An alternative attractor in gauged NJL inflation

We have investigated the attractor structure for the CMB fluctuations in composite inflation scenario within the gauged Nambu-Jona-Lasinio (NJL) model. Such composite inflation represents an attractor which can not be found in a fundamental scalar model. As is known, the number of inflationary models contains the attractor classified by the $\alpha$-attractor model. It is found that the attractor inflation in the gauged NJL model corresponds to the $\alpha = 2$ case.Comment: 7 pages, 2 figure

A Space-Optimal Grammar Compression

A grammar compression is a context-free grammar (CFG) deriving a single string deterministically. For an input string of length N over an alphabet of size sigma, the smallest CFG is O(log N)-approximable in the offline setting and O(log N log^* N)-approximable in the online setting. In addition, an information-theoretic lower bound for representing a CFG in Chomsky normal form of n variables is log (n!/n^sigma) + n + o(n) bits. Although there is an online grammar compression algorithm that directly computes the succinct encoding of its output CFG with O(log N log^* N) approximation guarantee, the problem of optimizing its working space has remained open. We propose a fully-online algorithm that requires the fewest bits of working space asymptotically equal to the lower bound in O(N log log n) compression time. In addition we propose several techniques to boost grammar compression and show their efficiency by computational experiments

Robustness of predicted CMB fluctuations in Cartan F(R)F(R) gravity

The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. This is called Cartan $F(R)$ gravity. The well-known $F(R)$ gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.Comment: 14pages, 4figure

Phase Structure of a Four- and Eight-Fermion Interaction Model at Finite Temperature and Chemical Potential in Arbitrary Dimensions

The phase structure of a four- and eight-fermion interaction model is investigated at finite temperature and chemical potential in arbitrary space-time dimensions, $2\leq D<4$. The effective potential and the gap equation are calculated in the leading order of the 1/N expansion. If the first order phase transition takes place, the phase boundary dividing the symmetric and the broken phase is modified by the eight-fermion interaction.Comment: 20 pages, 26 figures; revised argument and added reference for section

Vacuum Effects and Compressional Properties of Nuclear Matter in Cutoff Field Theory

Including the vacuum effects, the compressional properties of nuclear matter are studied in the cutoff field theory. Under the Hartree approximation, the low-energy effective Lagrangian is derived in the framework of the renormalization group methods. The coefficients are determined in a way where the physical results hardly depend on the value of the cutoff which is conveniently introduced into the theory. It is shown that, to reproduce the empirical data of the nucleus incompressibility, the compressibility of the nuclear matter is favorable to be 250$\sim$350MeV.Comment: PACS numbers, 21.65.+

High-grade Glioma Masquerading as a Small Cerebral Hemorrhage: A Case Report

We report a rare case of a high-grade glioma masquerading as a small subcortical hemorrhage. A 71-year-old woman came to a local hospital with sudden right upper extremity numbness. Computed tomography revealed a small subcortical hemorrhage with faint perifocal edema in the left postcentral gyrus. Conservative treatment was initiated, and she was discharged from the hospital with no neurological deficits. Six months later after discharge, she suffered an acute partial seizure of the right upper extremity. Magnetic resonance imaging with gadolinium demonstrated a ring-enhancing mass surrounded by severe perifocal edema in the hemorrhagic scar. We performed complete resection of the tumor, and the histological diagnosis was anaplastic oligodendroglioma. The diagnosis of a high-grade glioma was delayed due to intratumoral hemorrhages mimicking a small subcortical hemorrhage; consequently, we suspected the hemorrhage was induced by cerebral amyloid angiopathy. It may be important to repeat radiological follow up, if necessary, and to maintain clinical observance of possible intracranial neoplasm, even when the hemorrhage is small, particularly when the cause of bleeding is unknown