Minimum Cost Multicast with Decentralized Sources

In this paper we study the multisource multicast problem where every sink in a given directed acyclic graph is a client and is interested in a common file. We consider the case where each node can have partial knowledge about the file as a side information. Assuming that nodes can communicate over the capacity constrained links of the graph, the goal is for each client to gain access to the file, while minimizing some linear cost function of number of bits transmitted in the network. We consider three types of side-information settings:(ii) side information in the form of linearly correlated packets; and (iii) the general setting where the side information at the nodes have an arbitrary (i.i.d.) correlation structure. In this work we 1) provide a polynomial time feasibility test, i.e., whether or not all the clients can recover the file, and 2) we provide a polynomial-time algorithm that finds the optimal rate allocation among the links of the graph, and then determines an explicit transmission scheme for cases (i) and (ii)

Optimal Deterministic Polynomial-Time Data Exchange for Omniscience

We study the problem of constructing a deterministic polynomial time algorithm that achieves omniscience, in a rate-optimal manner, among a set of users that are interested in a common file but each has only partial knowledge about it as side-information. Assuming that the collective information among all the users is sufficient to allow the reconstruction of the entire file, the goal is to minimize the (possibly weighted) amount of bits that these users need to exchange over a noiseless public channel in order for all of them to learn the entire file. Using established connections to the multi-terminal secrecy problem, our algorithm also implies a polynomial-time method for constructing a maximum size secret shared key in the presence of an eavesdropper. We consider the following types of side-information settings: (i) side information in the form of uncoded fragments/packets of the file, where the users' side-information consists of subsets of the file; (ii) side information in the form of linearly correlated packets, where the users have access to linear combinations of the file packets; and (iii) the general setting where the the users' side-information has an arbitrary (i.i.d.) correlation structure. Building on results from combinatorial optimization, we provide a polynomial-time algorithm (in the number of users) that, first finds the optimal rate allocations among these users, then determines an explicit transmission scheme (i.e., a description of which user should transmit what information) for cases (i) and (ii)

Efficient Algorithms for the Data Exchange Problem

In this paper we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file while minimizing some communication cost. We assume that users can communicate over a noiseless broadcast channel, and that the communication cost is a sum of each user's cost function over the number of bits it transmits. For instance, the communication cost could simply be the total number of bits that needs to be transmitted. In the most general case studied in this paper, each user can have any arbitrary convex cost function. We provide deterministic, polynomial-time algorithms (in the number of users and packets) which find an optimal communication scheme that minimizes the communication cost. To further lower the complexity, we also propose a simple randomized algorithm inspired by our deterministic algorithm which is based on a random linear network coding scheme.Comment: submitted to Transactions on Information Theor

Data Exchange Problem with Helpers

In this paper we construct a deterministic polynomial time algorithm for the problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge of the file. We further assume the existence of another set of terminals in the system, called helpers, who are not interested in the common file, but who are willing to help the users. Given that the collective information of all the terminals is sufficient to allow recovery of the entire file, the goal is to minimize the (weighted) sum of bits that these terminals need to exchange over a noiseless public channel in order achieve this goal. Based on established connections to the multi-terminal secrecy problem, our algorithm also implies a polynomial-time method for constructing the largest shared secret key in the presence of an eavesdropper. We consider the following side-information settings: (i) side-information in the form of uncoded packets of the file, where the terminals' side-information consists of subsets of the file; (ii) side-information in the form of linearly correlated packets, where the terminals have access to linear combinations of the file packets; and (iii) the general setting where the the terminals' side-information has an arbitrary (i.i.d.) correlation structure. We provide a polynomial-time algorithm (in the number of terminals) that finds the optimal rate allocations for these terminals, and then determines an explicit optimal transmission scheme for cases (i) and (ii)

Gal-3 plays an important pro-inflammatory role in the induction phase of acute colitis by promoting activation of NLRP3 inflammasome and production of IL-β in macrophages

BACKGROUND AND AIMS: Galectin-3 [Gal-3] is an endogenous lectin with a broad spectrum of immunoregulatory effects: it plays an important role in autoimmune/inflammatory and malignant diseases, but the precise role of Gal-3 in pathogenesis of ulcerative colitis is still unknown. METHODS: We used a model of dextran sulphate sodium [DSS]-induced acute colitis. The role of Gal-3 in pathogenesis of this disease was tested by evaluating disease development in Gal-3 deficient mice and administration of Gal-3 inhibitor. Disease was monitored by clinical, histological, histochemical, and immunophenotypic investigations. Adoptive transfer was used to detect cellular events in pathogenesis. RESULTS: Genetic deletion or pharmacological inhibition of Gal-3 significantly attenuate DSS-induced colitis. Gal-3 deletion suppresses production of pro-inflammatory cytokines in colonic macrophages and favours their alternative activation, as well as significantly reducing activation of NOD-like receptor family, pyrin domain containing 3 [NLRP3] inflammasome in macrophages. Peritoneal macrophages isolated from untreated Gal-3(-/-) mice and treated in vitro with bacterial lipopolysaccharide or DSS produce lower amounts of tumour necrosis factor alpha [TNF-α] and interleukin beta [IL-1β] when compared with wild type [WT] cells. Genetic deletion of Gal-3 did not directly affect total neutrophils, inflammatory dendritic cells [DCs] or natural killer [NK] T cells. However, the total number of CD11c+ CD80+ DCs which produce pro-inflammatory cytokines, as well as TNF-α and IL-1β producing CD45+ CD11c- Ly6G+ neutrophils were significantly lower in colons of Gal-3(-/-) DSS-treated mice. Adoptive transfer of WT macrophages significantly enhanced the severity of disease in Gal-3(-/-) mice. CONCLUSIONS: Gal-3 expression promotes acute DSS-induced colitis and plays an important pro-inflammatory role in the induction phase of colitis by promoting the activation of NLRP3 inflammasome and production of IL-1β in macrophages

Data Exchange Problems: Algorithms and Complexity

In this thesis we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side- information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file while minimizing some communication cost. We assume that users can communicate over a noiseless broadcast channel, and that the communication cost is a sum of each user's cost function over the number of bits it transmits. For instance, the communication cost could simply be the total number of bits that needs to be transmitted. In the most general case studied in this thesis, each user can have any arbitrary convex cost function. We provide a polynomial time deterministic algorithm (in the number of users and packets) that finds an optimal communication scheme that minimizes the communication cost. To further lower the complexity, we also propose a simple randomized algorithm inspired by our deterministic algorithm which is based on a random linear network coding scheme. In the later chapters we consider a general form of side-information, where each user observes independent realizations of some joint random process. For such scenario, we provide a polynomial-time algorithm (in the number of users and packets) that finds an optimal communication rate allocations for all the users. Next, we study two extensions to the original data exchange problem. First, we consider the problem where not all users in the system are interested in obtaining the file, but they are willing to help users who are. Also, we explore the problem where each user can communicate only to its immediate neighbors through a wireline network. For both the problems, we provide a polynomial time algorithm that is inspired by the original data exchange problem

The Role of Game Theory in Key Agreement Over a Public Channel

In this work we study the problem of key agreement over a public noiseless channel when Alice, Bob and Charlie observe discrete memoryless sources of an unknown distribution. Alice and Bob want to agree on a key K-AB that is protected from Charlie. At the same time, Alice and Charlie want to agree on a key K-AC that is protected from Bob. In order to construct codebooks for the key agreement, Alice has to know how the sources are distributed. Therefore, she requests Bob and Charlie to send her sufficient information about their observations. We also assume that Bob and Charlie, besides agreeing with Alice on the keys, want to learn as much as possible about the other user's key: we call this quantity the leakage. We model these reports by having Bob and Charlie select discrete memoryless channels and passing their true observations through them. We approach this problem from a game-theoretic point of view. For a class of Bob and Charlie's objective functions which are linear in the key rate and the leakage rate, we characterize a Nash equilibrium. Also, we propose a strategy that Alice can apply in order to ensure that Bob and Charlie's honest reporting is a Nash equilibrium

Secure Communication using an Untrusted Relay via Sources and Channels

Confidential communication aided by a relay without security clearance is studied. General strategies and outer bounds are derived for the problem of secret communication and secret key generation when correlated observations at all terminals are available. In a variation of the problem, it is assumed that the quality of the channel to the relay is known only to the relay. If the throughput-maximizing strategy is used according to the relay's claimed channel quality, the question is: what should the relay claim about the channel in order to maximize its eavesdropping capabilities? We propose a strategy that Alice and Bob may agree on in order to suppress any leakage of confidential communication between the source and the receiver

Deterministic algorithm for the cooperative data exchange problem

Download Citation Email Print Request Permissions Save to Project In this paper we study the problem of data exchange, where each node in the system has a number of linear combinations of the data packets. Communicating over a public channel, the goal is for all nodes to reconstruct the entire set of the data packets in minimal total number of bits exchanged over the channel. We present a novel divide and conquer based architecture that determines the number of bits each node should transmit. This along with the well known fact, that it is sufficient for the nodes to broadcast linear combinations of their local information, provides a polynomial time deterministic algorithm for reconstructing the entire set of the data packets at all nodes in minimal amount of total communication