Causal inference in a nonlinear system of multivariate timeseries is
instrumental in disentangling the intricate web of relationships among
variables, enabling us to make more accurate predictions and gain deeper
insights into real-world complex systems. Causality methods typically identify
the causal structure of a multivariate system by considering the cause-effect
relationship of each pair of variables while ignoring the collective effect of
a group of variables or interactions involving more than two-time series
variables. In this work, we test model invariance by group-level interventions
on the trained deep networks to infer causal direction in groups of variables,
such as climate and ecosystem, brain networks, etc. Extensive testing with
synthetic and real-world time series data shows a significant improvement of
our method over other applied group causality methods and provides us insights
into real-world time series. The code for our method can be found
at:this https URL

我们在多元时间序列的非线性系统中通过组级别的干预，测试模型的不变性，识别变量组的因果方向，从而获得比其他应用组因果方法更显著的改进，并深入了解真实世界的时间序列。

基于深度学习的多元时间序列群体因果推断

Deep Learning-based Group Causal Inference in Multivariate Time-series

This work investigates conditions for quantitative image reconstruction in
multispectral computed tomography (MSCT), which remains a topic of active
research. In MSCT, one seeks to obtain from data the spatial distribution of
linear attenuation coefficient, referred to as a virtual monochromatic image
(VMI), at a given X-ray energy, within the subject imaged. As a VMI is
decomposed often into a linear combination of basis images with known
decomposition coefficients, the reconstruction of a VMI is thus tantamount to
that of the basis images. An empirical, but highly effective, two-step
data-domain-decomposition (DDD) method has been developed and used widely for
quantitative image reconstruction in MSCT. In the two-step DDD method, step (1)
estimates the so-called basis sinogram from data through solving a nonlinear
transform, whereas step (2) reconstructs basis images from their basis
sinograms estimated. Subsequently, a VMI can readily be obtained from the
linear combination of basis images reconstructed. As step (2) involves the
inversion of a straightforward linear system, step (1) is the key component of
the DDD method in which a nonlinear system needs to be inverted for estimating
the basis sinograms from data. In this work, we consider a {\it discrete} form
of the nonlinear system in step (1), and then carry out theoretical and
numerical analyses of conditions on the existence, uniqueness, and stability of
a solution to the discrete nonlinear system for accurately estimating the
discrete basis sinograms, leading to quantitative reconstruction of VMIs in
MSCT.

通过离散非线性系统的理论和数值分析，研究多光谱计算机断层扫描中基础正弦图像的存在性、唯一性、稳定性等问题，从而可实现定量图像重建。

多光谱 CT 离散基础正弦图谱的解的存在性、唯一性和稳定性

Solution existence, uniqueness, and stability of discrete basis  sinograms in multispectral CT

The paper introduces a technique that decomposes the dynamics of a nonlinear
system about an equilibrium into low order components, which then can be used
to reconstruct the full dynamics. This is a nonlinear analogue of linear modal
analysis. The dynamics is decomposed using Invariant Spectral Foliations (ISF),
which is defined as the smoothest invariant foliation about an equilibrium and
hence unique under general conditions. The conjugate dynamics of an ISF can be
used as a reduced order model. An ISF can be fitted to vibration data without
carrying out a model identification first. The theory is illustrated on a
analytic example and on free-vibration data of a clamped-clamped beam

本文介绍了将非线性系统动力学分解为低阶组件的技术，以便重构完整的动力学，该技术使用不变谱叶（ISF）来分解动力学，并且可以将 ISF 拟合到振动数据中，作为降阶模型。作者通过一个分析例子和夹紧梁自由振动数据来说明该理论。