Compact surfaces with no Bonnet mate

This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.Comment: 7 pages, LaTeX2

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

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

Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method

Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic halos relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify halos in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and -independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et. al. (2011), including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading order terms are included. We quantify these differences here. [abridged]Comment: Accepted for publication in MNRAS. Includes minor revisions recommended by referee, slightly revised notation for clarity, and corrected typo

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale \alpha' in the low-energy effective action through the stringy non-perturbative sector.Comment: 22 pages, 1 figur

TA treatment of depression : a hermeneutic single-case efficacy design study - ‘Caterina’

This study is the second of a series of seven, and belongs to the second Italian systematic replication of findings from two previous series (Widdowson 2012a, 2012b, 2012c, 2013; Benelli, 2016a, 2016b, 2016c) that investigated the effectiveness of a manualised transactional analysis treatment for depression through Hermeneutic Single-Case Efficacy Design. The therapist was a white Italian woman with 10 years of clinical experience and the client, Caterina, was a 28-year old white Italian woman who attended 16 sessions of transactional analysis psychotherapy. Caterina satisfied DSM-5 criteria for major depressive disorder with generalized anxiety disorder. The conclusion of the judges was that this was an outstanding good-outcome case: the depressive symptoms showed an early clinical and reliable improvement, maintained till the 6 months follow-up, accompanied by reductions in anxiety symptoms, global distress and severity of personal problems. Adherence to the manualised treatment for depression appears good to excellent. In this case study, transactional analysis treatment for depression has proven its efficacy in treating major depressive disorder in comorbidity with anxiety disorder

Retrospective Proteomic Screening of 100 Breast Cancer Tissues

The present investigation has been conducted on one hundred tissue fragments of breast cancer, collected and immediately cryopreserved following the surgical resection. The specimens were selected from patients with invasive ductal carcinoma of the breast, the most frequent and potentially aggressive type of mammary cancer, with the objective to increase the knowledge of breast cancer molecular markers potentially useful for clinical applications. The proteomic screening; by 2D-IPG and mass spectrometry; allowed us to identify two main classes of protein clusters: proteins expressed ubiquitously at high levels in all patients; and proteins expressed sporadically among the same patients. Within the group of ubiquitous proteins, glycolytic enzymes and proteins with anti-apoptotic activity were predominant. Among the sporadic ones, proteins involved in cell motility, molecular chaperones and proteins involved in the detoxification appeared prevalent. The data of the present study indicates that the primary tumor growth is reasonably supported by concurrent events: the inhibition of apoptosis and stimulation of cellular proliferation, and the increased expression of glycolytic enzymes with multiple functions. The second phase of the evolution of the tumor can be prematurely scheduled by the occasional presence of proteins involved in cell motility and in the defenses of the oxidative stress. We suggest that this approach on large-scale 2D-IPG proteomics of breast cancer is currently a valid tool that offers the opportunity to evaluate on the same assay the presence and recurrence of individual proteins, their isoforms and short forms, to be proposed as prognostic indicators and susceptibility to metastasis in patients operated on for invasive ductal carcinoma of the breast

A Simple Operator Check of the Effective Fermion Mode Function during Inflation

We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.Comment: 39 pages, no figuire.(1) New version has clarified the ultimate motivation by adding sentences to the abstract and to the penultimate paragraph of the introduction. (2) By combining a number of references and equations we have managed to reduce the length by 2 page

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic