The Expected Capacity of Concentrators

The expected capacity of a class of sparse concentrators called modular concentrators is determined. In these concentrators, each input is connected to exactly two outputs, each output is connected to exactly three inputs, and the girth (the length of the shortest cycle in the connexion graph) is large. Two definitions of expected capacity are considered. For the first (which is due to Masson and Morris), it is assumed that a batch of customers arrive at a random set of inputs and that a maximum matching of these customers to servers at the outputs is found. The number of unsatisfied requests is negligible if customers arrive at fewer than one-half of the inputs, and it grows quite gracefully even beyond this threshold. The situation in which customers arrive sequentially is considered, and the decision as to how to serve each is made randomly, without knowledge of future arrivals. In this case, the number of unsatisfied requests is larger but still quite modest

Expander Chunked Codes

Chunked codes are efficient random linear network coding (RLNC) schemes with low computational cost, where the input packets are encoded into small chunks (i.e., subsets of the coded packets). During the network transmission, RLNC is performed within each chunk. In this paper, we first introduce a simple transfer matrix model to characterize the transmission of chunks, and derive some basic properties of the model to facilitate the performance analysis. We then focus on the design of overlapped chunked codes, a class of chunked codes whose chunks are non-disjoint subsets of input packets, which are of special interest since they can be encoded with negligible computational cost and in a causal fashion. We propose expander chunked (EC) codes, the first class of overlapped chunked codes that have an analyzable performance,where the construction of the chunks makes use of regular graphs. Numerical and simulation results show that in some practical settings, EC codes can achieve rates within 91 to 97 percent of the optimum and outperform the state-of-the-art overlapped chunked codes significantly.Comment: 26 pages, 3 figures, submitted for journal publicatio

Randomized Routing on Fat-Trees

Fat-trees are a class of routing networks for hardware-efficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. We show that if a set of messages has load factor lambda on a fat-tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(lambda + lg n lg lg n) with probability 1-O(1/n). The best previous bound was O(lambda lg n) for the offline problem in which the set of messages is known in advance. In the context of a VLSI model that equates hardware cost with physical volume, the routing algorithm can be used to demonstrate that fat-trees are universal routing networks. Specifically, we prove that any routing network can be efficiently simulated by a fat-tree of comparable hardware cost

Teletraffic Engineering for Direct Load Control in Smart Grids

International audienceThe traditional paradigm for power grid operation is to continuously adapt energy production to demand. This paradigm is challenged by the increasing penetration of renewable sources, that are more variable and less predictable. An alternative approach is the direct load control of some inherently flexible electric loads to shape the demand. Direct control of deferrable loads presents analogies with flow admission control in telecommunication networks: a request for network resources (bandwidth or energy) can be delayed on the basis of the current network status in order to guarantee some performance metrics. In this paper we go beyond such an analogy, showing that usual teletraffic tools can be effectively used to control energy loads. In particular, we propose a family of control schemes which can be easily tuned to achieve the desired trade-off among resource usage, control overhead and privacy leakage

Speciation of Lanthanide Metal Ion Dopants in Microcrystalline All-Inorganic Halide Perovskite CsPbCl3

Lanthanides are versatile modulators of optoelectronic properties owing to their narrow optical emission spectra across the visible and near-infrared range. Their use in metal halide perovskites (MHPs) has recently gained prominence, although their fate in these materials has not yet been established at the atomic level. We use cesium-133 solid-state NMR to establish the speciation of all nonradioactive lanthanide ions (La3+, Ce3+, Pr3+, Nd3+, Sm3+, Sm2+, Eu3+, Eu2+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+, Lu3+) in microcrystalline CsPbCl3. Our results show that all lanthanides incorporate into the perovskite structure of CsPbCl3 regardless of their oxidation state (+2, +3).</p

Broadcasting on Random Directed Acyclic Graphs

We study a generalization of the well-known model of broadcasting on trees. Consider a directed acyclic graph (DAG) with a unique source vertex $X$, and suppose all other vertices have indegree $d\geq 2$. Let the vertices at distance $k$ from $X$ be called layer $k$. At layer $0$, $X$ is given a random bit. At layer $k\geq 1$, each vertex receives $d$ bits from its parents in layer $k-1$, which are transmitted along independent binary symmetric channel edges, and combines them using a $d$-ary Boolean processing function. The goal is to reconstruct $X$ with probability of error bounded away from $1/2$ using the values of all vertices at an arbitrarily deep layer. This question is closely related to models of reliable computation and storage, and information flow in biological networks. In this paper, we analyze randomly constructed DAGs, for which we show that broadcasting is only possible if the noise level is below a certain degree and function dependent critical threshold. For $d\geq 3$, and random DAGs with layer sizes $\Omega(\log k)$ and majority processing functions, we identify the critical threshold. For $d=2$, we establish a similar result for NAND processing functions. We also prove a partial converse for odd $d\geq 3$ illustrating that the identified thresholds are impossible to improve by selecting different processing functions if the decoder is restricted to using a single vertex. Finally, for any noise level, we construct explicit DAGs (using expander graphs) with bounded degree and layer sizes $\Theta(\log k)$ admitting reconstruction. In particular, we show that such DAGs can be generated in deterministic quasi-polynomial time or randomized polylogarithmic time in the depth. These results portray a doubly-exponential advantage for storing a bit in DAGs compared to trees, where $d=1$ but layer sizes must grow exponentially with depth in order to enable broadcasting.Comment: 33 pages, double column format. arXiv admin note: text overlap with arXiv:1803.0752

High ecosystem service delivery potential of small woodlands in agricultural landscapes

Global forest loss and fragmentation have strongly increased the frequency of forest patches smaller than a few hectares. Little is known about the biodiversity and ecosystem service supply potential of such small woodlands in comparison to larger forests. As it is widely recognized that high biodiversity levels increase ecosystem functionality and the delivery of multiple ecosystem services, small, isolated woodlands are expected to have a lower potential for ecosystem service delivery than large forests hosting more species. We collected data on the diversity of six taxonomic groups covering invertebrates, plants and fungi, and on the supply potential of five ecosystem services and one disservice within 224 woodlands distributed across temperate Europe. We related their ability to simultaneously provide multiple ecosystem services (multiservice delivery potential) at different performance levels to biodiversity of all studied taxonomic groups (multidiversity), forest patch size and age, as well as habitat availability and connectivity within the landscape, while accounting for macroclimate, soil properties and forest structure. Unexpectedly, despite their lower multidiversity, smaller woodlands had the potential to deliver multiple services at higher performance levels per area than larger woodlands of similar age, probably due to positive edge effects on the supply potential of several ecosystem services. Biodiversity only affected multiservice delivery potential at a low performance level as well as some individual ecosystem services. The importance of other drivers of ecosystem service supply potential by small woodlands in agricultural landscapes also depended on the level of performance and varied with the individual ecosystem service considered. Synthesis and applications. Large, ancient woodlands host high levels of biodiversity and can therefore deliver a number of ecosystem services. In contrast, smaller woodlands in agricultural landscapes, especially ancient woodlands, have a higher potential to deliver multiple ecosystem services on a per area basis. Despite their important contribution to agricultural landscape multifunctionality, small woodlands are not currently considered by public policies. There is thus an urgent need for targeted policy instruments to ensure their adequate management and future conservation in order to either achieve multiservice delivery at high levels or to maximize the delivery of specific ecosystem services

High ecosystem service delivery potential of small woodlands in agricultural landscapes

Global forest loss and fragmentation have strongly increased the frequency of forest patches smaller than a few hectares. Little is known about the biodiversity and ecosystem service supply potential of such small woodlands in comparison to larger forests. As it is widely recognized that high biodiversity levels increase ecosystem functionality and the delivery of multiple ecosystem services, small, isolated woodlands are expected to have a lower potential for ecosystem service delivery than large forests hosting more species. We collected data on the diversity of six taxonomic groups covering invertebrates, plants and fungi, and on the supply potential of five ecosystem services and one disservice within 224 woodlands distributed across temperate Europe. We related their ability to simultaneously provide multiple ecosystem services (multiservice delivery potential) at different performance levels to biodiversity of all studied taxonomic groups (multidiversity), forest patch size and age, as well as habitat availability and connectivity within the landscape, while accounting for macroclimate, soil properties and forest structure. Unexpectedly, despite their lower multidiversity, smaller woodlands had the potential to deliver multiple services at higher performance levels per area than larger woodlands of similar age, probably due to positive edge effects on the supply potential of several ecosystem services. Biodiversity only affected multiservice delivery potential at a low performance level as well as some individual ecosystem services. The importance of other drivers of ecosystem service supply potential by small woodlands in agricultural landscapes also depended on the level of performance and varied with the individual ecosystem service considered. Synthesis and applications. Large, ancient woodlands host high levels of biodiversity and can therefore deliver a number of ecosystem services. In contrast, smaller woodlands in agricultural landscapes, especially ancient woodlands, have a higher potential to deliver multiple ecosystem services on a per area basis. Despite their important contribution to agricultural landscape multifunctionality, small woodlands are not currently considered by public policies. There is thus an urgent need for targeted policy instruments to ensure their adequate management and future conservation in order to either achieve multiservice delivery at high levels or to maximize the delivery of specific ecosystem services

Source coding for communication concentrators

Originally presented as the author's thesis, (Ph.D.) in the M.I.T. Dept. of Electrical Engineering and Computer Science, 1978.Prepared under Advanced Research Projects Agency Grant ONR-N00014-75-C-1183.Bibliography: p. 194-198.by Pierre Am?e Humblet