The Onsager--Machlup functional for data assimilation

When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager--Machlup functional. Through numerical experiments, this study clarifies how the prior distribution should be incorporated into cost functions for discrete-time estimation problems. Consistent with previous theoretical studies, the divergence of the drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not nec essary in Markov chain Monte Carlo with the Euler scheme. Although the former property may cause difficulties when implementing w4D-Var in large systems, this paper proposes a new technique for estimating the divergence term and its derivative.Comment: Reprint from Nonlin. Processes Geophys. (ver.5). 12 pages, 5 figure

Principal Geodesic Analysis applied to climate time series

Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not applicable. Instead, we treat the signature space as a geodesic manifold. By replacing the notion of straight lines with that of geodesics, the domain of PCA can be extended to the curved space. Then, the first principal component is derived as the geodesic that minimizes the unexplained variance in the data. As an application, we computed the leading modes for one-year NINO SST time series, which are divided into segments that represent annual variations of monthly averages. It is interesting that some months in a year reveal characteristic undulations that could indicate the early signs of upcoming El Nin\~{o} events.Comment: draft, 23pages, 21figure

Machine learning technique using the signature method for automated quality control of the Argo profiles

A profile from the Argo ocean observation array is a sequence of three-dimensional vectors composed of pressure, salinity, and temperature, appearing as a continuous curve in three-dimensional space. The shape of this curve is faithfully represented by a path signature, which is a collection of all the iterated integrals. Moreover, the product of two terms of the signature of a path can be expressed as the sum of higher-order terms. Thanks to this algebraic property, a nonlinear function of profile shape can always be represented by a weighted linear combination of the iterated integrals, which enables machine learning of a complicated function of the profile shape. In this study, we performed supervised learning for existing Argo data with quality control flags by using the signature method, and demonstrated the estimation performance by cross-validation. Unlike rule-based approaches, which require several complicated and possibly subjective rules, this method is simple and objective in nature because it relies only on past knowledge regarding the shape of profiles. This technique should be critical to realizing automatic quality control for Argo profile data.Comment: 21 pages. 13 figures, 1 table, in revisio

The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures

We establish well-definedness of the barycenter for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). Our main motivation stems from measures induced by iterated-integrals signatures.Comment: 49 pages, 1 figur

B cell-derived GABA elicits IL-10⁺ macrophages to limit anti-tumour immunity

GABAを標的とする抗腫瘍免疫機構 --代謝産物を介した免疫細胞間制御の一端を解明--. 京都大学プレスリリース. 2021-11-10.Small, soluble metabolites not only are essential intermediates in intracellular biochemical processes, but can also influence neighbouring cells when released into the extracellular milieu1-3. Here we identify the metabolite and neurotransmitter GABA as a candidate signalling molecule synthesized and secreted by activated B cells and plasma cells. We show that B cell-derived GABA promotes monocyte differentiation into anti-inflammatory macrophages that secrete interleukin-10 and inhibit CD8⁺ T cell killer function. In mice, B cell deficiency or B cell-specific inactivation of the GABA-generating enzyme GAD67 enhances anti-tumour responses. Our study reveals that, in addition to cytokines and membrane proteins, small metabolites derived from B-lineage cells have immunoregulatory functions, which may be pharmaceutical targets allowing fine-tuning of immune responses