Estimating Graphlet Statistics via Lifting

Exploratory analysis over network data is often limited by the ability to efficiently calculate graph statistics, which can provide a model-free understanding of the macroscopic properties of a network. We introduce a framework for estimating the graphlet count---the number of occurrences of a small subgraph motif (e.g. a wedge or a triangle) in the network. For massive graphs, where accessing the whole graph is not possible, the only viable algorithms are those that make a limited number of vertex neighborhood queries. We introduce a Monte Carlo sampling technique for graphlet counts, called {\em Lifting}, which can simultaneously sample all graphlets of size up to $k$ vertices for arbitrary $k$. This is the first graphlet sampling method that can provably sample every graphlet with positive probability and can sample graphlets of arbitrary size $k$. We outline variants of lifted graphlet counts, including the ordered, unordered, and shotgun estimators, random walk starts, and parallel vertex starts. We prove that our graphlet count updates are unbiased for the true graphlet count and have a controlled variance for all graphlets. We compare the experimental performance of lifted graphlet counts to the state-of-the art graphlet sampling procedures: Waddling and the pairwise subgraph random walk

Preconditioning for the Geometric Transportation Problem

In the geometric transportation problem, we are given a collection of points P in d-dimensional Euclidean space, and each point is given a supply of mu(p) units of mass, where mu(p) could be a positive or a negative integer, and the total sum of the supplies is 0. The goal is to find a flow (called a transportation map) that transports mu(p) units from any point p with mu(p) > 0, and transports -mu(p) units into any point p with mu(p) < 0. Moreover, the flow should minimize the total distance traveled by the transported mass. The optimal value is known as the transportation cost, or the Earth Mover\u27s Distance (from the points with positive supply to those with negative supply). This problem has been widely studied in many fields of computer science: from theoretical work in computational geometry, to applications in computer vision, graphics, and machine learning. In this work we study approximation algorithms for the geometric transportation problem. We give an algorithm which, for any fixed dimension d, finds a (1+epsilon)-approximate transportation map in time nearly-linear in n, and polynomial in epsilon^{-1} and in the logarithm of the total supply. This is the first approximation scheme for the problem whose running time depends on n as n * polylog(n). Our techniques combine the generalized preconditioning framework of Sherman, which is grounded in continuous optimization, with simple geometric arguments to first reduce the problem to a minimum cost flow problem on a sparse graph, and then to design a good preconditioner for this latter problem

Computation over the Noisy Broadcast Channel with Malicious Parties

We study the n-party noisy broadcast channel with a constant fraction of malicious parties. Specifically, we assume that each non-malicious party holds an input bit, and communicates with the others in order to learn the input bits of all non-malicious parties. In each communication round, one of the parties broadcasts a bit to all other parties, and the bit received by each party is flipped with a fixed constant probability (independently for each recipient). How many rounds are needed? Assuming there are no malicious parties, Gallager gave an (n log log n)-round protocol for the above problem, which was later shown to be optimal. This protocol, however, inherently breaks down in the presence of malicious parties. We present a novel n ⋅ ̃(√{log n})-round protocol, that solves this problem even when almost half of the parties are malicious. Our protocol uses a new type of error correcting code, which we call a locality sensitive code and which may be of independent interest. Roughly speaking, these codes map "close" messages to "close" codewords, while messages that are not close are mapped to codewords that are very far apart. We view our result as a first step towards a theory of property preserving interactive coding, i.e., interactive codes that preserve useful properties of the protocol being encoded. In our case, the naive protocol over the noiseless broadcast channel, where all the parties broadcast their input bit and output all the bits received, works even in the presence of malicious parties. Our simulation of this protocol, unlike Gallager’s, preserves this property of the original protocol

Protecting Single-Hop Radio Networks from Message Drops

Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the n participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic message drops (i.e., erasures), where in every round, the message received by each party is erased (replaced by ?) with some small constant probability, independently. Our main result is a constant rate coding scheme, allowing one to run protocols designed to work over the (noiseless) SHRN model over the SHRN model with erasures. Our scheme converts any protocol ? of length at most exponential in n over the SHRN model to a protocol ?\u27 that is resilient to constant fraction of erasures and has length linear in the length of ?. We mention that for the special case where the protocol ? is non-adaptive, i.e., the order of communication is fixed in advance, such a scheme was known. Nevertheless, adaptivity is widely used and is known to hugely boost the power of wireless channels, which makes handling the general case of adaptive protocols ? both important and more challenging. Indeed, to the best of our knowledge, our result is the first constant rate scheme that converts adaptive protocols to noise resilient ones in any multi-party model

Near-Optimal Two-Pass Streaming Algorithm for Sampling Random Walks over Directed Graphs

For a directed graph G with n vertices and a start vertex u_start, we wish to (approximately) sample an L-step random walk over G starting from u_start with minimum space using an algorithm that only makes few passes over the edges of the graph. This problem found many applications, for instance, in approximating the PageRank of a webpage. If only a single pass is allowed, the space complexity of this problem was shown to be ??(n ? L). Prior to our work, a better space complexity was only known with O?(?L) passes. We essentially settle the space complexity of this random walk simulation problem for two-pass streaming algorithms, showing that it is ??(n ? ?L), by giving almost matching upper and lower bounds. Our lower bound argument extends to every constant number of passes p, and shows that any p-pass algorithm for this problem uses ??(n ? L^{1/p}) space. In addition, we show a similar ??(n ? ?L) bound on the space complexity of any algorithm (with any number of passes) for the related problem of sampling an L-step random walk from every vertex in the graph

ALGORITHM OF MULTIHARMONIC DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH ARBITRARY DELAY: INTERNAL MODEL APPROACH

Subject of Research. The problem of multiharmonic disturbance compensation for the class of linear time-invariant plants with known parameters and delay is considered. Method. The disturbance is presented as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally enables applying certainty equivalence principle. In order to remove undesirable influence of delay a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. As distinct from widespread approaches, the proposed algorithm does not require identification of disturbance parameters and gives the possibility to remove such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of proposed approach. Results illustrate the boundness of all signals in the closed-loop system and complete compensation of harmonic signal. It is shown that the proposed idea makes it possible to increase the adaptation gain for different delays without system stability loss. Practical Relevance. The algorithm of adaptive compensation is recommended for the use in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal; the problems of control of robotics systems with periodical behavior; the problems of ship roll compensation; the problems of space plants control in the presence of uncontrollable rotation

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements