A Survey on Distance Vector Routing Protocols

In this paper we give a brief introduction to five different distance vector routing protocols (RIP, AODV, EIGRP, RIP-MTI and Babel) and give some of our thoughts on how to solve the count to infinity problem. Our focus is how distance vector routing protocols, based on limited information, can prevent routing loops and the count to infinity problem.Comment: 15 pages, 8 figure

An Information Theoretic Converse for the "Consecutive Complete--SS" PICOD Problem

Pliable Index CODing (PICOD) is a variant of the Index Coding (IC) problem in which a user is satisfied whenever it can successfully decode any one message that is not in its side information set, as opposed to a fixed pre-determined message. The complete--$S$ PICOD with $m$ messages, for $S\subseteq[0:m-1]$, has $n = \sum_{s\in S} \binom{m}{s}$ users with distinct side information sets. Past work on PICOD provided tight converse results when either the sender is constrained to use linear codes, or for some special classes of complete--$S$ PICOD. This paper provides a tight information theoretic converse result (i.e., no restriction to linear codes) for the so-called "consecutive complete--$S$" PICOD, where the set $S$ satisfies $S=[s_{min} : s_{max}]$ for some $0\leq s_{min} \leq s_{max} \leq m-1$. This result extends existing converse results and shows that linear codes have the smallest possible code length given by $\min(m-s_{\min},1+s_{\max})$. The central contribution is a novel proof technique rooted in combinatorics. The main idea is to consider all the messages a user can eventually successfully decode, in addition to its own desired message. This allows us to circumvent the necessity of essentially considering all possible assignments of desired messages for the users. The keystone of the proof is to show that, for the case of $S=\{s\}$ and $m = 2s+1$, there exists at least one user who can decode $s+1$ messages. From this, the extension to the "consecutive complete--$S$" PICOD follows.Comment: Submitted to ITW 201

Private Pliable Index Coding

The Pliable Index CODing (PICOD) problem is a variant of the Index Coding (IC) problem, where the desired messages by the users, who are equipped with message side information, is part of the optimization. This paper studies the PICOD problem where users are subject to a privacy constraint. In particular, the following spacial class of private PICODs is investigated: 1) the side information structure is circular, and 2) each user can decode one and only one message. The first condition is a special case of the "circular-arc network topology hypergraph" class of PICOD studied in [Liu and D. Tuninetti, "Tight information theoretic converse results for some pliable index coding problems," ITW, 2018], for which an optimal solution was given without the privacy constraint. The second condition was first studied in [S. Sasi and B. S. Rajan, "On pliable index coding," arXiv:1901.05809] and was motivated by the need to keep content privacy is some distribution networks. This paper proposes both converse and achievable bounds. The proposed achievable scheme not only strictly outperforms the one in [S. Sasi and B. S. Rajan, "On pliable index coding," arXiv:1901.05809] for some values of the system parameters, but it is also information theoretically optimal in some settings. For the remaining cases, the proposed linear code is shown to require at most one more transmission than the converse bound derived by restricting the sender to only use linear codes.Comment: 6 pages. Submitted to ITW 2019. Eq. 4 changed for a constraint on individual messages in v

Decentralized Pliable Index Coding

This paper introduces the ${\it decentralized}$ Pliable Index CODing (PICOD) problem: a variant of the Index Coding (IC) problem, where a central transmitter serves ${\it pliable}$ users with message side information; here, pliable refers to the fact that a user is satisfied by decoding ${\it any}$ $t$ messages that are not in its side information set. In the decentralized PICOD, a central transmitter with knowledge of all messages is not present, and instead users share among themselves massages that can only depend on their local side information set. This paper characterizes the capacity of two classes of decentralized complete--$S$ PICOD$(t)$ problems with $m$ messages (where the set $S\subset[m]$ contains the sizes of the side information sets, and the number of users is $n=\sum_{s\in S}\binom{m}{s}$, with no two users having the same side information set): (i) the consecutive case: S=[s_\min:s_\max] for some 0 \leq s_\min\leq s_\max \leq m-t, and (ii) the complement-consecutive case: S=[0:m-t]\backslash[s_\min:s_\max], for some 0 < s_\min\leq s_\max < m-t. Interestingly, the optimal code-length for the decentralized PICOD in those cases is the same as for the classical (centralized) PICOD counterpart, except when the problem is no longer pliable, that is, it reduces to an IC problem where every user needs to decode all messages not in its side information set. Although the optimal code-length may be the same in both centralized and decentralized settings, the actual optimal codes are not. For the decentralized PICOD, sparse Maximum Distance Separable (MDS) codes and vector linear index codes are used (as opposed to scalar linear codes).Comment: 5 pages. To be presented at ISIT 201

The minimal number of generators for simple Lie superalgebras

Using the classification theorem due to Kac we prove that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by one element

Tight Information Theoretic Converse Results for some Pliable Index Coding Problems

This paper studies the Pliable Index CODing problem (PICOD), which models content-type distribution networks. In the PICOD$(t)$ problem there are $m$ messages, $n$ users and each user has a distinct message side information set, as in the classical Index Coding problem (IC). Differently from IC, where each user has a pre-specified set of messages to decode, in the PICOD$(t)$ a user is "pliable" and is satisfied if it can decode any $t$ messages that are not in its side information set. The goal is to find a code with the shortest length that satisfies all the users. This flexibility in determining the desired message sets makes the PICOD$(t)$ behave quite differently compared to the IC, and its analysis challenging. This paper mainly focuses on the \emph{complete--$S$} PICOD$(t)$ with $m$ messages, where the set $S\subset[m]$ contains the sizes of the side information sets, and the number of users is $n=\sum_{s\in S}\binom{m}{s}$, with no two users having the same side information set. Capacity results are shown for: (i) the \emph{consecutive} complete--$S$ PICOD$(t)$, where $S=[s_{\min}:s_{\max}]$ for some $0 \leq s_{\min} \leq s_{\max} \leq m-t$, and (ii) the \emph{complement-consecutive} complete--$S$ PICOD$(t)$, where $S=[0:m-t]\backslash[s_{\min}:s_{\max}]$, for some $0 < s_{\min} \leq s_{\max} < m-t$. The novel converse proof is inspired by combinatorial design techniques and the key insight is to consider all messages that a user can eventually decode successfully, even those in excess of the $t$ required ones. This allows one to circumvent the need to consider all possible desired message set assignments at the users in order to find the one that leads to the shortest code length. In addition, tight converse results are also shown for those PICOD$(1)$ with circular-arc network topology hypergraph.Comment: 38 pages, 4 figures, submitted to IEEE Transactions on Information Theor

Generators of simple Lie superalgebras in characteristic 0

It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements

Experience-based Optimization: A Coevolutionary Approach

This paper studies improving solvers based on their past solving experiences, and focuses on improving solvers by offline training. Specifically, the key issues of offline training methods are discussed, and research belonging to this category but from different areas are reviewed in a unified framework. Existing training methods generally adopt a two-stage strategy in which selecting the training instances and training instances are treated in two independent phases. This paper proposes a new training method, dubbed LiangYi, which addresses these two issues simultaneously. LiangYi includes a training module for a population-based solver and an instance sampling module for updating the training instances. The idea behind LiangYi is to promote the population-based solver by training it (with the training module) to improve its performance on those instances (discovered by the sampling module) on which it performs badly, while keeping the good performances obtained by it on previous instances. An instantiation of LiangYi on the Travelling Salesman Problem is also proposed. Empirical results on a huge testing set containing 10000 instances showed LiangYi could train solvers that perform significantly better than the solvers trained by other state-of-the-art training method. Moreover, empirical investigation of the behaviours of LiangYi confirmed it was able to continuously improve the solver through training

Directed flow of transported and non-transported protons in Au+Au collisions from UrQMD model

The directed flow of inclusive, transported and non-transported (including produced) protons, as well as antiprotons, has been studied in the framework of Ultra-Relativistic Quantum Molecular Dynamics approach (UrQMD model) for Au+Au collisions at\surdsNN =7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV. The rapidity, centrality and energy dependence of directed flow for various proton groups are presented. It is found that the integrated directed flow decreases monotonically as a function of collision energy for\surdsNN =11.5 GeV and beyond. However, the sign-change of directed flow of inclusive protons, seen in experimental data as a function of centrality and collision energy, can be explained by the competing effect of directed flow between transported and non-transported protons. Similarly the difference in directed flow between protons and antiprotons can be explained. Our study offers a conventional explanation on the cause of the v1 sign-change other than the antiflow component of protons alone which is argued to be linked to a phase transition.Comment: 5 pages,5 figure

Spin transfer in high energy fragmentation processes

We point out that measuring longitudinal polarizations of different hyperons produced in lepton induced reactions are ideal to study the spin transfer of the fragtmenting quark to produced hadron in high energy hadronization processes. We briefly summarize the method used in calculating the hyperon polarizations in these processes, then present some of the results for e+e- and e-p or \nu p reactions obtained using two different pictures for the spin structure of hyperon: that drawn from polarized deep inelastic lepton-nucleon scattering data or that using SU(6) symmetric wave functions. The results show in particular that measurements of such polarizations should provide useful information to the question of which picture is more suitable in describing the spin effects in the fragmentation processes.Comment: Talk given at the 14th International Spin Symposium, 5 page