Scaling limit of a limit order book model via the regenerative characterization of L\'evy trees

We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost atom. Interpreting atoms as limit buy orders, this process was introduced by Lakner et al. to model a one-sided limit order book. We consider this model in the regime where the total number of orders converges to a reflected Brownian motion, and complement the results of Lakner et al. by showing that, in the case where the mean displacement at which a new order is added is positive, the measure-valued process describing the whole limit order book converges to a simple functional of this reflected Brownian motion. Our results make it possible to derive useful and explicit approximations on various quantities of interest such as the depth or the total value of the book. Our approach leverages an unexpected connection with L\'evy trees. More precisely, the cornerstone of our approach is the regenerative characterization of L\'evy trees due to Weill, which provides an elegant proof strategy which we unfold.Comment: Accepted for publication in stochastic system

Delay Line as a Chemical Reaction Network

Chemistry as an unconventional computing medium presently lacks a systematic approach to gather, store, and sort data over time. To build more complicated systems in chemistries, the ability to look at data in the past would be a valuable tool to perform complex calculations. In this paper we present the first implementation of a chemical delay line providing information storage in a chemistry that can reliably capture information over an extended period of time. The delay line is capable of parallel operations in a single instruction, multiple data (SIMD) fashion. Using Michaelis-Menten kinetics, we describe the chemical delay line implementation featuring an enzyme acting as a means to reduce copy errors. We also discuss how information is randomly accessible from any element on the delay line. Our work shows how the chemical delay line retains and provides a value from a previous cycle. The system's modularity allows for integration with existing chemical systems. We exemplify the delay line capabilities by integration with a threshold asymmetric signal perceptron to demonstrate how it learns all 14 linearly separable binary functions over a size two sliding window. The delay line has applications in biomedical diagnosis and treatment, such as smart drug delivery.Comment: 9 pages, 11 figures, 6 table

Ghrelin axis genes, peptides and receptors : recent findings and future challenges

The ghrelin axis consists of the gene products of the ghrelin gene (GHRL), and their receptors, including the classical ghrelin receptor GHSR. While it is well-known that the ghrelin gene encodes the 28 amino acid ghrelin peptide hormone, it is now also clear that the locus encodes a range of other bioactive molecules, including novel peptides and non-coding RNAs. For many of these molecules, the physiological functions and cognate receptor(s) remain to be determined. Emerging research techniques, including proteogenomics, are likely to reveal further ghrelin axis-derived molecules. Studies of the role of ghrelin axis genes, peptides and receptors, therefore, promises to be a fruitful area of basic and clinical research in years to come

Editors\u27 Note

Editors\u27 note to the inaugural issue, volume 1 of Green Humanities (2015)

Interoceptive robustness through environment-mediated morphological development

Typically, AI researchers and roboticists try to realize intelligent behavior in machines by tuning parameters of a predefined structure (body plan and/or neural network architecture) using evolutionary or learning algorithms. Another but not unrelated longstanding property of these systems is their brittleness to slight aberrations, as highlighted by the growing deep learning literature on adversarial examples. Here we show robustness can be achieved by evolving the geometry of soft robots, their control systems, and how their material properties develop in response to one particular interoceptive stimulus (engineering stress) during their lifetimes. By doing so we realized robots that were equally fit but more robust to extreme material defects (such as might occur during fabrication or by damage thereafter) than robots that did not develop during their lifetimes, or developed in response to a different interoceptive stimulus (pressure). This suggests that the interplay between changes in the containing systems of agents (body plan and/or neural architecture) at different temporal scales (evolutionary and developmental) along different modalities (geometry, material properties, synaptic weights) and in response to different signals (interoceptive and external perception) all dictate those agents' abilities to evolve or learn capable and robust strategies

Editors’ Note

Editors\u27 note to volume 3 of Green Humanities (2021)