The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations

It is known that any explicit averaging scheme of the type essential for describing the large scale behaviour of the Universe, must necessarily yield corrections to the Einstein equations applied in the Cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant, is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov's Macroscopic Gravity (MG) which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on \emph{one} gauge choice -- which is inherent in the assumption of large scale homogeneity and isotropy -- it is however possible to construct \emph{spacetime scalar} corrections to the standard FLRW equations. This partially addresses the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.Comment: 18 pages, no figures, revtex4; v2 - minor clarifications added; v3 - minor changes in presentation to improve clarity, reference added, to appear in Phys. Rev.

Proximal Hypospadias

Hypospadias results from abnormal development of the penis that leaves the urethral meatus proximal to its normal glanular position. Meatal position may be located anywhere along the penile shaft, but more severe forms of hypospadias may have a urethral meatus located at the scrotum or perineum. The spectrum of abnormalities may also include ventral curvature of the penis, a dorsally redundant prepuce, and atrophic corpus spongiosum. Due to the severity of these abnormalities, proximal hypospadias often requires more extensive reconstruction in order to achieve an anatomically and functionally successful result. We review the spectrum of proximal hypospadias etiology, presentation, correction, and possible associated complications

Cosmic Inhomogeneities and the Average Cosmological Dynamics

If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a `dark energy'. However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on smaller scales. While GR governs the dynamics of the \emph{in}homogeneous Universe, the averaged \emph{homogeneous} Universe obeys modified Einstein equations. Can such modifications alone explain the acceleration? For a simple generic model with realistic initial conditions, we show the answer to be `no'. Averaging effects negligibly influence the cosmological dynamics.Comment: 5 pages, 2 figures, revtex4; v3 -- Text shortened to match published version. Some typos fixed. No physics change

Backreaction of Cosmological Perturbations in Covariant Macroscopic Gravity

The problem of corrections to Einstein's equations arising from averaging of inhomogeneities ("backreaction") in the cosmological context, has gained considerable attention recently. We present results of analysing cosmological perturbation theory in the framework of Zalaletdinov's fully covariant Macroscopic Gravity. We show that this framework can be adapted to the setting of cosmological perturbations in a manner which is free from gauge related ambiguities. We derive expressions for the backreaction which can be readily applied in \emph{any} situation (not necessarily restricted to the linear perturbations considered here) where the \emph{metric} can be brought to the perturbed FLRW form. In particular these expressions can be employed in toy models studying nonlinear structure formation, and possibly also in N-body simulations. Additionally, we present results of example calculations which show that the backreaction remains negligible well into the matter dominated era.Comment: 17 pages, 5 figures, revtex4; v2 -- typos fixed, 1 reference updated, to appear in Phys Rev

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $\delta_c$, the void excursion set problem involves two barriers $\delta_v$ and $\delta_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2, version published in PR

The Prognostic Significance of the Depth of Cervical Stromal Invasion in Women with FIGO Stage II Uterine Endometrioid Carcinoma

Purpose/Objective(s): To explore the prognostic significance of the depth of cervical stromal invasion (CSI) on survival endpoints in women with FIGO stage II uterine endometrioid adenocarcinoma. Materials/Methods: A total of 117 patients were included in this retrospective review. Between 1990 and 2021, all patients with FIGO stage II endometrial cancer (EC) underwent hysterectomy and oophorectomy at our institution, with or without lymph node dissection. Patients with synchronous ovarian or breast cancer, as well as those who had undergone adjuvant systemic chemotherapy for EC, were excluded from the study. Pathologic slides were retrieved for these patients and were reviewed by a gynecologic pathologist to determine stromal thickness and the depth of CSI. The depth of CSI was then measured as a percentage of invasion (% CSI) and used in the analysis as a continuous or dichotomous variable (\u3c 50% vs \u3e = 50%). Patients\u27 demographics, pathologic, and treatment characteristics were analyzed using univariate and multivariate analysis to calculate recurrence-free (RFS) and disease-specific (DSS) rates. Results: The median age for the study cohort was 65 years (range, 34–96), and the median follow-up was 131 months (range, 9–334). A total of 90 patients (77%) had lymph node dissection, with a median of 8 examined lymph nodes (range 0-18). Adjuvant radiation therapy (RT) with pelvic or vaginal cuff HDR brachytherapy, or a combination of the two, was completed in 92 patients (79 percent). The median % CSI was 27% (range, 1-100) with 68% of patients having ≥ 50% CSI. While there was a trend for a worse 5-year RFS and DSS for women with ≥ 50% CSI (69% vs. 83%, p = 0.093) and (78% vs. 91%, p = 0.034), respectively, the depth of CSI was not statistically significant as an independent predictor of 5-year RFS, DSS, or OS. The depth of CSI was not associated with a difference in the recurrence pattern (vaginal cuff, pelvic, paraaortic, or distant). In multivariate analysis, FIGO grade was the only predictor of 5-year OS. FIGO grade and the presence of lympho-vascular space invasion (LVSI) were independent predictors of 5-year RFS and DSS. Conclusion: Deep cervical stromal invasion does not appear to be an independent predictive factor for survival endpoints in women with stage II uterine endometroid cancer, according to our findings. The presence of LVSI and tumor grade were both independent predictors of recurrence-free and disease-specific survival. Pooled data analysis may be needed to validate our study findings

Emerging Views on the CTD Code

The C-terminal domain (CTD) of RNA polymerase II (Pol II) consists of conserved heptapeptide repeats that function as a binding platform for different protein complexes involved in transcription, RNA processing, export, and chromatin remodeling. The CTD repeats are subject to sequential waves of posttranslational modifications during specific stages of the transcription cycle. These patterned modifications have led to the postulation of the “CTD code” hypothesis, where stage-specific patterns define a spatiotemporal code that is recognized by the appropriate interacting partners. Here, we highlight the role of CTD modifications in directing transcription initiation, elongation, and termination. We examine the major readers, writers, and erasers of the CTD code and examine the relevance of describing patterns of posttranslational modifications as a “code.” Finally, we discuss major questions regarding the function of the newly discovered CTD modifications and the fundamental insights into transcription regulation that will necessarily emerge upon addressing those challenges

Politics, Governance, and Leadership: What Can We Learn From the Academy of Management’s Response to EO13769?

Organization design seeks to balance potentially conflicting objectives while achieving a broader mission. EO13769 created a challenge for the president of the Academy of Management in leading through these conflicts, as President Anita McGahan describes: how to be true to her own moral values while leading an organization with well-established design constraints, and members with diverse opinions. This article shares the perspectives of 12 scholars on the lessons we can learn from Professor McGahan’s leadership of a constraining organization through a challenging time