37 resultados para Semigroups of Operators
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For many years a combined analysis of pionic hydrogen and deuterium atoms has been known as a good tool to extract information on the isovector and especially on the isoscalar s-wave pN scattering length. However, given the smallness of the isoscalar scattering length, the analysis becomes useful only if the pion–deuteron scattering length is controlled theoretically to a high accuracy comparable to the experimental precision. To achieve the required few-percent accuracy one needs theoretical control over all isospin-conserving three-body pNN !pNN operators up to one order before the contribution of the dominant unknown (N†N)2pp contact term. This term appears at next-to-next-to-leading order in Weinberg counting. In addition, one needs to include isospin-violating effects in both two-body (pN) and three-body (pNN) operators. In this talk we discuss the results of the recent analysis where these isospin-conserving and -violating effects have been carefully taken into account. Based on this analysis, we present the up-to-date values of the s-wave pN scattering lengths.
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A close to native structure of bulk biological specimens can be imaged by cryo-electron microscopy of vitreous sections (CEMOVIS). In some cases structural information can be combined with X-ray data leading to atomic resolution in situ. However, CEMOVIS is not routinely used. The two critical steps consist of producing a frozen section ribbon of a few millimeters in length and transferring the ribbon onto an electron microscopy grid. During these steps, the first sections of the ribbon are wrapped around an eyelash (unwrapping is frequent). When a ribbon is sufficiently attached to the eyelash, the operator must guide the nascent ribbon. Steady hands are required. Shaking or overstretching may break the ribbon. In turn, the ribbon immediately wraps around itself or flies away and thereby becomes unusable. Micromanipulators for eyelashes and grids as well as ionizers to attach section ribbons to grids were proposed. The rate of successful ribbon collection, however, remained low for most operators. Here we present a setup composed of two micromanipulators. One of the micromanipulators guides an electrically conductive fiber to which the ribbon sticks with unprecedented efficiency in comparison to a not conductive eyelash. The second micromanipulator positions the grid beneath the newly formed section ribbon and with the help of an ionizer the ribbon is attached to the grid. Although manipulations are greatly facilitated, sectioning artifacts remain but the likelihood to investigate high quality sections is significantly increased due to the large number of sections that can be produced with the reported tool.
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INTRODUCTION Hemodynamic management in intensive care patients guided by blood pressure and flow measurements often do not sufficiently reveal common hemodynamic problems. Trans-esophageal echocardiography (TEE) allows for direct measurement of cardiac volumes and function. A new miniaturized probe for TEE (mTEE) potentially provides a rapid and simplified approach to monitor cardiac function. The aim of the study was to assess the feasibility of hemodynamic monitoring using mTEE in critically ill patients after a brief operator training period. METHODS In the context of the introduction of mTEE in a large ICU, 14 ICU staff specialists with no previous TEE experience received six hours of training as mTEE operators. The feasibility of mTEE and the quality of the obtained hemodynamic information were assessed. Three standard views were acquired in hemodynamically unstable patients: 1) for assessment of left ventricular function (LV) fractional area change (FAC) was obtained from a trans-gastric mid-esophageal short axis view, 2) right ventricular (RV) size was obtained from mid-esophageal four chamber view, and 3) superior vena cava collapsibility for detection of hypovolemia was assessed from mid-esophageal ascending aortic short axis view. Off-line blinded assessment by an expert cardiologist was considered as a reference. Inter-rater agreement was assessed using Chi-square tests or correlation analysis as appropriate. RESULTS In 55 patients, 148 mTEE examinations were performed. Acquisition of loops in sufficient quality was possible in 110 examinations for trans-gastric mid-esophageal short axis, 118 examinations for mid-esophageal four chamber and 125 examinations for mid-esophageal ascending aortic short axis view. Inter-rater agreement (Kappa) between ICU mTEE operators and the reference was 0.62 for estimates of LV function, 0.65 for RV dilatation, 0.76 for hypovolemia and 0.77 for occurrence of pericardial effusion (all P < 0.0001). There was a significant correlation between the FAC measured by ICU operators and the reference (r = 0.794, P (one-tailed) < 0.0001). CONCLUSIONS Echocardiographic examinations using mTEE after brief bed-side training were feasible and of sufficient quality in a majority of examined ICU patients with good inter-rater reliability between mTEE operators and an expert cardiologist. Further studies are required to assess the impact of hemodynamic monitoring by mTEE on relevant patient outcomes.
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Lesions of the ventromedial prefrontal cortex can result in a deficient decision-making behavior. So far, most experimental results in the neuropsychological decision-making research have been obtained with gambling tasks. Due to their high complexity, it is difficult to evaluate the underlying processes of the decision-making deficits. The aim of this study was to assess if patients with ventromedial prefrontal damage compared to patients with dorsolateral prefrontal damage and controls show a deficit in an early stage of the decision-making process. Nine patients with ventromedial prefrontal damage, three with dorsolateral prefrontal damage, and eleven healthy controls were tested with a newly developed decision task in which they had to search actively for the information they needed for their decisions. Our results show that patients with ventromedial prefrontal damage compared to the brain-lesioned dorsolateral prefrontal control group and healthy controls searched less for information with regard to risk defusing operators or consequences of their decisions indicating impairment already in the early stage of the decision-making process.
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Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.
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We consider black probes of Anti-de Sitter and Schrödinger spacetimes embedded in string theory and M-theory and construct perturbatively new black hole geometries. We begin by reviewing black string configurations in Anti-de Sitter dual to finite temperature Wilson loops in the deconfined phase of the gauge theory and generalise the construction to the confined phase. We then consider black strings in thermal Schrödinger, obtained via a null Melvin twist of the extremal D3-brane, and construct three distinct types of black string configurations with spacelike as well as lightlike separated boundary endpoints. One of these configurations interpolates between the Wilson loop operators, with bulk duals defined in Anti-de Sitter and another class of Wilson loop operators, with bulk duals defined in Schrödinger. The case of black membranes with boundary endpoints on the M5-brane dual to Wilson surfaces in the gauge theory is analysed in detail. Four types of black membranes, ending on the null Melvin twist of the extremal M5-brane exhibiting the Schrödinger symmetry group, are then constructed. We highlight the differences between Anti-de Sitter and Schrödinger backgrounds and make some comments on the properties of the corresponding dual gauge theories.
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We study lepton flavor observables in the Standard Model (SM) extended with all dimension-6 operators which are invariant under the SM gauge group. We calculate the complete one-loop predictions to the radiative lepton decays μ → eγ, τ → μγ and τ → eγ as well as to the closely related anomalous magnetic moments and electric dipole moments of charged leptons, taking into account all dimension-6 operators which can generate lepton flavor violation. Also the 3-body flavor violating charged lepton decays τ ± → μ ± μ + μ −, τ ± → e ± e + e −, τ ± → e ± μ + μ −, τ ± → μ ± e + e −, τ ± → e ∓ μ ± μ ±, τ ± → μ ∓ e ± e ± and μ ± → e ± e + e − and the Z 0 decays Z 0 → ℓ+iℓ−j are considered, taking into account all tree-level contributions.
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We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson’s classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.
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BACKGROUND There is great variability for the type of anaesthesia used during TAVI, with no clear consensus coming from comparative studies or guidelines. We sought to detect regional differences in the anaesthetic management of patients undergoing transcatheter aortic valve implantation (TAVI) in Europe and to evaluate the relationship between type of anaesthesia and in-hospital and 1year outcome. METHODS Between January 2011 and May 2012 the Sentinel European TAVI Pilot Registry enrolled 2807 patients treated via a transfemoral approach using either local (LA-group, 1095 patients, 39%) or general anaesthesia (GA-group, 1712 patients, 61%). RESULTS A wide variation in LA use was evident amongst the 10 participating countries. The use of LA has increased over time (from a mean of 37.5% of procedures in the first year, to 57% in last 6months, p<0.01). MI, major stroke as well as in-hospital death rate (7.0% LA vs 5.3% GA, p=0.053) had a similar incidence between groups, confirmed in multivariate regression analysis after adjusting for confounders. Dividing our population in tertiles according to the Log-EuroSCORE we found similar mortality under LA, whilst mortality was higher in the highest risk tertile under GA. Survival at 1year, compared by Kaplan-Meier analysis, was similar between groups (log-rank: p=0.1505). CONCLUSIONS Selection of anaesthesia appears to be more influenced by national practice and operator preference than patient characteristics. In the absence of an observed difference in outcomes for either approach, there is no compelling argument to suggest that operators and centres should change their anaesthetic practice.
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Background Concurrent cardiac diseases are frequent among elderly patients and invite simultaneous treatment to ensure an overall favourable patient outcome. Aim To investigate the feasibility of combined single-session percutaneous cardiac interventions in the era of transcatheter aortic valve implantation (TAVI). Methods This prospective, case–control study included 10 consecutive patients treated with TAVI, left atrial appendage occlusion and percutaneous coronary interventions. Some in addition had patent foramen ovale or atrial septal defect closure in the same session. The patients were matched in a 1:10 manner with TAVI-only cases treated within the same time period at the same institution regarding their baseline factors. The outcome was validated according to the Valve Academic Research Consortium (VARC) criteria. Results Procedural time (126±42 vs 83±40 min, p=0.0016), radiation time (34±8 vs 22±12 min, p=0.0001) and contrast dye (397±89 vs 250±105 mL, p<0.0001) were higher in the combined intervention group than in the TAVI-only group. Despite these drawbacks, no difference in the VARC endpoints was evident during the in-hospital period and after 30 days (VARC combined safety endpoint 32% for TAVI only and 20% for combined intervention, p=1.0). Conclusions Transcatheter treatment of combined cardiac diseases is feasible even in a single session in a high-volume centre with experienced operators.
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With the current growth of mobile devices usage, mobile net- works struggle to deliver content with an acceptable Quality of Experience. In this paper, we propose the integration of Information Centric Networking into 3GPP Long Term Evolution mobile networks, allowing its inherent caching feature to be explored in close proximity to the end users by deploying components inside the evolved Node B. Apart from the advantages brought by Information-Centric Networking’s content requesting paradigm, its inherent caching features enable lower latencies to access content and reduce traffic at the core network. Results show that the impact on the evolved Node B performance is low and ad- vantages coming from Information-Centric Networking are considerable. Thus, mobile network operators reduce operational costs and users end up with a higher perceived network quality even in peak utilization periods.
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We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.
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We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.
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We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.
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We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.