On the Computational Power of Shared Objects

Abstract. We propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. We use the strongest progress condition to associate with each object a number call the power number of that object. Objects with higher power numbers are considered stronger. Then, we define the power hierarchy which is an infinite hi-erarchy of objects such that the objects at level i of the hierarchy are exactly those objects with power number i. Comparing our classification with the traditional one which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Our equivalence and extended universality results, provide a deeper understanding of the nature of the relative computational power of shared objects

What Can Be Implemented Anonymously?

Abstract. The vast majority of papers on distributed computing assume that processes are assigned unique identifiers before computation begins. But is this assumption necessary? What if processes do not have unique identifiers or do not wish to divulge them for reasons of privacy? We consider asynchronous shared-memory systems that are anonymous. The shared memory contains only the most common type of shared objects, read/write registers. We investigate, for the first time, what can be implemented deterministically in this model when processes can fail. We give anonymous algorithms for some fundamental problems: timestamping, snapshots and consensus. Our solutions to the first two are wait-free and the third is obstruction-free. We also show that a shared object has an obstruction-free implementation if and only if it satisfies a simple property called idempotence. To prove the sufficiency of this condition, we give a universal construction that implements any idempotent object

The Computational Structure of Progress Conditions

Abstract. Understanding the effect of different progress conditions on the com-putability of distributed systems is an important and exciting research direction. For a system with n processes, we define exponentially many new progress con-ditions and explore their properties and strength. We cover all the known, sym-metric and asymmetric, progress conditions and many new interesting conditions. Together with our technical results, the new definitions provide a deeper under-standing of synchronization and concurrency

Uncertainty and Surprise Jointly Predict Musical Pleasure and Amygdala, Hippocampus, and Auditory Cortex Activity

Listening to music often evokes intense emotions [1, 2]. Recent research suggests that musical pleasure comes from positive reward prediction errors, which arise when what is heard proves to be better than expected [3]. Central to this view is the engagement of the nucleus accumbens—a brain region that processes reward expectations—to pleasurable music and surprising musical events [4, 5, 6, 7, 8]. However, expectancy violations along multiple musical dimensions (e.g., harmony and melody) have failed to implicate the nucleus accumbens [9, 10, 11], and it is unknown how music reward value is assigned [12]. Whether changes in musical expectancy elicit pleasure has thus remained elusive [11]. Here, we demonstrate that pleasure varies nonlinearly as a function of the listener’s uncertainty when anticipating a musical event, and the surprise it evokes when it deviates from expectations. Taking Western tonal harmony as a model of musical syntax, we used a machine-learning model [13] to mathematically quantify the uncertainty and surprise of 80,000 chords in US Billboard pop songs. Behaviorally, we found that chords elicited high pleasure ratings when they deviated substantially from what the listener had expected (low uncertainty, high surprise) or, conversely, when they conformed to expectations in an uninformative context (high uncertainty, low surprise). Neurally, we found using fMRI that activity in the amygdala, hippocampus, and auditory cortex reflected this interaction, while the nucleus accumbens only reflected uncertainty. These findings challenge current neurocognitive models of music-evoked pleasure and highlight the synergistic interplay between prospective and retrospective states of expectation in the musical experience