On The Robustness of a Neural Network

With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and capabilities. With the rise of neuromorphic hardware, it is even more critical to understand how a neural network, as a distributed system, tolerates the failures of its computing nodes, neurons, and its communication channels, synapses. Experimentally assessing the robustness of neural networks involves the quixotic venture of testing all the possible failures, on all the possible inputs, which ultimately hits a combinatorial explosion for the first, and the impossibility to gather all the possible inputs for the second. In this paper, we prove an upper bound on the expected error of the output when a subset of neurons crashes. This bound involves dependencies on the network parameters that can be seen as being too pessimistic in the average case. It involves a polynomial dependency on the Lipschitz coefficient of the neurons activation function, and an exponential dependency on the depth of the layer where a failure occurs. We back up our theoretical results with experiments illustrating the extent to which our prediction matches the dependencies between the network parameters and robustness. Our results show that the robustness of neural networks to the average crash can be estimated without the need to neither test the network on all failure configurations, nor access the training set used to train the network, both of which are practically impossible requirements.Comment: 36th IEEE International Symposium on Reliable Distributed Systems 26 - 29 September 2017. Hong Kong, Chin

Synthesis of methods to assess farms’ sustainability

Sustainability became a central exit in the agricultural sector, all for researchers, producers and decision makers. Sustainable agriculture is a mode which produces abundant food without exhausting the earth resources or polluting its environment. It is also the agriculture of the statutory values, one whose success is not distinguished from the vibrating rural communities, of the rich person lives for families, and safety for each one. Sustainability in agriculture is attached to broader exits of the total economy. The main aims of this review paper are: (1) formulate definitions of sustainable development, (2) identify and know the components and the aspects of sustainability at the farm level, and (3) mention methods of sustainability’s evaluation.Keywords: Sustainabilty; Scales; Aspects; Indicators; Evaluatio

Activité de la phosphatase alcaline bactérienne à l'interface eau-sédiment au sein du réservoir Sahela (Maroc)

Les variations temporelles des concentrations en phosphore, celles des abondances bactériennes et de l'activité de la phosphatase alcaline (APA) ont été estimées in situ en chambre benthique placée en deux points du réservoir Sahela (Maroc) durant les mois de septembre et octobre 98. En période de faible oxygénation, nous avons enregistré des élévations relativement faibles des concentrations en orthophosphates (de 0,020 à 0,035 mg. l-1 au point 1 et 0,015 à 0,025 mg. l-1 au point 2) par rapport au phosphore total (0,080 à 0,100 mg. l-1 au point 1 et de 0,035 à 0,040 mg. l-1 au point 2). À cette période, les abondances bactériennes et l'APA montrent des valeurs maximales (8. 106 bact. ml-1 et 0,323 mmol.PNP l-1.h-1 au point 1 et 6.106 bact. ml-1 et 0,438 mmol.PNP l-1.h-1 au point 2 respectivement). L'apparition des conditions anoxiques et la diminution du pH favorisaient la dissolution du phosphore particulaire et la libération du phosphore réactif soluble. Cette libération s'accompagne d'une élévation des abondances de bactéries anaérobies (de 5.106 à 9,2. 106 bact. ml-1 au point 1 et de 3,8.106 à 7,2. 106 bact. ml-1 au point 2) et une diminution progressive d'APA (de 0,200 à 0,025 mmol.PNP l-1.h-1 au point 1 et de 0,125 à 0,077 mmol.PNP l-1.h-1 au point 2). Ce relargage du phosphore à partir du sédiment est accentué par les rejets domestiques et industriels de la ville de Taounate, ce qui accélère le processus d'eutrophisation de ce réservoir.Temporal variations of phosphorus concentrations, bacterial abundance and alkaline phosphatase activity (APA) were estimated in situ in a benthic chamber. The chamber used has a surface of 0.4m2 and a volume of 90 l ; it resembles those used in oceanography, with a tube connecting the interior of the chamber to the lake surface. The water in the chamber was permanently mixed by an electric agitation system. The chamber was placed at two points in the Sahela reservoir (Morocco). Point 1 was located near Guelta El Haila, a site that receives both domestic and industrial effluent, and point 2 was located in the centre of the reservoir. During the two incubations, eight samples were taken over 24 d in September and October 1998 from point 1, and seven samples were taken from point 2 over 29 d in October. After each sampling, an equal volume of water was injected into the chamber to avoid bubble formation.Under low dissolved oxygen concentrations in the benthic chamber, we noticed a relatively small elevation in orthophosphate concentrations (from 0.020 to 0.035 mg×L-1 at point 1 and from 0.015 to 0.025 mg×L-1 at point 2) in relation to total phosphorus (from 0.080 to 0.100 mg×L-1 and from 0.035 to 0.040 mg×L-1 at points 1 and 2 respectively). The low residual oxygenation of hypolimnic layer allowed the oxidation of iron, manganese and led to their binding to phosphorus released from the interstitial water. Dissociation of calcium-phosphorus complexes as a result of a pH decrease may have contributed to phosphorus release. The orthophosphate concentrations were relatively low, a situation that favours the synthesis of alkaline phosphatase by aerobic bacteria and facultative aerobic bacteria. In this period, the bacterial abundance and APA were comparable and showed the maximal values (8. 106 bact. ml-1 and 0.323 mmol. PNP l-1.h-1 (phosphate nitrophenol) in point 1 and 6. 106 bact. ml-1and 0.438 mmol. PNP l-1.h-1 in point 2 respectively). The lack of a significant correlation between total APA and bacterial abundance at the two sampling points is probably due to the decrease of aerobic bacteria followed by a repopulation with anaerobic bacteria. However, the relative contribution of two bacterial populations that have different sizes, as at points 1 and 2, showed that the majority of total APA was produced by bacteria that are attached to organic matter. Therefore we suggest that attached bacteria contribute more than free bacteria to APA production.The beginning of anoxic conditions and the decrease in pH favored the dissolution of particulate phosphorus and the liberation of reactive phosphorus. We noted an elevation in orthophosphate concentrations (from 0.035 to 0.050 mg×L-1 at point 1 and stabilised at 0.025 mg×L-1 at point 2) and total phosphorus (from 0.100 to 0.150 mg×L-1 at point 1 and from 0.040 to 0.050 mg×L-1 at point 2). This liberation followed an increase in anaerobic bacterial abundance (from 5×106 to 9.2×106 bact×mL-1 at point 1 and from 3.8×106 to 7.2×106 bact×mL-1 at point 2) and the progressive decrease in APA (from 0.200 to 0.025 mmol PNP L-1 ×h-1 at point 1 and from 0.125 to 0.077 mmol PNP L-1 ×h-1 at point 2). The anaerobic bacteria did not activate their alkaline phosphatase and the synthesis of their enzyme was progressively inhibited by a de-repression phenomenon caused by high phosphorus concentrations.We conclude that low oxygen and a decrease in pH favoured the release of phosphorus by dissolution of chemical complexes: calcium-phosphorus, iron-phosphorus, manganese-phosphorus and aluminium-phosphorus. This release is also the result of bacterial phosphatase activity to which fixed bacteria contributed the most. The release of phosphorus from water-sediment interface is further amplified by phosphate import from domestic and industrial waste waters originating from Taounate, which accelerates the eutrophication process in this reservoir

Providing Performance Guarantees in Data Center Network Switching Fabrics

This paper proposes a novel and highly scalable multistage packet-switch design based on Networks-on-Chip (NoC). In particular, we describe a three-stage packet-switch fabric with a Round-Robin packets dispatching scheme where each central stage module is an Output-Queued Unidirectional NoC (OQ-UDN), instead of the conventional single-hop crossbar. We test the switch performance under different traffic profiles. In addition to experimental results, we present an analytical approximation for the theoretical throughput of the switch under Bernoulli i.i.d arrivals. We also provide an upper-bound estimation of the end-to-end blocking probability in the proposed switch to help predict performance and to optimize the design

High-Capacity Clos-Network Switch for Data Center Networks

Scaling-up Data Center Networks (DCNs) should be done at the network level as well as the switching elements level. The glaring reason for this, is that switches/routers deployed in the DCN can bound the network capacity and affect its performance if improperly chosen. Many multistage switching architectures have been proposed to fit for the next-generation networking needs. However all of them are either performance limited or too complex to be implemented. Targeting scalability and performance, we propose the design of a large-capacity switch in which we affiliate a multistage design with a Networks-on- Chip (NoC) design. The proposal falls into the category of buffered multistage switches. Still, it has a different architectural aspect and scheduling process. Dissimilar to common point-to-point crossbars, NoCs used at the heart of the three-stage Clos-network allow multiple packets simultaneously in the modules where they can be adaptively transported using a pipelined scheduling scheme. Our simulations show that the switch scales well with the load and size variation. It outperforms a variety of architectures under a range of traffic arrivals

High-radix Packet-Switching Architecture for Data Center Networks

We propose a highly scalable packet-switching architecture that suits for demanding Data center Networks (DCNs). The design falls into the category of buffered multistage switches. It affiliates a three-stage Clos-network and the Networks-on-Chip (NoC) paradigm. We also suggest a congestion-aware routing algorithm that shares the traffic load among the switch's central modules via interleaved connecting links. Unlike conventional switches, the current proposal provides better path diversity, simple scheduling, speedup and robustness to load variation. Simulation results show that the switch is scalable with the portcount and traffic fluctuation, and that it outperforms different switches under many traffic patterns