1,116 research outputs found
Dynamic energy budget approach to evaluate antibiotic effects on biofilms
Quantifying the action of antibiotics on biofilms is essential to devise
therapies against chronic infections. Biofilms are bacterial communities
attached to moist surfaces, sheltered from external aggressions by a polymeric
matrix. Coupling a dynamic energy budget based description of cell metabolism
to surrounding concentration fields, we are able to approximate survival curves
measured for different antibiotics. We reproduce numerically stratified
distributions of cell types within the biofilm and introduce ways to
incorporate different resistance mechanisms. Qualitative predictions follow
that are in agreement with experimental observations, such as higher survival
rates of cells close to the substratum when employing antibiotics targeting
active cells or enhanced polymer production when antibiotics are administered.
The current computational model enables validation and hypothesis testing when
developing therapies.Comment: to appear in Communications in Nonlinear Science and Numerical
Simulatio
Unifying Contests: from Noisy Ranking to Ratio-Form Contest Success Functions
This paper proposes a multi-winner noisy-ranking contest model. Contestants are ranked in a descending order by their perceived outputs, and rewarded by their ranks. A contestant's perceivable output increases with his/her autonomous effort, but is subject to random perturbation. We establish, under plausible conditions, the equivalence between our model and the family of (winner-take-all and multi-winner) lottery contests built upon ratio-form contest success functions. Our model thus provides a micro foundation for this family of often studied contests. In addition, our approach reveals a common thread that connects a broad class of seeming disparate competitive activities and unifies them in the nutshell of ratio-form success functions.Multi-Winner Contest; Contest Success Function; Noisy Ranking
Unifying Contests: from Noisy Ranking to Ratio-Form Contest Success Functions
This paper proposes a multi-winner noisy-ranking contest model. Contestants are ranked in a descending order by their perceived outputs, and rewarded by their ranks. A contestant's perceivable output increases with his/her autonomous effort, but is subject to random perturbation. We establish, under plausible conditions, the equivalence between our model and the family of (winner-take-all and multi-winner) lottery contests built upon ratio-form contest success functions. Our model thus provides a micro foundation for this family of often studied contests. In addition, our approach reveals a common thread that connects a broad class of seeming disparate competitive activities and unifies them in the nutshell of ratio-form success functions.Multi-Winner Contest; Contest Success Function; Noisy Ranking
From Micro to Macro: Uncovering and Predicting Information Cascading Process with Behavioral Dynamics
Cascades are ubiquitous in various network environments. How to predict these
cascades is highly nontrivial in several vital applications, such as viral
marketing, epidemic prevention and traffic management. Most previous works
mainly focus on predicting the final cascade sizes. As cascades are typical
dynamic processes, it is always interesting and important to predict the
cascade size at any time, or predict the time when a cascade will reach a
certain size (e.g. an threshold for outbreak). In this paper, we unify all
these tasks into a fundamental problem: cascading process prediction. That is,
given the early stage of a cascade, how to predict its cumulative cascade size
of any later time? For such a challenging problem, how to understand the micro
mechanism that drives and generates the macro phenomenons (i.e. cascading
proceese) is essential. Here we introduce behavioral dynamics as the micro
mechanism to describe the dynamic process of a node's neighbors get infected by
a cascade after this node get infected (i.e. one-hop subcascades). Through
data-driven analysis, we find out the common principles and patterns lying in
behavioral dynamics and propose a novel Networked Weibull Regression model for
behavioral dynamics modeling. After that we propose a novel method for
predicting cascading processes by effectively aggregating behavioral dynamics,
and propose a scalable solution to approximate the cascading process with a
theoretical guarantee. We extensively evaluate the proposed method on a large
scale social network dataset. The results demonstrate that the proposed method
can significantly outperform other state-of-the-art baselines in multiple tasks
including cascade size prediction, outbreak time prediction and cascading
process prediction.Comment: 10 pages, 11 figure
Distribution and asymptotics under beta random scaling
Let X,Y,B be three independent random variables such that has the same
distribution function as Y B. Assume that B is a Beta random variable with
positive parameters a,b and Y has distribution function H. Pakes and Navarro
(2007) show under some mild conditions that the distribution function H_{a,b}
of X determines H. Based on that result we derive in this paper a recursive
formula for calculation of H, if H_{a,b} is known. Furthermore, we investigate
the relation between the tail asymptotic behaviour of X and Y. We present three
applications of our asymptotic results concerning the extremes of two random
samples with underlying distribution functions H and H_{a,b}, respectively, and
the conditional limiting distribution of bivariate elliptical distributions.Comment: 12 page
The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures
Are there general principles governing the process by which certain products
or ideas become popular relative to other (often qualitatively similar)
competitors? To investigate this question in detail, we have focused on the
popularity of movies as measured by their box-office income. We observe that
the log-normal distribution describes well the tail (corresponding to the most
successful movies) of the empirical distributions for the total income, the
income on the opening week, as well as, the weekly income per theater. This
observation suggests that popularity may be the outcome of a linear
multiplicative stochastic process. In addition, the distributions of the total
income and the opening income show a bimodal form, with the majority of movies
either performing very well or very poorly in theaters. We also observe that
the gross income per theater for a movie at any point during its lifetime is,
on average, inversely proportional to the period that has elapsed after its
release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal
form of the overall gross income distribution, and (iii) the decay of gross
income per theater with time as a power law, constitute the fundamental set of
{\em stylized facts} (i.e., empirical "laws") that can be used to explain other
observations about movie popularity. We show that, in conjunction with an
assumption of a fixed lower cut-off for income per theater below which a movie
is withdrawn from a cinema, these laws can be used to derive a Weibull
distribution for the survival probability of movies which agrees with empirical
data. The connection to extreme-value distributions suggests that popularity
can be viewed as a process where a product becomes popular by avoiding failure
(i.e., being pulled out from circulation) for many successive time periods. We
suggest that these results may apply to popularity in general.Comment: 14 pages, 11 figure
On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels
Fading MIMO relay channels are studied analytically, when the source and
destination are equipped with multiple antennas and the relays have a single
one. Compact closed-form expressions are obtained for the outage probability
under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations
are derived, which reveal a number of insights, including the impact of
correlation, of the number of antennas, of relay noise and of relaying
protocol. The effect of correlation is shown to be negligible, unless the
channel becomes almost fully correlated. The SNR loss of relay fading channels
compared to the AWGN channel is quantified. The SNR-asymptotic
diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading
distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull,
which may be non-identical, spatially correlated and/or non-zero mean. The DMT
is shown to depend not on a particular fading distribution, but rather on its
polynomial behavior near zero, and is the same for the simple
"amplify-and-forward" protocol and more complicated "decode-and-forward" one
with capacity achieving codes, i.e. the full processing capability at the relay
does not help to improve the DMT. There is however a significant difference
between the SNR-asymptotic DMT and the finite-SNR outage performance: while the
former is not improved by using an extra antenna on either side, the latter can
be significantly improved and, in particular, an extra antenna can be
traded-off for a full processing capability at the relay. The results are
extended to the multi-relay channels with selection relaying and typical outage
events are identified.Comment: accepted by IEEE Trans. on Comm., 201
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