4,692 research outputs found
From fractions to complete Segal spaces
We show that the Rezk classification diagram of a relative category admitting
a homotopical version of the two-sided calculus of fractions is a Segal space
up to Reedy-fibrant replacement. This generalizes the result of Rezk and
Bergner on the classification diagram of a closed model category, as well as
the result of Barwick and Kan on the classification diagram of a partial model
category.Comment: 21 pages, LaTeX. Changes in v3: added some expository material,
following suggestions by anonymous referee. (N.B. numbering has changed.
Equilateral sets in the β1 sum of Euclidean spaces
Let En denote the (real) n-dimensional Euclidean space. It is not known whether an equilateral set in the β1 sum of Ea and Eb , denoted here as Eaβ1Eb , has maximum size at least dim(Eaβ1Eb)+1=a+b+1 for all pairs of a and b. We show, via some explicit constructions of equilateral sets, that this holds for all aβ©½27 , as well as some other instances
Near-Optimal Time and Sample Complexities for Solving Discounted Markov Decision Process with a Generative Model
In this paper we consider the problem of computing an -optimal
policy of a discounted Markov Decision Process (DMDP) provided we can only
access its transition function through a generative sampling model that given
any state-action pair samples from the transition function in time.
Given such a DMDP with states , actions , discount factor
, and rewards in range we provide an algorithm which
computes an -optimal policy with probability where
\emph{both} the time spent and number of sample taken are upper bounded by For fixed values
of , this improves upon the previous best known bounds by a factor of
and matches the sample complexity lower bounds proved in
Azar et al. (2013) up to logarithmic factors. We also extend our method to
computing -optimal policies for finite-horizon MDP with a generative
model and provide a nearly matching sample complexity lower bound.Comment: 31 pages. Accepted to NeurIPS, 201
Phase resetting reveals network dynamics underlying a bacterial cell cycle
Genomic and proteomic methods yield networks of biological regulatory
interactions but do not provide direct insight into how those interactions are
organized into functional modules, or how information flows from one module to
another. In this work we introduce an approach that provides this complementary
information and apply it to the bacterium Caulobacter crescentus, a paradigm
for cell-cycle control. Operationally, we use an inducible promoter to express
the essential transcriptional regulatory gene ctrA in a periodic, pulsed
fashion. This chemical perturbation causes the population of cells to divide
synchronously, and we use the resulting advance or delay of the division times
of single cells to construct a phase resetting curve. We find that delay is
strongly favored over advance. This finding is surprising since it does not
follow from the temporal expression profile of CtrA and, in turn, simulations
of existing network models. We propose a phenomenological model that suggests
that the cell-cycle network comprises two distinct functional modules that
oscillate autonomously and couple in a highly asymmetric fashion. These
features collectively provide a new mechanism for tight temporal control of the
cell cycle in C. crescentus. We discuss how the procedure can serve as the
basis for a general approach for probing network dynamics, which we term
chemical perturbation spectroscopy (CPS)
Extension of Public Warning System
This disclosure describes techniques to relay public warning system (PWS) messages from a host device to user devices that cannot receive broadcast messages from a cellular network. A PWS message broadcast by a cellular network is received by the host device and relayed to user devices within a personal area network (PAN). Fields from the incoming PWS message are compared to previously received PWS messages to avoid duplication of messages. Relay of the PWS message by the router enables reception of the PWS message by user devices in the PAN that are not connected to the cellular network. User configurable settings enable users to select or disable the feature of reception of PWS via the PAN
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