This study investigated in eight healthy male volunteers ( a) the gastric emptying pattern of 50 and 100 grams of glucose; (b) its relation to the phase of interdigestive motility (phase I or II) existing when glucose was ingested; and (c) the interplay between gastric emptying or duodenal perfusion of glucose (1.1 and 2.2 kcal/min; identical total glucose loads as orally given) and release of glucose-dependent insulinotropic peptide (GIP), glucagon-like peptide-1(7-36)amide (GLP-1), C-peptide, insulin, and plasma glucose. The phase of interdigestive motility existing at the time of glucose ingestion did not affect gastric emptying or any metabolic parameter. Gastric emptying of glucose displayed a power exponential pattern with a short initial lag period. Duodenal delivery of glucose was not constant but exponentially declined over time. Increasing the glucose load reduced the rate of gastric emptying by 27.5% (P Ͻ 0.05) but increased the fractional duodenal delivery of glucose. Both glucose loads induced a fed motor pattern which was terminated by an antral phase III when ‫ف‬ 95% of the meal had emptied. Plasma GLP-1 rose from basal levels of ‫ف‬ 1 pmol/liter to peaks of 3.2 Ϯ 0.6 pmol/liter with 50 grams of glucose and of 7.2 Ϯ 1.6 pmol/ liter with 100 grams of glucose. These peaks occurred 20 min after glucose intake irrespective of the load. A duodenal delivery of glucose exceeding 1.4 kcal/min was required to maintain GLP-1 release in contrast to ongoing GIP release with negligibly low emptying of glucose. Oral administration of glucose yielded higher GLP-1 and insulin releases but an equal GIP release compared with the isocaloric duodenal perfusion. We conclude that ( a) gastric emptying of glucose displays a power exponential pattern with duodenal delivery exponentially declining over time and (b) a threshold rate of gastric emptying of glucose must be exceeded to release GLP-1, whereas GIP release is not con-

Microtubule‐associated protein tau is the major constituent of the paired helical filament, the main fibrous component of the neurofibrillary lesions of Alzheimer's disease. Tau is an axonal phosphoprotein in normal adult brain. In Alzheimer's disease brain tau is hyperphosphorylated and is found not only in axons, but also in cell bodies and dendrites of affected nerve cells. We report the production and analysis of transgenic mice that express the longest human brain tau isoform under the control of the human Thy‐1 promoter. As in Alzheimer's disease, transgenic human tau protein was present in nerve cell bodies, axons and dendrites; moreover, it was phosphorylated at sites that are hyperphosphorylated in paired helical filaments. We conclude that transgenic human tau protein showed pre‐tangle changes similar to those that precede the full neurofibrillary pathology in Alzheimer's disease.

We have studied the impact of non-local electronic correlations at all length scales on the MottHubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed. Introduction.The Mott-Hubbard metal-insulator transition (MIT) [1] is one of the most fundamental hallmarks of the physics of electronic correlations. Nonetheless, astonishingly little is known exactly, even for its simplest modeling, i.e., the single-band Hubbard Hamiltonian [2]: Exact solutions for this model are available only in the extreme, limiting cases of one and infinite dimensions.In one dimension (1D), the Bethe ansatz shows that there is actually no Mott-Hubbard transition [3][4][5]; or, in other words, it occurs for a vanishingly small Hubbard interaction U : At any U > 0 the 1D-Hubbard model is insulating at half filling. One dimension is, however, rather peculiar: While there is no antiferromagnetic ordering even at temperature T = 0, antiferromagnetic spin fluctuations are strong and long-ranged, decaying slowly, i.e., algebraically. Also the (doped) metallic phase is not a standard Fermi liquid but a Luttinger liquid.For the opposite extreme, infinite dimensions, the dynamical mean field theory (DMFT) [6] becomes exact [7], which allows for a clear-cut and -to a certain extentalmost "idealized" description of a pure Mott-Hubbard MIT. In fact, since in D = ∞ only local correlations survive [7], the Mott-Hubbard insulator of DMFT consists of a collection of localized (but not long-range ordered) magnetic moments. This way, if antiferromagnetic order is neglected or sufficiently suppressed, DMFT describes a first-order MIT [6,8], ending with a critical endpoint.As an approximation, DMFT is applicable to the more realistic cases of the three-and two-dimensional Hubbard models. However, the DMFT description of the MIT is the very same here, since only the non-interacting density of states (DOS) and in particular its second moment enter. This is a natural shortcoming of the mean-field nature of DMFT: antiferromagnetic fluctuations have no effect at all on the DMFT spectral function or self-energy above the antiferromagnetic ordering temperature T N .In 3D, antiferromagnetic fluctuations reduce T N siz-

Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first nonperturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. In the low-temperature limit this occurs for interaction values where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic limit.

We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength. Introduction.-Correlated electron systems display some of the most fascinating phenomena in condensed matter physics, but their understanding still represents a formidable challenge for theory and experiments. For photoemission [1] or STM [2,3] spectra, which measure single-particle quantities, information about correlation is encoded in the electronic self-energy Σ. However, due to the intrinsically many-body nature of the problems, even an exact knowledge of Σ is not sufficient for an unambiguous identification of the underlying physics. A perfect example of this is the pseudogap observed in the single-particle spectral functions of underdoped cuprates [4], and, more recently, of their nickelate analogues [5]. Although relying on different assumptions, many theoretical approaches provide self-energy results compatible with the experimental spectra. This explains the lack of a consensus about the physical origin of the pseudogap: In the case of cuprates, the pseudogap has been attributed to spin fluctuations [6-10], preformed pairs [11][12][13][14][15], Mottness [16,17], and, recently, to the interplay with charge fluctuations [18][19][20][21] or to Fermi-liquid scenarios [22]. The existence and the role of (d-wave) superconducting fluctuations [11][12][13][14][15] in the pseudogap regime are still openly debated for the basic model of correlated electrons, the Hubbard model.Experimentally, the clarification of many-body physics is augmented by a simultaneous investigation at the two-particle level, i.e., via neutron scattering [23], infrared or optical [24] and pump-probe spectroscopy [25], muon-spin relaxation [26], and correlation or coincidence two-particle spectroscopies [27][28][29]. Analogously, theoretical studies of Σ can also be supplemented by a corresponding analysis at the two-particle level. In this

We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory (DMFT) calculations at the two-particle level. By extending the results of Schäfer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. By comparing our numerical data for the Hubbard model with analytical calculations for exactly solvable systems of increasing complexity [disordered binary mixture (BM), Falicov-Kimball (FK) and atomic limit (AL)], we have (i) identified two different kinds of divergence lines; (ii) classified them in terms of the frequency-structure of the associated singular eigenvectors; (iii) investigated their relation to the emergence of multiple branches in the Luttinger-Ward functional. In this way, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, single energy scale ν * below which perturbation theory is no longer applicable, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Green function, G→G_{0}, is strongly violated, by providing numerous explicit examples of different G_{0} leading to the same physical G. We argue that there are indeed infinitely many such G_{0}, with numerous crossings with the physical solution. We show that this rich functional structure is directly related to the divergence of certain classes of (irreducible vertex) diagrams, with important consequences for traditional many-body physics based on diagrammatic expansions. Physically, we ascribe the onset of these highly nonperturbative manifestations to the progressive suppression of the charge susceptibility induced by the formation of local magnetic moments and/or resonating valence bond (RVB) states in strongly correlated electron systems.

We have implemented the dynamical vertex approximation (D rA ) in its full parquet-based version to include spatial correlations on all length scales and in all scattering channels. The algorithm is applied to study the electronic self-energies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution allow us to evaluate the performance of the DF A algorithm in the most challenging situation of low dimensions. From a physical perspective, our results unveil how nonlocal correlations affect the spectral properties of nanoscopic systems of various sizes in different regimes of interaction strength.