The Writhe of Permutations and Random Framed Knots

We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution. This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model. The distribution of the framing in this model is equivalent to the writhe of random permutations

Jet-like Correlations with Direct-Photon and Neutral-Pion Triggers at sNN=200 GeV

Azimuthal correlations of charged hadrons with direct-photon (γdir) and neutral-pion (π0) trigger particles are analyzed in central Au+Au and minimum-bias p + p collisions at √sN N = 200 GeV in the STAR experiment. The charged-hadron per-trigger yields at mid-rapidity from central Au+Au collisions are compared with p + p collisions to quantify the suppression in Au+Au collisions. The suppression of the away-side associated-particle yields per γdir trigger is independent of the transverse momentum of the trigger particle (ptrig T ), whereas the suppression is smaller at low transverse momentum of the associated charged hadrons (passoc T ). Within uncertainty, similar levels of suppression are observed for γdir and π0 triggers as a function of zT (≡ passoc T /ptrig T ). The results are compared with energy-lossinspired theoretical model predictions. Our studies support previous conclusions that the lost energy reappears predominantly at low transverse momentum, regardless of the trigger energy

A theorem prover-based analysis tool for object-oriented databases

We present a theorem-prover based analysis tool for object-oriented database systems with integrity constraints. Object-oriented database specifications are mapped to higher-order logic (HOL). This allows us to reason about the semantics of database operations using a mechanical theorem prover such as Isabelle or PVS. The tool can be used to verify various semantics requirements of the schema (such as transaction safety, compensation, and commutativity) to support the advanced transaction models used in workflow and cooperative work. We give an example of method safety analysis for the generic structure editing operations of a cooperative authoring system

Faster and Simpler Distributed Algorithms for Testing and Correcting Graph Properties in the CONGEST-Model

In this paper we present distributed testing algorithms of graph properties in the CONGEST-model [Censor-Hillel et al. 2016]. We present one-sided error testing algorithms in the general graph model. We first describe a general procedure for converting $\epsilon$-testers with a number of rounds $f(D)$, where $D$ denotes the diameter of the graph, to $O((\log n)/\epsilon)+f((\log n)/\epsilon)$ rounds, where $n$ is the number of processors of the network. We then apply this procedure to obtain an optimal tester, in terms of $n$, for testing bipartiteness, whose round complexity is $O(\epsilon^{-1}\log n)$, which improves over the $poly(\epsilon^{-1} \log n)$-round algorithm by Censor-Hillel et al. (DISC 2016). Moreover, for cycle-freeness, we obtain a \emph{corrector} of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. In the second part of the paper we design algorithms for testing whether the network is $H$-free for any connected $H$ of size up to four with round complexity of $O(\epsilon^{-1})$. This improves over the $O(\epsilon^{-2})$-round algorithms for testing triangle freeness by Censor-Hillel et al. (DISC 2016) and for testing excluded graphs of size $4$ by Fraigniaud et al. (DISC 2016). In the last part we generalize the global tester by Iwama and Yoshida (ITCS 2014) of testing $k$-path freeness to testing the exclusion of any tree of order $k$. We then show how to simulate this algorithm in the CONGEST-model in $O(k^{k^2+1}\cdot\epsilon^{-k})$ rounds

Deterministic Rateless Codes for BSC

A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for every channel in the family, reliable communication is obtained by a prefix of the code whose rate is arbitrarily close to the channel's capacity. As a result, a universal encoder can communicate over all channels in the family while simultaneously achieving optimal communication overhead. In this paper, we construct the first \emph{deterministic} rateless code for the binary symmetric channel. Our code can be encoded and decoded in $O(\beta)$ time per bit and in almost logarithmic parallel time of $O(\beta \log n)$, where $\beta$ is any (arbitrarily slow) super-constant function. Furthermore, the error probability of our code is almost exponentially small $\exp(-\Omega(n/\beta))$. Previous rateless codes are probabilistic (i.e., based on code ensembles), require polynomial time per bit for decoding, and have inferior asymptotic error probabilities. Our main technical contribution is a constructive proof for the existence of an infinite generating matrix that each of its prefixes induce a weight distribution that approximates the expected weight distribution of a random linear code

Centrality and Transverse Momentum Dependence of Elliptic Flow of Multistrange Hadrons and ϕ Meson in Au + Au Collisions at √ sNN = 200 GeV

We present high precision measurements of elliptic flow near midrapidity (|y|\u3c1.0) for multistrange hadrons and ϕ meson as a function of centrality and transverse momentum in Au+Au collisions at center of mass energy √sNN=200 GeV. We observe that the transverse momentum dependence of ϕ and Ω v2 is similar to that of π and p, respectively, which may indicate that the heavier strange quark flows as strongly as the lighter up and down quarks. This observation constitutes a clear piece of evidence for the development of partonic collectivity in heavy-ion collisions at the top RHIC energy. Number of constituent quark scaling is found to hold within statistical uncertainty for both 0%–30% and 30%–80% collision centrality. There is an indication of the breakdown of previously observed mass ordering between ϕ and proton v2 at low transverse momentum in the 0%–30% centrality range, possibly indicating late hadronic interactions affecting the proton v2