Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $\omega^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where the players receive all the inputs at the same time and produce all the outputs at the same time. They win $G^n$ if they win each instance of $G$. In this paper we show that for any game $G$ such that $\omega^*(G) = 1 - \varepsilon < 1$, $\omega^*(G^n)$ decreases exponentially in $n$. First, for any game $G$ on the uniform distribution, we show that $\omega^*(G^n) = (1 - \varepsilon^2)^{\Omega\left(\frac{n}{\log(|I||O|)} - |\log(\varepsilon)|\right)}$, where $|I|$ and $|O|$ are the sizes of the input and output sets. From this result, we show that for any entangled game $G$, $\omega^*(G^n) \le (1 - \varepsilon^2)^{\Omega(\frac{n}{Q\log(|I||O|)} - \frac{|\log(\varepsilon)|}{Q})}$ where $p$ is the input distribution of $G$ and $Q= \frac{|I|^2 \max_{xy} p_{xy}^2 }{\min_{xy} p_{xy} }$. This implies parallel repetition with exponential decay as long as $\min_{xy} \{p_{xy}\} \neq 0$ for general games. To prove this parallel repetition, we introduce the concept of \emph{Superposed Information Cost} for entangled games which is inspired from the information cost used in communication complexity.Comment: In the first version of this paper we presented a different, stronger Corollary 1 but due to an error in the proof we had to modify it in the second version. This third version is a minor update. We correct some typos and re-introduce a proof accidentally commented out in the second versio

Quantified Derandomization of Linear Threshold Circuits

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing approach to prove such lower bounds is to construct a non-trivial derandomization algorithm for $TC^0$. In this work we take a first step towards the latter goal, by proving the first positive results regarding the derandomization of $TC^0$ circuits of depth $d>2$. Our first main result is a quantified derandomization algorithm for $TC^0$ circuits with a super-linear number of wires. Specifically, we construct an algorithm that gets as input a $TC^0$ circuit $C$ over $n$ input bits with depth $d$ and $n^{1+\exp(-d)}$ wires, runs in almost-polynomial-time, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs. In fact, our algorithm works even when the circuit $C$ is a linear threshold circuit, rather than just a $TC^0$ circuit (i.e., $C$ is a circuit with linear threshold gates, which are stronger than majority gates). Our second main result is that even a modest improvement of our quantified derandomization algorithm would yield a non-trivial algorithm for standard derandomization of all of $TC^0$, and would consequently imply that $NEXP\not\subseteq TC^0$. Specifically, if there exists a quantified derandomization algorithm that gets as input a $TC^0$ circuit with depth $d$ and $n^{1+O(1/d)}$ wires (rather than $n^{1+\exp(-d)}$ wires), runs in time at most $2^{n^{\exp(-d)}}$, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs, then there exists an algorithm with running time $2^{n^{1-\Omega(1)}}$ for standard derandomization of $TC^0$.Comment: Changes in this revision: An additional result (a PRG for quantified derandomization of depth-2 LTF circuits); rewrite of some of the exposition; minor correction

Mycobacteriumsmegmatis bio¢lm formationand slidingmotility are a¡ected by the serine/threonine protein kinase PknF

Eighteen ‘eukaryotic-like’ serine/threonine kinases are present in the Mycobacterium smegmatis genome. One of them encoded by the ORF 3677 demonstrates high similarity to the Mycobacterium tuberculosis protein kinase PknF. A merodiploid strain was generated, which showed reduced growth associated with irregular cell structure. The merodiploid strain displayed altered colony morphology, defective slidingmotility and biofilm formation. These data indicate a role for PknF in biofilm formation, possibly associated with alterations in glycopeptidolipid composition

FLEET: Butterfly Estimation from a Bipartite Graph Stream

We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different partitions. We present a space lower bound for any streaming algorithm that can estimate the number of butterflies accurately, as well as FLEET, a suite of algorithms for accurately estimating the number of butterflies in the graph stream. Estimates returned by the algorithms come with provable guarantees on the approximation error, and experiments show good tradeoffs between the space used and the accuracy of approximation. We also present space-efficient algorithms for estimating the number of butterflies within a sliding window of the most recent elements in the stream. While there is a significant body of work on counting subgraphs such as triangles in a unipartite graph stream, our work seems to be one of the few to tackle the case of bipartite graph streams.Comment: This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Seyed-Vahid Sanei-Mehri, Yu Zhang, Ahmet Erdem Sariyuce and Srikanta Tirthapura. "FLEET: Butterfly Estimation from a Bipartite Graph Stream". The 28th ACM International Conference on Information and Knowledge Managemen

Sublinear Estimation of Weighted Matchings in Dynamic Data Streams

This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. We also give the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs (or any graph with bounded arboricity) using $\tilde{O}(n^{4/5})$ space which also extends to weighted matching. Using previous results by Kapralov, Khanna, and Sudan (2014) we obtain a $\mathrm{polylog}(n)$ approximation for general graphs using $\mathrm{polylog}(n)$ space in random order streams, respectively. In addition, we give a space lower bound of $\Omega(n^{1-\varepsilon})$ for any randomized algorithm estimating the size of a maximum matching up to a $1+O(\varepsilon)$ factor for adversarial streams

Selectivity estimation on set containment search

© Springer Nature Switzerland AG 2019. In this paper, we study the problem of selectivity estimation on set containment search. Given a query record Q and a record dataset S, we aim to accurately and efficiently estimate the selectivity of set containment search of query Q over S. The problem has many important applications in commercial fields and scientific studies. To the best of our knowledge, this is the first work to study this important problem. We first extend existing distinct value estimating techniques to solve this problem and develop an inverted list and G-KMV sketch based approach IL-GKMV. We analyse that the performance of IL-GKMV degrades with the increase of vocabulary size. Motivated by limitations of existing techniques and the inherent challenges of the problem, we resort to developing effective and efficient sampling approaches and propose an ordered trie structure based sampling approach named OT-Sampling. OT-Sampling partitions records based on element frequency and occurrence patterns and is significantly more accurate compared with simple random sampling method and IL-GKMV. To further enhance performance, a divide-and-conquer based sampling approach, DC-Sampling, is presented with an inclusion/exclusion prefix to explore the pruning opportunities. We theoretically analyse the proposed techniques regarding various accuracy estimators. Our comprehensive experiments on 6 real datasets verify the effectiveness and efficiency of our proposed techniques

Using the Minnesota Multiphasic Personality Inventory-2-Restructured Form Cutoffs to Predict Lack of Pre-surgical Exercise

Previous studies suggest the importance of understanding what factors increase risk of lack of physical activity (PA) prior to bariatric surgery, which may increase risk of suboptimal postoperative outcomes. Therefore, the current study sought to explore which Minnesota Multiphasic Personality Inventory-2-Restructured Form (MMPI-2-RF) scales were associated with lack of pre-surgical PA. The mean age of the sample (N=1170) was 45.97 years [standard deviation (SD)=11.59]. Bivariate correlations and relative risk ratios were utilized to examine associations between MMPI-2-RF scale scores and regular preoperative PA. Of the ten hypothesized associations, seven MMPI-2-RF scales in the internalizing and somatic domains were associated with increased risk of preoperative lack of PA. Interventions designed to increase levels of preoperative PA are especially important because individuals with higher levels of preoperative cardiorespiratory fitness experience less complications in surgery and greater weight loss postoperativel

Antimicrobial, Anti-Inflammatory, Antiparasitic, and Cytotoxic Activities of Laennecia confusa

The current paper investigated the potential benefit of the traditional Mexican medicinal plant Laennecia confusa (Cronquist) G. L. Nesom (Asteraceae). Fractions from the hexane, chloroform, methanol, and aqueous extracts were analyzed for antibacterial, antifungal, anti-inflammatory, and antiparasitic activities. The antimicrobial activity of the extracts and fractions was assessed on bacterial and fungal strains, in addition to the protozoa Leishmania donovani, using a microdilution assay. The propensity of the plant's compounds to produce adverse effects on human health was also evaluated using propidium iodine to identify damage to human macrophages. The anti-inflammatory activity of the extracts and fractions was investigated by measuring the secretion of interleukin-6. Chemical analyses demonstrated the presence of flavonoids, cyanogenic and cardiotonic glycosides, saponins, sesquiterpene lactones, and triterpenes in the chloroform extract. A number of extracts and fractions show antibacterial activity. Of particular interest is antibacterial activity against Staphylococcus aureus and its relative methicillin-resistant strain, MRSA. Hexanic and chloroformic fractions also exhibit antifungal activity and two extracts and the fraction CE 2 antiparasitic activity against Leishmania donovani. All bioactive extracts and fractions assayed were also found to be cytotoxic to macrophages. In addition, the hexane and methane extracts show anti-inflammatory activity by suppressing the secretion of interleukine-6