An evaluation of free nonprojected visual aids for use in teaching general business.

Thesis (Ed.M.)--Boston Universit

The holonomy groupoid of a singular foliation

We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper ([H. E. Winkelnkemper, The graph of a foliation, Ann. Glob. Anal. Geom. 1 (3) (1983), 51-75.]); the same holds in the singular cases of [J. Pradines, How to define the differentiable graph of a singular foliation, C. Top. Geom. Diff. Cat. XXVI(4) (1985), 339-381.], [B. Bigonnet, J. Pradines, Graphe d'un feuilletage singulier, C. R. Acad. Sci. Paris 300 (13) (1985), 439-442.], [C. Debord, Local integration of Lie algebroids, Banach Center Publ. 54 (2001), 21-33.], [C. Debord, Holonomy groupoids of singular foliations, J. Diff. Geom. 58 (2001), 467-500.], which from our point of view can be thought of as being "almost regular”. In the general case, the holonomy groupoid can be quite an ill behaved geometric object. On the other hand it often has a nice longitudinal smooth structure. Nonetheless, we use this groupoid to generalize to the singular case Connes' construction of the C*-algebra of the foliation. We also outline the construction of a longitudinal pseudo-differential calculus; the analytic index of a longitudinally elliptic operator takes place in the K-theory of our C*-algebra. In our construction, the key notion is that of a bi-submersion which plays the role of a local Lie groupoid defining the foliation. Our groupoid is the quotient of germs of these bi-submersions with respect to an appropriate equivalence relatio

On infinite tensor products of factors of type I2

It is proved, using Krieger's theorem, that ITPFI's of bounded type are ITPFI2. This answers a question asked by E. J. Wood

Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture

We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic K-theoretic (split) Novikov conjecture over \cpt and \S, where \cpt denotes the C^*-algebra of compact operators and \S denotes the algebra of Schatten class operators. We introduce assembly maps with finite coefficients and under an additional hypothesis, we prove that such a group also satisfies the algebraic K-theoretic Novikov conjecture over \bar{\mathbb{Q}} and \mathbb{C} with finite coefficients. For all torsion free Gromov hyperbolic groups G, we demonstrate that the canonical algebra homomorphism \cpt[G]\map C^*_r(G)\hat{\otimes}\cpt induces an isomorphism between their algebraic K-theory groups.Comment: v2 Exposition improved; one lemma and grant acknowledgement added; v3 some terminology changed and details added, Theorems 4.5 and 4.7 in v3 need an extra hypothesis; v4 abridged version accepted for publication in JHR

A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA]

A Short Survey of Noncommutative Geometry

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the Riemann-Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illustration of the spectral formulation of geometry in the ordinary commutative case, we give a polynomial equation for geometries on the four dimensional sphere with fixed volume. The equation involves an idempotent e, playing the role of the instanton, and the Dirac operator D. It expresses the gamma five matrix as the pairing between the operator theoretic chern characters of e and D. It is of degree five in the idempotent and four in the Dirac operator which only appears through its commutant with the idempotent. It determines both the sphere and all its metrics with fixed volume form. We also show using the noncommutative analogue of the Polyakov action, how to obtain the noncommutative metric (in spectral form) on the noncommutative tori from the formal naive metric. We conclude on some questions related to string theory.Comment: Invited lecture for JMP 2000, 45

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page

Versican but not decorin accumulation is related to malignancy in mammographically detected high density and malignant-appearing microcalcifications in non-palpable breast carcinomas

<p>Abstract</p> <p>Background</p> <p>Mammographic density (MD) and malignant-appearing microcalcifications (MAMCs) represent the earliest mammographic findings of non-palpable breast carcinomas. Matrix proteoglycans versican and decorin are frequently over-expressed in various malignancies and are differently involved in the progression of cancer. In the present study, we have evaluated the expression of versican and decorin in non-palpable breast carcinomas and their association with high risk mammographic findings and tumor characteristics.</p> <p>Methods</p> <p>Three hundred and ten patients with non-palpable suspicious breast lesions, detected during screening mammography, were studied. Histological examination was carried out and the expression of decorin, versican, estrogen receptor α (ERα), progesterone receptor (PR) and c-erbB2 (HER-2/neu) was assessed by immunohistochemistry.</p> <p>Results</p> <p>Histological examination showed 83 out of 310 (26.8%) carcinomas of various subtypes. Immunohistochemistry was carried out in 62/83 carcinomas. Decorin was accumulated in breast tissues with MD and MAMCs independently of the presence of malignancy. In contrast, versican was significantly increased only in carcinomas with MAMCs (median ± SE: 42.0 ± 9.1) and MD (22.5 ± 10.1) as compared to normal breast tissue with MAMCs (14.0 ± 5.8), MD (11.0 ± 4.4) and normal breast tissue without mammographic findings (10.0 ± 2.0). Elevated levels of versican were correlated with higher tumor grade and invasiveness in carcinomas with MD and MAMCs, whereas increased amounts of decorin were associated with <it>in situ </it>carcinomas in MAMCs. Stromal deposition of both proteoglycans was related to higher expression of ERα and PR in tumor cells only in MAMCs.</p> <p>Conclusions</p> <p>The specific accumulation of versican in breast tissue with high MD and MAMCs only in the presence of malignant transformation and its association with the aggressiveness of the tumor suggests its possible use as molecular marker in non-palpable breast carcinomas.</p

Broad targeting of resistance to apoptosis in cancer

Apoptosis or programmed cell death is natural way of removing aged cells from the body. Most of the anti-cancer therapies trigger apoptosis induction and related cell death networks to eliminate malignant cells. However, in cancer, de-regulated apoptotic signaling, particularly the activation of an anti-apoptotic systems, allows cancer cells to escape this program leading to uncontrolled proliferation resulting in tumor survival, therapeutic resistance and recurrence of cancer. This resistance is a complicated phenomenon that emanates from the interactions of various molecules and signaling pathways. In this comprehensive review we discuss the various factors contributing to apoptosis resistance in cancers. The key resistance targets that are discussed include (1) Bcl-2 and Mcl-1 proteins; (2) autophagy processes; (3) necrosis and necroptosis; (4) heat shock protein signaling; (5) the proteasome pathway; (6) epigenetic mechanisms; and (7) aberrant nuclear export signaling. The shortcomings of current therapeutic modalities are highlighted and a broad spectrum strategy using approaches including (a) gossypol; (b) epigallocatechin-3-gallate; (c) UMI-77 (d) triptolide and (e) selinexor that can be used to overcome cell death resistance is presented. This review provides a roadmap for the design of successful anti-cancer strategies that overcome resistance to apoptosis for better therapeutic outcome in patients with cancer

Alternative Splicing and Nonsense-Mediated RNA Decay Contribute to the Regulation of SHOX Expression

The human SHOX gene is composed of seven exons and encodes a paired-related homeodomain transcription factor. SHOX mutations or deletions have been associated with different short stature syndromes implying a role in growth and bone formation. During development, SHOX is expressed in a highly specific spatiotemporal expression pattern, the underlying regulatory mechanisms of which remain largely unknown. We have analysed SHOX expression in diverse embryonic, fetal and adult human tissues and detected expression in many tissues that were not known to express SHOX before, e.g. distinct brain regions. By using RT-PCR and comparing the results with RNA-Seq data, we have identified four novel exons (exon 2a, 7-1, 7-2 and 7-3) contributing to different SHOX isoforms, and also established an expression profile for the emerging new SHOX isoforms. Interestingly, we found the exon 7 variants to be exclusively expressed in fetal neural tissues, which could argue for a specific role of these variants during brain development. A bioinformatical analysis of the three novel 3′UTR exons yielded insights into the putative role of the different 3′UTRs as targets for miRNA binding. Functional analysis revealed that inclusion of exon 2a leads to nonsense-mediated RNA decay altering SHOX expression in a tissue and time specific manner. In conclusion, SHOX expression is regulated by different mechanisms and alternative splicing coupled with nonsense-mediated RNA decay constitutes a further component that can be used to fine tune the SHOX expression level