Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Pharmaceutical Polymorph Control in a Drug-Mimetic Supramolecular Gel

We report the synthesis of a bis(urea) gelator designed to specifically mimic the chemical structure of the highly polymorphic drug substance ROY. Crystallization of ROY from toluene gels of this gelator results in the formation of the metastable red form instead of the thermodynamic yellow polymorph. In contrast, all other gels and solution control experimetns give the yellow form. Conformational and crystal structure prediction methods have been used to propose the structure of the gel and shows that the templation of the red form by the targetted gel results from conformational matching of the gelator to the ROY substrate coupled with overgorwth of ROY onto the the local periodic structure of the gel fibres

Dot/Icm Type IVB Secretion System Requirements for Coxiella burnetii Growth in Human Macrophages

Central to Q fever pathogenesis is replication of the causative agent, Coxiella burnetii, within a phagolysosome-like parasitophorous vacuole (PV) in mononuclear phagocytes. C. burnetii modulates PV biogenesis and other host cell functions, such as apoptotic signaling, presumably via the activity of proteins delivered to the host cytosol by a Dot/Icm type IVB secretion system (T4BSS). In this study, we utilized a C. burnetii strain carrying IcmD inactivated by the Himar1 transposon to investigate the requirements for Dot/Icm function in C. burnetii parasitism of human THP-1 macrophage-like cells. The icmD::Tn mutant failed to secrete characterized T4BSS substrates, a defect that correlated with deficient replication, PV development, and apoptosis protection. Restoration of type IVB secretion and intracellular growth of the icmD::Tn mutant required complementation with icmD, -J, and -B, indicating a polar effect of the transposon insertion on downstream dot/icm genes. Induction of icmDJB expression at 1 day postinfection resulted in C. burnetii replication and PV generation. Collectively, these data prove that T4BSS function is required for productive infection of human macrophages by C. burnetii. However, illustrating the metabolic flexibility of C. burnetti, the icmD::Tn mutant could replicate intracellularly when sequestered in a PV generated by wild-type bacteria, where Dot/Icm function is provided in trans, and within a phenotypically similar PV generated by the protozoan parasite Leishmania amazonensis, where host cells are devoid of Dot/Icm T4BSS effector proteins

Dirac's Representation Theory as a Framework for Signal Theory. I. Discrete Finite Signals

We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection operators is stressed. A Dirac space is defined, which is spanned by an orthonormal basis labeled with the time points. An infinite number of orthonormal bases is found which are labeled with frequencies, they are distinguished by the continuous parameter a. In a way, similar to one used in quantum mechanics, self-adjoint operators (observables) and averages (expectation values) are defined. Non orthonormal bases are discussed and it is shown, in an example, that they are less stable compared to the orthonormal ones. A variant of the sampling theorem for finite signals is derived. The aliasing phenomenon is described in the paper in terms of aliasing symmetry. Relations between different bases are derived. The uncertainty principle for finite signals is discussed.Comment: 31 pages (including 3 figures

Dirac's Representation Theory as a Framework for Signal Theory. II. Infinite Duration and Continuous Signals

We generalize previous results and demonstrate that the Dirac representation theory can be effectively adjusted and applied to continuous or discrete signals of infinite time duration. The role of the identity and projection operators is emphasized. The sampling theorem is viewed from the point of view of orthogonal physical states. An orthogonal basis which spanned the time space, ceases to be orthogonal and becomes overcomplete if the domain of frequencies is restricted in a bandwidth. In this case there exists an infinite number of sub-bases of discrete times which are orthogonal and complete. The relation between the overcomplete bases and a complete one is the essence of the sampling theorem. The signal theory is reformulated in the framework of the Dirac bra-kets. The case of signals existing for positive time is treated in detail.Comment: 33 page

A Microbial Strategy to Multiply in Macrophages: The Pregnant Pause

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72518/1/j.1600-0854.2002.030302.x.pd

Quantal time asymmetry: mathematical foundation and physical interpretation

For a quantum theory that includes exponentially decaying states and Breit-Wigner resonances, which are related to each other by the lifetime-width relation $\tau=\frac{\hbar}{\Gamma}$, where $\tau$ is the lifetime of the decaying state and $\Gamma$ the width of the resonance, one has to go beyond the Hilbert space and beyond the Schwartz-Rigged Hilbert Space $\Phi\subset\mathcal{H}\subset\Phi^\times$ of the Dirac formalism. One has to distinguish between prepared states, using a space \Phi_-\subset\mat hcal{H}, and detected observables, using a space $\Phi_+\subset\mathcal{H}$, where $-(+)$ refers to analyticity of the energy wave function in the lower (upper) complex energy semiplane. This differentiation is also justified by causality: A state needs to be prepared first, before an observable can be measured in it. The axiom that will lead to the lifetime-width relation is that $\Phi_+$ and $\Phi_-$ are Hardy spaces of the upper and lower semiplane, respectively. Applying this axiom to the relativistic case for the variable \s=p_\mu p^\mu leads to semigroup transformations into the forward light cone (Einstein causality) and a precise definition of resonance mass and width.Comment: Plenary talk at the 5th International Symposium on Quantum Theory and Symmetries, July 22-28, 2007, Valladolid, Spai

Specific In Vivo Staining of Astrocytes in the Whole Brain after Intravenous Injection of Sulforhodamine Dyes

Fluorescent staining of astrocytes without damaging or interfering with normal brain functions is essential for intravital microscopy studies. Current methods involved either transgenic mice or local intracerebral injection of sulforhodamine 101. Transgenic rat models rarely exist, and in mice, a backcross with GFAP transgenic mice may be difficult. Local injections of fluorescent dyes are invasive. Here, we propose a non-invasive, specific and ubiquitous method to stain astrocytes in vivo. This method is based on iv injection of sulforhodamine dyes and is applicable on rats and mice from postnatal age to adulthood. The astrocytes staining obtained after iv injection was maintained for nearly half a day and showed no adverse reaction on astrocytic calcium signals or electroencephalographic recordings in vivo. The high contrast of the staining facilitates the image processing and allows to quantify 3D morphological parameters of the astrocytes and to characterize their network. Our method may become a reference for in vivo staining of the whole astrocytes population in animal models of neurological disorders

Reuse of medical face masks in domestic and community settings without sacrificing safety: Ecological and economical lessons from the Covid-19 pandemic

The need for personal protective equipment increased exponentially in response to the Covid-19 pandemic. To cope with the mask shortage during springtime 2020, a French consortium was created to find ways to reuse medical and respiratory masks in healthcare departments. The consortium addressed the complex context of the balance between cleaning medical masks in a way that maintains their safety and functionality for reuse, with the environmental advantage to manage medical disposable waste despite the current mask designation as single-use by the regulatory frameworks. We report a Workflow that provides a quantitative basis to determine the safety and efficacy of a medical mask that is decontaminated for reuse. The type IIR polypropylene medical masks can be washed up to 10 times, washed 5 times and autoclaved 5 times, or washed then sterilized with radiations or ethylene oxide, without any degradation of their filtration or breathability properties. There is loss of the antiprojection properties. The Workflow rendered the medical masks to comply to the AFNOR S76-001 standard as “type 1 non-sanitory usage masks”. This qualification gives a legal status to the Workflow-treated masks and allows recommendation for the reuse of washed medical masks by the general population, with the significant public health advantage of providing better protection than cloth-tissue masks. Additionally, such a legal status provides a basis to perform a clinical trial to test the masks in real conditions, with full compliance with EN 14683 norm, for collective reuse. The rational reuse of medical mask and their end-of-life management is critical, particularly in pandemic periods when decisive turns can be taken. The reuse of masks in the general population, in industries, or in hospitals (but not for surgery) has significant advantages for the management of waste without degrading the safety of individuals wearing reused masks