Enumerating (2+2)-free posets by the number of minimal elements and other statistics

An unlabeled poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Let $p_n$ denote the number of (2+2)-free posets of size $n$. In a recent paper, Bousquet-M\'elou et al.\cite{BCDK} found, using so called ascent sequences, the generating function for the number of (2+2)-free posets of size $n$: $P(t)=\sum_{n \geq 0} p_n t^n = \sum_{n\geq 0} \prod_{i=1}^{n} (1-(1-t)^i)$. We extend this result in two ways. First, we find the generating function for (2+2)-free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if $p_{n,k}$ equals the number of (2+2)-free posets of size $n$ with $k$ minimal elements, then $P(t,z)=\sum_{n,k \geq 0} p_{n,k} t^n z^k = 1+ \sum_{n \geq 0} \frac{zt}{(1-zt)^{n+1}} \prod_{i=1}^n (1-(1-t)^i)$. The second result cannot be derived from the first one by a substitution. On the other hand, $P(t)$ can easily be obtained from $P(t,z)$ thus providing an alternative proof for the enumeration result in \cite{BCDK}. Moreover, we conjecture a simpler form of writing $P(t,z)$. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in \cite{BCDK,cdk}. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with (2+2)- and (3+1)-free posets

Transcription start site scanning and the requirement for ATP during transcription initiation by RNA polymerase II

Saccharomyces cerevisiae RNA polymerase (Pol) II locates transcription start sites (TSS) at TATA-containing promoters by scanning sequences downstream from the site of preinitiation complex formation, a process that involves the translocation of downstream promoter DNA toward Pol II. To investigate a potential role of yeast Pol II transcription in TSS scanning, HIS4 promoter derivatives were generated that limited transcripts in the 30-bp scanned region to two nucleotides in length. Although we found that TSS scanning does not require RNA synthesis, our results revealed that transcription in the purified yeast basal system is largely ATP-independent despite a requirement for the TFIIH DNA translocase subunit Ssl2. This result is rationalized by our finding that, although they are poorer substrates, UTP and GTP can also be utilized by Ssl2. ATPγS is a strong inhibitor of rNTP-fueled translocation, and high concentrations of ATPγS make transcription completely dependent on added dATP. Limiting Pol II function with low ATP concentrations shifted the TSS position downstream. Combined with prior work, our results show that Pol II transcription plays an important role in TSS selection but is not required for the scanning reaction

Hedging Effectiveness under Conditions of Asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution

Going from Theory to Practice: The Mixed Success of Approval Voting

Approval voting (AV) is a voting system in which voters can vote for, or approve of, as many candidates as they like in multicandidate elections. In 1987 and 1988, four scientific and engineering societies, collectively comprising several hundred thousand members, used AV for the first time. Since then, about half a dozen other societies have adopted AV. Usually its adoption was seriously debated, but other times pragmatic or political considerations proved decisive in its selection. While AV has an ancient pedigree, its recent history is the focus of this paper. Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected. Although the use of AV is generally considered to have been successful in the societies-living up to the rhetoric of its proponents-AV has been a controversial reform. AV is not currently used in any public elections, despite efforts to institute it, so its success should be judged as mixed. The chief reason for its nonadoption in public elections, and by some societies, seems to be a lack of key "insider" support.APPROVAL VOTING; ELECTIONS; PROFESSIONAL SOCIETIES; CONDORCET CANDIDATE.

Price Elasticity Estimates of Cigarette Demand in Vietnam

In this paper, we analyze a complete demand system to estimate the price elasticity for cigarette demand in Vietnam. Following Deaton (1990), we build a spatial panel using cross sectional household survey data. We consider a model of simultaneous choice of quantity and quality. This allows us to exploit unit values from cigarette consumption in order to disentangle quality choice from exogenous price variations. We then rely on spatial variations in prices and quantities demanded to estimate an Almost Ideal Demand System. The estimated price elasticity for cigarette demand is centered around -0.53, which is in line with previous empirical studies for developing countries.Price elasticity; Cigarette Demand; Taxation; Consumption; Vietnam

Kronecker products and the RSK correspondence

The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that realizes combinatorially this identity. As a consequence we obtain an algorithm that to each minimal matrix associates a minimal component, with respect to the dominance order, in a Kronecker product, and a combinatorial description of the corresponding Kronecker coefficient in terms of minimal matrices and tableau insertion. Our bijection follows from a generalization of the dual RSK correspondence to 3-dimensional binary matrices, which we state and prove. With the same tools we also obtain a generalization of the RSK correspondence to 3-dimensional integer matrices

An extremal problem on crossing vectors

For positive integers $w$ and $k$, two vectors $A$ and $B$ from $\mathbb{Z}^w$ are called $k$-crossing if there are two coordinates $i$ and $j$ such that $A[i]-B[i]\geq k$ and $B[j]-A[j]\geq k$. What is the maximum size of a family of pairwise $1$-crossing and pairwise non-$k$-crossing vectors in $\mathbb{Z}^w$? We state a conjecture that the answer is $k^{w-1}$. We prove the conjecture for $w\leq 3$ and provide weaker upper bounds for $w\geq 4$. Also, for all $k$ and $w$, we construct several quite different examples of families of desired size $k^{w-1}$. This research is motivated by a natural question concerning the width of the lattice of maximum antichains of a partially ordered set.Comment: Corrections and improvement

Strategic Audit of National Instruments

The research and analyses compiled in this paper provide a holistic view into the current situation that National Instruments faces as a company and what strategies it can take to overcome current and pressing issues. The goal of the audit is to determine a strategic recommendation for National Instruments that will achieve any number of goals and objectives set by the auditor in accordance to the situation at hand. In addition to this strategic recommendation, an implementation and contingency plan are developed to further expand upon how such a strategy would be created in the real world. The strategic recommendation and corresponding plans have been crafted through extensive background research of National Instruments in combination with various tools such as a SWOT Analysis and Porter’s Five Forces to analyze the current state of National Instruments. Through analysis and extensive thought regarding possible alternatives, this paper concluded that investing in 5G Test & Measurement development was of highest importance to overcome the low net income issues that National Instruments currently faces

Betancourt, Sonia. Oriente no es una pieza de museo: Jorge Luis Borges, la clave orientalista y el manuscrito de Qué es el budismo. Salamanca: Ediciones Universidad de Salamanca, 2018. 312 pp.

Betancourt, Sonia.  Oriente no es una pieza de museo: Jorge Luis Borges, la clave orientalista y el manuscrito de Qué es el budismo. Salamanca: Ediciones Universidad de Salamanca, 2018. 312 pp