52 research outputs found
Krausz dimension and its generalizations in special graph classes
A {\it krausz -partition} of a graph is the partition of into
cliques, such that any vertex belongs to at most cliques and any two
cliques have at most vertices in common. The {\it -krausz} dimension
of the graph is the minimum number such that has a
krausz -partition. 1-krausz dimension is known and studied krausz
dimension of graph .
In this paper we prove, that the problem is polynomially
solvable for chordal graphs, thus partially solving the problem of P. Hlineny
and J. Kratochvil. We show, that the problem of finding -krausz dimension is
NP-hard for every , even if restricted to (1,2)-colorable graphs, but
the problem is polynomially solvable for -polar
graphs for every fixed
-product and -threshold graphs
This paper is the continuation of the research of the author and his
colleagues of the {\it canonical} decomposition of graphs. The idea of the
canonical decomposition is to define the binary operation on the set of graphs
and to represent the graph under study as a product of prime elements with
respect to this operation. We consider the graph together with the arbitrary
partition of its vertex set into subsets (-partitioned graph). On the
set of -partitioned graphs distinguished up to isomorphism we consider the
binary algebraic operation (-product of graphs), determined by the
digraph . It is proved, that every operation defines the unique
factorization as a product of prime factors. We define -threshold graphs as
graphs, which could be represented as the product of one-vertex
factors, and the threshold-width of the graph as the minimum size of
such, that is -threshold. -threshold graphs generalize the classes of
threshold graphs and difference graphs and extend their properties. We show,
that the threshold-width is defined for all graphs, and give the
characterization of graphs with fixed threshold-width. We study in detail the
graphs with threshold-widths 1 and 2
Antigenic cooperation in Viral Populations: Transformation of Functions of Intra-Host Viral Variants
In this paper we study intra-host viral adaptation by antigenic cooperation -
a mechanism of immune escape that serves as an alternative to the standard
mechanism of escape by continuous genomic diversification and allows to explain
a number of experimental observations associated with the establishment of
chronic infections by highly mutable viruses. Within this mechanism, the
topology of a cross-immunoreactivity network forces intra-host viral variants
to specialize for complementary roles and adapt to host's immune response as a
quasi-social ecosystem. Here we study dynamical changes in immune adaptation
caused by evolutionary and epidemiological events. First, we show that the
emergence of a viral variant with altered antigenic features may result in a
rapid re-arrangement of the viral ecosystem and a change in the roles played by
existing viral variants. In particular, it may push the population under immune
escape by genomic diversification towards the stable state of adaptation by
antigenic cooperation. Next, we study the effect of a viral transmission
between two chronically infected hosts, which results in merging of two
intra-host viral populations in the state of stable immune-adapted equilibrium.
In this case, we also describe how the newly formed viral population adapts to
the host's environment by changing the functions of its members. The results
are obtained analytically for minimal cross-immunoreactivity networks and
numerically for larger populations.Comment: 39 pages (including Appendix), 21 image
Scale-free spanning trees: complexity, bounds and algorithms
We introduce and study the general problem of finding a most
"scale-free-like" spanning tree of a connected graph. It is motivated by a
particular problem in epidemiology, and may be useful in studies of various
dynamical processes in networks. We employ two possible objective functions for
this problem and introduce the corresponding algorithmic problems termed -SF
and -SF Spanning Tree problems. We prove that those problems are APX- and
NP-hard, respectively, even in the classes of cubic, bipartite and split
graphs. We study the relations between scale-free spanning tree problems and
the max-leaf spanning tree problem, which is the classical algorithmic problem
closest to ours. For split graphs, we explicitly describe the structure of
optimal spanning trees and graphs with extremal solutions. Finally, we propose
two Integer Linear Programming formulations and two fast heuristics for the
-SF Spanning Tree problem, and experimentally assess their performance using
simulated and real data
Predicting Opioid Epidemic by Using Twitter Data
Opioid crisis was declared as a public health emergency in 2017 by the President of USA. According to the Centers for Disease Control and Prevention, more than 91 Americans die every day from an opioid overdose. Nearly $4B is provided to address the opioid epidemic in the 2018 spending bill and help fulfill the President’s Opioid Initiative.
How to monitor and predict the opioid epidemic accurately and in real time? The traditional methods mainly use the hospital data and usually have a lag of several years. Even though they are accurate, the long lag period prevents us from monitoring and predicting the epidemic in real time. We observe that people discuss things related to the epidemic a lot in social media platforms. These user behavior data collected from social media platforms can potentially help us monitor and predict the epidemic in real time.
In this paper, we study how to use Twitter to monitor the epidemic. We collect the historic tweets containing the set of keywords related to the epidemic. We count the frequency of the tweets posted at each month and each state. We compare the frequency values with the real-world death rates at each month and each state. We identify high correlation between tweet frequency values and real-world death rates. The statistical significance demonstrates that the Twitter data can be used for predicting the death rate and epidemic in future
Detecting Illicit Drug Ads in Google+ Using Machine Learning
Opioid abuse epidemics is a major public health emergency in the US. Social media platforms have facilitated illicit drug trading, with significant amount of drug advertisement and selling being carried out online. In order to understand dynamics of drug abuse epidemics and design efficient public health interventions, it is essential to extract and analyze data from online drug markets. In this paper, we present a computational framework for automatic detection of illicit drug ads in social media, with Google+ being used for a proof-of-concept. The proposed SVM- and CNN-based methods have been extensively validated on the large dataset containing millions of posts collected using Google+ API. Experimental results demonstrate that our methods can efficiently identify illicit drug ads with high accuracy. Both approaches have been extensively validated using the dataset containing millions of posts collected using Google+ API. Experimental results demonstrate that both methods allow for accurate identification of illicit drug ads
Next-generation sequencing reveals large connected networks of intra-host HCV variants
Background: Next-generation sequencing (NGS) allows for sampling numerous viral variants from infected patients. This provides a novel opportunity to represent and study the mutational landscape of Hepatitis C Virus (HCV) within a single host. Results: Intra-host variants of the HCV E1/E2 region were extensively sampled from 58 chronically infected patients. After NGS error correction, the average number of reads and variants obtained from each sample were 3202 and 464, respectively. The distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is 1. The work focused on large components having > 5% of all reads, which in average account for 93.7% of all reads found in a patient. The distance between any two variants calculated over the component correlated strongly with nucleotide distances (r = 0.9499; p = 0.0001), a better correlation than the one obtained with Neighbour-Joining trees (r = 0.7624; p = 0.0001). In each patient, components were well separated, with the average distance between (6.53%) being 10 times greater than within each component (0.68%). The ratio of nonsynonymous to synonymous changes was calculated and some patients (6.9%) showed a mixture of networks under strong negative and positive selection. All components were robust to in silico stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved 82.4% of remaining nodes. In vitro sampling showed that 93.02% of components present in the original sample were also found in experimental replicas, with 81.6% of reads found in both. When syringe-sharing transmission events were simulated, 91.2% of all simulated transmission events seeded all components present in the source. Conclusions: Most intra-host variants are organized into distinct single-mutation components that are: well separated from each other, represent genetic distances between viral variants, robust to sampling, reproducible and likely seeded during transmission events. Facilitated by NGS, large components offer a novel evolutionary framework for genetic analysis of intra-host viral populations and understanding transmission, immune escape and drug resistance
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