pinecone/core-2020-05-10-deduplication huggingface dataset:
Harnessing the Bethe free energy

A wide class of problems in combinatorics, computer science and physics can
be described along the following lines. There are a large number of variables
ranging over a finite domain that interact through constraints that each bind a
few variables and either encourage or discourage certain value combinations.
Examples include the $k$-SAT problem or the Ising model. Such models naturally
induce a Gibbs measure on the set of assignments, which is characterised by its
partition function. The present paper deals with the partition function of
problems where the interactions between variables and constraints are induced
by a sparse random (hyper)graph. According to physics predictions, a generic
recipe called the "replica symmetric cavity method" yields the correct value of
the partition function if the underlying model enjoys certain properties
[Krzkala et al., PNAS 2007]. Guided by this conjecture, we prove general
sufficient conditions for the success of the cavity method. The proofs are
based on a "regularity lemma" for probability measures on sets of the form
$\Omega^n$ for a finite $\Omega$ and a large $n$ that may be of independent
interest.Comment: This version replaces version 1 and the RANDOM 2015 version of the
  paper, which contained critical errors affecting the main result
A universal result for consecutive random subdivision of polygons

We consider consecutive random subdivision of polygons described as follows.
Given an initial convex polygon with $d\ge 3$ edges, we choose a point at
random on each edge, such that the proportions in which these points divide
edges are i.i.d. copies of some random variable $\xi$. These new points form a
new (smaller) polygon. By repeatedly implementing this procedure we obtain a
sequence of random polygons. The aim of this paper is to show that under very
mild non-degenerateness conditions on $\xi$, the shapes of these polygons
eventually become "flat" The convergence rate to flatness is also investigated;
in particular, in the case of triangles ($d=3$), we show how to calculate the
exact value of the rate of convergence, connected to Lyapunov exponents. Using
the theory of products of random matrices our paper greatly generalizes the
results of Volkov (2013) which are achieved mostly by using ad hoc methods.Comment: 35 pages, 2 figure
The Writhe of Permutations and Random Framed Knots

We introduce and study the writhe of a permutation, a circular variant of the
well-known inversion number. This simple permutation statistics has several
interpretations, which lead to some interesting properties. For a permutation
sampled uniformly at random, we study the asymptotics of the writhe, and obtain
a non-Gaussian limit distribution.
  This work is motivated by the study of random knots. A model for random
framed knots is described, which refines the Petaluma model. The distribution
of the framing in this model is equivalent to the writhe of random
permutations
Chromatic thresholds in dense random graphs

The chromatic threshold δχ(H,p) of a graph H with respect to the random graph G(n,p) is the infimum over d>0 such that the following holds with high probability: the family of H-free graphs G⊂G(n,p) with minimum degree δ(G)≥dpn has bounded chromatic number. The study of the parameter δχ(H):=δχ(H,1) was initiated in 1973 by Erd\H{o}s and Simonovits, and was recently determined for all graphs H. In this paper we show that δχ(H,p)=δχ(H) for all fixed p∈(0,1), but that typically δχ(H,p)≠δχ(H) if p=o(1). We also make significant progress towards determining δχ(H,p) for all graphs H in the range p=n−o(1). In sparser random graphs the problem is somewhat more complicated, and is studied in a separate paper
Cliques in dense inhomogeneous random graphs

The theory of dense graph limits comes with a natural sampling process which
yields an inhomogeneous variant G(n,W) of the Erdos-Renyi random graph. Here we
study the clique number of these random graphs. We establish the concentration
of the clique number of G(n,W) for each fixed n, and give examples of graphons
for which G(n,W) exhibits wild long-term behavior. Our main result is an
asymptotic formula which gives the almost sure clique number of these random
graphs. We obtain a similar result for the bipartite version of the problem. We
also make an observation that might be of independent interest: Every graphon
avoiding a fixed graph is countably-partite.Comment: 30 pages, 2 figure; accepted to publication in Random Structures and
  Algorithm
Subgraph statistics in subcritical graph classes

Let $H$ be a fixed graph and $\mathcal{G}$ a subcritical graph class. In this
paper we show that the number of occurrences of $H$ (as a subgraph) in a
uniformly at random graph of size $n$ in $\mathcal{G}$ follows a normal
limiting distribution with linear expectation and variance. The main ingredient
in our proof is the analytic framework developed by Drmota, Gittenberger and
Morgenbesser to deal with infinite systems of functional equations. As a case
study, we get explicit expressions for the number of triangles and cycles of
length four for the family of series-parallel graphs.Comment: 32 pages, 6 figure
Sharp thresholds for Ramsey properties of strictly balanced nearly
  bipartite graphs

For a given graph $F$ we consider the family of (finite) graphs $G$ with the
Ramsey property for $F$, that is the set of such graphs $G$ with the property
that every two-colouring of the edges of $G$ yields a monochromatic copy of
$F$. For $F$ being a triangle Friedgut, R\"odl, Ruci\'nski, and Tetali (2004)
established the sharp threshold for the Ramsey property in random graphs. We
obtained a simpler proof of this result which extends to a more general class
of graphs $F$ including all cycles.
  The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on
the recently developed container method for independent sets in hypergraphs by
Saxton and Thomason, and Balogh, Morris and Samotij. The proof builds on some
recent work of Friedgut et al. who established a similar result for van der
Waerden's theorem.Comment: 40 pages, second version addresses changes arising from the referee
  report
The random connection model: Connectivity, edge lengths, and degree distributions

Consider the random graph G(Pn,r) whose vertex set Pn is a Poisson point process of intensity n on (-12,12]d,d2. Any two vertices Xi,XjPn are connected by an edge with probability g(d(Xi,Xj)r), independently of all other edges, and independent of the other points of Pn. d is the toroidal metric, r > 0 and g:0,)0,1] is non-increasing and =dg(|x|)dx <. Under suitable conditions on g, almost surely, the critical parameter M-n for which G(Pn,<bold></bold>) does not have any isolated nodes satisfies lim?nnMndlog?n=1. Let =inf?{x > 0:xg(x)> 1}, and be the volume of the unit ball in d. Then for all >, G(Pn,(log?nn)1d) is connected with probability approaching one as n. The bound can be seen to be tight for the usual random geometric graph obtained by setting g=10,1]. We also prove some useful results on the asymptotic behavior of the length of the edges and the degree distribution in the connectivity regime. The results in this paper work for connection functions g that are not necessarily compactly supported but satisfy g(r)=o(r-c)
High degrees of random recursive trees

For $n\ge 1$, let $T_n$ be a random recursive tree on the vertex set
$[n]=\{1,\ldots,n\}$. Let $\mathrm{deg}_{T_n}(v)$ be the degree of vertex $v$
in $T_n$, that is, the number of children of $v$ in $T_n$. Devroye and Lu
showed that the maximum degree $\Delta_n$ of $T_n$ satisfies $\Delta_n/\lfloor
\log_2 n\rfloor \to 1$ almost surely; Goh and Schmutz showed distributional
convergence of $\Delta_n - \lfloor \log_2 n \rfloor$ along suitable
subsequences. In this work we show how a version of Kingman's coalescent can be
used to access much finer properties of the degree distribution in $T_n$.
  For any $i\in \mathbb{Z}$, let $X_i^{(n)}=|\{v\in [n]: \mathrm{deg}_{T_n}(v)=
\lfloor \log n\rfloor +i\}|$. Also, let $\mathcal{P}$ be a Poisson point
process on $\mathbb{R}$ with rate function $\lambda(x)=2^{-x}\cdot \ln 2$. We
show that, up to lattice effects, the vectors $(X_i^{(n)},\, i\in \mathbb{Z})$
converge weakly in distribution to $(\mathcal{P}[i,i+1),\, i\in \mathbb{Z})$.
We also prove asymptotic normality of $X_i^{(n)}$ when $i=i(n) \to -\infty$
slowly, and obtain precise asymptotics for $\mathbb{P}(\Delta_n - \log_2 n >
i)$ when $ i(n) \to \infty$ and $i(n)/\log n$ is not too large. Our results
recover and extends the previous results on maximal and near-maximal degrees in
random recursive trees.Comment: 15 pages, 3 figures. Revised proof of Proposition 4.5, results
  unchange
Complex martingales and asymptotic enumeration

Many enumeration problems in combinatorics, including such fundamental
questions as the number of regular graphs, can be expressed as high-dimensional
complex integrals. Motivated by the need for a systematic study of the
asymptotic behaviour of such integrals, we establish explicit bounds on the
exponentials of complex martingales. Those bounds applied to the case of
truncated normal distributions are precise enough to include and extend many
enumerative results of Barvinok, Canfield, Gao, Greenhill, Hartigan, Isaev,
McKay, Wang, Wormald, and others. Our method applies to sums as well as
integrals.
  As a first illustration of the power of our theory, we considerably
strengthen existing results on the relationship between random graphs or
bipartite graphs with specified degrees and the so-called $\beta$-model of
random graphs with independent edges, which is equivalent to the Rasch model in
the bipartite case.Comment: Minor changes as accepted by Random Structures and Algorithm
Counting dense connected hypergraphs via the probabilistic method

In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number
of connected graphs on $[n]=\{1,2,\ldots,n\}$ with $m$ edges, whenever
$n\to\infty$ and $n-1\le m=m(n)\le \binom{n}{2}$. We give an asymptotic formula
for the number $C_r(n,m)$ of connected $r$-uniform hypergraphs on $[n]$ with
$m$ edges, whenever $r\ge 3$ is fixed and $m=m(n)$ with $m/n\to\infty$, i.e.,
the average degree tends to infinity. This complements recent results of
Behrisch, Coja-Oghlan and Kang (the case $m=n/(r-1)+\Theta(n)$) and the present
authors (the case $m=n/(r-1)+o(n)$, i.e., `nullity' or `excess' $o(n)$). The
proof is based on probabilistic methods, and in particular on a bivariate local
limit theorem for the number of vertices and edges in the largest component of
a certain random hypergraph. The arguments are much simpler than in the sparse
case; in particular, we can use `smoothing' techniques to directly prove the
local limit theorem, without needing to first prove a central limit theorem.Comment: 37 pages, 1 figure. Minor changes only. To appear in Random
  Structures and Algorithm
Scaling limits of random bipartite planar maps with a prescribed degree
  sequence

We study the asymptotic behaviour of uniform random maps with a prescribed
face-degree sequence, in the bipartite case, as the number of faces tends to
infinity. Under mild assumptions, we show that, properly rescaled, such maps
converge in distribution towards the Brownian map in the Gromov-Hausdorff
sense. This result encompasses a previous one of Le Gall for uniform random
$q$-angulations where $q$ is an even integer. It applies also to random maps
sampled from a Boltzmann distribution, under a second moment assumption only,
conditioned to be large in either of the sense of the number of edges,
vertices, or faces. The proof relies on the convergence of so-called "discrete
snakes" obtained by adding spatial positions to the nodes of uniform random
plane trees with a prescribed child sequence recently studied by Broutin &
Marckert. This paper can alternatively be seen as a contribution to the study
of the geometry of such trees.Comment: 46 pages, 5 figures. Minor revisions since the first versio
On the Cycle Space of a Random Graph

Write $\mathcal{C}(G)$ for the cycle space of a graph $G$,
$\mathcal{C}_\kappa(G)$ for the subspace of $\mathcal{C}(G)$ spanned by the
copies of the $\kappa$-cycle $C_\kappa$ in $G$, $\mathcal{T}_\kappa$ for the
class of graphs satisfying $\mathcal{C}_\kappa(G)=\mathcal{C}(G)$, and
$\mathcal{Q}_\kappa$ for the class of graphs each of whose edges lies in a
$C_\kappa$. We prove that for every odd $\kappa \geq 3$ and $G=G_{n,p}$,
\[\max_p \, \Pr(G \in \mathcal{Q}_\kappa \setminus \mathcal{T}_\kappa)
\rightarrow 0;\] so the $C_\kappa$'s of a random graph span its cycle space as
soon as they cover its edges. For $\kappa=3$ this was shown by DeMarco, Hamm
and Kahn (2013).Comment: 38 page
Asymptotically optimal bound on the adjacent vertex distinguishing edge
  choice number

An adjacent vertex distinguishing edge colouring of a graph $G$ without
isolated edges is its proper edge colouring such that no pair of adjacent
vertices meets the same set of colours in $G$. We show that such colouring can
be chosen from any set of lists associated to the edges of $G$ as long as the
size of every list is at least $\Delta+C\Delta^{\frac{1}{2}}(\log\Delta)^4$,
where $\Delta$ is the maximum degree of $G$ and $C$ is a constant. The proof is
probabilistic. The same is true in the environment of total colourings.Comment: 12 page
Wildlife speed cameras: measuring animal travel speed and day range using camera traps

Travel speed (average speed of travel while active) and day range (average speed over the daily activity cycle) are behavioural metrics that influence processes including energy use, foraging success, disease transmission and human-wildlife interactions, and which can therefore be applied to a range of questions in ecology and conservation. These metrics are usually derived from telemetry or direct observations. Here, we describe and validate an entirely new alternative approach, using camera traps recording passing animals to measure movement paths at very fine scale. Dividing the length of a passage by its duration gives a speed observation, and average travel speed is estimated by fitting size-biased probability distributions to a sample of speed observations. Day range is then estimated as the product of travel speed and activity level (proportion of time spent active), which can also be estimated from camera-trap data. We field tested the procedure with data from a survey of terrestrial mammals on Barro Colorado Island, Panama. Travel speeds and day ranges estimated for 12 species scaled positively with body mass, and were higher in faunivores than in herbivores, patterns that are consistent with those obtained using independent estimates derived from tracked individuals. Comparisons of our day range estimates with independent telemetry-based estimates for three species also showed very similar values in absolute terms. We conclude that these methods are accurate and ready to use for estimating travel speed and day range in wildlife. Key advantages of the methods are that they are non-invasive, and that measurements are made at very high resolution in time and space, yielding estimates that are comparable across species and studies. Combined with emerging techniques in computer vision, we anticipate that these methods will help to expand the range of species for which we can estimate movement rate in the wild
Ultrasonic monitoring to assess the impacts of forest conversion on Solomon Island bats

Paleotropical islands are experiencing extensive land-use change, yet little is known about how such changes are impacting wildlife in these biodiversity hotspots. To address this knowledge gap, we characterized bat responses to forest conversion in a biodiverse, human-threatened coastal rainforest habitat on Makira, Solomon Islands. We analysed ~200hrs of acoustic recordings from echolocating bats in the four dominant types of land-use on Makira: intact forest, secondary forest, food gardens and cacao plantations. Bat calls were identified to the species level using a supervised classification model (where labelled data are used to train the system). We examined relative activity levels and morphological traits across habitats. Relative activity levels were highest in intermediately disturbed habitats and lowest in the most heavily disturbed habitat, although these differences were not significant. There were significant differences in the mean forearm length of bat assemblages across habitats, with the highest mean forearm length found in the most open habitat (Cacao). Overall, our study constitutes the first detailed exploration of anthropogenic effects on mammalian diversity in the Solomon Islands and includes the first acoustic and morphological information for many bat species in Melanesia. We use our experience to discuss the challenges of acoustic monitoring in such a remote and poorly studied region.Publisher PDFPeer reviewe
Upland vegetation mapping using Random Forests with optical and radar satellite data

Uplands represent unique landscapes that provide a range of vital benefits to society, but are under increasing pressure from the management needs of a diverse number of stakeholders (e.g. farmers, conservationists, foresters, government agencies and recreational users). Mapping the spatial distribution of upland vegetation could benefit management and conservation programmes and allow for the impacts of environmental change (natural and anthropogenic) in these areas to be reliably estimated. The aim of this study was to evaluate the use of medium spatial resolution optical and radar satellite data, together with ancillary soil and topographic data, for identifying and mapping upland vegetation using the Random Forests (RF) algorithm. Intensive field survey data collected at three study sites in Ireland as part of the National Parks and Wildlife Service (NPWS) funded survey of upland habitats was used in the calibration and validation of different RF models. Eight different datasets were analysed for each site to compare the change in classification accuracy depending on the input variables. The overall accuracy values varied from 59.8% to 94.3% across the three study locations and the inclusion of ancillary datasets containing information on the soil and elevation further improved the classification accuracies (between 5 and 27%, depending on the input classification dataset). The classification results were consistent across the three different study areas, confirming the applicability of the approach under different environmental contexts
Best practices and software for themanagement and sharing\ud
of camera trap data for small and large scales studies

Camera traps typically generate large amounts of bycatch data of non-target species that are secondary to the study’s objectives. Bycatch data pooled from multiple\ud
studies can answer secondary research questions; however, variation in field and data management techniques creates problems when pooling data from multiple sources. Multi-collaborator projects that use standardized methods to answer broad-scale research questions are rare and limited in geographical scope. Many small, fixed-term independent camera trap studies operate in poorly represented\ud
regions, often using field and data management methods tailored to their own objectives. Inconsistent data management practices lead to loss of bycatch data, or\ud
an inability to share it easily. As a case study to illustrate common problems that limit use of bycatch data, we discuss our experiences processing bycatch data\ud
obtained by multiple research groups during a range-wide assessment of sun bears Helarctos malayanus in Southeast Asia. We found that the most significant barrier to using bycatch data for secondary research was the time required, by the owners of the data and by the secondary researchers (us), to retrieve, interpret and process data into a form suitable for secondary analyses. Furthermore, large quantities of data were lost due to incompleteness and ambiguities in data entry. From our experiences, and from a review of the published literature and online resources, we generated nine recommendations on data management best practices for field site metadata, camera trap deployment metadata, image classification data and derived data products. We cover simple techniques that can be\ud
employed without training, special software and Internet access, as well as options for more advanced users, including a review of data management software and\ud
platforms. From the range of solutions provided here, researchers can employ those that best suit their needs and capacity. Doing so will enhance the usefulness of their camera trap bycatch data by improving the ease of data sharing, enabling collaborations and expanding the scope of research
Satellite remote sensing of ecosystem functions: opportunities, challenges and way forward

Societal, economic and scientific interests in knowing where biodiversity is, how it is faring and what can be done to efficiently mitigate further biodiversity loss and the associated loss of ecosystem services are at an all-time high. So far, however, biodiversity monitoring has primarily focused on structural and compositional features of ecosystems despite growing evidence that ecosystem functions are key to elucidating the mechanisms through which biological diversity generates services to humanity. This monitoring gap can be traced to the current lack of consensus on what exactly ecosystem functions are and how to track them at scales beyond the site level. This contribution aims to advance the development of a global biodiversity monitoring strategy by proposing the adoption of a set of definitions and a typology for ecosystem functions, and reviewing current opportunities and potential limitations for satellite remote sensing technology to support the monitoring of ecosystem functions worldwide. By clearly defining ecosystem processes, functions and services and their interrelationships, we provide a framework to improve communication between ecologists, land and marine managers, remote sensing specialists and policy makers, thereby addressing a major barrier in the field.publishersversionPeer reviewe