Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naïve estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.

Canines and carnassials as indicators of sociality in durophagous hyaenids: analyzing the past to understand the present

We analyzed the lower and upper dentition of the family Hyaenidae along its evolutionary history from a multivariate point of view. A total of 13,103 individual measurements of the lengths and widths of canines and the main post-canine teeth (lower third and fourth premolar, lower first molar, and upper second, third, and fourth premolars) were collected for 39 extinct and extant species of this family. We analyzed these measurements using principal component analyses. The multivariate structure characterized the main groups of previously defined hyaenid ecomorphs. Strikingly, our analyses also detected differences between social hunting durophages (such as Crocuta crocuta) and solitary scavengers (such as Hyaena hyaena or Parahyaena brunnea). Concerning the hyaenid bauplan, social hunters have large carnassials and smaller canines, whereas solitary scavengers show the exact opposite morphological adaptations. Additionally, scavengers exhibited upper canines larger than lower ones, whereas hunters have upper and lower canines of similar size. It is hypothesized that sociality has led to an increase in carnassial length for hunting durophages via scramble competition at feeding. Such competition also penalizes adults from bringing food to cubs, which are consequently breastfed. On the other hand, it is also hypothesized that natural selection has led to solitary scavengers having large canines to transport carcasses to cubs. Our results indicate that these functional aspects are also better reflected by lower teeth than the upper dentition, which leads to a mosaic evolution.

Multivariate General Compound Point Processes in Limit Order Books

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

Analytical construction of relay dynamic system point mappings taking into account delays

The article considers solving the problem of analytical construction of Poincare maps for finding simple and complex limit cycles in a relay dynamic system involving constant perturbation and delay. Application of Neymark’s theory of multivariate point transformations allows reducing the problem under consideration to the search for a multifold fixed point thus overcoming the difficulty of finding complex periodic motions. The choice of switching lines as arcs without contact taking into account delays significantly simplified the task of analytical construction of point mapping. The results of analytical constructions are confirmed by numerical simulation of movements. The results obtained can find practical application in developing reactive systems for controlling the orientation and stabilization of the spacecraft. Compared with the previously known solution, a more complete result is obtained, which is of particular importance in the study of systems with high efficiency of executive bodies.