Rumor Spreading on Random Regular Graphs and Expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d, which is at least 3, i.e., the underlying graph is drawn uniformly at random from the set of all d-regular graphs with n vertices. We show that with probability 1 - o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d ln n rounds, where C_d = 1/ ln(2(1-1/d)) - 1/(d ln(1 - 1/d)). In particular, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo-random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1+o(1))C ln n with probability 1 - o(1), where C= 1/ ln 2 + 1, is the limit of C_d as d grows.Comment: 18 page

On the Insertion Time of Cuckoo Hashing

Cuckoo hashing is an efficient technique for creating large hash tables with high space utilization and guaranteed constant access times. There, each item can be placed in a location given by any one out of k different hash functions. In this paper we investigate further the random walk heuristic for inserting in an online fashion new items into the hash table. Provided that k > 2 and that the number of items in the table is below (but arbitrarily close) to the theoretically achievable load threshold, we show a polylogarithmic bound for the maximum insertion time that holds with high probability.Comment: 27 pages, final version accepted by the SIAM Journal on Computin

The Multiple-orientability Thresholds for Random Hypergraphs

A $k$-uniform hypergraph $H = (V, E)$ is called $\ell$-orientable, if there is an assignment of each edge $e\in E$ to one of its vertices $v\in e$ such that no vertex is assigned more than $\ell$ edges. Let $H_{n,m,k}$ be a hypergraph, drawn uniformly at random from the set of all $k$-uniform hypergraphs with $n$ vertices and $m$ edges. In this paper we establish the threshold for the $\ell$-orientability of $H_{n,m,k}$ for all $k\ge 3$ and $\ell \ge 2$, i.e., we determine a critical quantity $c_{k, \ell}^*$ such that with probability $1-o(1)$ the graph $H_{n,cn,k}$ has an $\ell$-orientation if $c c_{k, \ell}^*$. Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.Comment: An extended abstract appeared in the proceedings of SODA 201

Bootstrap percolation in inhomogeneous random graphs

A bootstrap percolation process on a graph G is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round every uninfected node which has at least r infected neighbours becomes infected and remains so forever. The parameter r > 1 is fixed. We consider this process in the case where the underlying graph is an inhomogeneous random graph whose kernel is of rank 1. Assuming that initially every vertex is infected independently with probability p > 0, we provide a law of large numbers for the number of vertices that will have been infected by the end of the process. We also focus on a special case of such random graphs which exhibit a power-law degree distribution with exponent in (2,3). The first two authors have shown the existence of a critical function a_c(n) such that a_c(n)=o(n) with the following property. Let n be the number of vertices of the underlying random graph and let a(n) be the number of the vertices that are initially infected. Assume that a set of a(n) vertices is chosen randomly and becomes externally infected. If a(n) << a_c(n), then the process does not evolve at all, with high probability as n grows, whereas if a(n)>> a_c(n), then with high probability the final set of infected vertices is linear. Using the techniques of the previous theorem, we give the precise asymptotic fraction of vertices which will be eventually infected when a(n) >> a_c (n) but a(n) = o(n). Note that this corresponds to the case where p approaches 0.Comment: 42 page

Extracellular vesicles, ageing, and therapeutic interventions

A more comprehensive understanding of the human ageing process is required to help mitigate the increasing burden of age-related morbidities in a rapidly growing global demographic of elderly individuals. One exciting novel strategy that has emerged to intervene involves the use of extracellular vesicles to engender tissue regeneration. Specifically, this employs their molecular payloads to confer changes in the epigenetic landscape of ageing cells and ameliorate the loss of functional capacity. Understanding the biology of extracellular vesicles and the specific roles they play during normative ageing will allow for the development of novel cell-free therapeutic interventions. Hence, the purpose of this review is to summarise the current understanding of the mechanisms that drive ageing, critically explore how extracellular vesicles affect ageing processes and discuss their therapeutic potential to mitigate the effects of age-associated morbidities and improve the human health span

Microvesicles as vehicles for tissue regeneration: Changing of the guards

Purpose of Review: Microvesicles (MVs) have been recognised as mediators of stem cell function, enabling and guiding their regenerative effects. Recent Findings: MVs constitute one unique size class of extracellular vesicles (EVs) directly shed from the cell plasma membrane. They facilitate cell-to-cell communication via intercellular transfer of proteins, mRNA and microRNA (miRNA). MVs derived from stem cells, or stem cell regulatory cell types, have proven roles in tissue regeneration and repair processes. Their role in the maintenance of healthy tissue function throughout the life course and thus in age related health span remains to be elucidated. Summary: Understanding the biogenesis and mechanisms of action of MVs may enable the development of cell-free therapeutics capable of assisting in tissue maintenance and repair for a variety of age-related degenerative diseases. This review critically evaluates recent work published in this area and highlights important new findings demonstrating the use of MVs in tissue regeneration

The Multiple-Orientability Thresholds for Random Hypergraphs

A k-uniform hypergraph H = (V, E) is called l-orientable if there is an assignment of each edge e is an element of E to one of its vertices v is an element of e such that no vertex is assigned more than l edges. Let H-n,H-m,H-k be a hypergraph, drawn uniformly at random from the set of all k-uniform hypergraphs with n vertices and m edges. In this paper we establish the threshold for the l-orientability of H-n,H-m,H-k for all k >= 3 and l >= 2, that is, we determine a critical quantity c(*)k,l such that with probability 1-o(1) the graph H-n,H-cn,(k) has an l-orientation if c c(k,l)(*) . Our result has various applications, including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays

Prognostic factors of atrial fibrillation following elective coronary artery bypass grafting: the impact of quantified intraoperative myocardial ischemia

<p>Abstract</p> <p>Background</p> <p>Atrial fibrillation (AF) occurs in 28-33% of the patients undergoing coronary artery revascularization (CABG). This study focuses on both pre- and peri-operative factors that may affect the occurrence of AF. The aim is to identify those patients at higher risk to develop AF after CABG.</p> <p>Patients and methods</p> <p>Two patient cohorts undergoing CABG were retrospectively studied. The first group (group A) consisted of 157 patients presenting AF after elective CABG. The second group (group B) consisted of 191 patients without AF postoperatively.</p> <p>Results</p> <p>Preoperative factors presenting significant correlation with the incidence of post-operative AF included: 1) age > 65 years (p = 0.029), 2) history of AF (p = 0.022), 3) chronic obstructive pulmonary disease (p = 0.008), 4) left ventricular dysfunction with ejection fraction < 40% (p = 0.015) and 5) proximal lesion of the right coronary artery (p = 0.023). The intraoperative factors that appeared to have significant correlation with the occurrence of postoperative AF were: 1) CPB-time > 120 minutes (p = 0.011), 2) myocardial ischemia index < 0.27 ml.m²/Kg.min (p = 0.011), 3) total positive fluid-balance during ICU-stay (p < 0.001), 4) FiO₂/PO₂> 0, 4 after extubation and during the ICU-stay (p = 0.021), 5) inotropic support with doses 15-30 μg/Kg/min (p = 0.016), 6) long ICU-stay recovery for any reason (p < 0.001) and perioperative myocardial infarction (p < 0.001).</p> <p>Conclusions</p> <p>Our results suggest that the incidence of post-CABG atrial fibrillation can be predicted by specific preoperative and intraoperative measures. The intraoperative myocardial ischemia can be sufficiently quantified by the myocardial ischemia index. For those patients at risk we would suggest an early postoperative precautionary anti-arrhythmic treatment.</p