Christian Hirsch, Christian Mönch.

Source: Bernoulli, Volume 26, Number 2, 927--947.

Abstract:
This paper considers two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. Mörters (In Algorithms and Models for the Web Graph (2013) 14–25 Springer). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. Second, we derive a large deviation principle for the empirical neighbourhood structure and express the rate function as solution to an entropy minimisation problem in the space of stationary marked point processes.

Jie Yen Fan, Kais Hamza, Peter Jagers, Fima Klebaner.

Source: Bernoulli, Volume 26, Number 2, 893--926.

Abstract:
We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes are Markovian in the age structure. In a previous paper ( Proc. Steklov Inst. Math. 282 (2013) 90–105), the Law of Large Numbers as $K o infty $ was derived. Here we prove the central limit theorem, namely the weak convergence of the fluctuation processes in an appropriate Skorokhod space. We also show that the limit is driven by a stochastic partial differential equation.

Alexander Schnurr.

Source: Bernoulli, Volume 26, Number 1, 642--663.

Abstract:
We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space $mathbb{R}^{d}$. In particular, Markov processes related to sub-Markovian kernels, but also non-Markovian processes with path-dependent behavior. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Lévy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.

Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons.

Source: Bernoulli, Volume 26, Number 1, 352--386.

Abstract:
In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $Hin (0,1)$. The drift term is assumed to be globally Lipschitz. We prove that the solution of each of the above equations is continuous in terms of the index $H$, with respect to the convergence in law in the space of continuous functions.

Kay Bogerd, Rui M. Castro, Remco van der Hofstad.

Source: Bernoulli, Volume 26, Number 1, 253--285.

Abstract:
We study the asymptotic behavior of the clique number in rank-1 inhomogeneous random graphs, where edge probabilities between vertices are roughly proportional to the product of their vertex weights. We show that the clique number is concentrated on at most two consecutive integers, for which we provide an expression. Interestingly, the order of the clique number is primarily determined by the overall edge density, with the inhomogeneity only affecting multiplicative constants or adding at most a $log log (n)$ multiplicative factor. For sparse enough graphs the clique number is always bounded and the effect of inhomogeneity completely vanishes.

Stepan Mazur, Dmitry Otryakhin, Mark Podolskij.

Source: Bernoulli, Volume 26, Number 1, 226--252.

Abstract:
In this paper, we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $sigma>0$, the self-similarity parameter $Hin(0,1)$ and the stability index $alphain(0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in ( Ann. Probab. 45 (2017) 4477–4528). More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(sigma,alpha,H)$. We present the law of large numbers and some fully feasible weak limit theorems.

Thomson (Family)

St. Philip and St. James Church (Noarlunga, S.A.)

Moore, Amy, 1908-2005.

Moore, Amy, 1908-2005 -- Family.

Siekmann, Francis Heinrich Ernst, 1830-1917.

Hewish Henry -- Family.

Grant (Family)

Hicks (Family)

St. Philip and St. James Church (Noarlunga, S.A.)

Penney, Anna -- Travels.

Klemm (Family)

King's Orphan Schools (New Town, Tas.)

Kuerschner (Family)

Daws, Revell.

Traeger, Ernst Wilhelm, 1805-1874.

Urlwin (Family).

Huppatz (Family).

Nixon, Geoffrey Owen, 1921-2011.

Scott Marion, who consults states on testing, talks about why it's important for vendors and public officials to work cooperatively in renegotiating contracts amid assessment cancellations caused by COVID-19.

The post How States, Assessment Companies Can Work Together Amid Coronavirus Testing Cancellations appeared first on Market Brief.

State funding for K-12 is likely to fall sharply, though districts could look to protect essentials like distance-learning support and professional development, says school finance expert Mike Griffith.

The post As States’ Budgets Reel During COVID-19, Districts to Feel the Wrath appeared first on Market Brief.

EdWeek Market Brief asked district officials in a nationwide survey about their most urgent assessment needs, as they cope with COVID-19 and tentatively plan for reopening schools.

The post What Districts Want From Assessments, as They Grapple With the Coronavirus appeared first on Market Brief.

Vice President Pence’s trip to Iowa shows how the Trump administration’s aims to move past coronavirus are sometimes complicated by the virus itself.

Boeing CEO Dave Calhoun said the company was aiming to resume production this month, despite the ongoing grounding and coronavirus pandemic.

For millions of Americans, working at home isn't an option. NBC News identified seven occupations in which employees are at especially high risk of COVID-19.

Delta said it is making the move to protect employees amid the coronavirus pandemic, but planes have been flying near empty

While President Donald Trump traveled to the battleground state of Arizona this week, his Democratic opponent for the White House, Joe Biden, campaigned from his basement as he has done throughout the coronavirus pandemic. The freeze on in-person campaigning during the outbreak has had an upside for Biden, giving the former vice president more time to court donors and shielding him from on-the-trail gaffes. "I personally would like to see him out more because he's in his element when he's meeting people," said Tom Sacks-Wilner, a fundraiser for Biden who is on the campaign's finance committee.

Austin-Bergstrom International Airport said it was "aware of an individual that was struck and killed on runway 17-R by a landing aircraft."

Some Buckeyes are not comfortable being told by a "woman in power" to quarantine, one expert said.

Georgia is one of four states that doesn't have a hate crime law. Arbery's killing has reignited calls for legislation.

The Justice Department announced Thursday that it is dropping its criminal case against President Trump's first national security adviser Michael Flynn. Flynn twice admitted in court he lied to the FBI about his conversations with Russia's U.S. ambassador, and then cooperated in Special Counsel Robert Mueller's investigation. It was an unusual move by the Justice Department, and CNN's legal and political analysts smelled a rat."Attorney General [William] Barr is already being accused of creating a special justice system just for President Trump's friends," and this will only feed that perception, CNN's Jake Tapper suggested. Political correspondent Sara Murray agreed, noting that the prosecutor in the case, Brandon Van Grack, withdrew right before the Justice Department submitted its filing, just like when Barr intervened to request a reduced sentence for Roger Stone.National security correspondent Jim Sciutto laid out several reason why the substance of Flynn's admitted lie was a big deal, and chief legal analyst Jeffrey Toobin was appalled. "It is one of the most incredible legal documents I have read, and certainly something that I never expected to see from the United States Department of Justice," Toobin said. "The idea that the Justice Department would invent an argument -- an argument that the judge in this case has already rejected -- and say that's a basis for dropping a case where a defendant admitted his guilt shows that this is a case where the fix was in."Barr told CBS News' Cathrine Herridge on Thursday that dropping Flynn's case actually "sends the message that there is one standard of justice in this country." Herridge told Barr he would take flak for this, asking: "When history looks back on this decision, how do you think it will be written?" Barr laughed: "Well, history's written by the winners. So it largely depends on who's writing the history." Watch below. More stories from theweek.com Outed CIA agent Valerie Plame is running for Congress, and her launch video looks like a spy movie trailer 7 scathing cartoons about America's rush to reopen Trump says he couldn't have exposed WWII vets to COVID-19 because the wind was blowing the wrong way

Some Democrats took "Believe Women" literally until Joe Biden was accused. Now they're relearning that guilt-by-accusation doesn't serve justice.

The ongoing investigation of the fatal shooting in Brunswick, Georgia, will also look at a neighbor of suspects Gregory and Travis McMichael who recorded video of the incident, authorities said.

Qingpo Cai, Jian Kang, Tianwei Yu.

Source: Bayesian Analysis, Volume 15, Number 1, 79--102.

Abstract:
Selecting informative nodes over large-scale networks becomes increasingly important in many research areas. Most existing methods focus on the local network structure and incur heavy computational costs for the large-scale problem. In this work, we propose a novel prior model for Bayesian network marker selection in the generalized linear model (GLM) framework: the Thresholded Graph Laplacian Gaussian (TGLG) prior, which adopts the graph Laplacian matrix to characterize the conditional dependence between neighboring markers accounting for the global network structure. Under mild conditions, we show the proposed model enjoys the posterior consistency with a diverging number of edges and nodes in the network. We also develop a Metropolis-adjusted Langevin algorithm (MALA) for efficient posterior computation, which is scalable to large-scale networks. We illustrate the superiorities of the proposed method compared with existing alternatives via extensive simulation studies and an analysis of the breast cancer gene expression dataset in the Cancer Genome Atlas (TCGA).