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Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

 

В статье приведены доказательства результатов, сформулированных в работе C. Banerjee, L. Sakhanenko, D. C. Zhu Global rate optimality of integral curve estimators in high order tensor models, опубликованной в журнале Теория вероятностей и ее применения, 2023, 68(2), с. 95-115.

 

Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis—the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.

 

Functional magnetic resonance imaging faces inherent challenges when applied to deep-brain areas in rodents, e.g. entorhinal cortex, due to the signal loss near the ear cavities induced by susceptibility artifacts and reduced sensitivity induced by the long distance from the surface array coil. Given the pivotal roles of deep brain regions in various diseases, optimized imaging techniques are needed. To mitigate susceptibility-induced signal losses, we introduced baby cream into the middle ear. To enhance the detection sensitivity of deep brain regions, we implemented inductively coupled ear-bars, resulting in approximately a 2-fold increase in sensitivity in entorhinal cortex. Notably, the inductively coupled ear-bar can be seamlessly integrated as an add-on device, without necessitating modifications to the scanner interface. To underscore the versatility of inductively coupled ear-bars, we conducted echo-planner imaging-based task functional magnetic resonance imaging in rats modeling Alzheimer’s disease. As a proof of concept, we also demonstrated resting-state-functional magnetic resonance imaging connectivity maps originating from the left entorhinal cortex—a central hub for memory and navigation networks-to amygdala hippocampal area, Insular Cortex, Prelimbic Systems, Cingulate Cortex, Secondary Visual Cortex, and Motor Cortex. This work demonstrates an optimized procedure for acquiring large-scale networks emanating from a previously challenging seed region by conventional magnetic resonance imaging detectors, thereby facilitating improved observation of functional magnetic resonance imaging outcomes.

 

Вдохновленные применениями в нейровизуализации, мы рассматриваем проблему установления глобальной минимаксной нижней границы в модели тензора высокого порядка. В частности, описываемая нами методология позволяет получить глобальную минимаксную границу для оценок интегральных кривых, предложенных в работе О. Кармайкла и второго автора 2015 г., при полупараметрической постановке задачи. Теоретические результаты настоящей работы гарантируют, что оценки, используемые для отслеживания сложной структуры волокон внутри живого человеческого мозга и построенные по данным, полученным из диффузионной тензорной МРТ с высоким угловым разрешением (HARDI), оптимальны не только локально, но и глобально. Таким образом, глобальная минимаксная граница асимптотического риска оценок предоставит квантификацию неопределенности для метода оценки во всей области изображения. В дополнение к теоретическим результатам проводится подробное эмпирическое исследование с целью определить оптимальное число градиентных направлений для протоколов нейровизуализации, которые мы далее иллюстрируем анализом сканирования мозга живого человека по реальным данным. 

Neurophysiological measurements suggest that human information processing is evinced by neuronal activity. However, the quantitative relationship between the activity of a brain region and its information processing capacity remains unclear. We introduce and validate a mathematical model of the information processing capacity of a brain region in terms of neuronal activity, input storage capacity, and the arrival rate of afferent information. We applied the model to fMRI data obtained from a flanker paradigm in young and old subjects. Our analysis showed that—for a given cognitive task and subject—higher information processing capacity leads to lower neuronal activity and faster responses. Crucially, processing capacity—as estimated from fMRI data—predicted task and age-related differences in reaction times, speaking to the model’s predictive validity. This model offers a framework for modelling of brain dynamics in terms of information processing capacity, and may be exploited for studies of predictive coding and Bayes-optimal decision-making.