A stability result for balanced dictatorships in Sn

We prove that a balanced Boolean function on S_n whose Fourier transform is highly concentrated on the first two irreducible representations of S_n, is close in structure to a dictatorship, a function which is determined by the image or pre‐image of a single element. As a corollary, we obtain a stability result concerning extremal isoperimetric sets in the Cayley graph on S_n generated by the transpositions. Our proof works in the case where the expectation of the function is bounded away from 0 and 1. In contrast, [6] deals with Boolean functions of expectation O(1/ n) whose Fourier transform is highly concentrated on the first two irreducible representations of S_n. These need not be close to dictatorships; rather, they must be close to a union of a constant number of cosets of point‐stabilizers. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 494–530, 2015     

Steady-state chemotaxis in Escherichia coli

The bacterium E. coli maneuvers itself to regions with high chemoattractant concentrations by performing two stereotypical moves: "runs," in which it moves in near-straight lines, and "tumbles," in which it does not advance but changes direction randomly. The duration of each move is stochastic and depends upon the chemoattractant concentration experienced in the recent past. We relate this stochastic behavior to the steady-state density of a bacterium population, and we derive the latter as a function of chemoattractant concentration. In contrast to earlier treatments, here we account for the effects of temporal correlations and variable tumbling durations. A range of behaviors is obtained that depends subtly upon several aspects of the system -- memory, correlation, and tumbling stochasticity, in particular.     

The Metabolostasis Network and the Cellular Depository of Aggregation-Prone Metabolites

The vital role of metabolites across all branches of life and their involvement in various disorders have been investigated for decades. Many metabolites are poorly soluble in water or in physiological buffers and tend to form supramolecular aggregates. On the other hand, in the cell, they should be preserved in a pool and be readily available for the execution of biochemical functions. We thus propose that a quality-control network, termed “metabolostasis”, has evolved to regulate the storage and retrieval of aggregation-prone metabolites. Such a system should control metabolite concentration, subcellular localization, supramolecular arrangement, and interaction in dynamic environments, thus enabling normal cellular physiology, healthy development, and preventing disease onset. The paradigm-shifting concept of metabolostasis calls for a reevaluation of the traditional view of metabolite storage and dynamics in physiology and pathology and proposes unprecedented directions for therapeutic targets under conditions where metabolostasis is imbalanced.