E9.5 Ts65Dn mandible precursor. We hypothesize that the previously documented Ts65Dn bone phenotype originates during embryonic development, and the presence of an extra copy of Dyrk1a contributes to the abnormal bone phenotype observed in Ts65Dn mice and humans with DS. To test our first hypothesis, analysis of the cartilage template and early bone precursor is being conducted on the femurs from embryonic day 17.5 trisomic and euploid embryos. To implicate the involvement of Dyrk1a in the DS bone phenotype, Ts65Dn mice are be-ing treated with a known Dyrk1a inhibitor, EGCG, to determine if correcting the functional expression of Dyrk1a impacts the development of the Ts65Dn postnatal bone phenotype. Understanding the molecular mechanisms under-lying DS bone phenotypes may help improve the quality of life for individuals with DS and provide viable options for the treatment of osteoporosis

EMBRYONIC BONE DEVELOPMENT AND NFAT EXPRESSION IN THE TS65DN MOUSE MODEL FOR DOWN SYNDROME

poster abstractDown syndrome (DS) is a common genetic disorder that occurs in ap-proximately 1 out of every 750 live births. DS phenotypes include cognitive deficits, altered craniofacial features, muscle hypotonia, heart defects, and abnormal bone structure. The Ts65Dn mouse model is the most common or-ganismal model used to study DS phenotypes. This model exhibits a number of phenotypic traits comparable to those of humans with DS, including bone anomalies. Past studies have shown that Ts65Dn mice exhibit weaker tra-becular bone due to less trabeculae. They have also been shown to have less bone mineral density and bone mineral content at 6 weeks of age when compared to their euploid counterparts, with the severity of these defects lessening by 16 weeks. No studies of bone development have yet decisively identified the origin of these defects. We hypothesized that abnormal endochondral ossification is responsible for the presence of these deficien-cies in bone mineral content and bone mineral density. Aberrant expression of Nfat has been implicated as the molecular cause of many DS-related phe-notypes, and activity of Nfat can be determined based upon its localization. Specifically, Nfat has been shown to control many aspects of bone develop-ment, which makes it of special interest to this research. To test our hypoth-esis of a bone deficit present during embryonic development of Ts65Dn em-bryos, we are comparing cartilaginous template characteristics, progression of the mineralization front, osteoclast activity, percent bone volume, and Nfat localization in euploid and trisomic mouse femurs at embryonic day 17.5. Our preliminary data show lower percent bone volumes in trisomic fe-murs, suggesting that endochondral ossification in Ts65Dn mice lags behind that of their euploid counterparts. These results indicate that DS bone phe-notypes do indeed originate during embryonic development and create a foundation for future work on their treatment. Supported by: National Science Foundation GK-12 Fellowship; Jerome Lejeune Foundatio

Rescue of the abnormal skeletal phenotype in Ts65Dn Down syndrome mice using genetic and therapeutic modulation of trisomic Dyrk1a

Trisomy 21 causes skeletal alterations in individuals with Down syndrome (DS), but the causative trisomic gene and a therapeutic approach to rescue these abnormalities are unknown. Individuals with DS display skeletal alterations including reduced bone mineral density, modified bone structure and distinctive facial features. Due to peripheral skeletal anomalies and extended longevity, individuals with DS are increasingly more susceptible to bone fractures. Understanding the genetic and developmental origin of DS skeletal abnormalities would facilitate the development of therapies to rescue these and other deficiencies associated with DS. DYRK1A is found in three copies in individuals with DS and Ts65Dn DS mice and has been hypothesized to be involved in many Trisomy 21 phenotypes including skeletal abnormalities. Return of Dyrk1a copy number to normal levels in Ts65Dn mice rescued the appendicular bone abnormalities, suggesting that appropriate levels of DYRK1A expression are critical for the development and maintenance of the DS appendicular skeleton. Therapy using the DYRK1A inhibitor epigallocatechin-3-gallate improved Ts65Dn skeletal phenotypes. These outcomes suggest that the osteopenic phenotype associated with DS may be rescued postnatally by targeting trisomic Dyrk1a

EGCG from different sources: differential stability and effects on treating bone phenotypes related to Down syndrome

poster abstractDown Syndrome (DS) is a genetic disorder caused by trisomy of human chromosome 21 (Hsa21). DS phenotypes include cognitive impairment, craniofacial abnormalities, low muscle tone, and skeletal deficiencies. The Ts65Dn mouse model exhibits similar phenotypes as found in humans with DS, including deficits in skeletal bone. Over-expression of DYRK1A, a serine-threonine kinase encoded on Hsa21, has been linked to deficiencies in DS bone homeostasis. Epigallocatechin-3-gallate (EGCG), an aromatic polyphenol found in green tea (GT), is a known inhibitor of Dyrk1a activity. Normalization of Dyrk1a activity by EGCG may have the potential to regulate bone homeostasis, by increasing bone mineral density (BMD) and bone strength. We hypothesized that EGCG obtained from different vendors would differ in stability as well as success in ameliorating skeletal deficiencies. EGCG from different sources was subjected to degradation analysis because of its low bioavailability due to strong antioxidative characteristics. We also hypothesized that phosphoric acid would stabilize EGCG and prevent breakdown in an aqueous solution. We performed High Performance Liquid Chromatography–Mass Spectrometry (HPLC-MS) on EGCG from different sources to determine the amount of EGCG degradation in solution. Our analyses showed differential stability in EGCG from different sources or with phosphoric acid. We chose EGCG from three sources to test the hypothesis that these compounds would have differing effects treating bone phenotypes associated with DS. Three-week-old Ts65Dn and control male mice were treated with EGCG for three weeks. At six weeks of age, mice were sacrificed and femurs were extracted. BMD, bone strength, as well as architecture of the femur were assessed. Our results indicate that EGCG from different sources has diverse effects on the correction of bone phenotypes associated with DS. Our work is important to understand how EGCG from different sources may affect DS phenotypes as the EGCG is translated to human use

Evaluation of the Effects of Green Tea Extracts on Bone Homeostasis in the Ts65Dn Down Syndrome Mouse Model

poster abstractDown Syndrome (DS) is a genetic disorder that affects ~1 in 700 live births, caused by trisomy of human chromosome 21 (Hsa21), and results in cognitive impairment, craniofacial abnormalities, low muscle tone, and skeletal deficiencies. To study these phenotypes, we utilized the Ts65Dn mouse model, which contains three copies of approximately half the orthologous found on Hsa21 and exhibits similar phenotypes as found in humans with DS. Individuals with DS and Ts65Dn mice have deficits in bone mineral density (BMD), architecture, and bone strength. Over-expression of DYRK1A, a serine-threonine kinase encoded on Hsa21, has been linked to deficiencies in DS bone homeostasis. Epigallocatechin-3- gallate (EGCG), an aromatic polyphenol found in high concentrations in green tea, is a known inhibitor of Dyrk1a activity. Normalization of Dyrk1a activity by EGCG may have the potential to regulate bone homeostasis and increase BMD and bone strength in individuals with DS. In this study, we hypothesized that EGCG obtained from different sources would have differential effects in correcting bone deficits associated with DS. To test our hypothesis, we performed Liquid chromatography–mass spectrometry (LC-MS) on EGCG and related compounds from different sources. The LC-MS analysis determined the amount of EGCG and the degradation in our stock solution. Next, we treated three-weekold Ts65Dn and control male mice with EGCG for three weeks. At six weeks of age, mice were sacrificed. DXA and micro CT analysis were performed on the femurs and skulls of the mice to assess trabecular and cortical bone structure and BMD. Our results indicate the ability of EGCG to ameliorate skeletal deficiencies and compared pure EGCG with EGCG purchased from commercial vendors in correcting skeletal deficits associated with DS

Testing Yukawa-unified SUSY during year 1 of LHC: the role of multiple b-jets, dileptons and missing E_T

We examine the prospects for testing SO(10) Yukawa-unified supersymmetric models during the first year of LHC running at \sqrt{s}= 7 TeV, assuming integrated luminosity values of 0.1 to 1 fb^-1. We consider two cases: the Higgs splitting (HS) and the D-term splitting (DR3) models. Each generically predicts light gluinos and heavy squarks, with an inverted scalar mass hierarchy. We hence expect large rates for gluino pair production followed by decays to final states with large b-jet multiplicity. For 0.2 fb^-1 of integrated luminosity, we find a 5 sigma discovery reach of m(gluino) ~ 400 GeV even if missing transverse energy, E_T^miss, is not a viable cut variable, by examining the multi-b-jet final state. A corroborating signal should stand out in the opposite-sign (OS) dimuon channel in the case of the HS model; the DR3 model will require higher integrated luminosity to yield a signal in the OS dimuon channel. This region may also be probed by the Tevatron with 5-10 fb^-1 of data, if a corresponding search in the multi-b+ E_T^miss channel is performed. With higher integrated luminosities of ~1 fb^-1, using E_T^miss plus a large multiplicity of b-jets, LHC should be able to discover Yukawa-unified SUSY with m(gluino) up to about 630 GeV. Thus, the year 1 LHC reach for Yukawa-unified SUSY should be enough to either claim a discovery of the gluino, or to very nearly rule out this class of models, since higher values of m(gluino) lead to rather poor Yukawa unification.Comment: 32 pages including 31 EPS figure

The Duck Redux: An Improved Proper Motion Upper Limit for the Pulsar B1757-24 Near the Supernova Remnant G5.4-1.2

"The Duck" is a complicated non-thermal radio system, consisting of the energetic radio pulsar B1757-24, its surrounding pulsar wind nebula G5.27-0.90 and the adjacent supernova remnant (SNR) G5.4-1.2. PSR B1757-24 was originally claimed to be a young (~15 000 yr) and extreme velocity (>~1500 km/s) pulsar which had penetrated and emerged from the shell of the associated SNR G5.4-1.2, but recent upper limits on the pulsar's motion have raised serious difficulties with this interpretation. We here present 8.5 GHz interferometric observations of the nebula G5.27-0.90 over a 12-year baseline, doubling the time-span of previous measurements. These data correspondingly allow us to halve the previous upper limit on the nebula's westward motion to 14 milliarcseconds/yr (5-sigma), allowing a substantive reevaluation of this puzzling object. We rule out the possibility that the pulsar and SNR were formed from a common supernova explosion ~15 000 yrs ago as implied by the pulsar's characteristic age, but conclude that an old (>~70 000 yr) pulsar / SNR association, or a situation in which the pulsar and SNR are physically unrelated, are both still viable explanations.Comment: 9 pages, including 1 color and 1 B/W figure. Minor changes following referee's report. ApJ, in pres