First principle calculation of the QCD spectral functions (SPFs) based on the lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian inference theory and the Maximum Entropy Method (MEM), which is a useful tool to extract SPFs from the imaginary-time correlation functions numerically obtained by the Monte Carlo method. Three important aspects of MEM are (i) it does not require a priori assumptions or parametrizations of SPFs, (ii) for given data, a unique solution is obtained if it exists, and (iii) the statistical significance of the solution can be quantitatively analyzed.The ability of MEM is explicitly demonstrated by using mock data as well as lattice QCD data. When applied to lattice data, MEM correctly reproduces the low-energy resonances and shows the existence of high-energy continuum in hadronic correlation functions. This opens up various possibilities for studying hadronic properties in QCD beyond the conventional way of analyzing the lattice data. Future problems to be studied by MEM in lattice QCD are also summarized.
QCD spectral functions of hadrons in the pseudoscalar and vector channels are extracted from lattice Monte Carlo data of the imaginary time Green's functions. The maximum entropy method works well for this purpose, and the resonance and continuum structures in the spectra are obtained in addition to the ground state peaks. ͓S0556-2821͑99͒50119-7͔ PACS number͑s͒: 12.38. Gc, 12.38.Aw Among various dynamical quantities in quantum chromodynamics ͑QCD͒, the spectral functions ͑SPFs͒ of hadrons play a special role in physical observables ͑see, e.g. ͓1,2͔͒. A well-known example is the cross section of the e ϩ e Ϫ annihilation into hadrons, which can be expressed by SPF in the vector channel. SPF at finite temperature ͑T͒ and/or baryon density is also a key concept to understand the medium modification of hadrons ͓3͔. The enhancement in low-mass dileptons observed in relativistic heavy ion collisions at the CERN Super Proton Synchrotron ͑SPS͒ ͓4͔ is a typical example which may indicate a spectral shift in the medium ͓5͔.However, the Monte Carlo simulations of QCD on the lattice, which have been successful in measuring static observables ͓6͔, have difficulties in accessing the dynamical quantities in the Minkowski space such as SPFs and the real time correlation functions. This is because measurements on the lattice can only be carried out for discrete points in imaginary time. The analytic continuation from the imaginary time to the real time using the finite number of lattice data with noise is highly nontrivial and is even classified as an ill-posed problem.In this paper, we make a first serious attempt to extract SPFs of hadrons from lattice QCD data without making a priori assumptions on the spectral shape. For this purpose, we use the maximum entropy method ͑MEM͒, which has been successfully applied for similar problems in quantum Monte Carlo simulations in condensed matter physics, image reconstruction in crystallography and astrophysics, and so forth ͓7,8͔. Due to the limitation of space, we present only the results for the pseudoscalar ͑PS͒ and vector ͑V͒ channels at Tϭ0. The results for other channels will be given in ͓9͔.The Euclidean correlation function D() of an operator O(,x ជ ) and its spectral decomposition at zero threemomentum readwhere Ͼ0, is a real frequency, and A() is SPF ͑or sometimes called the image in this paper͒, which is positive semidefinite by definition. The kernel K(,) is proportional to the Fourier transform of a free boson propagator with mass : At Tϭ0, K(,)ϭexp(Ϫ).Monte Carlo simulation provides D( i ) for the discrete set of points 0р i /aрN , where N is the temporal lattice size and a is the lattice spacing. In the actual analysis, we use data points for min р i р max . From this data set with noise, we need to reconstruct the continuous function A() on the right-hand side of ͑1͒, or to make the inverse Laplace transform. This is a typical ill-posed problem, where the number of data is much smaller than the number of degrees of freedom to be reconstructed. This makes the standard l...
We recently identified CD8+CD122+ regulatory T cells that directly control CD8+ and CD4+ cells without intervention of APCs. In this study, we investigated the effector mechanism of CD8+CD122+ regulatory T cells by using an in vitro regulation system. The profile of cytokine expression revealed that IL-10 was predominantly produced by CD8+CD122+ cells, whereas other cytokines were similarly expressed in CD8+CD122+ cells and CD8+CD122− cells. Suppression of both proliferation and IFN-γ production by CD8+CD122− cells by CD8+CD122+ cells was blocked by adding anti-IL-10 Ab to the culture but not by adding anti-TGF-β Ab. When IL-10 was removed from the conditioned medium from CD8+CD122+ cells, the conditioned medium no longer showed regulatory activity. Finally, CD8+CD122+ cells from IL-10-deficient mice had no regulatory activity in vitro and reduced regulatory activity in vivo. Our results clearly indicate that IL-10 is produced by CD8+CD122+ cells and mediates the regulatory activity of these cells.
Tissues and organs consist of a complex organization of cells, extracellular matrix (ECM), and signaling molecules. In particular, blood vessels and skin are a highly organized hierarchical layer composed of various types of cells and ECM layers. The construction in vitro of three-dimensional (3D) cell-polymeric material composites has created notable advances in tissue regeneration.[1] However, an effective methodology to fabricate a 3D multilayer composed of cells and an ECM layer with the appropriate components and thickness has not yet been achieved. Recently, new technologies such as a cell sheet, [2a] magnetic liposomes, [2b] and a chitosan membrane [2c] have been reported to fabricate layered tissues. Although these methods are intriguing, complicated manipulation is required and the thickness of the ECM layer is not controllable.We focused on a layer-by-layer (LbL) technique, which is an appropriate method to prepare nanometer-sized films on a substrate through the alternate immersion into interactive polymer solutions.[3] The preparation of nanometer-sized multilayer films composed of ECM components on the surface of the first layer of cells provides a cell-adhesive surface for the second layer of cells. Rajagopalan et al. demonstrated a bilayer structure composed of hepatocytes and other cells by preparing a polyelectrolyte multilayer consisting of chitosan and DNA on the hepatocyte surface.[4a]However, chitosan cannot dissolve in neutral buffer solutions and fabrication of polyelectrolyte multilayers onto the cell surface is limited owing to the cytotoxicity of polycations. [4b,c] Furthermore, a highly organized cellular multilayer with more than three layers will be required for the creation of functional artificial tissues that are similar to natural tissues. The use of natural ECM components for nanofilms is significant because the typical ECM presents with celladhesive moieties such as RGD (arginine-glycine-aspartic acid) and other amino acid sequences for cellular functions. [5] In the present study, fibronectin (FN) and gelatin were selected to prepare nanometer-sized ECM films (nano-ECM film) on the cell surface. FN is a flexible multifunctional glycoprotein that plays an important role in cell attachment, migration, differentiation, etc. [6a,b] FN is well known to interact not only with a variety of ECM proteins, such as collagens (gelatins) and glycosaminoglycans, but also with the a 5 b 1 integrin receptor on the cell surface.[6c] Recently, we reported FN-based protein multilayers composed of FN and ECM components, such as gelatin, heparin, and elastin, constructed by LbL assembly.[7] Although FN and gelatin have a negative charge under physiological conditions, they interact with each other because FN has a collagen binding domain.[6b] The preparation of FN-gelatin nanofilms on the surface of the first layer of cells will provide a suitable celladhesive surface that is similar to the natural ECM for the second layer of cells. Herein, we report well-organized, fourlayered architectures...
We extract the spectral functions in the scalar, pseudo-scalar, vector, and axial-vector channels above the deconfinement phase transition temperature (Tc) using the maximum entropy method (MEM). We use anisotropic lattices, 32 3 × 32, 40, 54, 72, 80, and 96 (corresponding to T = 2.3Tc → 0.8Tc), with the renormalized anisotropy ξ = 4.0 to have enough temporal data points to carry out the MEM analysis. Our result suggests that the spectral functions continue to possess non-trivial structures even above Tc and in addition that there is a qualitative change in the state of the deconfined matter between 1.5Tc and 2Tc.
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