On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Against the Vagueness Argument

In this paper I offer a counterexample to the so called vagueness argument against restricted composition. This will be done in the lines of a recent suggestion by Trenton Merricks, namely by challenging the claim that there cannot be a sharp cut-off point in a composition sequence. It will be suggested that causal powers which emerge when composition occurs can serve as an indicator of such sharp cut-off points. The main example will be the case of a heap. It seems that heaps might provide a very plausible counterexample to the vagueness argument if we accept the idea that four grains of sand is the least number required to compose a heap—the case has been supported by W. D. Hart. My purpose here is not to put forward a new theory of composition, I only wish to refute the vagueness argument and point out that we should be wary of arguments of its form.

Differential influence of ions on the copy number of plasmids in Thiobacillus ferrooxidans

Thiobacillus ferrooxidans MAL4-1, an isolate from Malanjkhand copper mines, India, was adapted to grow in the presence of high concentration (30 gL(-1)) of Cu2+, resulting in a 15-fold increase in its tolerance to Cu2+. While wild-type T. ferrooxidans MAL4-1 contained multiple plasmids, cultures adapted to Cu2+ concentrations of 20 gL(-1) or more showed a drastic reduction in the copy number of the plasmids. The reduction for three of the plasmids was estimated to be over 50-fold. Examination of the plasmid profiles of the strains adapted to high concentration of SO42- anion (as Na2SO4 or ZnSO4) indicated that the reduction in plasmid copy number is not owing to SO42- anion, but is specific for Cu2+. The effect of mercury on the plasmids was similar to that of copper. Deadaptation of the Cu2+- Or Hg2+-adapted T. ferrooxidans resulted in restoration of the plasmids to the original level within the first passage. The fact that the plasmid copy number, in general, is drastically reduced in Cu2+-adapted T. ferrooxidans suggests that resistance to copper is chromosome mediated. This is the first report of a selective negative influence of copper ions on the copy number of plasmids in T. ferrooxidans.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

On the Maximum Number of Linearly Independent Cycles and Paths in a Network

Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the ``link rank'' of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

The Least of These: American Evangelical Parachurch Missions to the Poor, 1947-2005

This dissertation narrates the historical development of American evangelical missions to the poor from 1947-2005 and analyzes the discourse of its main parachurch proponents, especially World Vision, Compassion International, Food for the Hungry, Samaritan's urse, Sojourners, Evangelicals for Social Action, and the Christian Community Development Association. Although recent scholarship on evangelicalism has been prolific, much of the historical work has focused on earlier periods. Sociological and political scientific scholarship on the postwar period has been attracted mostly to controversies surrounding the Religious Right, leaving evangelicalism's resurgent concern for the poor relatively understudied. This dissertation addresses these lacunae. The study consists of three chronological parts, each marked by a distinctive model of mission to the poor. First, the 1950s were characterized by compassionate charity for individual emergencies, a model that cohered neatly with evangelicalism's individualism and emotionalism. This model should be regarded as the quintessential, bedrock evangelical theory of mission to the poor. It remained strong throughout the entire postwar period. Second, in the 1970s, a strong countercurrent emerged that advocated for penitent protest against structural injustice and underdevelopment. In contrast to the first model, it was distinguished by going against the grain of many aspects of evangelical culture, especially its reflexive patriotism and individualism. Third, in the 1990s, an important movement towards developing potential through hopeful holism gained prominence. Its advocates were confident that their integration of biblical principles with insights from contemporary economic development praxis would contribute to drastic, widespread reductions in poverty. This model signaled a new optimism in evangelicalism's engagement with the broader world. The increasing prominence of missions to the poor within American evangelicalism led to dramatic changes within the movement's worldview: by 2005, evangelicals were mostly unified in their expressed concern for the physical and social needs of the poor, a position that radically reversed their immediate postwar worldview of near-exclusive focus on the spiritual needs of individuals. Nevertheless, missions to the poor also paralleled, reinforced, and hastened the increasing fragmentation of evangelicalism's identity, as each missional model advocated for highly variant approaches to poverty amelioration that were undergirded by diverse sociological, political, and theological assumptions.

Finding the magic number

Paul Wilson and Colin Cooper investigate methods used to extract the number of factors in a factor analysis