An
topological graph
(briefly an
AT-graph
) is a pair
A
=
(
G
,
X
)
where
G
=
(
V
,
E
)
is a graph and
X
⊆
E
2
is a set of pairs of its edges. The AT-graph
A
is
simply realizable
if
G
can be drawn in ...the plane so that each pair of edges from
X
crosses exactly once and no other pair crosses. We show that simply realizable complete AT-graphs are characterized by a finite set of forbidden AT-subgraphs, each with at most six vertices. This implies a straightforward polynomial algorithm for testing simple realizability of complete AT-graphs, which simplifies a previous algorithm by the author. We also show an analogous result for independent
Z
2
-realizability, where only the parity of the number of crossings for each pair of independent edges is specified.
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A
simple topological graph
T
=
(
V
(
T
)
,
E
(
T
)
)
is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass ...through a single crossing. Topological graphs
G
and
H
are
isomorphic
if
H
can be obtained from
G
by a homeomorphism of the sphere, and
weakly isomorphic
if
G
and
H
have the same set of pairs of crossing edges. We generalize results of Pach and Tóth and the author’s previous results on counting different drawings of a graph under both notions of isomorphism. We prove that for every graph
G
with
n
vertices,
m
edges and no isolated vertices the number of weak isomorphism classes of simple topological graphs that realize
G
is at most
2
O
(
n
2
log
(
m
/
n
)
)
, and at most
2
O
(
m
n
1
/
2
log
n
)
if
m
≤
n
3
/
2
. As a consequence we obtain a new upper bound
2
O
(
n
3
/
2
log
n
)
on the number of intersection graphs of
n
pseudosegments. We improve the upper bound on the number of weak isomorphism classes of simple complete topological graphs with
n
vertices to
2
n
2
·
α
(
n
)
O
(
1
)
, using an upper bound on the size of a set of permutations with bounded VC-dimension recently proved by Cibulka and the author. We show that the number of isomorphism classes of simple topological graphs that realize
G
is at most
2
m
2
+
O
(
m
n
)
and at least
2
Ω
(
m
2
)
for graphs with
m
>
(
6
+
ε
)
n
.
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Spiraling and Folding: The Topological View Kynčl, Jan; Schaefer, Marcus; Sedgwick, Eric ...
Discrete & computational geometry,
07/2024, Volume:
72, Issue:
1
Journal Article
Peer reviewed
Open access
For every
n
, we construct two arcs in the plane that intersect at least
n
times and do not form spirals. The construction is in three stages: we first exhibit two closed curves on the torus that do ...not form double spirals, then two arcs on the torus that do not form spirals, and finally two arcs in the plane that do not form spirals. The planar arcs provide a counterexample to a proof of Pach and Tóth concerning string graphs.
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We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem ...cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus.
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The aim of our study was to analyse the influence of air temperature and implemented veterinary measures on salmonellosis incidence in the Czech Republic (CZ).
We conducted a descriptive analysis of ...salmonellosis as reported to the Czech national surveillance system during 1998-2017 and evaluated the influence of applied veterinary measures (started in January 2008) on salmonellosis incidence by comparing two 9-year periods (1998-2006, 2009-2017). Using a generalized additive model, we analysed association between monthly mean air temperature and log-transformed salmonellosis incidence over the entire twenty-year period.
A total of 410,533 salmonellosis cases were reported during the study period in the CZ. Annual mean incidences of salmonellosis were 313.0/100,000 inhabitants before and 99.0/100,000 inhabitants after implementation of the veterinary measures. The time course of incidence was non-linear, with a sharp decline during 2006-2010. Significant association was found between disease incidence and air temperature. On average, the data indicated that within a common temperature range every 1 °C rise in air temperature contributed to a significant 6.2% increase in salmonellosis cases.
Significant non-linear effects of annual trend, within-year seasonality, and air temperature on the incidence of salmonellosis during 1998-2017 were found. Our study also demonstrates significant direct effect of preventive veterinary measures taken in poultry in reducing incidence of human salmonellosis in the CZ. The annual mean number of salmonellosis cases in the period after introducing the veterinary measures was only 32.5% of what it had been in the previous period.
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The hamburger theorem Kano, Mikio; Kynčl, Jan
Computational geometry : theory and applications,
March 2018, 2018-03-00, Volume:
68
Journal Article
Peer reviewed
Open access
We generalize the ham sandwich theorem to d+1 measures on Rd as follows. Let μ1,μ2,…,μd+1 be absolutely continuous finite Borel measures on Rd. Let ωi=μi(Rd) for i∈d+1, ω=min{ωi;i∈d+1} and assume ...that ∑j=1d+1ωj=1. Assume that ωi≤1/d for every i∈d+1. Then there exists a hyperplane h such that each open halfspace H defined by h satisfies μi(H)≤(∑j=1d+1μj(H))/d for every i∈d+1 and ∑j=1d+1μj(H)≥min{1/2,1−dω}≥1/(d+1). As a consequence we obtain that every (d+1)-colored set of nd points in Rd such that no color is used for more than n points can be partitioned into n disjoint rainbow (d−1)-dimensional simplices.
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Pregnant women are among the priority groups to receive influenza vaccines in the Czech Republic since 2011, data on vaccination coverage are not yet available. The aim of the study was to determine ...the influenza vaccination coverage (IVC) and provide source data for further activities.
A prospective observational study was performed in a large maternity hospital in Prague. The self-completed questionnaire was distributed to 5,475 pregnant women between September 1, 2020 and August 31, 2021. Questions included maternal sociodemographic characteristics, influenza vaccination status and sources of maternal vaccination recommendations during pregnancy.
A total of 4,617 completed questionnaires have been analysed. The median age of study participants (N = 4,592) was 33 years (range: 18-51 years). The majority (69.7%) of women had completed their university education, most women were childless (58.5%) or had one child (32.5%) before the start of the study. Less than 2% of women reported being vaccinated against influenza during their pregnancy (1.5%; 95% CI, 1.1-1.9%). Only 21% of women knew that it's possible to get vaccinated against influenza during pregnancy. Participants considered influenza vaccination in pregnancy as important (3.3%), useful (41.1%) and useless (44.4%). Out of 959 pregnant women who had information about influenza vaccination during pregnancy, only 6.9% were vaccinated, while among those who did not have this information, 0.1% were vaccinated during pregnancy (p < 0.001). The most frequent source of information was Internet, then media and a general practitioner.
The IVC during pregnancy in our study was extremely low. In order to improve IVC among pregnant women, it is necessary to increase awareness of recommendations and vaccination options among the public and professionals and incorporating vaccination recommendation in routine antenatal practice.
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8.
On crossing-families in planar point sets Aichholzer, Oswin; Kynčl, Jan; Scheucher, Manfred ...
Computational geometry : theory and applications,
December 2022, 2022-12-00, Volume:
107
Journal Article
Peer reviewed
Open access
A k-crossing family in a point set S in general position is a set of k segments spanned by points of S such that all k segments mutually cross. In this short note we present two statements on ...crossing families which are based on sets of small cardinality: (1) Any set of at least 15 points contains a crossing family of size 4. (2) There are sets of n points which do not contain a crossing family of size larger than 8⌈n41⌉. Both results improve the previously best known bounds.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
An
topological graph
(briefly an
AT-graph
) is a pair
where
G
=(
V
,
E
) is a graph and
is a set of pairs of its edges. An AT-graph
A
is
simply realizable
if
G
can be drawn in the plane in such a way ...that each pair of edges from
crosses exactly once and no other pair crosses. We present a polynomial algorithm which decides whether a given complete AT-graph is simply realizable. On the other hand, we show that other similar realizability problems for (complete) AT-graphs are NP-hard.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Many studies have reported associations between temperature extremes and cardiovascular mortality but little has been understood about differences in the effects on acute and chronic diseases. The ...present study examines hot and cold spell effects on ischaemic heart disease (IHD) mortality in the Czech Republic during 1994-2009, with emphasis upon differences in the effects on acute myocardial infarction (AMI) and chronic IHD.
We use analogous definitions for hot and cold spells based on quantiles of daily average temperature anomalies, thus allowing for comparison of results for summer hot spells and winter cold spells. Daily mortality data were standardised to account for the long-term trend and the seasonal and weekly cycles. Periods when the data were affected by epidemics of influenza and other acute respiratory infections were removed from the analysis.
Both hot and cold spells were associated with excess IHD mortality. For hot spells, chronic IHD was responsible for most IHD excess deaths in both male and female populations, and the impacts were much more pronounced in the 65+ years age group. The excess mortality from AMI was much lower compared to chronic IHD mortality during hot spells. For cold spells, by contrast, the relative excess IHD mortality was most pronounced in the younger age group (0-64 years), and we found different pattern for chronic IHD and AMI, with larger effects on AMI.
The findings show that while excess deaths due to IHD during hot spells are mainly of persons with chronic diseases whose health had already been compromised, cardiovascular changes induced by cold stress may result in deaths from acute coronary events rather than chronic IHD, and this effect is important also in the younger population. This suggests that the most vulnerable population groups as well as the most affected cardiovascular diseases differ between hot and cold spells, which needs to be taken into account when designing and implementing preventive actions.
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