Optimal Budget Allocation in Social Networks: Quality or Seeding

In this paper, we study a strategic model of marketing and product consumption in social networks. We consider two competing firms in a market providing two substitutable products with preset qualities. Agents choose their consumptions following a myopic best response dynamics which results in a local, linear update for the consumptions. At some point in time, firms receive a limited budget which they can use to trigger a larger consumption of their products in the network. Firms have to decide between marginally improving the quality of their products and giving free offers to a chosen set of agents in the network in order to better facilitate spreading their products. We derive a simple threshold rule for the optimal allocation of the budget and describe the resulting Nash equilibrium. It is shown that the optimal allocation of the budget depends on the entire distribution of centralities in the network, quality of products and the model parameters. In particular, we show that in a graph with a higher number of agents with centralities above a certain threshold, firms spend more budget on seeding in the optimal allocation. Furthermore, if seeding budget is nonzero for a balanced graph, it will also be nonzero for any other graph, and if seeding budget is zero for a star graph, it will be zero for any other graph too. We also show that firms allocate more budget to quality improvement when their qualities are close, in order to distance themselves from the rival firm. However, as the gap between qualities widens, competition in qualities becomes less effective and firms spend more budget on seeding.Comment: 7 page

Nontrivial t-Designs over Finite Fields Exist for All t

A $t$-$(n,k,\lambda)$ design over \F_q is a collection of $k$-dimensional subspaces of \F_q^n, called blocks, such that each $t$-dimensional subspace of \F_q^n is contained in exactly $\lambda$ blocks. Such $t$-designs over \F_q are the $q$-analogs of conventional combinatorial designs. Nontrivial $t$-$(n,k,\lambda)$ designs over \F_q are currently known to exist only for $t \leq 3$. Herein, we prove that simple (meaning, without repeated blocks) nontrivial $t$-$(n,k,\lambda)$ designs over \F_q exist for all $t$ and $q$, provided that $k > 12t$ and $n$ is sufficiently large. This may be regarded as a $q$-analog of the celebrated Teirlinck theorem for combinatorial designs

Morphometric evidences for regional variation in potential of neural plasticity

The neural plasticity showing the ability of nervous system to change its structure and function is a well-documented fact. However regional variation within a CNS structure to undergo plastic changes has been shown by limited studies. Along medial-lateral sequences of parasagittal sections, the molecular layer thickness of primary fissure borderlands in rat cerebellar left hemisphere was studied to assess the regional difference in plasticibility. Despite the homogeneity of cerebellar histology, this study showed that there is a significant interlobular difference between ML thicknesses of Prf borderlands. In addition, it revealed that the thickness alters in a significant trend within each borderland. The quantitative heterogeneity of cerebellar architecture such as variation of cortical thickness may provide some evidences to show that different regions of a homogenous cortex, even two adjacent borderlands and areas within them, can have different potentials for plasticity. © 2006 Sociedad Chilena de Anatomía

Design and implementation of 30kW 200/900V LCL modular multilevel based DC/DC converter for high power applications

This paper presents the design, development and testing of a 30kW, 200V/900V modular multilevel converter (MMC) based DC/DC converter prototype. An internal LCL circuit is used to provide voltage stepping and fault tolerance property. The converter comprises two five level MMC based on insulated gate bipolar transistors (IGBTs) and metal oxide semiconductor field effect transistor (MOSFET). Due to low number of levels, selective harmonic elimination modulation (SHE) is used, which determines the switching angles in such a way that third harmonic is minimized whereas the fundamental component is a linear function of the modulation index. In addition, instead of using an expensive control board, three commercial control boards are embedded. This is required to implement the sophisticated DC/DC converter control algorithm. Simulation and experimental results are presented to demonstrate the converter performance in step up and down modes