Beyond Structural Causal Models: Causal Constraints Models

Structural Causal Models (SCMs) provide a popular causal modeling framework. In this work, we show that SCMs are not flexible enough to give a complete causal representation of dynamical systems at equilibrium. Instead, we propose a generalization of the notion of an SCM, that we call Causal Constraints Model (CCM), and prove that CCMs do capture the causal semantics of such systems. We show how CCMs can be constructed from differential equations and initial conditions and we illustrate our ideas further on a simple but ubiquitous (bio)chemical reaction. Our framework also allows to model functional laws, such as the ideal gas law, in a sensible and intuitive way.Comment: Published in Proceedings of the 35th Annual Conference on Uncertainty in Artificial Intelligence (UAI-19

A Vector-Integration-to-Endpoint Model for Performance of Viapoint Movements

Viapoint (VP) movements are movements to a desired point that are constrained to pass through an intermediate point. Studies have shown that VP movements possess properties, such as smooth curvature around the VP, that are not explicable by treating VP movements as strict concatenations of simpler point-to-point (PTP) movements. Such properties have led some theorists to propose whole-trajectory optimization models, which imply that the entire trajectory is pre-computed before movement initiation. This paper reports new experiments conducted to systematically compare VP with PTP trajectories. Analyses revealed a statistically significant early directional deviation in VP movements but no associated curvature change. An explanation of this effect is offered by extending the Vector-Integration-To-Endpoint (VITE) model (Bullock and Grossberg, 1988), which postulates that voluntary movement trajectories emerge as internal gating signals control the integration of continuously computed vector commands based on the evolving, perceptible difference between desired and actual position variables. The model explains the observed trajectories of VP and PTP movements as emergent properties of a dynamical system that does not precompute entire trajectories before movement initiation. The new model includes a working memory and a stage sensitive to time-to-contact information. These cooperate to control serial performance. The structural and functional relationships proposed in the model are consistent with available data on forebrain physiology and anatomy.Office of Naval Research (N00014-92-J-1309, N00014-93-1-1364, N0014-95-1-0409

Multiple solutions of the quasirelativistic Choquard equation

We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential

A glycinergic projection from the ventromedial lower brainstem to spinal motoneurons. An ultrastructural double labeling study in rat

__Abstract__ In the present study it was determined whether glycine was present in the descending brainstem projections to spinal motoneurons in the rat. For this purpose injections of wheatgerm agglutinin-horseradish peroxidase (WGA-HRP) were made in the ventromedial part of the lower brainstem at the levels of the rostral inferior olive and the caudal facial nucleus. After perfusion, WGA-HRP histochemistry was performed, followed by the postembedding immunogold tehncque with an antbody against glycine. Electron microscopical examination of the lumbar motoneuronal cell groups showed that 15% of the WGA-HRP labeled terminals, derived from the ventromedial reticular formation, were also labeled for glycine. The majority (91%) of these double labeled terminal were of the F-type (containing many flattened vesicles), while the remaining 9% were of the S-type (containing mostly sphetical vesicles). Many of the double labeled terminals established a synapse, mostly with proximal and distal dendrites. The present data, combined with our previous findings that 40% of the projections from the same ventromedial brainstem area to lumbar motoneurons contained γ-aminobutyric acid (GABA), indicate that over 50% of these brainstem projections contain GABA and/or glycine, exerting a direct inhibition effect on spinal motoneurons. The possibility that the glycinergic fibers within these projections play an important role in producing muscle atonia during rapid eye movement (REM) sleep is discussed

Old adults preserve motor flexibility during rapid reaching

Purpose Our ability to flexibly coordinate the available degrees of freedom allows us to perform activities of daily living under various task constraints. Healthy old adults exhibit subclinical peripheral and central nervous system dysfunctions, possibly compromising the flexibility in inter-joint coordination during voluntary movements and the ability to adapt to varying task constraints. Method We examined how healthy old (75.4 +/- 5.2 years, n = 14) compared with young adults (24.3 +/- 2 years, n = 15) make use of the available motor flexibility to adapt to physical and dexterity constraints during a rapid goal-directed reaching task. We manipulated physical and dexterity demands by changing, respectively, external resistance and target size. Motor flexibility was quantified by an uncontrolled manifold (UCM) analysis. Results We found that healthy young and old adults employ similar motor flexibility as quantified by the ratio between goal equivalent and non-goal equivalent variability (V-Ratio) and were similarly able to adapt to increases in physical and dexterity demands during goal-directed rapid reaching (V-Ratio: p = .092; young: 0.548 +/- 0.113; old: 0.264 +/- 0.117). Age affected end-effector kinematics. Motor flexibility and end-effector kinematics did not correlate. Conclusions The data challenge the prevailing view that old age affects movement capabilities in general and provide specific evidence that healthy old adults preserve motor flexibility during a reaching task. Future studies applying UCM analysis should examine if experimental set-ups limit movement exploration, leaving possible age differences undetected

Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

On fractional Choquard equations

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 page