Complex pathways and memory in compressed corrugated sheets

The nonlinear response of driven complex materials—disordered magnets, amorphous media, and crumpled sheets—features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry. We show how manipulation of the boundaries allows us to elicit multiple targeted pathways from a single sample. In all cases, each state in the pathway can be encoded by the binary state of material bits called hysterons, and the strength of their interactions plays a crucial role. In particular, as function of increasing interaction strength, we observe Preisach pathways, expected in systems of independently switching hysterons; scrambled pathways that evidence hitherto unexplored interactions between these material bits; and accumulator pathways which leverage these interactions to perform an elementary computation. Our work opens a route to probe, manipulate, and understand complex pathways, impacting future applications in soft robotics and information processing in materials.

Bounded Rational Decision-Making from Elementary Computations That Reduce Uncertainty

In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou–Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. Consequently, we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.

Is Cognitive Psychopathology Plausible? Illustrations from Memory Research

Objective: To examine the strengths and weaknesses of cognitive psychopathology through the specific examples of the memory impairments associated with the administration of benzodiazepines, with schizophrenia, and with depression. Method: These examples are analyzed with reference to a model of memory based on the principle of division between specialized and central processing structures. A basic contention is that it is useful to consider 2 broad classes of processes—automatic, associative, or sensory/perceptual processes on the one hand and intentional, strategic, or reflective processes on the other hand—as being separate. Results: The functional mechanisms of the memory impairments associated with these conditions are beginning to be identified, and there is preliminary evidence that a deficit in an elementary computation may have dramatic consequences on highest cognitive functions. There is also evidence that certain memory impairments are linked to specific dysfunctional outcomes in everyday life. By showing that specific rate-limiting factors of cognitive performance can be identified and are amenable to cognitive interventions, existing data open the door for theoretically and empirically based cognitive remediation of mental disorders. Conclusion: The bulk of available evidence (albeit limited) makes the enterprise of cognitive psychopathology quite plausible and convincing.