Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Distribution and density of the partition function zeros for the diamond-decorated Ising model

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.Comment: 8 pages,8figure

Silent Myocardial Infarction and Long-Term Risk of Heart Failure: The ARIC Study

Background Although silent myocardial infarction (SMI) accounts for about one-half of the total number of myocardial infarctions (MIs), the risk of heart failure (HF) among patients with SMI is not well established. Objectives The purpose of this study was to examine the association of SMI and clinically manifested myocardial infarction (CMI) with HF, as compared with patients with no MI. Methods This analysis included 9,243 participants from the ARIC (Atherosclerosis Risk In Communities) study who were free of cardiovascular disease at baseline (ARIC visit 1: 1987 to 1989). SMI was defined as electrocardiographic evidence of MI without CMI after the baseline until ARIC visit 4 (1996 to 1998). HF events were ascertained starting from ARIC visit 4 until 2010 in individuals free of HF before that visit. Results Between ARIC visits 1 and 4, 305 SMIs and 331 CMIs occurred. After ARIC visit 4 and during a median follow-up of 13.0 years, 976 HF events occurred. The incidence rate of HF was higher in both CMI and SMI participants than in those without MI (incidence rates per 1,000 person-years were 30.4, 16.2, and 7.8, respectively; p < 0.001). In a model adjusted for demographics and HF risk factors, both SMI (hazard ratio [HR]: 1.35; 95% confidence interval [CI]: 1.02 to 1.78) and CMI (HR: 2.85; 95% CI: 2.31 to 3.51) were associated with increased risk of HF compared with no MI. These associations were consistent in subgroups of participants stratified by several HF risk predictors. However, the risk of HF associated with SMI was stronger in those younger than the median age (53 years) (HR: 1.66; 95% CI: 1.00 to 2.75 vs. HR: 1.19; 95% CI: 0.85 to 1.66, respectively; overall interaction p by MI type <0.001). Conclusions SMI is associated with an increased risk of HF. Future research is needed to examine the cost effectiveness of screening for SMI as part of HF risk assessment, and to identify preventive therapies to improve the risk of HF among patients with SMI

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Roles of the RAF/MEK/ERK Pathway in Cell Growth, Malignant Transformation and Drug Resistance

Growth factors and mitogens use the Ras/Raf/MEK/ERK signaling cascade to transmit signals from their receptors to regulate gene expression and prevent apoptosis. Some components of these pathways are mutated or aberrantly expressed in human cancer (e.g., Ras, B-Raf). Mutations also occur at genes encoding upstream receptors (e.g., EGFR and Flt-3) and chimeric chromosomal translocations (e.g., BCR-ABL) which transmit their signals through these cascades. Even in the absence of obvious genetic mutations, this pathway has been reported to be activated in over 50% of acute myelogenous leukemia and acute lymphocytic leukemia and is also frequently activated in other cancer types (e.g., breast and prostate cancers). Importantly, this increased expression is associated with a poor prognosis. The Ras/Raf/MEK/ERK and Ras/PI3K/PTEN/Akt pathways interact with each other to regulate growth and in some cases tumorigenesis. For example, in some cells, PTEN mutation may contribute to suppression of the Raf/MEK/ERK cascade due to the ability of activated Akt to phosphorylate and inactivate different Rafs. Although both of these pathways are commonly thought to have anti-apoptotic and drug resistance effects on cells, they display different cell lineage specific effects. For example, Raf/MEK/ERK is usually associated with proliferation and drug resistance of hematopoietic cells, while activation of the Raf/MEK/ERK cascade is suppressed in some prostate cancer cell lines which have mutations at PTEN and express high levels of activated Akt. Furthermore the Ras/Raf/MEK/ERK and Ras/PI3K/PTEN/Akt pathways also interact with the p53 pathway. Some of these interactions can result in controlling the activity and subcellular localization of Bim, Bak, Bax, Puma and Noxa. Raf/MEK/ERK may promote cell cycle arrest in prostate cells and this may be regulated by p53 as restoration of wild-type p53 in p53 deficient prostate cancer cells results in their enhanced sensitivity to chemotherapeutic drugs and increased expression of Raf/MEK/ERK pathway. Thus in advanced prostate cancer, it may be advantageous to induce Raf/MEK/ERK expression to promote cell cycle arrest, while in hematopoietic cancers it may be beneficial to inhibit Raf/MEK/ERK induced proliferation and drug resistance. Thus the Raf/MEK/ERK pathway has different effects on growth, prevention of apoptosis, cell cycle arrest and induction of drug resistance in cells of various lineages which may be due to the presence of functional p53 and PTEN and the expression of lineage specific factors. Originally published Biochim Biophys Acta, Vol. 1773, No. 8, August 200

The fully differential single-top-quark cross section in next-to-leading order QCD

We present a new next-to-leading order calculation for fully differential single-top-quark final states. The calculation is performed using phase space slicing and dipole subtraction methods. The results of the methods are found to be in agreement. The dipole subtraction method calculation retains the full spin dependence of the final state particles. We show a few numerical results to illustrate the utility and consistency of the resulting computer implementations.Comment: 37 pages, latex, 2 ps figure

Measurements of exclusive B_s^0 decays at the Y(5S) resonance

Several exclusive $B_s^0$ decays are studied using a 1.86 fb-1 data sample collected at the Y(5S) resonance with the Belle detector at the KEKB asymmetric energy e^+ e^- collider. In the $B_s^0 \to D_s^- \pi^+$ decay mode we find 10 $B_s^0$ candidates and measure the corresponding branching fraction. Combining the B_s^0 -> D_s^{(*)-} \pi^+, B_s^0 -> D_s^{(*)-} \rho^+, B_s^0 -> J/\psi \phi and B_s^0 -> J/\psi \eta decay modes, a significant $B_s^0$ signal is observed. The ratio \sigma (e^+ e^- -> B_s^* \bar{B}_s^*) / \sigma (e^+ e^- -> B_s^{(*)} \bar{B}_s^{(*)}) = (93^{+7}_{-9} \pm 1)% is obtained at the Y(5S) energy, indicating that $B_s^0$ meson production proceeds predominantly through the creation of $B^*_s \bar{B}^*_s$ pairs. The $B_s^0$ and $B_s^*$ meson masses are measured to be M(B_s^0)=(5370 \pm 1 \pm 3)MeV/c^2 and M(B_s^*)=(5418 \pm 1 \pm 3)MeV/c^2. Upper limits on the B_s^0 -> \gamma \gamma, B_s^0 -> \phi \gamma, B_s^0 -> K^+ K^- and B_s^0 -> D_s^{(*)+} D_s^{(*)-} branching fractions are also reported.Comment: 9 pages, 5 figures, published in Phys. Rev. D76, 012002 (2007

Evidence of the Purely Leptonic Decay B- --> tau- nu_tau-bar

We present the first evidence of the decay B- --> tau- nu_tau-bar using 414 fb^-1 of data collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. Events are tagged by fully reconstructing one of the B mesons in hadronic modes. We detect the signal with a significance of 3.5 standard deviations including systematics, and measure the branching fraction to be Br(B- --> tau- nu_tau-bar) = (1.79 +0.56-0.49(stat) +0.46-0.51(syst))*10^-4. This implies that f_B = 0.229 +0.036-0.031(stat) +0.034-0.037(syst) GeV and is the first direct measurement of this quantity.Comment: 6 pages, 3 figures, to appear in Physical Review Letter

Search for tau -> e gamma decay at Belle

We have searched for the lepton-flavor-violating decay tau -> e gamma using a data sample of 86.7/fb collected with the Belle detector at the KEKB asymmetric e^+ e^- collider. No evidence for a signal is obtained, and we set an upper limit for the branching fraction Br(tau -> e gamma) < 3.9 x 10^-7 at the 90% C.L.Comment: 11 pages, 10 figures, ReVTeX4, eps