Endogenous trading bloc formation in a North-South global economy

Majority of the trading blocs to date are between similar countries, rather than between developed and developing countries. This paper provides a rationale for why trading blocs among similar countries may arise as an equilibrium phenomenon. It develops a model of an asymmetric world economy, in which there are at least four countries. The countries are differentiated with respect to their market size and market structure.

Bidirectional motion of filaments: Role of motor proteins and passive cross linkers

In eukaryotic cells, motor proteins (MP) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules (MT) form whose stability and dynamics under the influence of MPs has been studied extensively. Although passive cross linkers (PCL) were known to provide structural stability to filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on MT overlap remains largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the MTs of overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.Comment: 13 pages, 9 figure

Fixed points of generalized cyclic contractions without continuity and application to fractal generation

In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces

Exclusion and Inclusion -- A model agnostic approach to feature importance in DNNs

Deep Neural Networks in NLP have enabled systems to learn complex non-linear relationships. One of the major bottlenecks towards being able to use DNNs for real world applications is their characterization as black boxes. To solve this problem, we introduce a model agnostic algorithm which calculates phrase-wise importance of input features. We contend that our method is generalizable to a diverse set of tasks, by carrying out experiments for both Regression and Classification. We also observe that our approach is robust to outliers, implying that it only captures the essential aspects of the input.Comment: 8 pages, 4 figure

Study of organized and biological systems using an ultrafast laser

In an aqueous solution, weak ('soft') molecular interactions lead to the formation of many supramolecular assemblies. In such an assembly, the reactive chemical species remain confined in a nanocavity. Confinement and the local interactions render chemistry in these assemblies markedly different from that in an ordinary solution. Very recently, ultrafast time resolved spectroscopy has been applied to unravel the dynamics in these systems. The new experiments and the computer simulations reveal many surprising and highly interesting features. First, in such a confined system there is almost invariably a new ultraslow component which is slower by 100-1000 times compared to bulk water. Second, in spite of the restrictions imposed inside a nanocavity, dynamics of several processes displays an ultrafast component (in <10 ps time scale). In this review, we discuss five ultrafast processes in many organized and biological systems. The ultrafast processes include solvation dynamics, proton transfer, energy transfer (FRET), electron transfer and anisotropy decay

Excited-state proton transfer from pyranine to acetate in methanol

Excited-state proton transfer (ESPT) of pyranine (8-hydroxypyrene-1,3,6-trisulphonate, HPTS) to acetate in methanol has been studied by steady-state and time-resolved fluorescence spectroscopy. The rate constant of direct proton transfer from pyranine to acetate (k1) is calculated to be ~1 × 109 M-1 s-1. This is slower by about two orders of magnitude than that in bulk water (8 × 1010 M-1 s-1) at 4 M acetate