Bounds for self-stabilization in unidirectional networks

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional networks, and focus on the classical vertex coloring problem. When deterministic solutions are considered, we prove a lower bound of $n$ states per process (where $n$ is the network size) and a recovery time of at least $n(n-1)/2$ actions in total. We present a deterministic algorithm with matching upper bounds that performs in arbitrary graphs. When probabilistic solutions are considered, we observe that at least $\Delta + 1$ states per process and a recovery time of $\Omega(n)$ actions in total are required (where $\Delta$ denotes the maximal degree of the underlying simple undirected graph). We present a probabilistically self-stabilizing algorithm that uses $\mathtt{k}$ states per process, where $\mathtt{k}$ is a parameter of the algorithm. When $\mathtt{k}=\Delta+1$, the algorithm recovers in expected $O(\Delta n)$ actions. When $\mathtt{k}$ may grow arbitrarily, the algorithm recovers in expected O(n) actions in total. Thus, our algorithm can be made optimal with respect to space or time complexity

Sur le Coloriage Auto-stabilisant dans les Réseaux Unidirectionnels Anonymes

International audienceNous considérons des réseaux unidirectionnels anonymes. Nous démontrons que contrairement aux réseaux bidirectionnels, l'auto-stabilisation de tâches locales peut y être aussi difficile que l'auto-stabilisation de tâches globales. Pour ce faire, nous prenons comme exemple le problème du coloriage des nœuds d'un réseau. Plus précisément, nous démontrons que le coloriage auto-stabilisant est intrinsèquement aussi difficile à résoudre de manière déterministe qu'une tâche globale. Nous proposons ensuite une approche probabiliste pour retrouver une complexité locale

A New Self-Stabilizing Maximal Matching Algorithm

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it stabilizes in the same number of moves as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best moves complexities for the distributed adversarial daemon from O(n^2) and O(delta m) to O(m) where n is the number of processes, m is thenumber of edges, and delta is the maximum degree in the graph

Aspects of Grafting Influence on Carbon and Nitrogen Movement of Some Pear (Pyrus sativa) Cultivars

Among carbon and nitrogen contents, the interaction residing in the Interdependence Theory is one of the important components of plants. To elucidate how grafting influences the flow of carbon from shoots to tree roots and nitrogen from the roots to the shoots two sets of tests were carried out that have targeted the dosage of soluble sugars (to emphasize the relative flow of carbon) and nitrogen content dosage around the grafting union area. After many laboratory analyses, we obtained average values that reflect the dynamics of soluble sugars content depending on grafting, namely: 24% in the scion, 41% into the union area and 35% in the rootstock, in a ratio of about 1:1.7:1.4. In what concerns the total nitrogen content, we observed that the values are very similar between variants. Instead, somewhat higher nitrogen quantities (36%) were obtained in the rootstocks compared to the union area (32%) and scions (32%) representing a ratio of 1:1:1.1. Performing our experiments we found that the distribution of soluble sugars and nitrogen, in particular, in the grafting union area and the flow of photoassimilates and mineral elements, in general, for first year grafted trees depends not so much on the compatibility between scion and rootstock, but on grafting itself. Furthermore, we concluded that grafting itself is a barrier in photoassimilates and mineral elements flow in trees

Graft Incompatibility Influence on Assimilating Pigments and Soluble Sugars Amount of some Pear (Pyrus sativa) Cultivars

Graft incompatibility in fruit trees is one of the greatest obstacles in rootstocks and cultivars breeding. The mechanism in which incompatibility is expressed is not yet fully understood and several hypotheses have been advanced in an attempt to explain it. In many cases (pear on quince grafts, apricot on Prunus grafts), incompatibility is manifested by the breaking of the trees at the point of the union particularly when they have been growing for some years. Many reports focus on this problem in order to understand the mechanisms of graft development. These reports refer to both cytological and biochemical responses occurring at an early phase in response to grafting, as well as to the consequences of these events on the future graft response. In this experiment, we tried to highlight how affinity between scion and rootstock can influence the photosynthetic apparatus and carbohydrates synthesis. The results showed that grafting affinity has an influence on total assimilating pigments content. Thus, on the pear cultivars grafted on an incompatible rootstock (cultivars/Cydonia oblonga) the total pigments content ratio (reported to the ungrafted rootstock) ranged between 0.58 and 0.69. However, the combinations had a ratio ranging between 0.79 and 0.98. Nevertheless, the assimilating pigments ratio reduction had no influence on photosynthetic rate. The soluble sugars amount was close in both variants (cultivars/Cydonia oblonga and cultivars/Pyrus sativa)

Sodium-Based Osmotherapy in Continuous Renal Replacement Therapy: a Mathematical Approach

Cerebral edema, in a variety of circumstances, may be accompanied by states of hyponatremia. The threat of brain injury from hypotonic stress-induced astrocyte demyelination is more common when vulnerable patients with hyponatremia who have end stage liver disease, traumatic brain injury, heart failure, or other conditions undergo overly rapid correction of hyponatremia. These scenarios, in the context of declining urinary output from CKD and/or AKI, may require controlled elevations of plasma tonicity vis-à-vis increases of the plasma sodium concentration. We offer a strategic solution to this problem via sodium-based osmotherapy applied through a conventional continuous RRT modality: predilution continuous venovenous hemofiltration