Defining Recursive Predicates in Graph Orders

We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary. We define the notion of a recursive predicate over graphs using Turing Machine recognizable string encodings of graphs. We also define the notion of an arithmetical relation over graphs using a total order $\leq_t$ on the set $\mathcal{G}$ such that ($\mathcal{G},\leq_t$) is isomorphic to ($\mathbb{N},\leq$). We introduce the notion of a \textit{capable} structure over graphs, which is one satisfying the conditions : (1) definability of arithmetic, (2) definability of cardinality of a graph, and (3) definability of two particular graph predicates related to vertex labellings of graphs. We then show any capable structure can define every arithmetical predicate over graphs. As a corollary, any capable structure also defines every recursive graph relation. We identify capable structures which are expansions of graph orders, which are structures of the form ($\mathcal{G},\leq$) where $\leq$ is a partial order. We show that the subgraph order i.e. ($\mathcal{G},\leq_s$), induced subgraph order with one constant $P_3$ i.e. ($\mathcal{G},\leq_i,P_3$) and an expansion of the minor order for counting edges i.e. ($\mathcal{G},\leq_m,sameSize(x,y)$) are capable structures. In the course of the proof, we show the definability of several natural graph theoretic predicates in the subgraph order which may be of independent interest. We discuss the implications of our results and connections to Descriptive Complexity

Induced abortion potential among Indian women

Information on abortion is limited and inaccurate especially in the developing world, which has led to several speculations on the prevalence of abortion in this region. A rise in prevalence of abortion is mostly accounted for in terms of increase in the prevalence of induced abortions, which reflects on the reproductive health of women. With the growing concern for reproductive health of women, the study of abortion phenomenon has drawn serious attention of researchers world wide. In such circumstances, this is an attempt to assess the induced abortion potential among Indian women by utilising information on proportion of unwanted and ill-timed pregnancies obtained through National Family Health Survey, India.

Concentration in Knowledge Output:A Case of Economics Journals

Journals moderate knowledge activity in economics. The activity of publishing article in professional journal forms significant part of knowledge output. Output of economics articles has been growing over the time. We examine an important question: Is there any case of institutional or location concentration in knowledge production? This paper analyses concentration indicators specific to economics journals and explores link between publication process and concentration. The analysis of various concentration measures present evidence for institutional-geographic-area-author concentration in Knowledge production in Economics. High concentration levels indicate possibility of institutional lock-in. The literature provides evidence for myopic refereeing, editorial favouritism and the presence of ‘lock-in’ effect. The achievement in journal publication is influenced by factors like institutional affiliation, propitious circumstances etc. Discussion carried out in this paper hints the possibility of causal link between unfair process and unfair outcome.Knowledge,Lotka's Law,Fourier Series

Neural reactivations during sleep determine network credit assignment.

A fundamental goal of motor learning is to establish the neural patterns that produce a desired behavioral outcome. It remains unclear how and when the nervous system solves this 'credit assignment' problem. Using neuroprosthetic learning, in which we could control the causal relationship between neurons and behavior, we found that sleep-dependent processing was required for credit assignment and the establishment of task-related functional connectivity reflecting the casual neuron-behavior relationship. Notably, we observed a strong link between the microstructure of sleep reactivations and credit assignment, with downscaling of non-causal activity. Decoupling of spiking to slow oscillations using optogenetic methods eliminated rescaling. Thus, our results suggest that coordinated firing during sleep is essential for establishing sparse activation patterns that reflect the causal neuron-behavior relationship