Balanced Allocations: A Simple Proof for the Heavily Loaded Case

We provide a relatively simple proof that the expected gap between the maximum load and the average load in the two choice process is bounded by $(1+o(1))\log \log n$, irrespective of the number of balls thrown. The theorem was first proven by Berenbrink et al. Their proof uses heavy machinery from Markov-Chain theory and some of the calculations are done using computers. In this manuscript we provide a significantly simpler proof that is not aided by computers and is self contained. The simplification comes at a cost of weaker bounds on the low order terms and a weaker tail bound for the probability of deviating from the expectation

Parallel Load Balancing on Constrained Client-Server Topologies

We study parallel \emph{Load Balancing} protocols for a client-server distributed model defined as follows. There is a set \sC of $n$ clients and a set \sS of $n$ servers where each client has (at most) a constant number $d \geq 1$ of requests that must be assigned to some server. The client set and the server one are connected to each other via a fixed bipartite graph: the requests of client $v$ can only be sent to the servers in its neighborhood $N(v)$. The goal is to assign every client request so as to minimize the maximum load of the servers. In this setting, efficient parallel protocols are available only for dense topolgies. In particular, a simple symmetric, non-adaptive protocol achieving constant maximum load has been recently introduced by Becchetti et al \cite{BCNPT18} for regular dense bipartite graphs. The parallel completion time is \bigO(\log n) and the overall work is \bigO(n), w.h.p. Motivated by proximity constraints arising in some client-server systems, we devise a simple variant of Becchetti et al's protocol \cite{BCNPT18} and we analyse it over almost-regular bipartite graphs where nodes may have neighborhoods of small size. In detail, we prove that, w.h.p., this new version has a cost equivalent to that of Becchetti et al's protocol (in terms of maximum load, completion time, and work complexity, respectively) on every almost-regular bipartite graph with degree $\Omega(\log^2n)$. Our analysis significantly departs from that in \cite{BCNPT18} for the original protocol and requires to cope with non-trivial stochastic-dependence issues on the random choices of the algorithmic process which are due to the worst-case, sparse topology of the underlying graph

Balanced Allocation on Graphs: A Random Walk Approach

In this paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$, $1\le t\le n$, ball $t$ picks a node of $G$ uniformly at random and performs a non-backtracking random walk of length $l$ from the chosen node.Then it allocates itself on one of the visited nodes with minimum load (ties are broken uniformly at random). Suppose that $G$ has a sufficiently large girth and $d=\omega(\log n)$. Then we establish an upper bound for the maximum number of balls at any bin after allocating $n$ balls by the algorithm, called {\it maximum load}, in terms of $l$ with high probability. We also show that the upper bound is at most an $O(\log\log n)$ factor above the lower bound that is proved for the algorithm. In particular, we show that if we set $l=\lfloor(\log n)^{\frac{1+\epsilon}{2}}\rfloor$, for every constant $\epsilon\in (0, 1)$, and $G$ has girth at least $\omega(l)$, then the maximum load attained by the algorithm is bounded by $O(1/\epsilon)$ with high probability.Finally, we slightly modify the algorithm to have similar results for balanced allocation on $d$-regular graph with $d\in[3, O(\log n)]$ and sufficiently large girth

ATP-induced reversed thermal sensitivity of O2 binding in both major haemoglobin polymorphs of the non-endothermic Atlantic cod, Gadus morhua.

Atlantic cod is a species that is affected by climate change, with some populations being exposed to higher temperatures than others. The two polymorphs of its major haemoglobin type (HbI) show an inverse change in frequency along a latitudinal temperature cline in the North East Atlantic, which has been associated with differences in population performance and behavioural traits. An earlier study at the northern distribution limit of the species reported differential temperature sensitivities of red blood cell oxygen (O2) affinity between the northern cold-water HbI-2 polymorph and its southern, warm-water HbI-1 counter-part, which has since widely been held as adaptive for the species across its distributional range. The present study critically re-examined this hypothesis by comparing the thermal sensitivity of O2 binding in both purified HbI polymorphs from the southern, high-temperature distribution limit of the species under controlled conditions of allosteric modifiers of Hb function. Contrary to the prevailing view, the O2 affinity of the major HbI polymorphs did not differ from each other under any of the tested conditions. Depending on pH and ATP concentration, the temperature-sensitive and temperature-insensitive Hb–O2 affinity phenotypes – previously exclusively ascribed to HbI-1 and HbI-2, respectively – could be induced in both HbI polymorphs. These results are the first to establish a molecular mechanism behind a reversed temperature dependence of red blood cell O2 affinity in a non-endotherm fish and lay the basis for future studies on alternative mechanisms behind the differences in distribution, performance and behavioural traits associated with the different HbI polymorphs of Atlantic cod

Almost Logarithmic-Time Space Optimal Leader Election in Population Protocols

The model of population protocols refers to a large collection of simple indistinguishable entities, frequently called {\em agents}. The agents communicate and perform computation through pairwise interactions. We study fast and space efficient leader election in population of cardinality $n$ governed by a random scheduler, where during each time step the scheduler uniformly at random selects for interaction exactly one pair of agents. We propose the first $o(\log^2 n)$-time leader election protocol. Our solution operates in expected parallel time $O(\log n\log\log n)$ which is equivalent to $O(n \log n\log\log n)$ pairwise interactions. This is the fastest currently known leader election algorithm in which each agent utilises asymptotically optimal number of $O(\log\log n)$ states. The new protocol incorporates and amalgamates successfully the power of assorted {\em synthetic coins} with variable rate {\em phase clocks}

How Many Nodes are Effectively Accessed in Complex Networks?

The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility, including its relationship with the average minimal time to visit all nodes reachable after $h$ steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics, namely: traditional random walks, self-avoiding random walks, and preferential random walks.Comment: 8 pages and 7 figure

Evidence for the adaptation of protein pH-dependence to subcellular pH

<p>Abstract</p> <p>Background</p> <p>The availability of genome sequences, and inferred protein coding genes, has led to several proteome-wide studies of isoelectric points. Generally, isoelectric points are distributed following variations on a biomodal theme that originates from the predominant acid and base amino acid sidechain pKas. The relative populations of the peaks in such distributions may correlate with environment, either for a whole organism or for subcellular compartments. There is also a tendency for isoelectric points averaged over a subcellular location to not coincide with the local pH, which could be related to solubility. We now calculate the correlation of other pH-dependent properties, calculated from 3D structure, with subcellular pH.</p> <p>Results</p> <p>For proteins with known structure and subcellular annotation, the predicted pH at which a protein is most stable, averaged over a location, gives a significantly better correlation with subcellular pH than does isoelectric point. This observation relates to the cumulative properties of proteins, since maximal stability for individual proteins follows the bimodal isoelectric point distribution. Histidine residue location underlies the correlation, a conclusion that is tested against a background of proteins randomised with respect to this feature, and for which the observed correlation drops substantially.</p> <p>Conclusion</p> <p>There exists a constraint on protein pH-dependence, in relation to the local pH, that is manifested in the pKa distribution of histidine sub-proteomes. This is discussed in terms of protein stability, pH homeostasis, and fluctuations in proton concentration.</p

O2-Filled Swimbladder Employs Monocarboxylate Transporters for the Generation of O2 by Lactate-Induced Root Effect Hemoglobin

The swimbladder volume is regulated by O2 transfer between the luminal space and the blood In the swimbladder, lactic acid generation by anaerobic glycolysis in the gas gland epithelial cells and its recycling through the rete mirabile bundles of countercurrent capillaries are essential for local blood acidification and oxygen liberation from hemoglobin by the “Root effect.” While O2 generation is critical for fish flotation, the molecular mechanism of the secretion and recycling of lactic acid in this critical process is not clear. To clarify molecules that are involved in the blood acidification and visualize the route of lactic acid movement, we analyzed the expression of 17 members of the H+/monocarboxylate transporter (MCT) family in the fugu genome and found that only MCT1b and MCT4b are highly expressed in the fugu swimbladder. Electrophysiological analyses demonstrated that MCT1b is a high-affinity lactate transporter whereas MCT4b is a low-affinity/high-conductance lactate transporter. Immunohistochemistry demonstrated that (i) MCT4b expresses in gas gland cells together with the glycolytic enzyme GAPDH at high level and mediate lactic acid secretion by gas gland cells, and (ii) MCT1b expresses in arterial, but not venous, capillary endothelial cells in rete mirabile and mediates recycling of lactic acid in the rete mirabile by solute-specific transcellular transport. These results clarified the mechanism of the blood acidification in the swimbladder by spatially organized two lactic acid transporters MCT4b and MCT1b

Genomic organization and evolution of the Atlantic salmon hemoglobin repertoire

<p>Abstract</p> <p>Background</p> <p>The genomes of salmonids are considered pseudo-tetraploid undergoing reversion to a stable diploid state. Given the genome duplication and extensive biological data available for salmonids, they are excellent model organisms for studying comparative genomics, evolutionary processes, fates of duplicated genes and the genetic and physiological processes associated with complex behavioral phenotypes. The evolution of the tetrapod hemoglobin genes is well studied; however, little is known about the genomic organization and evolution of teleost hemoglobin genes, particularly those of salmonids. The Atlantic salmon serves as a representative salmonid species for genomics studies. Given the well documented role of hemoglobin in adaptation to varied environmental conditions as well as its use as a model protein for evolutionary analyses, an understanding of the genomic structure and organization of the Atlantic salmon α and β hemoglobin genes is of great interest.</p> <p>Results</p> <p>We identified four bacterial artificial chromosomes (BACs) comprising two hemoglobin gene clusters spanning the entire α and β hemoglobin gene repertoire of the Atlantic salmon genome. Their chromosomal locations were established using fluorescence <it>in situ </it>hybridization (FISH) analysis and linkage mapping, demonstrating that the two clusters are located on separate chromosomes. The BACs were sequenced and assembled into scaffolds, which were annotated for putatively functional and pseudogenized hemoglobin-like genes. This revealed that the tail-to-tail organization and alternating pattern of the α and β hemoglobin genes are well conserved in both clusters, as well as that the Atlantic salmon genome houses substantially more hemoglobin genes, including non-Bohr β globin genes, than the genomes of other teleosts that have been sequenced.</p> <p>Conclusions</p> <p>We suggest that the most parsimonious evolutionary path leading to the present organization of the Atlantic salmon hemoglobin genes involves the loss of a single hemoglobin gene cluster after the whole genome duplication (WGD) at the base of the teleost radiation but prior to the salmonid-specific WGD, which then produced the duplicated copies seen today. We also propose that the relatively high number of hemoglobin genes as well as the presence of non-Bohr β hemoglobin genes may be due to the dynamic life history of salmon and the diverse environmental conditions that the species encounters.</p> <p>Data deposition: BACs S0155C07 and S0079J05 (fps135): GenBank <ext-link ext-link-id="GQ898924" ext-link-type="gen">GQ898924</ext-link>; BACs S0055H05 and S0014B03 (fps1046): GenBank <ext-link ext-link-id="GQ898925" ext-link-type="gen">GQ898925</ext-link></p