Sharing storage using dirty vectors

Consider a computation F with n inputs (independent variables) and m outputs (dependent variables) and suppose that we wish to evaluate the Jacobian of F. Automatic differentiation commonly performs this evaluation by associating vector storage either with the program variables (in the case of forward-mode automatic differentiation) or with the adjoint variables (in the case of reverse). Each vector component contains a partial derivative with respect to an independent variable, or a partial derivative of a dependent variable, respectively. The vectors may be full vectors, or they may be dynamically managed sparse data structures. In either case, many of these vectors will be scalar multiples of one another. For example, any intermediate variable produced by a unary operation in the forward mode will have a derivative vector that is a multiple of the derivative for the argument. Any computational graph node that is read just once during its lifetime will have an adjoint vector that is a multiple of the adjoint of the node that reads it. It is frequently wasteful to perform component multiplications explicitly. A scalar multiple of another vector can be replaced by a single multiplicative "scale factor" together with a pointer to the other vector. Automated use of this "dirty vector" technique can save considerable memory management overhead and dramatically reduce the number of floating-point operations required. In particular, dirty vectors often allow shared threads of computation to be reverse-accumulated cheaply. The mechanism permits a number of generalizations, some of which give efficient techniques for preaccumulation

Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction

Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we present a space-optimal \emph{silent} self-stabilizing construction of minimum-degree spanning trees in this model. Computing a spanning tree with minimum degree is NP-hard. Therefore, we actually focus on constructing a spanning tree whose degree is within one from the optimal. Our algorithm uses registers on $O(\log n)$ bits, converges in a polynomial number of rounds, and performs polynomial-time computation at each node. Specifically, the algorithm constructs and stabilizes on a special class of spanning trees, with degree at most $OPT+1$. Indeed, we prove that, unless NP $=$ coNP, there are no proof-labeling schemes involving polynomial-time computation at each node for the whole family of spanning trees with degree at most $OPT+1$. Up to our knowledge, this is the first example of the design of a compact silent self-stabilizing algorithm constructing, and stabilizing on a subset of optimal solutions to a natural problem for which there are no time-efficient proof-labeling schemes. On our way to design our algorithm, we establish a set of independent results that may have interest on their own. In particular, we describe a new space-optimal silent self-stabilizing spanning tree construction, stabilizing on \emph{any} spanning tree, in $O(n)$ rounds, and using just \emph{one} additional bit compared to the size of the labels used to certify trees. We also design a silent loop-free self-stabilizing algorithm for transforming a tree into another tree. Last but not least, we provide a silent self-stabilizing algorithm for computing and certifying the labels of a NCA-labeling scheme

Transducers based on networks of evolutionary processors LOS FINANCIADORES NO ESTÁN BIEN

We consider a new type of transducer that does not scan sequentially the input word. Instead, it consists of a directed graph whose nodes are processors which work in parallel and are specialized in just one type of a very simple evolutionary operation: inserting, deleting or substituting a symbol by another one. The computation on an input word starts with this word placed in a designated node, the input node, of the network an alternates evolutionary and communication steps. The computation halts as soon as another designated node, the output node, is nonempty. The translation of the input word is the set of words existing in the output node when the computation halts. We prove that these transducers can simulate the work of generalized sequential machines on every input. Furthermore, all words obtained by a given generalized sequential machine by the shortest computations on a given word can also be computed by the new transducers. Unlike the case of generalized sequential machines, every recursively enumerable language can be the transduction de?ned by the new transducer of a very simple regular language. The same idea may be used for proving that these transducers can simulate the shortest computations of an arbitrary Turing machine, used as a transducer, on every input word. Finally, we consider a restricted variant of NEP transducer, namely pure NEP transducers and prove that there are still regular languages whose pure NEP transductions are not semilinear

Popularity versus Similarity in Growing Networks

Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks, or duplication. Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity. We develop a framework where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon

Beyond the ego network: The effect of distant connections on node anonymity

Ensuring privacy of individuals is of paramount importance to social network analysis research. Previous work assessed anonymity in a network based on the non-uniqueness of a node's ego network. In this work, we show that this approach does not adequately account for the strong de-anonymizing effect of distant connections. We first propose the use of d-k-anonymity, a novel measure that takes knowledge up to distance d of a considered node into account. Second, we introduce anonymity-cascade, which exploits the so-called infectiousness of uniqueness: mere information about being connected to another unique node can make a given node uniquely identifiable. These two approaches, together with relevant "twin node" processing steps in the underlying graph structure, offer practitioners flexible solutions, tunable in precision and computation time. This enables the assessment of anonymity in large-scale networks with up to millions of nodes and edges. Experiments on graph models and a wide range of real-world networks show drastic decreases in anonymity when connections at distance 2 are considered. Moreover, extending the knowledge beyond the ego network with just one extra link often already decreases overall anonymity by over 50%. These findings have important implications for privacy-aware sharing of sensitive network data

Security for Multi-hop Communication of Two-tier Wireless Networks with Different Trust Degrees

Many effective strategies for enhancing network performance have been put forth for wireless communications' physical-layer security. Up until now, wireless communications security and privacy have been optimized based on a set assumption on the reliability or network tiers of certain wireless nodes. Eavesdroppers, unreliable relays, and trustworthy cooperative nodes are just a few examples of the various sorts of nodes that are frequently categorized. When working or sharing information for one another, wireless nodes in various networks may not always have perfect trust in one another. Modern wireless networks' security and privacy may be enhanced in large part by optimizing the network based on trust levels. To determine the path with the shortest total transmission time between the source and the destination while still ensuring that the private messages are not routed through the untrusted network tier, we put forth a novel approach. To examine the effects of the transmit SNR, node density, and the percentage of the illegitimate nodes on various network performance components, simulation results are provided