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We initiate a systematic study of the class of theories without the tree property of the second kind -- NTP2. Most importantly, we show: the burden is "sub-multiplicative" in arbitrary theories (in pa...
We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between ...
In many parts of mainland Southeast Asia rubber plantations are expanding rapidly in areas where the crop was not historically found. Monitoring and mapping the distribution of rubber trees in the reg...
The net benefits of mutualism depend directly on the costs and effectiveness of mutualistic services and indirectly on the interactions that affect those services. We examined interactions amo...
Abstract: In this paper we consider a nearest-neighbor $p$-adic hard core (HC) model, with fugacity $\lambda$, on a homogeneous Cayley tree of order $k$ (with $k + 1$ neighbors). We focus on $p$-adic ...
Abstract: We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which t...
Dark matter halo merger trees are now routinely extracted from cosmological simulations of structure formation. These trees are frequently used as inputs to semi-analytic models of galaxy formation to...
Abstract: We consider the number of cuts $X_n^*$ needed to isolate the root of the sub-tree spanned by $n$ leaves uniformly chosen at random in Aldous's continuum random tree $\ct$. We prove the almos...
Abstract: The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by P. Hubert...
Abstract: The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of the scatter...
Abstract: The paper considers a variable length Markov chain model associated with a group of stationary processes that share the same context tree but potentially different conditional probabilities....
Abstract: The degree chromatic polynomial $Pm(G,k)$ of a graph $G$ counts the number of $k$-colorings in which no vertex has $m$ adjacent vertices of its same color. We prove Humpert and Martin's conj...
Molecular composition and compound-specific carbon and hydrogen stable isotope ratios of n-alkanes are presented for leaves of grass, reeds and trees from five regions extending between latitudes 22°...
A conjecture of I. H´avel asserts that all middle-levels graphs Mk of the (2k + 1)-cubes possess Hamilton cycles. In this work, a tree containing all vertices of certain reduced graphs of the Mk...
It is shown that a group defined by forbidding all patterns of size s + 1 that do not appear in a given self-simialr group of tree automorphisms is the topological closure of a self-similar, countable...

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