Topology Change in (2+1)-Dimensional Gravity

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-9

PERCEIVED IMPACT OF AMBIENT OPERATING ROOM NOISE BY CERTIFIED REGISTERED NURSE ANESTHETISTS

It is widely acknowledged that elevated levels of noise are commonplace in the healthcare environment, particularly in high acuity areas such as the operating room (OR). Excessive ambient noise may pose a threat to patient safety by adversely impacting provider performance and interfering with communication among perioperative care team members. With respect to the certified registered nurse anesthetist (CRNA), increased ambient OR noise may engender distractibility, diminish situation awareness and cause untoward health effects, thereby increasing the possibility for the occurrence of error and patient injury. This research project analytically examines the perceived impact of ambient noise in the operating room by CRNAs. Findings from this study reveal that CRNAs perceive elevated noise to be regularly present in the OR, specifically during the critical emergence phase of the anesthetic. However, CRNAs feel that increased noise only occasionally limits their ability to perform procedures, concentrate and communicate with the perioperative team. OR noise rarely interferes with memory retrieval. CRNAs perceive that noise is sometimes a threat to patient safety but infrequently engenders adverse patient outcomes. CRNAs do not perceive noise in the OR to be detrimental to their health but strongly agree that excessive noise can and should be controlled. Increased ambient OR noise is a veritable reality that may pose a potential threat to patient safety. Further research to identify elevations in noise during critical phases of the anesthetic and delineation of significant contributors to its genesis is warranted

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit

Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $N \times N$ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general $N$ case. For N=1 and N=2 the probabilities and thus the solution of the equations are given explicitly. An asymptotic expansion for large gap size is obtained from the equation in the Hermite case, and also studied is the scaling at the edge of the Hermite spectrum as $N \to \infty$, and the Jacobi to Hermite limit; these last two studies make correspondence to other cases reported here or known previously. Moreover, the differential equation arising in the Hermite ensemble is solved in terms of an explicit rational function of a {Painlev\'e-V} transcendent and its derivative, and an analogous solution is provided in the two Jacobi cases but this time involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2

On the Choice and Number of Microarrays for Transcriptional Regulatory Network Inference

<p>Abstract</p> <p>Background</p> <p>Transcriptional regulatory network inference (TRNI) from large compendia of DNA microarrays has become a fundamental approach for discovering transcription factor (TF)-gene interactions at the genome-wide level. In correlation-based TRNI, network edges can in principle be evaluated using standard statistical tests. However, while such tests nominally assume independent microarray experiments, we expect dependency between the experiments in microarray compendia, due to both project-specific factors (e.g., microarray preparation, environmental effects) in the multi-project compendium setting and effective dependency induced by gene-gene correlations. Herein, we characterize the nature of dependency in an <it>Escherichia coli </it>microarray compendium and explore its consequences on the problem of determining which and how many arrays to use in correlation-based TRNI.</p> <p>Results</p> <p>We present evidence of substantial effective dependency among microarrays in this compendium, and characterize that dependency with respect to experimental condition factors. We then introduce a measure <it>n</it>_{<it>eff </it>}of the effective number of experiments in a compendium, and find that corresponding to the dependency observed in this particular compendium there is a huge reduction in effective sample size i.e., <it>n</it>_{<it>eff </it>}= 14.7 versus <it>n </it>= 376. Furthermore, we found that the <it>n</it>_{<it>eff </it>}of select subsets of experiments actually exceeded <it>n</it>_{<it>eff </it>}of the full compendium, suggesting that the adage 'less is more' applies here. Consistent with this latter result, we observed improved performance in TRNI using subsets of the data compared to results using the full compendium. We identified experimental condition factors that trend with changes in TRNI performance and <it>n</it>_{<it>eff </it>}, including growth phase and media type. Finally, using the set of known E. coli genetic regulatory interactions from RegulonDB, we demonstrated that false discovery rates (FDR) derived from <it>n</it>_{<it>eff </it>}-adjusted p-values were well-matched to FDR based on the RegulonDB truth set.</p> <p>Conclusions</p> <p>These results support utilization of <it>n</it>_{<it>eff </it>}as a potent descriptor of microarray compendia. In addition, they highlight a straightforward correlation-based method for TRNI with demonstrated meaningful statistical testing for significant edges, readily applicable to compendia from any species, even when a truth set is not available. This work facilitates a more refined approach to construction and utilization of mRNA expression compendia in TRNI.</p

Constructing Integrable Third Order Systems:The Gambier Approach

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlev\'e method for ODE's and the singularity confinement method for mappings).Comment: 14 pages, TEX FIL

Factorization of Ising correlations C(M,N) for ν= −k \nu= \, -k and M+N odd, M≤NM \le N, T<TcT < T_c and their lambda extensions

We study the factorizations of Ising low-temperature correlations C(M,N) for $\nu=-k$ and M+N odd, $M \le N$, for both the cases $M\neq 0$ where there are two factors, and $M=0$ where there are four factors. We find that the two factors for $M \neq 0$ satisfy the same non-linear differential equation and, similarly, for M=0 the four factors each satisfy Okamoto sigma-form of Painlev\'e VI equations with the same Okamoto parameters. Using a Landen transformation we show, for $M\neq 0$, that the previous non-linear differential equation can actually be reduced to an Okamoto sigma-form of Painlev\'e VI equation. For both the two and four factor case, we find that there is a one parameter family of boundary conditions on the Okamoto sigma-form of Painlev\'e VI equations which generalizes the factorization of the correlations C(M,N) to an additive decomposition of the corresponding sigma's solutions of the Okamoto sigma-form of Painlev\'e VI equation which we call lambda extensions. At a special value of the parameter, the lambda-extensions of the factors of C(M,N) reduce to homogeneous polynomials in the complete elliptic functions of the first and second kind. We also generalize some Tracy-Widom (Painlev\'e V) relations between the sum and difference of sigma's to this Painlev\'e VI framework.Comment: 45 page