8,672 research outputs found
Maximum Entropy Models of Shortest Path and Outbreak Distributions in Networks
Properties of networks are often characterized in terms of features such as
node degree distributions, average path lengths, diameters, or clustering
coefficients. Here, we study shortest path length distributions. On the one
hand, average as well as maximum distances can be determined therefrom; on the
other hand, they are closely related to the dynamics of network spreading
processes. Because of the combinatorial nature of networks, we apply maximum
entropy arguments to derive a general, physically plausible model. In
particular, we establish the generalized Gamma distribution as a continuous
characterization of shortest path length histograms of networks or arbitrary
topology. Experimental evaluations corroborate our theoretical results
Kinetic analysis of drug release from nanoparticles
PURPOSE. Comparative drug release kinetics from nanoparticles was carried out using conventional and our novel models with the aim of finding a general model applicable to multi mechanistic release. Theoretical justification for the two best general models was also provided for the first time. METHODS. Ten conventional models and three models developed in our laboratory were applied to release data of 32 drugs from 106 nanoparticle formulations collected from literature. The accuracy of the models was assessed employing mean percent error (E) of each data set, overall mean percent error (OE) and number of Es less than 10 percent. RESULTS. Among the models the novel reciprocal powered time (RPT), Weibull (W) and log-probability (LP) ones produced OE values of 6.47, 6.39 and 6.77, respectively. The OEs of other models were higher than 10%. Also the number of errors less than 10% for the models was 84.9, 80.2 and 78.3 percents of total number of data sets. CONCLUSIONS. Considering the accuracy criteria the reciprocal powered time model could be suggested as a general model for analysis of multi mechanistic drug release from nanoparticles. Also W and LP models were the closest to the suggested model RPT
Modeling Adoption and Usage of Competing Products
The emergence and wide-spread use of online social networks has led to a
dramatic increase on the availability of social activity data. Importantly,
this data can be exploited to investigate, at a microscopic level, some of the
problems that have captured the attention of economists, marketers and
sociologists for decades, such as, e.g., product adoption, usage and
competition.
In this paper, we propose a continuous-time probabilistic model, based on
temporal point processes, for the adoption and frequency of use of competing
products, where the frequency of use of one product can be modulated by those
of others. This model allows us to efficiently simulate the adoption and
recurrent usages of competing products, and generate traces in which we can
easily recognize the effect of social influence, recency and competition. We
then develop an inference method to efficiently fit the model parameters by
solving a convex program. The problem decouples into a collection of smaller
subproblems, thus scaling easily to networks with hundred of thousands of
nodes. We validate our model over synthetic and real diffusion data gathered
from Twitter, and show that the proposed model does not only provides a good
fit to the data and more accurate predictions than alternatives but also
provides interpretable model parameters, which allow us to gain insights into
some of the factors driving product adoption and frequency of use
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
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An Overview of Models for Response Times and Processes in Cognitive Tests.
Response times (RTs) are a natural kind of data to investigate cognitive processes underlying cognitive test performance. We give an overview of modeling approaches and of findings obtained with these approaches. Four types of models are discussed: response time models (RT as the sole dependent variable), joint models (RT together with other variables as dependent variable), local dependency models (with remaining dependencies between RT and accuracy), and response time as covariate models (RT as independent variable). The evidence from these approaches is often not very informative about the specific kind of processes (other than problem solving, information accumulation, and rapid guessing), but the findings do suggest dual processing: automated processing (e.g., knowledge retrieval) vs. controlled processing (e.g., sequential reasoning steps), and alternative explanations for the same results exist. While it seems well-possible to differentiate rapid guessing from normal problem solving (which can be based on automated or controlled processing), further decompositions of response times are rarely made, although possible based on some of model approaches
Change of Scaling and Appearance of Scale-Free Size Distribution in Aggregation Kinetics by Additive Rules
The idealized general model of aggregate growth is considered on the basis of
the simple additive rules that correspond to one-step aggregation process. The
two idealized cases were analytically investigated and simulated by Monte Carlo
method in the Desktop Grid distributed computing environment to analyze
"pile-up" and "wall" cluster distributions in different aggregation scenarios.
Several aspects of aggregation kinetics (change of scaling, change of size
distribution type, and appearance of scale-free size distribution) driven by
"zero cluster size" boundary condition were determined by analysis of evolving
cumulative distribution functions. The "pile-up" case with a \textit{minimum}
active surface (singularity) could imitate piling up aggregations of
dislocations, and the case with a \textit{maximum} active surface could imitate
arrangements of dislocations in walls. The change of scaling law (for pile-ups
and walls) and availability of scale-free distributions (for walls) were
analytically shown and confirmed by scaling, fitting, moment, and bootstrapping
analyses of simulated probability density and cumulative distribution
functions. The initial "singular" \textit{symmetric} distribution of pile-ups
evolves by the "infinite" diffusive scaling law and later it is replaced by the
other "semi-infinite" diffusive scaling law with \textit{asymmetric}
distribution of pile-ups. In contrast, the initial "singular"
\textit{symmetric} distributions of walls initially evolve by the diffusive
scaling law and later it is replaced by the other ballistic (linear) scaling
law with \textit{scale-free} exponential distributions without distinctive
peaks. The conclusion was made as to possible applications of such approach for
scaling, fitting, moment, and bootstrapping analyses of distributions in
simulated and experimental data.Comment: 37 pages, 16 figures, 1 table; accepted preprint version after
comments of reviewers, Physica A: Statistical Mechanics and its Applications
(2014
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