An approximation principle for congruence subgroups

The motivating question of this paper is roughly the following: given a group scheme $G$ over $\mathbb{Z}_p$, $p$ prime, with semisimple generic fiber $G_{\mathbb{Q}_p}$, how far are open subgroups of $G(\mathbb{Z}_p)$ from subgroups of the form $X(\mathbb{Z}_p)\mathbf{K}_p(p^n)$, where $X$ is a subgroup scheme of $G$ and $\mathbf{K}_p(p^n)$ is the principal congruence subgroup $\operatorname{Ker} (G(\mathbb{Z}_p)\rightarrow G(\mathbb{Z}/p^n\mathbb{Z}))$? More precisely, we will show that for $G_{\mathbb{Q}_p}$ simply connected there exist constants $J\ge1$ and $\varepsilon>0$, depending only on $G$, such that any open subgroup of $G (\mathbb{Z}_p)$ of level $p^n$ admits an open subgroup of index $\le J$ which is contained in $X(\mathbb{Z}_p)\mathbf{K}_p(p^{\lceil \varepsilon n\rceil})$ for some proper connected algebraic subgroup $X$ of $G$ defined over $\mathbb{Q}_p$. Moreover, if $G$ is defined over $\mathbb{Z}$, then $\varepsilon$ and $J$ can be taken independently of $p$. We also give a correspondence between natural classes of $\mathbb{Z}_p$-Lie subalgebras of $\mathfrak{g}_{\mathbb{Z}_p}$ and of closed subgroups of $G(\mathbb{Z}_p)$ that can be regarded as a variant over $\mathbb{Z}_p$ of Nori's results on the structure of finite subgroups of $\operatorname{GL}(N_0,\mathbb{F}_p)$ for large $p$. As an application we give a bound for the volume of the intersection of a conjugacy class in the group $G (\hat{\mathbb{Z}}) = \prod_p G (\mathbb{Z}_p)$, for $G$ defined over $\mathbb{Z}$, with an arbitrary open subgroup. In a future paper, this result will be applied to the limit multiplicity problem for arbitrary congruence subgroups of the arithmetic lattice $G (\mathbb{Z})$

Why is there no queer international theory?

Over the last decade, Queer Studies have become Global Queer Studies, generating significant insights into key international political processes. Yet, the transformation from Queer to Global Queer has left the discipline of International Relations largely unaffected, which begs the question: if Queer Studies has gone global, why has the discipline of International Relations not gone somewhat queer? Or, to put it in Martin Wight’s provocative terms, why is there no Queer International Theory? This article claims that the presumed non-existence of Queer International Theory is an effect of how the discipline of International Relations combines homologization, figuration, and gentrification to code various types of theory as failures in order to manage the conduct of international theorizing in all its forms. This means there are generalizable lessons to be drawn from how the discipline categorizes Queer International Theory out of existence to bring a specific understanding of International Relations into existence

On unitarizability in the case of classical p-adic groups

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give additional evidence in generalized cuspidal rank (up to) three.Comment: This paper is a merged and revised version of ealier preprints arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul

Functional immunomics: Microarray analysis of IgG autoantibody repertoires predicts the future response of NOD mice to an inducer of accelerated diabetes

One's present repertoire of antibodies encodes the history of one's past immunological experience. Can the present autoantibody repertoire be consulted to predict resistance or susceptibility to the future development of an autoimmune disease? Here we developed an antigen microarray chip and used bioinformatic analysis to study a model of type 1 diabetes developing in non-obese diabetic (NOD) male mice in which the disease was accelerated and synchronized by exposing the mice to cyclophosphamide at 4 weeks of age. We obtained sera from 19 individual mice, treated the mice to induce cyclophosphamide-accelerated diabetes (CAD), and found, as expected, that 9 mice became severely diabetic while 10 mice permanently resisted diabetes. We again obtained serum from each mouse afterCAD induction. We then analyzed the patterns of antibodies in the individualmice to 266 different antigens spotted on the antigen chip. We identified a select panel of 27 different antigens (10% of the array) that revealed a pattern of IgG antibody reactivity in the pre-CAD serathat discriminated between the mice resistant or susceptible to CAD with 100% sensitivity and 82% specificity (p=0.017). Surprisingly, the set of IgG antibodies that was informative before CAD induction did not separate the resistant and susceptible groups after the onset of CAD; new antigens became criticalfor post-CAD repertoire discrimination. Thus, at least for a model disease, present antibody repertoires can predict future disease; predictive and diagnostic repertoires can differ; and decisive information about immune system behavior can be mined by bioinformatic technology. Repertoires matter.Comment: See Advanced Publication on the PNAS website for final versio

Spontaneous regression of congenital epulis: a case report and review of the literature

<p>Abstract</p> <p>Introduction</p> <p>Congenital epulis is a rare lesion found on the alveolar process of a newborn child, diagnosed soon after birth. The lesion has a site predilection for the anterior maxillary alveolar process and a 9:1 sex predilection for females. Once diagnosed the traditional management of the lesion has been surgical excision under general anesthesia.</p> <p>Case presentation</p> <p>The purpose of this case report is to describe spontaneous regression of congenital epulis in a three week old healthy African American female child. She presented with a 1.5 cm bilobed sessile nodular lesion in the region of the right maxillary cuspid. The clinical impression was congenital epulis. Since the lesion was not interfering with feeding and respiration, a conservative approach was taken. The child was followed-up for 18 months, during which the lesion progressively regressed.</p> <p>Conclusions</p> <p>Conservative management prevented unnecessary surgery and anesthesia exposure in a neonate.</p

The detection rate of early UV emission from supernovae: A dedicated GALEX/PTF survey and calibrated theoretical estimates

The radius and surface composition of an exploding massive star,as well as the explosion energy per unit mass, can be measured using early UV observations of core collapse supernovae (SNe). We present the first results from a simultaneous GALEX/PTF search for early UV emission from SNe. Six Type II SNe and one Type II superluminous SN (SLSN-II) are clearly detected in the GALEX NUV data. We compare our detection rate with theoretical estimates based on early, shock-cooling UV light curves calculated from models that fit existing Swift and GALEX observations well, combined with volumetric SN rates. We find that our observations are in good agreement with calculated rates assuming that red supergiants (RSGs) explode with fiducial radii of 500 solar, explosion energies of 10^51 erg, and ejecta masses of 10 solar masses. Exploding blue supergiants and Wolf-Rayet stars are poorly constrained. We describe how such observations can be used to derive the progenitor radius, surface composition and explosion energy per unit mass of such SN events, and we demonstrate why UV observations are critical for such measurements. We use the fiducial RSG parameters to estimate the detection rate of SNe during the shock-cooling phase (<1d after explosion) for several ground-based surveys (PTF, ZTF, and LSST). We show that the proposed wide-field UV explorer ULTRASAT mission, is expected to find >100 SNe per year (~0.5 SN per deg^2), independent of host galaxy extinction, down to an NUV detection limit of 21.5 mag AB. Our pilot GALEX/PTF project thus convincingly demonstrates that a dedicated, systematic SN survey at the NUV band is a compelling method to study how massive stars end their life.Comment: See additional information including animations on http://www.weizmann.ac.il/astrophysics/ultrasa

Rituals of World Politics: On (Visual) Practices Disordering Things

Rituals are customarily muted into predictable and boring routines aimed to stabilise social orders and limit conflict. As a result, their magic lure recedes into the background, and the unexpected, disruptive and disordered elements are downplayed. Our collaborative contribution counters this move by foregrounding rituals of world politics as social practices with notable disordering effects. The collective discussion recovers the disruptive work of a range of rituals designed to sustain the sovereign exercise of violence and war. We do so through engaging a series of ‘world pictures' (Mitchell 2007). We show the worlding enacted in rituals such as colonial treaty-making, state commemoration, military/service dog training, cyber-security podcasts,algorithmically generated maps, the visit of Prince Harry to a joint NATO exercise and border ceremonies in India, respectively. We do so highlighting rituals’ immanent potential for disruption of existing orders, the fissures, failures and unforeseen repercussions. Reappraising the disordering role of ritual practices sheds light on the place of rituals in rearticulating the boundaries of the political. It emphasises the role of rituals in generating dissensus and re-divisions of the sensible rather than in imposing a consensus by policing the boundaries of the political, as Rancière might phrase it. Our images are essential to the account. They help disinterring the fundamentals and ambiguities of the current worldings of security, capturing the affective atmosphere of rituals

Protective versus pathogenic anti-CD4 immunity: insights from the study of natural resistance to HIV infection

HIV-1 exposure causes several dramatic unbalances in the immune system homeostasis. Here, we will focus on the paradox whereby CD4 specific autoimmune responses, which are expected to contribute to the catastrophic loss of most part of the T helper lymphocyte subset in infected patients, may display the characteristics of an unconventional protective immunity in individuals naturally resistant to HIV-1 infection. Reference to differences in fine epitope mapping of these two oppositely polarized outcomes will be presented, with particular reference to partially or totally CD4-gp120 complex-specific antibodies. The fine tuning of the anti-self immune response to the HIV-1 receptor may determine whether viral exposure will result in infection or, alternatively, protective immunity