Abstract:
In an unbiased approach to biomarker discovery, we applied a highly multiplexed proteomic technology (SOMAscan, SomaLogic, Inc, Boulder, CO) to understand changes in proteins from paired serum samples at enrollment and after 8 weeks of TB treatment from 39 patients with pulmonary TB from Kampala, Uganda enrolled in the Center for Disease Control and Prevention’s Tuberculosis Trials Consortium (TBTC) Study 29. This work represents the first large-scale proteomic analysis employing modified DNA aptamers in a study of active tuberculosis (TB). We identified multiple proteins that exhibit significant expression differences during the intensive phase of TB therapy. There was enrichment for proteins in conserved networks of biological processes and function including antimicrobial defense, tissue healing and remodeling, acute phase response, pattern recognition, protease/anti-proteases, complement and coagulation cascade, apoptosis, immunity and inflammation pathways. Members of cytokine pathways such as interferon-gamma, while present, were not as highly represented as might have been predicted. The top proteins that changed between baseline and 8 weeks of therapy were TSP4, TIMP-2, SEPR, MRC-2, Antithrombin III, SAA, CRP, NPS-PLA2, LEAP-1, and LBP. The novel proteins elucidated in this work may provide new insights for understanding TB disease, its treatment and subsequent healing processes that occur in response to effective therapy.

Abstract:
The lengthy treatment regimen for tuberculosis is necessary to eradicate a small sub-population of M. tuberculosis that persists in certain host locations under drug pressure. Limited information is available on persisting bacilli and their location within the lung during disease progression and after drug treatment. Here we provide a comprehensive histopathological and microscopic evaluation to elucidate the location of bacterial populations in animal models for TB drug development.

Abstract:
In this paper we start with the development of a theory of presheaves on a lattice, in particular on the quantum lattice $\LL(\kH)$ of closed subspaces of a complex Hilbert space $\kH$, and their associated etale spaces. Even in this early state the theory has interesting applications to the theory of operator algebras and the foundations of quantum mechanics. Among other things we can show that classical observables (continuous functions on a topological space) and quantum observables (selfadjoint linear operators on a Hilbert space) are on the same structural footing.

Abstract:
\noindent{In} this paper, we clarify the structure of the Stone spectrum of an arbitrary finite von Neumann algebra $\rr$ of type $\rm{I}_{n}$. The main tool for this investigation is a generalized notion of rank for projections in von Neumann algebras of this type.

Abstract:
In this fourth of our series of papers on observables we show that one can associate to each von Neumann algebra R a pair of isomorphic presheaves, the upper presheaf O^{+}_{R} and the lower presheaf O^{-}_{R}, on the category of abelian von Neumann subalgebras of R. Each $A \in R_{sa}$ induces a global section of O^{+}_{R} and of O^{-}_{R} respectively. We call them \emph {contextual observables}. But we show that, in general, not every global section of these presheaves arises in this way. Moreover, we discuss states of a von Neumann algebra in the presheaf context.

Abstract:
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background structure for quantum and classical observables. Moreover, a contextual generalization of the notion of quantum observable is proposed.

Abstract:
Let R be a von Neumann algebra acting on a Hilbert space H and let R_sa be the set of selfadjoint elements of R. It is well known that R_sa is a lattice with respect to the usual partial order ≤ if and only if R is abelian. We define and study a new partial order on R_sa, the spectral order ≤_s, which extends ≤ on projections, is coarser than the usual one, but agrees with it on abelian subalgebras, and turns R_sa into a boundedly complete lattice. The effect algebra E(R) := {A | 0 ≤ A ≤ I} is then a complete lattice and we show that the mapping A --> R(A), where R(A) denotes the range projection of A, is a homomorphism from the lattice E(R) onto the projection lattice P(R) of A if and only if R is a finite von Neumann algebra.

Abstract:
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's approach to) quantum physics, an observable is represented as a bonded selfadjoint operator on Hilbert space. We will show in part II of this work that there is a common structure behind these two different concepts. If $\mathcal{R}$ is a von Neumann algebra, a selfadjoint element $A \in \mathcal{R}$ induces a continuous function $f_{A} : \mathcal{Q}(\mathcal{P(R)}) \to \mathbb{R}$ defined on the \emph{Stone spectrum} $\mathcal{Q}(\mathcal{P(R)})$ of the lattice $\mathcal{P(R)}$ of projections in $\mathcal{R}$. The Stone spectrum $\mathcal{Q}(\mathbb{L})$ of a general lattice $\mathbb{L}$ is the set of maximal dual ideals in $\mathbb{L}$, equipped with a canonical topology. $\mathcal{Q}(\mathbb{L})$ coincides with Stone's construction if $\mathbb{L}$ is a Boolean algebra (thereby ``Stone'') and is homeomorphic to the Gelfand spectrum of an abelian von Neumann algebra $\mathcal{R}$ in case of $\mathbb{L} = \mathcal{P(R)}$ (thereby ``spectrum'').

Abstract:
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's approach to) quantum physics, an observable is represented as a bonded selfadjoint operator on Hilbert space. We will show in the present part II and the forthcoming part III of this work that there is a common structure behind these two different concepts. If $\mathcal{R}$ is a von Neumann algebra, a selfadjoint element $A \in \mathcal{R}$ induces a continuous function $f_{A} : \mathcal{Q}(\mathcal{P(R)}) \to \mathbb{R}$ defined on the \emph{Stone spectrum} $\mathcal{Q}(\mathcal{P(R)})$ (\cite{deg3}) of the lattice $\mathcal{P(R)}$ of projections in $\mathcal{R}$. $f_{A}$ is called the observable function corresponding to $A$. The aim of this part is to study observable functions and its various characterizations.

Abstract:
In the second part of our work on observables we have shown that quantum observables in the sense of von Neumann, i.e.bounded selfadjoint operators in some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded continuous functions on the Stone spectrum $Q(R)$ of $R$. Moreover, we have shown that this representation is linear if and only if $R$ is abelian, and that in this case it coincides with the Gelfand transformation of $R$. In this part we discuss classical observables, i.e. measurable and continuous functions, under the same point of view. We obtain results that are quite similar to the quantum case, thus showing up the common structural features of quantum and classical observables.