### 229910 results

Contributors: Agić, Željko, Vulić, Ivan

Date: 2019-09-19

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Contributors: Benjamini, Itai, Fontes, Luiz Renato, Hermon, Jonathan, Machado, Fabio Prates

Date: 2019-09-19

... We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple graph $G=(V,E)$. Initially, only the particles occupying $\mathbf{o}$ are active. Active particles perform $t \in \mathbb{N} \cup \{\infty \}$ steps of the walk they picked before vanishing and activate all inactive particles they hit. This system is often taken as a model for the spread of an epidemic over a population. Let $\mathcal{R}_t$ be the set of vertices which are visited by the process, when active particles vanish after $t$ steps. We study the susceptibility of the process on the underlying graph, defined as the random quantity $\mathcal{S}(G):=\inf \{t:\mathcal{R}_t=V \}$ (essentially, the shortest particles' lifetime required for the entire population to get infected). We consider the cases that the underlying graph is either a regular expander or a $d$-dimensional torus of side length $n$ (for all $d \ge 1$) $\mathbb{T}_d(n)$ and determine the asymptotic behavior of $\mathcal{S} $ up to a constant factor. In fact, throughout we allow the particle density $\lambda$ to depend on $n$ and for $d \ge 2$ we determine the asymptotic behavior of $\mathcal{S}(\mathbb{T}_d(n))$ up to smaller order terms for a wide range of $\lambda=\lambda_n$.

Contributors: Smith, Ewan

Date: 2019-09-19

... Excel files with raw data and protocols to support published data, covering both electrophysiology and cell viability assays.

Contributors: Glavaš, Goran, Vulić, Ivan

Date: 2019-09-19

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Contributors: Benjamini, Itai, Hermon, Jonathan

Date: 2019-09-19

... It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the square grid $\mathbb{Z}^2$. In particular, the $d$-dimensional grid $\mathbb{Z}^d$ admits such a Markov chain only when $d=2$. For $d=2$ we present a relevant example due to Gady Kozma, while the general statement for transient graphs is obtained by proving that for every transient irreducible Markov chain on a countable state space, which admits a stationary measure, its trace is a.s. recurrent for simple random walk. The case that the Markov chain is reversible is due to Gurel-Gurevich, Lyons and the first named author (2007). We exploit recent results in potential theory of non-reversible Markov chains in order to extend their result to the non-reversible setup.

Contributors: Lin, Qing, Qu, Mengke, Zhou, Bingjie, Patra, Hirak, Sun, Zihan, Luo, Qiong, Yang, Wenyu, Wu, Yongcui, Zhang, Yu, Li, Lin

Date: 2019-09-19

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Contributors: Glavaš, Goran, Litschko, Robert, Ruder, Sebastian, Vulić, Ivan

Date: 2019-09-19

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Contributors: Hermon, Jonathan

Date: 2019-09-19

... Let $G$ be a connected graph of uniformly bounded degree. A $k$ non-backtracking random walk ($k$-NBRW) $(X_n)_{n =0}^{\infty}$ on $G$ evolves according to the following rule: Given $ (X_n)_{n =0}^{s}$, at time $s+1$ the walk picks at random some edge which is incident to $X_s$ that was not crossed in the last $k$ steps and moves to its other end-point. If no such edge exists then it makes a simple random walk step. Assume that for some $R>0$ every ball of radius $R$ in $G$ contains a simple cycle of length at least $k$. We show that under some "nice" random time change the $k$-NBRW becomes reversible. This is used to prove that it is recurrent iff the simple random walk is.

Contributors: Nelson, Jennifer Emily

Date: 2019-09-18

... The development of novel bioconjugation strategies for the functionalisation of polypeptides and proteins has been of great benefit to the fields of chemical biology and medicine. Selective protein functionalisation has enabled the development of technologies such as targeted drug delivery, enzyme activity profiling and imaging of cells in vivo. Many strategies for bioconjugation target the nucleophilic side chains of the amino acids cysteine and lysine. However, many strategies remain sequence specific and some require pre-installation of recognition units to achieve high selectivity. Due to the low natural abundance and ancillary protein function of methionine, selective functionalisation of this amino acid presents an opportunity to develop a strategy complementary to current technologies. Strategies targeting methionine remain under-explored, with few truly biocompatible methods reported to date. This thesis describes the development of a novel bioconjugation method employing hypervalent iodine reagents for the selective functionalisation of methionine residues. The broad scope and excellent biocompatibility of the reaction is demonstrated, with a number of different polypeptide and protein substrates tolerated. Additionally, through the synthesis of different hypervalent iodine reagents, varying the ester group of the iodonium salt (R), a number of different payloads can be transferred to polypeptides and proteins. The highly reactive diazo group which is introduced using this methodology can be exploited in subsequent bioorthogonal transformations. Firstly, phosphine reagents can be employed for the cleavage of the methionine label, in a stimuli-responsive reversal of the conjugation. Secondly, a visible light-mediated reduction was developed, forming trialkylsulfonium products which exhibited improved stability. Finally, a C-benzylation has been developed using photoredox catalysis to enable functionalisation of this diazo moiety. The methionine bioconjugation strategy has also been used in tandem with a literature procedure for the functionalisation of tryptophan residues. Through the combination of two bioconjugation techniques, a simultaneous dual functionalisation of polypeptides has been developed, forming dually- or triply-functionalised scaffolds in a single step from native polypeptides.

Contributors: GBD 2017 Population and Fertility Collaborators,

Date: 2019-09-18

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