1,547 research outputs found
Preventing Unraveling in Social Networks Gets Harder
The behavior of users in social networks is often observed to be affected by
the actions of their friends. Bhawalkar et al. \cite{bhawalkar-icalp}
introduced a formal mathematical model for user engagement in social networks
where each individual derives a benefit proportional to the number of its
friends which are engaged. Given a threshold degree the equilibrium for
this model is a maximal subgraph whose minimum degree is . However the
dropping out of individuals with degrees less than might lead to a
cascading effect of iterated withdrawals such that the size of equilibrium
subgraph becomes very small. To overcome this some special vertices called
"anchors" are introduced: these vertices need not have large degree. Bhawalkar
et al. \cite{bhawalkar-icalp} considered the \textsc{Anchored -Core}
problem: Given a graph and integers and do there exist a set of
vertices such that and
every vertex has degree at least is the induced
subgraph . They showed that the problem is NP-hard for and gave
some inapproximability and fixed-parameter intractability results. In this
paper we give improved hardness results for this problem. In particular we show
that the \textsc{Anchored -Core} problem is W[1]-hard parameterized by ,
even for . This improves the result of Bhawalkar et al.
\cite{bhawalkar-icalp} (who show W[2]-hardness parameterized by ) as our
parameter is always bigger since . Then we answer a question of
Bhawalkar et al. \cite{bhawalkar-icalp} by showing that the \textsc{Anchored
-Core} problem remains NP-hard on planar graphs for all , even if
the maximum degree of the graph is . Finally we show that the problem is
FPT on planar graphs parameterized by for all .Comment: To appear in AAAI 201
On Directed Feedback Vertex Set parameterized by treewidth
We study the Directed Feedback Vertex Set problem parameterized by the
treewidth of the input graph. We prove that unless the Exponential Time
Hypothesis fails, the problem cannot be solved in time on general directed graphs, where is the treewidth of
the underlying undirected graph. This is matched by a dynamic programming
algorithm with running time .
On the other hand, we show that if the input digraph is planar, then the
running time can be improved to .Comment: 20
Anaesthetic challenges in a patient with Klippel–Feil syndrome scheduled for panendoscopy and biopsy
Klippel–Feil syndrome is one of the congenital causes of difficult airway. It is characterised by a classic triad of a short neck, restricted cervical spine movement, and a low posterior hairline, which can pose a significant challenge to the anaesthetist during airway management. A case of Klippel Feil Syndrome type 2 with associated Sprengel’s deformity for panendoscopy under general anaesthesia is presented. The anaesthetic considerations in the management of this patient are also discussed.Keywords: awake-fibreoptic intubation, difficult airway, Klippel-Feil syndrome, panendoscopy, Sprengel's deformit
Study of underlying particle spectrum during huge X-ray flare of Mkn 421 in April 2013
Context: In April 2013, the nearby (z=0.031) TeV blazar, Mkn 421, showed one
of the largest flares in X-rays since the past decade. Aim: To study all
multiwavelength data available during MJD 56392 to 56403, with special emphasis
on X-ray data, and understand the underlying particle energy distribution.
Methods: We study the correlations between the UV and gamma bands with the
X-ray band using the z-transformed discrete correlation function. We model the
underlying particle spectrum with a single population of electrons emitting
synchrotron radiation, and do a statistical fitting of the simultaneous,
time-resolved data from the Swift-XRT and the NuSTAR. Results: There was rapid
flux variability in the X-ray band, with a minimum doubling timescale of hrs. There were no corresponding flares in UV and gamma bands. The
variability in UV and gamma rays are relatively modest with and
respectively, and no significant correlation was found with the
X-ray light curve. The observed X-ray spectrum shows clear curvature which can
be fit by a log parabolic spectral form. This is best explained to originate
from a log parabolic electron spectrum. However, a broken power law or a power
law with an exponentially falling electron distribution cannot be ruled out
either. Moreover, the excellent broadband spectrum from keV allows us
to make predictions of the UV flux. We find that this prediction is compatible
with the observed flux during the low state in X-rays. However, during the
X-ray flares, the predicted flux is a factor of smaller than the
observed one. This suggests that the X-ray flares are plausibly caused by a
separate population which does not contribute significantly to the radiation at
lower energies. Alternatively, the underlying particle spectrum can be much
more complex than the ones explored in this work.Comment: 11 pages, 7 figures, Accepted in A&
Seasonality in epidemic models: a literature review
We provide a review of some key literature results on the influence of seasonality and other time heterogeneities of contact rates, and other parameters, such as vaccination rates, on the spread of infectious diseases. This is a classical topic where highly theoretical methodologies have provided new insight on the seemingly random behavior observed in epidemic time-series. We follow the line of providing a highly personal non-systematic review of this topic, mainly based on the history of mathematical epidemiology and on the impact of reviewed articles. Our aim is to stress some issues of increasing interest, such as the public health implications of the biomathematical literature and the impact of seasonality on epidemic extinction or elimination
Time heterogeneous programs of vaccination awareness: modeling and analysis
We investigate the role of time heterogeneity of public health systems efforts in favoring the propensity of parents to vaccinate their newborns against a target childhood disease. The starting point of our investigation is the behavioral-epidemiology model proposed by d’Onofrio et al. (PLoS ONE 7:e45653, 2012), where the PHS effort was assumed to be constant. We also consider the co-presence of another layer of temporal heterogeneity: seasonality in the contact rate of the disease. We mainly assume that the effort is periodic with a 1-year period because of alternating working and holiday periods. We show that if the average effort is larger than a threshold, then the disease can be eliminated leading to an ideal equilibrium point with 100% of vaccinated newborns. A more realistic disease-free equilibrium can also be reached, under a condition that depends on the whole form of the time profile describing the PHS effort. We also generalize our disease elimination-related results to a wide class of time-heterogenous PHS efforts. Finally, we analytically show that if the disease elimination is not reached, then the disease remains uniformly persistent
Preface to the special issue on “Demographic and temporal heterogeneities in infectious disease epidemiology
No Abstrac
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