We introduce gradient flow aggregation, a random growth model. Given existing particles $\{x_1,\ldots,x_n\} \subset \mathbb{R}^2$, a new particle arrives from a random direction at $\infty$ and flows in direction of the vector field $\nabla E$ where $ E(x) = \sum_{i=1}^{n}{1}/{\|x-x_i\|^{\alpha}}$, $0 < \alpha < \infty$. The case $\alpha = 0$ refers to the logarithmic energy ${-}\sum\log\|x-x_i\|$. Particles stop once they are at distance 1 from one of the existing particles, at which point they are added to the set and remain fixed for all time. We prove, under a non-degeneracy assumption, a Beurling-type estimate which, via Kesten’s method, can be used to deduce sub-ballistic growth for $0 \leq \alpha < 1$, $\text{diam}(\{x_1,\ldots,x_n\}) \leq c_{\alpha} \cdot n^{({3 \alpha +1})/({2\alpha + 2})}$. This is optimal when $\alpha = 0$. The case $\alpha = 0$ leads to a ‘round’ full-dimensional tree. The larger the value of $\alpha$, the sparser the tree. Some instances of the higher-dimensional setting are also discussed.

New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self-normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self-normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications, new self-normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.

In this paper, we provide a theoretical framework justifying the existence of a correlation risk premium in a market with two traded assets. We prove that risk-neutral dependence can differ substantially from real-world dependence by characterizing the set of risk-neutral martingale measures. This implies that implied correlation can be significantly different with the realized correlation. Depending on the choice of the market regarding the pricing measure, implied correlation can be high or low. We label the difference between risk-neutral and real-world correlation the “correlation gap” and make the connection with correlation risk premium. We show how dispersion trading can be used to exploit this correlation gap and demonstrate how there can exist a negative correlation risk premium in the financial market.

Ethical guidelines and policy documents destined to guide AI innovations have been heralded as the solution to guard us against harmful effects or to increase public value. However, these guidelines and policy documents face persistent challenges. While these documents are often criticized for their abstraction and disconnection from real-world contexts, it also occurs that stakeholders may influence them for political or strategic reasons. While this last issue is frequently acknowledged, there is seldom a means or a method provided to explore it. To address this gap, the paper employs a combination of social constructivism and science & technology studies perspectives, along with desk research, to investigate whether prior research has examined the influence of stakeholder interests, strategies, or agendas on guidelines and policy documents. The study contributes to the discourse on AI governance by proposing a theoretical framework and methodologies to better analyze this underexplored area, aiming to enhance comprehension of the policymaking process within the rapidly evolving AI landscape. The findings underscore the need for a critical evaluation of the methodologies found and a further exploration of their utility. In addition, the results aim to stimulate ongoing critical debates on this subject.

Since the outbreak of the COVID-19 epidemic, it has posed a great crisis to the health and economy of the world. The objective is to provide a simple deep-learning approach for predicting, modelling, and evaluating the time evolutions of the COVID-19 epidemic. The Dove Swarm Search (DSS) algorithm is integrated with the echo state network (ESN) to optimize the weight. The ESN-DSS model is constructed to predict the evolution of the COVID-19 time series. Specifically, the self-driven ESN-DSS is created to form a closed feedback loop by replacing the input with the output. The prediction results, which involve COVID-19 temporal evolutions of multiple countries worldwide, indicate the excellent prediction performances of our model compared with several artificial intelligence prediction methods from the literature (e.g., recurrent neural network, long short-term memory, gated recurrent units, variational auto encoder) at the same time scale. Moreover, the model parameters of the self-driven ESN-DSS are determined which acts as a significant impact on the prediction performance. As a result, the network parameters are adjusted to improve the prediction accuracy. The prediction results can be used as proposals to help governments and medical institutions formulate pertinent precautionary measures to prevent further spread. In addition, this study is not only limited to COVID-19 time series forecasting but also applicable to other nonlinear time series prediction problems.

We derive large-sample and other limiting distributions of components of the allele frequency spectrum vector, $\mathbf{M}_n$, joint with the number of alleles, $K_n$, from a sample of n genes. Models analysed include those constructed from gamma and $\alpha$-stable subordinators by Kingman (thus including the Ewens model), the two-parameter extension by Pitman and Yor, and a two-parameter version constructed by omitting large jumps from an $\alpha$-stable subordinator. In each case the limiting distribution of a finite number of components of $\mathbf{M}_n$ is derived, joint with $K_n$. New results include that in the Poisson–Dirichlet case, $\mathbf{M}_n$ and $K_n$ are asymptotically independent after centering and norming for $K_n$, and it is notable, especially for statistical applications, that in other cases the limiting distribution of a finite number of components of $\mathbf{M}_n$, after centering and an unusual $n^{\alpha/2}$ norming, conditional on that of $K_n$, is normal.

During the 20th century, dealing with grief through an ongoing involvement with the deceased (such as speaking to their grave) was seen as pathological by Western authors such as Sigmund Freud. Nowadays, we are presented with the opportunity to continue interacting with digital representations of the deceased. As a result, the paper adopts an Ubuntu perspective, i.e., a sub-Saharan African philosophy focussed on community and relationship to provide a toolkit for using this emerging technology. I will argue that the Ubuntu framework I propose contributes to the use of griefbots in two ways. The first is that it shows that it is morally permissible to use griefbots to assuage our grief. The second is that it delineates how we can ethically use the technology. To do so, I split my analysis into four sections. In the first section, I show that meaningful relationships can occur between the bereaved and griefbots. This will be done by exploring the Western theory of continuing bonds proposed by Dennis Klass, Phyllis Silverman and Steven Nickman. In my second, I flesh out my Ubuntu framework according to Thaddeus Metz’s accounts on Ubuntu as a modal-relational theory. In my third section, I apply my Ubuntu framework to the case of Roman Mazurenko. Furthermore, I consider some counterarguments to the Ubuntu framework regarding privacy, commercialisation and people replacement. Finally, I conclude that, despite these limitations, the Ubuntu framework positively contributes to determining whether we should communicate with the dead through griefbots to assuage our grief.

We consider linear-fractional branching processes (one-type and two-type) with immigration in varying environments. For $n\ge0$, let $Z_n$ count the number of individuals of the nth generation, which excludes the immigrant who enters the system at time n. We call n a regeneration time if $Z_n=0$. For both the one-type and two-type cases, we give criteria for the finiteness or infiniteness of the number of regeneration times. We then construct some concrete examples to exhibit the strange phenomena caused by the so-called varying environments. For example, it may happen that the process is extinct, but there are only finitely many regeneration times. We also study the asymptotics of the number of regeneration times of the model in the example.

We prove that any increasing sequence of real numbers with average gap $1$ and Poisson pair correlations has some gap that is at least $3/2+10^{-9}$. This improves upon a result of Aistleitner, Blomer, and Radziwiłł.