Nonparametric estimation of a convex bathtub-shaped hazard function

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ202 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Estimation of a discrete monotone distribution

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distribution is uniform on $\{0, ..., y \}$, the asymptotic risk of the method of rearrangements estimator (in squared $\ell_2$ norm) is $y/(y+1)$, while the asymptotic risk of the MLE is of order $(\log y)/(y+1)$. For strictly decreasing distributions, the estimators are asymptotically equivalent.Comment: 39 pages. See also http://www.stat.washington.edu/www/research/reports/2009/ http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.htm

Probing Limits of Information Spread with Sequential Seeding

We consider here information spread which propagates with certain probability from nodes just activated to their not yet activated neighbors. Diffusion cascades can be triggered by activation of even a small set of nodes. Such activation is commonly performed in a single stage. A novel approach based on sequential seeding is analyzed here resulting in three fundamental contributions. First, we propose a coordinated execution of randomized choices to enable precise comparison of different algorithms in general. We apply it here when the newly activated nodes at each stage of spreading attempt to activate their neighbors. Then, we present a formal proof that sequential seeding delivers at least as large coverage as the single stage seeding does. Moreover, we also show that, under modest assumptions, sequential seeding achieves coverage provably better than the single stage based approach using the same number of seeds and node ranking. Finally, we present experimental results showing how single stage and sequential approaches on directed and undirected graphs compare to the well-known greedy approach to provide the objective measure of the sequential seeding benefits. Surprisingly, applying sequential seeding to a simple degree-based selection leads to higher coverage than achieved by the computationally expensive greedy approach currently considered to be the best heuristic

Effects of the interaction between slurry, soil conditioners, and mineral NPK fertilizers on selected nutritional parameters of Festulolium braunii (K. Richt.) A. Camus

The research was aimed at assessing the biomass yield of Festulolium braunii and its content of raw protein and crude ash after application of slurry, both on its own and together with soil conditioners (UGmax and Humus Active), and mineral fertilizers. The studies were conducted on the basis of a two-year field experiment. The interaction between slurry and soil conditioners and between slurry and mineral fertilizers was studied on the Sulino variety of Festulolium braunii, a hybrid between Lolium multiflorum and Festuca pratensis. Compared with plants treated with liquid manure on its own, slurry applied with soil conditioners and mineral fertilizer did not significantly increase the biomass yield of the grass. However, there was higher protein content in Festulolium braunii, even if statistically insignificant, as a response to slurry supplemented with mineral fertilizer than in plants treated with slurry only. Various forms of treatment did not differentiate crude ash content in plant dry matter in a statistically significant way

AirNet: Neural Network Transmission over the Air

State-of-the-art performance for many emerging edge applications is achieved by deep neural networks (DNNs). Often, the employed DNNs are location- and time-dependent, and the parameters of a specific DNN must be delivered from an edge server to the edge device rapidly and efficiently to carry out time-sensitive inference tasks. This can be considered as a joint source-channel coding (JSCC) problem, in which the goal is not to recover the DNN coefficients with the minimal distortion, but in a manner that provides the highest accuracy in the downstream task. For this purpose we introduce AirNet, a novel training and analog transmission method to deliver DNNs over the air. We first train the DNN with noise injection to counter the wireless channel noise. We also employ pruning to identify the most significant DNN parameters that can be delivered within the available channel bandwidth, knowledge distillation, and nonlinear bandwidth expansion to provide better error protection for the most important network parameters. We show that AirNet achieves significantly higher test accuracy compared to the separation-based alternative, and exhibits graceful degradation with channel quality

Interacting Spreading Processes in Multilayer Networks: A Systematic Review

© 2013 IEEE. The world of network science is fascinating and filled with complex phenomena that we aspire to understand. One of them is the dynamics of spreading processes over complex networked structures. Building the knowledge-base in the field where we can face more than one spreading process propagating over a network that has more than one layer is a challenging task, as the complexity comes both from the environment in which the spread happens and from characteristics and interplay of spreads' propagation. As this cross-disciplinary field bringing together computer science, network science, biology and physics has rapidly grown over the last decade, there is a need to comprehensively review the current state-of-the-art and offer to the research community a roadmap that helps to organise the future research in this area. Thus, this survey is a first attempt to present the current landscape of the multi-processes spread over multilayer networks and to suggest the potential ways forward

Convergence of linear functionals of the Grenander estimator under misspecification

Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate $n^{1/3}$ if the true density is curved [Sankhy\={a} Ser. A 31 (1969) 23-36] and at rate $n^{1/2}$ if the density is flat [Ann. Probab. 11 (1983) 328-345; Canad. J. Statist. 27 (1999) 557-566]. In the case that the true density is misspecified, the results of Patilea [Ann. Statist. 29 (2001) 94-123] tell us that the global convergence rate is of order $n^{1/3}$ in Hellinger distance. Here, we show that the local convergence rate is $n^{1/2}$ at a point where the density is misspecified. This is not in contradiction with the results of Patilea [Ann. Statist. 29 (2001) 94-123]: the global convergence rate simply comes from locally curved well-specified regions. Furthermore, we study global convergence under misspecification by considering linear functionals. The rate of convergence is $n^{1/2}$ and we show that the limit is made up of two independent terms: a mean-zero Gaussian term and a second term (with nonzero mean) which is present only if the density has well-specified locally flat regions.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1196 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

IMPACT: The Journal of the Center for Interdisciplinary Teaching and Learning. Volume 8, Issue 1, Winter 2019

IMPACT: The Journal of the Center for Interdisciplinary Teaching & Learning is a peer-reviewed, biannual online journal that publishes scholarly and creative non-fiction essays about the theory, practice and assessment of interdisciplinary education. Impact is produced by the Center for Interdisciplinary Teaching & Learning at the College of General Studies, Boston University (www.bu.edu/cgs/citl).In this issue of Impact you will find a humanities scholar deeply engaged with the arcing out of a new territory: the interdisciplinary study of the Grateful Dead. Impact’s own Christopher Coffman’s review essay should be required reading for scholars of popular music, performance studies and history. His review also serves as an important reference for those who aspire to teach a course on the Grateful Dead, as well as for those who wish to write review essays. In this issue we also hear from those who are engaged in teaching people who are incarcerated. Importantly, Stephanie Cage’s essay looks to incarcerated people themselves to find out what they think about prison education. Peter Wakefield encourages us to see The Great Gatsby anew, in particular in the context of American racism and White supremacy. Wakefield’s essay is important too because it had its genesis in Writing, the State, and the Rise of Neo-Nationalism: Historical Contexts and Contemporary Concerns, a conference sponsored by the Center for Interdisciplinary Teaching & Learning