A Succinct Four Russians Speedup for Edit Distance Computation and One-against-many Banded Alignment

The classical Four Russians speedup for computing edit distance (a.k.a. Levenshtein distance), due to Masek and Paterson [Masek and Paterson, 1980], involves partitioning the dynamic programming table into k-by-k square blocks and generating a lookup table in O(psi^{2k} k^2 |Sigma|^{2k}) time and O(psi^{2k} k |Sigma|^{2k}) space for block size k, where psi depends on the cost function (for unit costs psi = 3) and |Sigma| is the size of the alphabet. We show that the O(psi^{2k} k^2) and O(psi^{2k} k) factors can be improved to O(k^2 lg{k}) time and O(k^2) space. Thus, we improve the time and space complexity of that aspect compared to Masek and Paterson [Masek and Paterson, 1980] and remove the dependence on psi. We further show that for certain problems the O(|Sigma|^{2k}) factor can also be reduced. Using this technique, we show a new algorithm for the fundamental problem of one-against-many banded alignment. In particular, comparing one string of length m to n other strings of length m with maximum distance d can be performed in O(n m + m d^2 lg{d} + n d^3) time. When d is reasonably small, this approaches or meets the current best theoretic result of O(nm + n d^2) achieved by using the best known pairwise algorithm running in O(m + d^2) time [Myers, 1986][Ukkonen, 1985] while potentially being more practical. It also improves on the standard practical approach which requires O(n m d) time to iteratively run an O(md) time pairwise banded alignment algorithm. Regarding pairwise comparison, we extend the classic result of Masek and Paterson [Masek and Paterson, 1980] which computes the edit distance between two strings in O(m^2/log{m}) time to remove the dependence on psi even when edits have arbitrary costs from a penalty matrix. Crochemore, Landau, and Ziv-Ukelson [Crochemore, 2003] achieved a similar result, also allowing for unrestricted scoring matrices, but with variable-sized blocks. In practical applications of the Four Russians speedup wherein space efficiency is important and smaller block sizes k are used (notably k < |Sigma|), Kim, Na, Park, and Sim [Kim et al., 2016] showed how to remove the dependence on the alphabet size for the unit cost version, generating a lookup table in O(3^{2k} (2k)! k^2) time and O(3^{2k} (2k)! k) space. Combining their work with our result yields an improvement to O((2k)! k^2 lg{k}) time and O((2k)! k^2) space

Gender Essentialisms and the Abject: Understanding Transgender Identity in Jackie Kay's Trumpet

This article focuses on the tensions between essentialist and fluid conceptions of gender identity in Jackie Kay's Trumpet (1998). Joss Moody, a Black Scottish jazz trumpeter who is posthumously revealed to have been biologically female, is constructed largely through external characterisations. The most significant of these narratives are his wife Millie's and his son Colman's. I first illustrate the importance of performativity in understanding gender identity through the work of Judith Butler. This provides context for my discussion of Millie and Joss, focused on the relationship between the pellicular and the sartorial. The narrative focus on skin and the body versus clothing serves to illustrate Millie's understanding of gender as fluid and performative. In the second section of the essay, I outline the abject and address Colman's expulsion of that which threatens his sense of self. Positing that his perception of Joss as a representative of the maternal that must be expelled in order to enter the Symbolic and constitute a self, his understanding of gender on binary terms is the key element in his internal struggle. Embarking on a journey to learn about his father's life, Colman's refocusing on personal, lived experience allows his views to align with Millie's by the end of the novel. Thereby, Kay illustrates the tension between binary and nuanced understandings of gender in Trumpet, and the method by which this can be overcome: an inclusive understanding that undermines notions of a hegemonic masculinity from which non-conformants can be excluded based on bodily attributes

Structural transitions in alumina nanoparticles by heat treatment

γ-alumina nanoparticles were annealed sequentially at 800°C, 950°C and 1100°C and structural transitions as a function of heat treatment were studied by X-ray diffraction (XRD), Differential Scanning Calorimetry (DSC) and 27Al Magic Angle Spinning Nuclear Magnetic Resonance (MAS-NMR) methods.. XRD studies found that γ-Al2O3 is stable upto a temperature of at least 950°C and transforms to the thermodynamically stable α-phase after annealing at 1100°C. MAS-NMR revealed that γ-alumina contains AlO4 and AlO6 structural units in the ratio 1: 2, while α-phase contains only AlO6 units. DSC confirmed that γ → α transition initiates at 1060°C

Explorer News: November 1971

https://digitalcommons.lasalle.edu/explorer_news/1003/thumbnail.jp

Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path Based Formulation

The problem of online matching with stochastic rewards is a generalization of the online bipartite matching problem where each edge has a probability of success. When a match is made it succeeds with the probability of the corresponding edge. Introducing this model, Mehta and Panigrahi (FOCS 2012) focused on the special case of identical edge probabilities. Comparing against a deterministic offline LP, they showed that the Ranking algorithm of Karp et al. (STOC 1990) is 0.534 competitive and proposed a new online algorithm with an improved guarantee of $0.567$ for vanishingly small probabilities. For the case of vanishingly small but heterogeneous probabilities Mehta et al. (SODA 2015), gave a 0.534 competitive algorithm against the same LP benchmark. For the more general vertex-weighted version of the problem, to the best of our knowledge, no results being $1/2$ were previously known even for identical probabilities. We focus on the vertex-weighted version and give two improvements. First, we show that a natural generalization of the Perturbed-Greedy algorithm of Aggarwal et al. (SODA 2011), is $(1-1/e)$ competitive when probabilities decompose as a product of two factors, one corresponding to each vertex of the edge. This is the best achievable guarantee as it includes the case of identical probabilities and in particular, the classical online bipartite matching problem. Second, we give a deterministic $0.596$ competitive algorithm for the previously well studied case of fully heterogeneous but vanishingly small edge probabilities. A key contribution of our approach is the use of novel path-based analysis. This allows us to compare against the natural benchmarks of adaptive offline algorithms that know the sequence of arrivals and the edge probabilities in advance, but not the outcomes of potential matches.Comment: Preliminary version in EC 202

THz and ft-ir study of 18-o isotopologues of sulfur dioxide: 32S16O18O and 32S18O2

Sulfur dioxide is a molecule that have a great interest in different domains: for atmospheric and planetology chemistry, it is also ubiquitous and abundant in interstellar medium. If the $^{16}$O species were extensively studied, this is not the case of the $^{18}$O isotopologues. The aim of this study is first to complete the rotational spectra of the ground state with these new measurements up to 1.5 THz, previous measurements are up to 1050 GHz for the $^{32}$S$^{16}$O$^{18}$O species\footnote{Belov, S. P.{\em et al.}, 1998, {\em J. Mol. Spectrosc.}~{\bf191}, 17}, and 145 GHz concerning the $^{32}$S$^{18}$O$_2$ species\footnote{Lindermayer, J.{\em et al.}, 1985, {\em J. Mol. Spectrosc.}~{\bf110}, 357}. The second part is making a global fit of the rotational and vibrational transitions for the excited vibrational states. For the $v_2$ band, we will complete the recent I.R. analysis\footnote{Gueye, F.{\em et al.} {\em Mol. Phys.}~{\bf in press}}. About the triad ($v_1, 2v_2, v_3$): $^{32}$S$^{18}$O$_2$ species was studied\footnote{Ulenikov, O. N.{\em et al.}, 2015, {\em JQSRT}~{\bf166}, 13}, but not the $^{32}$S$^{16}$O$^{18}$O one.\\ The FT-IR spectra were recorded on the AILES Beamline at Synchrotron SOLEIL using the Synchrotron light source, coupled to the Bruker IFS125HR Fourier transform spectrometer\footnote{Brubach, J.{\em et al.}, 2010, {\em AIP Conf. Proc.}~{\bf1214}, 81}. The THz spectra were obtained from 150 to 1500 GHz using the Lille's solid state spectrometer\footnote{Zakharenko, O.{\em et al.}, 2015, {\em J. Mol. Spectrosc.}~{\bf317}, 41}. The analysis is in progress, the latest results will be presented.\\ \em{Support from the French Laboratoire d'Excellence CaPPA (Chemical and Physical Properties of the Atmosphere) through contract ANR-10-LABX-0005 of the Programme d'Investissements d'Avenir is acknowledged

You\u27re a Good Man, Charlie Brown

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