1,680 research outputs found
Two-Source Condensers with Low Error and Small Entropy Gap via Entropy-Resilient Functions
In their seminal work, Chattopadhyay and Zuckerman (STOC\u2716) constructed a two-source extractor with error epsilon for n-bit sources having min-entropy {polylog}(n/epsilon). Unfortunately, the construction\u27s running-time is {poly}(n/epsilon), which means that with polynomial-time constructions, only polynomially-small errors are possible. Our main result is a {poly}(n,log(1/epsilon))-time computable two-source condenser. For any k >= {polylog}(n/epsilon), our condenser transforms two independent (n,k)-sources to a distribution over m = k-O(log(1/epsilon)) bits that is epsilon-close to having min-entropy m - o(log(1/epsilon)). Hence, achieving entropy gap of o(log(1/epsilon)).
The bottleneck for obtaining low error in recent constructions of two-source extractors lies in the use of resilient functions. Informally, this is a function that receives input bits from r players with the property that the function\u27s output has small bias even if a bounded number of corrupted players feed adversarial inputs after seeing the inputs of the other players. The drawback of using resilient functions is that the error cannot be smaller than ln r/r. This, in return, forces the running time of the construction to be polynomial in 1/epsilon.
A key component in our construction is a variant of resilient functions which we call entropy-resilient functions. This variant can be seen as playing the above game for several rounds, each round outputting one bit. The goal of the corrupted players is to reduce, with as high probability as they can, the min-entropy accumulated throughout the rounds. We show that while the bias decreases only polynomially with the number of players in a one-round game, their success probability decreases exponentially in the entropy gap they are attempting to incur in a repeated game
Detecting and characterizing phase transitions in active matter using entropy
A major challenge in the study of active matter lies in quantitative
characterization of phases and transitions between them. We show how the
entropy of a collection of active objects can be used to classify regimes and
spatial patterns in their collective behavior. Specifically, we estimate the
contributions to the total entropy from correlations between the degrees of
freedom of position and orientation. This analysis pin-points the flocking
transition in the Vicsek model while clarifying the physical mechanism behind
the transition. When applied to experiments on swarming Bacillus subtilis with
different cell aspect ratios and overall bacterial area fractions, the entropy
analysis reveals a rich phase diagram with transitions between qualitatively
different swarm statistics. We discuss physical and biological implications of
these findings.Comment: 18 pages, 5 figures. arXiv admin note: text overlap with
arXiv:2208.0529
Antibiotic-Induced Anomalous Statistics of Collective Bacterial Swarming
Under sublethal antibiotics concentrations, the statistics of collectively swarming Bacillus subtilis transitions from normal to anomalous, with a heavy-tailed speed distribution and a two-step temporal correlation of velocities. The transition is due to changes in the properties of the bacterial motion and the formation of a motility-defective subpopulation that self-segregates into regions. As a result, both the colonial expansion and the growth rate are not affected by antibiotics. This phenomenon suggests a new strategy bacteria employ to fight antibiotic stress
BLiRF: Bandlimited Radiance Fields for Dynamic Scene Modeling
Reasoning the 3D structure of a non-rigid dynamic scene from a single moving
camera is an under-constrained problem. Inspired by the remarkable progress of
neural radiance fields (NeRFs) in photo-realistic novel view synthesis of
static scenes, extensions have been proposed for dynamic settings. These
methods heavily rely on neural priors in order to regularize the problem. In
this work, we take a step back and reinvestigate how current implementations
may entail deleterious effects, including limited expressiveness, entanglement
of light and density fields, and sub-optimal motion localization. As a remedy,
we advocate for a bridge between classic non-rigid-structure-from-motion
(\nrsfm) and NeRF, enabling the well-studied priors of the former to constrain
the latter. To this end, we propose a framework that factorizes time and space
by formulating a scene as a composition of bandlimited, high-dimensional
signals. We demonstrate compelling results across complex dynamic scenes that
involve changes in lighting, texture and long-range dynamics
Collective Dynamics Of Two-dimensional Swimming Bacteria: Experiments And Models
The physical properties of collectively swimming bacteria have been thoroughly investigated both experimentally and theoretically using simulations. While models successfully predict some aspects of the dynamics observed in experiments, both models and experiments vary in their underlying assumptions and physical conditions. Hence, it is not clear which models are appropriate for which experimental setups. Here, we study, both experimentally and using two types of models (agent-based and continuous), the statistics of two strains of Serratia marcescens, wild-type and a nontumbling strain, swimming on a two-dimensional monolayer at varying concentrations. The experimental setup allows for a direct comparison with simulation results. Both models capture some aspects of the dynamics but fail at displaying others, especially at high densities. In particular, the effect of tumbling is much more significant than mere rotational (angular) diffusion
Collective Dynamics Of Two-dimensional Swimming Bacteria: Experiments And Models
The physical properties of collectively swimming bacteria have been thoroughly investigated both experimentally and theoretically using simulations. While models successfully predict some aspects of the dynamics observed in experiments, both models and experiments vary in their underlying assumptions and physical conditions. Hence, it is not clear which models are appropriate for which experimental setups. Here, we study, both experimentally and using two types of models (agent-based and continuous), the statistics of two strains of Serratia marcescens, wild-type and a nontumbling strain, swimming on a two-dimensional monolayer at varying concentrations. The experimental setup allows for a direct comparison with simulation results. Both models capture some aspects of the dynamics but fail at displaying others, especially at high densities. In particular, the effect of tumbling is much more significant than mere rotational (angular) diffusion
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