On multi-party communication complexity of random functions

We prove that almost all Boolean function has a high $k$--party communication complexity. The 2--party case was settled by {\it Papadimitriou} and {\it Sipser}. Proving the $k$--party case needs a deeper investigation of the underlying structure of the $k$--cylinder--intersections; (the 2--cylinder--intersections are the rectangles). \noindent First we examine the basic properties of $k$--cylinder--intersections, then an upper estimation is given for their number, which facilitates to prove the lower--bound theorem for the $k$--party communication complexity of randomly chosen Boolean functions. In the last section we extend our results to the $\varepsilon$--distributional communication complexity of random functions

Separating the communication complexities of MOD m and MOD p circuits

We prove in this paper that it is much harder to evaluate depth--2, size--$N$ circuits with MOD $m$ gates than with MOD $p$ gates by $k$--party communication protocols: we show a $k$--party protocol which communicates $O(1)$ bits to evaluate circuits with MOD $p$ gates, while evaluating circuits with MOD $m$ gates needs $\Omega(N)$ bits, where $p$ denotes a prime, and $m$ a composite, non-prime power number. Let us note that using $k$--party protocols with $k\geq p$ is crucial here, since there are depth--2, size--$N$ circuits with MOD $p$ gates with $p>k$, whose $k$--party evaluation needs $\Omega(N)$ bits. As a corollary, for all $m$, we show a function, computable with a depth--2 circuit with MOD $m$ gates, but not with any depth--2 circuit with MOD $p$ gates. It is easy to see that the $k$--party protocols are not weaker than the $k'$--party protocols, for $k'>k$. Our results imply that if there is a prime $p$ between $k$ and $k'$: $k<p\leq k'$, then there exists a function which can be computed by a $k'$--party protocol with a constant number of communicated bits, while any $k$--party protocol needs linearly many bits of communication. This result gives a hierarchy theorem for multi--party protocols

Harmonic analysis, real approximation, and the communication complexity of Boolean functions

In this paper we prove several fundamental theorems, concerning the multi--party communication complexity of Boolean functions. Let $g$ be a real function which approximates Boolean function $f$ of $n$ variables with error less than $1/5$. Then --- from our Theorem 1 --- there exists a k=O(\log (n\L_1(g)))--party protocol which computes $f$ with a communication of O(\log^3(n\L_1(g))) bits, where \L_1(g) denotes the \L_1 spectral norm of $g$. We show an upper bound to the symmetric $k$--party communication complexity of Boolean functions in terms of their \L_1 norms in our Theorem 3. For $k=2$ it was known that the communication complexity of Boolean functions are closely related with the {\it rank} of their communication matrix [Ya1]. No analogous upper bound was known for the k--party communication complexity of {\it arbitrary} Boolean functions, where $k>2$

NASCENT: an automatic protein interaction network generation tool for non-model organisms.

Large quantity of reliable protein interaction data are available for model organisms in public depositories (e.g., MINT, DIP, HPRD, INTERACT). Most data correspond to experiments with the proteins of Saccharomyces cerevisiae, Drosophila melanogaster, Homo sapiens, Caenorhabditis elegans, Escherichia coli and Mus musculus. For other important organisms the data availability is poor or non-existent. Here we present NASCENT, a completely automatic web-based tool and also a downloadable Java program, capable of modeling and generating protein interaction networks even for non-model organisms. The tool performs protein interaction network modeling through gene-name mapping, and outputs the resulting network in graphical form and also in computer-readable graph-forms, directly applicable by popular network modeling software. AVAILABILITY: http://nascent.pitgroup.org

2-Server PIR with sub-polynomial communication

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. In this work we construct a 1-round 2-server PIR with total communication cost $n^{O({\sqrt{\log\log n/\log n}})}$. This improves over the currently known 2-server protocols which require $O(n^{1/3})$ communication and matches the communication cost of known 3-server PIR schemes. Our improvement comes from reducing the number of servers in existing protocols, based on Matching Vector Codes, from 3 or 4 servers to 2. This is achieved by viewing these protocols in an algebraic way (using polynomial interpolation) and extending them using partial derivatives

Bidirectional PageRank Estimation: From Average-Case to Worst-Case

We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average-case sense, for a uniformly random choice of target node. Crucially, we show how the reversibility of random walks on undirected networks can be exploited to convert average-case to worst-case guarantees. While past bidirectional methods combine forward random walks with reverse local pushes, our algorithm combines forward local pushes with reverse random walks. We also discuss how to modify our methods to estimate random-walk probabilities for any length distribution, thereby obtaining fast algorithms for estimating general graph diffusions, including the heat kernel, on undirected networks.Comment: Workshop on Algorithms and Models for the Web-Graph (WAW) 201

Access Structure Hiding Secret Sharing from Novel Set Systems and Vector Families

Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public access structures, which violates privacy and facilitates the adversary by revealing high-value targets. In this paper, we address this shortcoming by introducing \emph{hidden access structures}, which remain secret until some authorized subset of parties collaborate. The central piece of this work is the construction of a set-system $\mathcal{H}$ with strictly greater than $\exp\left(c \dfrac{1.5 (\log h)^2}{\log \log h}\right)$ subsets of a set of $h$ elements. Our set-system $\mathcal{H}$ is defined over $\mathbb{Z}_m$, where $m$ is a non-prime-power, such that the size of each set in $\mathcal{H}$ is divisible by $m$ but the sizes of their pairwise intersections are not divisible by $m$, unless one set is a subset of another. We derive a vector family $\mathcal{V}$ from $\mathcal{H}$ such that superset-subset relationships in $\mathcal{H}$ are represented by inner products in $\mathcal{V}$. We use $\mathcal{V}$ to "encode" the access structures and thereby develop the first \emph{access structure hiding} secret sharing scheme. For a setting with $\ell$ parties, our scheme supports $2^{2^{\ell/2 - O(\log \ell) + 1}}$ out of the $2^{2^{\ell - O(\log \ell)}}$ total monotone access structures, and its maximum share size for any access structures is $(1+ o(1)) \dfrac{2^{\ell+1}}{\sqrt{\pi \ell/2}}$. The scheme assumes semi-honest polynomial-time parties, and its security relies on the Generalized Diffie-Hellman assumption.Comment: This is the full version of the paper that appears in D. Kim et al. (Eds.): COCOON 2020 (The 26th International Computing and Combinatorics Conference), LNCS 12273, pp. 246-261. This version contains tighter bounds on the maximum share size, and the total number of access structures supporte

Antimycobacterial activity of peptide conjugate of pyridopyrimidine derivative against Mycobacterium tuberculosis in a series of in vitro and in vivo models

New pyridopyrimidine derivatives were defined using a novel HTS in silico docking method (FRIGATE). The target protein was a dUTPase enzyme (EC 3.6.1.23; Rv2697) which plays a key role in nucleotide biosynthesis of Mycobacterium tuberculosis (Mtb). Top hit molecules were assayed in vitro for their antimycobacterial effect on Mtb H37Rv culture. In order to enhance the cellular uptake rate, the TB820 compound was conjugated to a peptid-based carrier and a nanoparticle type delivery system (polylactide-co-glycolide, PLGA) was applied. The conjugate had relevant in vitro antitubercular activity with low in vitro and in vivo toxicity. In a Mtb H37Rv infected guinea pig model the in vivo efficacy of orally administrated PLGA encapsulated compound was proved: animals maintained a constant weight gain and no external clinical signs of tuberculosis were observed. All tissue homogenates from lung, liver and kidney were found negative for Mtb, and diagnostic autopsy showed that no significant malformations on the tissues occurred

Testing non-uniform k-wise independent distributions over product spaces (extended abstract)

A distribution D over Σ1× ⋯ ×Σ n is called (non-uniform) k-wise independent if for any set of k indices {i 1, ..., i k } and for any z1zki1ik, PrXD[Xi1Xik=z1zk]=PrXD[Xi1=z1]PrXD[Xik=zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.National Science Foundation (U.S.) (NSF grant 0514771)National Science Foundation (U.S.) (grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Marie Curie International Reintegration Grants (Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09)Massachusetts Institute of Technology (Akamai Presidential Fellowship