Simplification Methods for Sum-of-Squares Programs

A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem. The computation required to solve the feasibility problem depends on the number of monomials used in the decomposition. The Newton polytope is a method to prune unnecessary monomials from the decomposition. This method requires the construction of a convex hull and this can be time consuming for polynomials with many terms. This paper presents a new algorithm for removing monomials based on a simple property of positive semidefinite matrices. It returns a set of monomials that is never larger than the set returned by the Newton polytope method and, for some polynomials, is a strictly smaller set. Moreover, the algorithm takes significantly less computation than the convex hull construction. This algorithm is then extended to a more general simplification method for sum-of-squares programming.Comment: 6 pages, 2 figure

R&D and Technology Transfer: Firm-Level Evidence from Chinese Industry

The capacity of developing economies to narrow the gap in living standards with the OECD nations depends critically on their ability to imitate and innovate new technologies. Toward this end, developing economies have access to three avenues of technological advance: technology transfer, domestic R&D, and foreign direct investment. This paper examines the contributions of each of these avenues, as well as their interactions, to productivity and knowledge production within Chinese industry. Based on a large data set for China’s large and medium-size enterprises, the estimation results show that technology transfer – whether domestic or foreign – affects productivity only through its interactions with in-house R&D. Foreign direct investment does not appear to facilitate the adoption of market-mediated foreign technology transfer. Firms wishing to produce patentable knowledge do not benefit from technology transfer; patentable knowledge is created exclusively through in-house R&D operations.http://deepblue.lib.umich.edu/bitstream/2027.42/39968/3/wp582.pd

Mimicry, Knowledge Spillover and Expatriate Assignment Strategy in Overseas Subsidiaries

Based on neo-institutional theory and knowledge spillover, we argue that the probability of a firm assigning an expatriate manager to a foreign subsidiary is influenced by a combination of mimicry and knowledge spillover from any existing expatriate community in the foreign location. The expatriate community's influence is hypothesized to be weaker when the firm's ownership share in its foreign subsidiary is greater but stronger when the cultural distance between a firm's home country and the foreign host country is greater. Data on 95,156 foreign-invested manufacturing ventures in China is used to test these predictions. The findings show an inverted U-shaped relationship between the assignment of expatriates and the number of expatriates previously sent to the same location by prior foreign investors. This relationship is shown to be moderated by subsidiary ownership, but not by the cultural distance between the investor's home country and the host country. Implications for research and practice are discussed

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

Noninflammatory Changes of Microglia Are Sufficient to Cause Epilepsy.

Microglia are well known to play a critical role in maintaining brain homeostasis. However, their role in epileptogenesis has yet to be determined. Here, we demonstrate that elevated mTOR signaling in mouse microglia leads to phenotypic changes, including an amoeboid-like morphology, increased proliferation, and robust phagocytosis activity, but without a significant induction of pro-inflammatory cytokines. We further provide evidence that these noninflammatory changes in microglia disrupt homeostasis of the CNS, leading to reduced synapse density, marked microglial infiltration into hippocampal pyramidal layers, moderate neuronal degeneration, and massive proliferation of astrocytes. Moreover, the mice thus affected develop severe early-onset spontaneous recurrent seizures (SRSs). Therefore, we have revealed an epileptogenic mechanism that is independent of the microglial inflammatory response. Our data suggest that microglia could be an opportune target for epilepsy prevention

Validation of an Impulse Measurement Technique with High Temporal and Spatial Resolutions

AbstractWe present a new experimental technique to measure the force-time history of high-velocity impacts and high pressure blast waves. The technique is based on the classic Hopkinson-type strain bar, coupled with an interferometric velocimeter instead of strain gauges. The major benefits of this setup are its accuracy, temporal resolution, and its imperviousness to electromagnetic interferences. We explain the keys concepts behind the technique and describe the experimental setup. We present experimental and numerical data as proof-of-concept and discuss preliminary studies on the effect of plastic deformation of the bar and its consequences on the interpretation of the measured impulse-history

Diffusion in a multi-component Lattice Boltzmann Equation model

Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is found to have correct diffusion behavior and the multiple diffusion coefficients are obtained analytically. The analytical results are further confirmed by numerical simulations in a few solvable limiting cases. The LBE model is established as a useful computational tool for the simulation of mass transfer in fluid systems with external forces.Comment: To appear in Aug 1 issue of PR

Single image watermark retrieval from 3D printed surfaces via convolutional neural networks.

In this paper we propose and analyse a method for watermarking 3D printed objects, concentrating on the watermark retrieval problem. The method embeds the watermark in a planar region of the 3D printed object in the form of small semi-spherical or cubic bumps arranged at the nodes of a regular grid. The watermark is extracted from a single image of the watermarked planar region through a Convolutional Neural Network. Experiments with 3D printed objects, produced by filaments of various colours, show that in most cases the retrieval method has a high accuracy rate