Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+

We perform amplitude analyses of the decays $B^0 \to K^+K^-K^0_S$, $B^+ \rightarrow K^+K^-K^+$, and $B^+ \to K^0_S K^0_S K^+$, and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\times 10^6$ $B\bar{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For $B^+ \to K^+K^-K^+$, we find a direct CP asymmetry in $B^+ \to \phi(1020)K^+$ of $A_{CP}= (12.8\pm 4.4 \pm 1.3)$, which differs from zero by $2.8 \sigma$. For $B^0 \to K^+K^-K^0_S$, we measure the CP-violating phase $\beta_{\rm eff} (\phi(1020)K^0_S) = (21\pm 6 \pm 2)^\circ$. For $B^+ \to K^0_S K^0_S K^+$, we measure an overall direct CP asymmetry of $A_{CP} = (4 ^{+4}_{-5} \pm 2)$. We also perform an angular-moment analysis of the three channels, and determine that the $f_X(1500)$ state can be described well by the sum of the resonances $f_0(1500)$, $f_2^{\prime}(1525)$, and $f_0(1710)$.Comment: 35 pages, 68 postscript figures. v3 - minor modifications to agree with published versio

A multi-Frey approach to Fermat equations of signature (r,r,p)(r,r,p)

In this paper, we give a resolution of the generalized Fermat equations $$x^5 + y^5 = 3 z^n \text{ and } x^{13} + y^{13} = 3 z^n,$$ for all integers $n \ge 2$, and all integers $n \ge 2$ which are not a multiple of $7$, respectively, using the modular method with Frey elliptic curves over totally real fields. The results require a refined application of the multi-Frey technique, which we show to be effective in new ways to reduce the bounds on the exponents $n$. We also give a number of results for the equations $x^5 + y^5 = d z^n$, where $d = 1, 2$, under additional local conditions on the solutions. This includes a result which is reminiscent of the second case of Fermat's Last Theorem, and which uses a new application of level raising at $p$ modulo $p$.Comment: Includes more details regarding the connection of this paper with its sequel 'Some extensions of the modular method and Fermat-equations of signature (13,13,n)'. More precisely: extended Remark 7.4; added details on the computational parts of the proofs of Proposition 9 and Theorem 2; included new comments and polished the auxiliary Magma files for Proposition 9 and Theorem

A result on the equation xp+yp=zrx^p + y^p = z^r using Frey abelian varieties

We prove a diophantine result on generalized Fermat equations of the form $x^p + y^p = z^r$ which for the first time requires the use of Frey abelian varieties of dimension $\geq 2$ in Darmon's program. For that, we provide an irreducibility criterion for the mod $\mathfrak{p}$ representations attached to certain abelian varieties of $\text{GL}_2$-type over totally real fields

Correlation between visual analog scale, Melbourne pain scale and Von Frey filaments in post-operatory pain evaluation in bitches submitted to ovaryhysterectomy

A avaliação da dor em animais necessita da utilização de escalas de avaliação, que dependem da interpretação realizada por observadores. O objetivo do presente estudo foi avaliar a correlação entre a escala visual analógica (EVA), escala de Melbourne e os filamentos de Von Frey, na avaliação da dor pós-operatória em 42 cadelas adultas e saudáveis, submetidas à ovariossalpingohisterectomia (OSH). A dor pós-operatória foi avaliada por dois observadores cegos aos tratamentos analgésicos, em intervalos de uma hora, utilizando a EVA, a escala de Melbourne e os filamentos de Von Frey, aplicados ao redor da incisão cirúrgica. Foram considerados como critérios para realização da analgesia resgate uma pontuação de 50mm na EVA ou de 13 pontos na escala de Melbourne. A EVA revelou-se a escala mais sensível, uma vez que 100% dos animais receberam resgate seguindo esse método. Os valores obtidos na EVA e na escala de Melbourne determinaram boa correlação, com r=0,74, o que não ocorreu com os filamentos de Von Frey (r=-0,18). Já a correlação entre a escala de Melbourne e os filamentos de Von Frey foi de -0.37. Apesar de a EVA e a escala de Melbourne apresentarem boa correlação, sugere-se que se considere uma pontuação menor na escala de Melbourne como critério para administração de analgesia resgate.Pain evaluation in animals requires the use of evaluation scales, which depend on the interpretation made by observers. The present study aimed to evaluate the correlation between visual analog scale (VAS), Melbourne pain scale and Von Frey filaments in the evaluation of post-operatory pain in fourty two healthy adult bitches submited to ovariohysterectomy. Post-operatory pain was evaluated by two observers unaware of the analgesic protocol used, in one-hour intervals, using VAS, Melbourne pain scale and Von Frey filaments, applied around the surgical wound. A score of 50mm in VAS or 13 points in the Melbourne pain scale were considered as the criterion for analgesic administration. VAS and Melbourne pain scale showed a good correlation, with r=0.74. Correlation between VAS and Von Frey filaments was weak (r=-0.18). Correlation between Melbourne pain scale and Von Frey filaments was -0.37. VAS revealed to be the most sensitive scale. VAS and Melbourne pain scale showed a good correlation degree. It was concluded that a lower score in the Melbourne pain scale can be considered as criterion for analgesic administration

Nociceptive neuropeptide increases and periorbital allodynia in a model of traumatic brain injury.

OBJECTIVE: This study tests the hypothesis that injury to the somatosensory cortex is associated with periorbital allodynia and increases in nociceptive neuropeptides in the brainstem in a mouse model of controlled cortical impact (CCI) injury. METHODS: Male C57BL/6 mice received either CCI or craniotomy-only followed by weekly periorbital von Frey (mechanical) sensory testing for up to 28 days post-injury. Mice receiving an incision only and naïve mice were included as control groups. Changes in calcitonin gene-related peptide (CGRP) and substance P (SP) within the brainstem were determined using enzyme-linked immunosorbent assay and immunohistochemistry, respectively. Activation of ionized calcium-binding adaptor molecule-1-labeled macrophages/microglia and glial fibrillary acidic protein (GFAP)-positive astrocytes were evaluated using immunohistochemistry because of their potential involvement in nociceptor sensitization. RESULTS: Incision-only control mice showed no changes from baseline periorbital von Frey mechanical thresholds. CCI significantly reduced mean periorbital von Frey thresholds (periorbital allodynia) compared with baseline and craniotomy-only at each endpoint, analysis of variance P \u3c .0001. Craniotomy significantly reduced periorbital threshold at 14 days but not 7, 21, or 28 days compared with baseline threshold, P \u3c .01. CCI significantly increased SP immunoreactivity in the brainstem at 7 and 14 days but not 28 days compared with craniotomy-only and controls, P \u3c .001. CGRP levels in brainstem tissues were significantly increased in CCI groups compared with controls (incision-only and naïve mice) or craniotomy-only mice at each endpoint examined, P \u3c .0001. There was a significant correlation between CGRP and periorbital allodynia (P \u3c .0001, r = -0.65) but not for SP (r = 0.20). CCI significantly increased the number of macrophage/microglia in the injured cortex at each endpoint up to 28 days, although cell numbers declined over weeks post-injury, P \u3c .001. GFAP(+) immunoreactivity was significantly increased at 7 but not 14 or 28 days after CCI, P \u3c .001. Craniotomy resulted in transient periorbital allodynia accompanied by transient increases in SP, CGRP, and GFAP immunoreactivity compared with control mice. There was no increase in the number of macrophage/microglia cells compared with controls after craniotomy. CONCLUSION: Injury to the somatosensory cortex results in persistent periorbital allodynia and increases in brainstem nociceptive neuropeptides. Findings suggest that persistent allodynia and increased neuropeptides are maintained by mechanisms other than activation of macrophage/microglia or astrocyte in the injured somatosensory cortex

Crossover from Isotropic to Directed Percolation

Directed percolation is one of the generic universality classes for dynamic processes. We study the crossover from isotropic to directed percolation by representing the combined problem as a random cluster model, with a parameter $r$ controlling the spontaneous birth of new forest fires. We obtain the exact crossover exponent $y_{DP}=y_T-1$ at $r=1$ using Coulomb gas methods in 2D. Isotropic percolation is stable, as is confirmed by numerical finite-size scaling results. For $D \geq 3$, the stability seems to change. An intuitive argument, however, suggests that directed percolation at $r=0$ is unstable and that the scaling properties of forest fires at intermediate values of $r$ are in the same universality class as isotropic percolation, not only in 2D, but in all dimensions.Comment: 4 pages, REVTeX, 4 epsf-emedded postscript figure