Testing Conditional Independence of Discrete Distributions

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with probability at least $2/3$, between the case that $X$ and $Y$ are conditionally independent given $Z$ from the case that $(X, Y, Z)$ is $\epsilon$-far, in $\ell_1$-distance, from every distribution that has this property. Conditional independence is a concept of central importance in probability and statistics with a range of applications in various scientific domains. As such, the statistical task of testing conditional independence has been extensively studied in various forms within the statistics and econometrics communities for nearly a century. Perhaps surprisingly, this problem has not been previously considered in the framework of distribution property testing and in particular no tester with sublinear sample complexity is known, even for the important special case that the domains of $X$ and $Y$ are binary. The main algorithmic result of this work is the first conditional independence tester with {\em sublinear} sample complexity for discrete distributions over $[\ell_1]\times[\ell_2] \times [n]$. To complement our upper bounds, we prove information-theoretic lower bounds establishing that the sample complexity of our algorithm is optimal, up to constant factors, for a number of settings. Specifically, for the prototypical setting when $\ell_1, \ell_2 = O(1)$, we show that the sample complexity of testing conditional independence (upper bound and matching lower bound) is \[ \Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,. \

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition

Site pleiotropy of a stickleback Bmp6 enhancer

Development and regeneration are orchestrated by gene regulatory networks that operate in part through transcriptional enhancers. Although many enhancers are pleiotropic and are active in multiple tissues, little is known about whether enhancer pleiotropy is due to 1) site pleiotropy, in which individual transcription factor binding sites (TFBS) are required for activity in multiple tissues, or 2) multiple distinct sites that regulate expression in different tissues. Here, we investigated the pleiotropy of an intronic enhancer of the stickleback Bone morphogenetic protein 6 (Bmp6) gene. This enhancer was previously shown to regulate evolved changes in tooth number and tooth regeneration, and is highly pleiotropic, with robust activity in both fins and teeth throughout embryonic, larval, and adult life, and in the heart and kidney in adult fish. We tested the hypothesis that the pleiotropy of this enhancer is due to site pleiotropy of an evolutionarily conserved predicted Foxc1 TFBS. Transgenic analysis and site-directed mutagenesis experiments both deleting and scrambling this predicted Foxc1 TFBS revealed that the binding site is required for enhancer activity in both teeth and fins throughout embryonic, larval, and adult development, and in the heart and kidney in adult fish. Collectively these data support a model where the pleiotropy of this Bmp6 enhancer is due to site pleiotropy and this putative binding site is required for enhancer activity in multiple anatomical sites from the embryo to the adult

Localization and Broadband Follow-Up of the Gravitational-Wave Transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser InterferometerGravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimatesof the time, significance, and sky location of the event were shared with 63 teams of observers covering radio,optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter wedescribe the low-latency analysis of the GW data and present the sky localization of the first observed compactbinary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-rayCoordinates Network circulars, giving an overview of the participating facilities, the GW sky localizationcoverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger,there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadbandcampaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broadcapabilities of the transient astronomy community and the observing strategies that have been developed to pursueneutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-upcampaign are being disseminated in papers by the individual teams

Mobilising Urban Policies: The Policy Transfer of US Business Improvement Districts to England and Wales

This paper examines the ways in which policies are transferred between places: how they are disembedded from, and re-embedded into, new political, economic and social contexts. To do this, the paper will draw upon a case study of the transfer of Business Improvement Districts (BIDs) from the US to England and Wales. Within this, the paper demonstrates how they were a response to fiscal problems facing city-centre management in England and Wales; how US BIDs were socially constructed as `successful' and `transferable'; and how the BID `model' was reshaped prior to and following its rolling-out in England and Wales. The paper concludes by stressing six wider conceptual points about the nature of urban policy transfer

Serum and cerebrospinal fluid biomarker profiles in acute SARS-CoV-2-associated neurological syndromes

Preliminary pathological and biomarker data suggest that SARS-CoV-2 infection can damage the nervous system. To understand what, where and how damage occurs, we collected serum and CSF from patients with COVID-19 and characterized neurological syndromes involving the PNS and CNS (n = 34). We measured biomarkers of neuronal damage and neuroinflammation, and compared these with non-neurological control groups, which included patients with (n = 94) and without (n = 24) COVID-19. We detected increased concentrations of neurofilament light, a dynamic biomarker of neuronal damage, in the CSF of those with CNS inflammation (encephalitis and acute disseminated encephalomyelitis) [14 800 pg/ml (400, 32 400)], compared to those with encephalopathy [1410 pg/ml (756, 1446)], peripheral syndromes (Guillain–Barré syndrome) [740 pg/ml (507, 881)] and controls [872 pg/ml (654, 1200)]. Serum neurofilament light levels were elevated across patients hospitalized with COVID-19, irrespective of neurological manifestations. There was not the usual close correlation between CSF and serum neurofilament light, suggesting serum neurofilament light elevation in the non-neurological patients may reflect peripheral nerve damage in response to severe illness. We did not find significantly elevated levels of serum neurofilament light in community cases of COVID-19 arguing against significant neurological damage. Glial fibrillary acidic protein, a marker of astrocytic activation, was not elevated in the CSF or serum of any group, suggesting astrocytic activation is not a major mediator of neuronal damage in COVID-19

Supplement: "Localization and broadband follow-up of the gravitational-wave transient GW150914" (2016, ApJL, 826, L13)

This Supplement provides supporting material for Abbott et al. (2016a). We briefly summarize past electromagnetic (EM) follow-up efforts as well as the organization and policy of the current EM follow-up program. We compare the four probability sky maps produced for the gravitational-wave transient GW150914, and provide additional details of the EM follow-up observations that were performed in the different bands

Localization and Broadband Follow-up of the Gravitational-wave Transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams. </p