Exact renormalization group equation for the Lifshitz critical point

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the $O(\epsilon ^{2})$ calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations $O(\epsilon)$ finally unstable.Comment: Final versio

Flow Equations for U_k and Z_k

By considering the gradient expansion for the wilsonian effective action S_k of a single component scalar field theory truncated to the first two terms, the potential U_k and the kinetic term Z_k, I show that the recent claim that different expansion of the fluctuation determinant give rise to different renormalization group equations for Z_k is incorrect. The correct procedure to derive this equation is presented and the set of coupled differential equations for U_k and Z_k is definitely established.Comment: 5 page

Wegner-Houghton equation and derivative expansion

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic coefficient $Z_k$, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differential equation for $Z_k$, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the $Z_k$ equation are obtained. Finally a numerical analysis of the coupled equations for $U_k$ and $Z_k$ is performed at the non-gaussian fixed point in $D<4$ dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure

Stability of a cubic fixed point in three dimensions. Critical exponents for generic N

The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D) within an assumption of isotropic exchange. Perturbative expansions for RG functions are calculated for arbitrary $N$ up to the four-loop order and resummed by means of the generalized Pad$\acute{\rm e}$-Borel-Leroy technique. Coordinates and stability matrix eigenvalues for the cubic fixed point are found under the optimal value of the transformation parameter. Critical dimensionality of the model is proved to be equal to $N_c=2.89 \pm 0.02$ that agrees well with the estimate obtained on the basis of the five-loop \ve-expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B342, 284 (1995)] resummed by the above method. As a consequence, the cubic fixed point should be stable in 3D for $N\ge3$, and the critical exponents controlling phase transitions in three-dimensional magnets should belong to the cubic universality class. The critical behavior of the random Ising model being the nontrivial particular case of the cubic model when N=0 is also investigated. For all physical quantities of interest the most accurate numerical estimates with their error bounds are obtained. The results achieved in the work are discussed along with the predictions given by other theoretical approaches and experimental data.Comment: 33 pages, LaTeX, 7 PostScript figures. Final version corrected and added with an Appendix on the six-loop stud

Goal-directed and habitual control in the basal ganglia: implications for Parkinson's disease

Progressive loss of the ascending dopaminergic projection in the basal ganglia is a fundamental pathological feature of Parkinson's disease. Studies in animals and humans have identified spatially segregated functional territories in the basal ganglia for the control of goal-directed and habitual actions. In patients with Parkinson's disease the loss of dopamine is predominantly in the posterior putamen, a region of the basal ganglia associated with the control of habitual behaviour. These patients may therefore be forced into a progressive reliance on the goal-directed mode of action control that is mediated by comparatively preserved processing in the rostromedial striatum. Thus, many of their behavioural difficulties may reflect a loss of normal automatic control owing to distorting output signals from habitual control circuits, which impede the expression of goal-directed action. © 2010 Macmillan Publishers Limited. All rights reserved

O6-methylguanine DNA methyltransferase (MGMT) expression in U1242 glioblastoma cells enhances in vitro clonogenicity, tumor implantation in vivo, and sensitivity to alisertib-carboplatin combination treatment

Glioblastoma (GBM) is the most common and aggressive primary adult CNS tumor. Increased understanding of glioma biology is needed for novel treatment strategies and maximization of current therapies. The action of the widely used antiglioma drug, temozolomide (TMZ), relies on its ability to methylate DNA guanine bases leading to DNA double strand breaks and apoptosis. However, glioma cells capable of reversing guanine methylation via the repair enzyme O6-methylguanine DNA methyltransferase (MGMT) are resistant to TMZ. GBMs exhibiting high MGMT expression, reflected by MGMT gene promoter hypomethylation, respond poorly to both chemo- and radiation therapy. To investigate possible non-canonical biological effects of MGMT and develop a tool to investigate drug sensitivity and resistance, we generated MGMT knockout (KO) U1242 GBM cells. MGMT KO U1242 cells showed substantially increased sensitivity to TMZ in vivo, and unlike wildtype U1242 cells, failed to form tumors in nude mouse brains. They also showed reduced growth in soft agar, as did wildtype U1242 and additional glioma cell lines in which MGMT expression was knocked down by siRNA. MGMT thus possesses cellular functions related to tumor cell engraftment and anchorage-independent growth beyond guanine methyltransferase repair. We additionally show that the combination of the AURKA inhibitor alisertib and carboplatin selectively induces apoptosis in high MGMT expressing wildtype U1242 cells versus MGMT KO U1242 cells and extends survival of mice orthotopically implanted with wildtype U1242 cells. This or other platinum-based drug combinations may represent a potentially effective treatment approach to chemotherapy for GBM with MGMT promoter hypomethylation

Resolved Psychosis after Liver Transplantation in a Patient with Wilson’s Disease

A psychiatric involvement is frequently present in Wilson’s disease. Psychiatric symptoms are sometimes the first and only manifestation of Wilson’s disease. More often a psychiatric involvement is present beside a neurologic or hepatic disease

Three-loop renormalization group analysis of a complex model with stable fixed point: Critical exponents up to ϵ3\epsilon^3 and ϵ4\epsilon^4

The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach in $D=4-2\epsilon$ dimensions. Perturbation expansions for RG functions are calculated using dimensional regularization and the minimal subtraction (MS) scheme. It is shown that for $N\ge 2$ the model does possess a stable fixed point in three dimensional space of coupling constants, in accordance with predictions made earlier on the base of the lower-order approximations. Numerical estimate for critical (marginal) value of the order parameter dimensionality $N_c$ is given using Pad\'e-Borel summation of the corresponding $\epsilon$--expansion series obtained. It is observed that two-fold degeneracy of the eigenvalue exponents in the one-loop approximation for the unique stable fixed point leads to the substantial decrease of the accuracy expected within three loops and may cause powers of $\sqrt{\epsilon}$ to appear in the expansions. The critical exponents $\gamma$ and $\eta$ are calculated for all fixed points up to $\epsilon^3$ and $\epsilon^4$, respectively, and processed by the Borel summation method modified with a conformal mapping. For the unique stable fixed point the magnetic susceptibility exponent $\gamma$ for N=2 is found to differ in third order in $\epsilon$ from that of an O(4)--symmetric point. Qualitative comparison of the results given by $\epsilon$--expansion, three-dimensional RG analysis, non-perturbative RG arguments, and experimental data is performed.Comment: 30 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57, Jan. issue (1998