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

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

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

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

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

An Alternative Yukawa Unified SUSY Scenario

Supersymmetric SO(10) Grand Unified Theories with Yukawa unification represent an appealing possibility for physics beyond the Standard Model. However Yukawa unification is made difficult by large threshold corrections to the bottom mass. Generally one is led to consider models where the sfermion masses are large in order to suppress these corrections. Here we present another possibility, in which the top and bottom GUT scale Yukawa couplings are equal to a component of the charged lepton Yukawa matrix at the GUT scale in a basis where this matrix is not diagonal. Physically, this weak eigenstate Yukawa unification scenario corresponds to the case where the charged leptons that are in the 16 of SO(10) containing the top and bottom quarks mix with their counterparts in another SO(10) multiplet. Diagonalizing the resulting Yukawa matrix introduces mixings in the neutrino sector. Specifically we find that for a large region of parameter space with relatively light sparticles, and which has not been ruled out by current LHC or other data, the mixing induced in the neutrino sector is such that $sin^2 2\Theta_{23} \approx 1$, in agreement with data. The phenomenological implications are analyzed in some detail.Comment: 32 pages, 22 Figure

Viability of MSSM scenarios at very large tan(beta)

We investigate the MSSM with very large tan(beta) > 50, where the fermion masses are strongly affected by loop-induced couplings to the "wrong" Higgs, imposing perturbative Yukawa couplings and constraints from flavour physics. Performing a low-energy scan of the MSSM with flavour-blind soft terms, we find that the branching ratio of B->tau nu and the anomalous magnetic moment of the muon are the strongest constraints at very large tan(beta) and identify the viable regions in parameter space. Furthermore we determine the scale at which the perturbativity of the Yukawa sector breaks down, depending on the low-energy MSSM parameters. Next, we analyse the very large tan(beta) regime of General Gauge Mediation (GGM) with a low mediation scale. We investigate the requirements on the parameter space and discuss the implied flavour phenomenology. We point out that the possibility of a vanishing Bmu term at a mediation scale M = 100 TeV is challenged by the experimental data on B->tau nu and the anomalous magnetic moment of the muon.Comment: 29 pages, 7 figures. v2: discussion in sections 1 and 4 expanded, conclusions unchanged. Matches version published in JHE

Supersymmetric Flavor Models and the B --> phi K_S Anomaly

We consider the flavor structure of supersymmetric theories that can account for the deviation of the observed time-dependent CP asymmetry in B --> phi K_S from the standard model prediction. Assuming simple flavor symmetries and effective field theory, we investigate possible correlations between sizable supersymmetric contributions to b --> s transitions and to flavor changing processes that are more tightly constrained. With relatively few assumptions, we determine the properties of minimal Yukawa and soft mass textures that are compatible with the desired supersymmetric flavor-changing effect and constraints. We then present explicit models that are designed (at least approximately) to realize these textures. In particular, we present an Abelian model based on a single U(1) factor and a non-trivial extra-dimensional topography that can explain the CP asymmetry in B --> phi K_S, while suppressing other supersymmetric flavor changing effects through a high degree of squark-quark alignment.Comment: 18 pages LaTeX, 3 eps figure

Bi-large Neutrino Mixing and Mass of the Lightest Neutrino from Third Generation Dominance in a Democratic Approach

We show that both small mixing in the quark sector and large mixing in the lepton sector can be obtained from a simple assumption of universality of Yukawa couplings and the right-handed neutrino Majorana mass matrix in leading order. We discuss conditions under which bi-large mixing in the lepton sector is achieved with a minimal amount of fine-tuning requirements for possible models. From knowledge of the solar and atmospheric mixing angles we determine the allowed values of sin \theta_{13}. If embedded into grand unified theories, the third generation Yukawa coupling unification is a generic feature while masses of the first two generations of charged fermions depend on small perturbations. In the neutrino sector, the heavier two neutrinos are model dependent, while the mass of the lightest neutrino in this approach does not depend on perturbations in the leading order. The right-handed neutrino mass scale can be identified with the GUT scale in which case the mass of the lightest neutrino is given as (m_{top}^2/M_{GUT}) sin^2 \theta_{23} sin^2 \theta_{12} in the limit sin \theta_{13} = 0. Discussing symmetries we make a connection with hierarchical models and show that the basis independent characteristic of this scenario is a strong dominance of the third generation right-handed neutrino, M_1, M_2 < 10^{-4} M_3, M_3 = M_{GUT}.Comment: typos correcte