Jigsaw percolation: What social networks can collaboratively solve a puzzle?

We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social network has a unique piece of a jigsaw puzzle. Acquainted people with compatible puzzle pieces merge their puzzle pieces. More generally, groups of people with merged puzzle pieces merge if the groups know one another and have a pair of compatible puzzle pieces. The social network solves the puzzle if it eventually merges all the puzzle pieces. For an Erd\H{o}s-R\'{e}nyi social network with $n$ vertices and edge probability $p_n$, we define the critical value $p_c(n)$ for a connected puzzle graph to be the $p_n$ for which the chance of solving the puzzle equals $1/2$. We prove that for the $n$-cycle (ring) puzzle, $p_c(n)=\Theta(1/\log n)$, and for an arbitrary connected puzzle graph with bounded maximum degree, $p_c(n)=O(1/\log n)$ and $\omega(1/n^b)$ for any $b>0$. Surprisingly, with probability tending to 1 as the network size increases to infinity, social networks with a power-law degree distribution cannot solve any bounded-degree puzzle. This model suggests a mechanism for recent empirical claims that innovation increases with social density, and it might begin to show what social networks stifle creativity and what networks collectively innovate.Comment: Published at http://dx.doi.org/10.1214/14-AAP1041 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Seeing the vibrational breathing of a single molecule through time-resolved coherent anti-Stokes Raman scattering

The motion of chemical bonds within molecules can be observed in real time, in the form of vibrational wavepackets prepared and interrogated through ultrafast nonlinear spectroscopy. Such nonlinear optical measurements are commonly performed on large ensembles of molecules, and as such, are limited to the extent that ensemble coherence can be maintained. Here, we describe vibrational wavepacket motion on single molecules, recorded through time-resolved, surface-enhanced, coherent anti-Stokes Raman scattering. The required sensitivity to detect the motion of a single molecule, under ambient conditions, is achieved by equipping the molecule with a dipolar nano-antenna (a gold dumbbell). In contrast with measurements in ensembles, the vibrational coherence on a single molecule does not dephase. It develops phase fluctuations with characteristic statistics. We present the time evolution of discretely sampled statistical states, and highlight the unique information content in the characteristic, early-time probability distribution function of the signal.Comment: 17 pages, 5 figure

New approach towards imaging λ-DNA using scanning tunneling microscopy/spectroscopy (STM/STS)

A new methodology to anchor λ-DNA to silanized n-Si(111) surface using Langmuir Blodget trough was developed. The n-Si (111) was silanized by treating it with low molecular weight octyltrichlorosilane in toluene. Scanning tunneling microscopy (STM) image of λ-DNA on octyltrichlorosilane deposited Si substrate shows areas exhibiting arrayed structures of 700 nm length and 40 nm spacing. Scanning tunneling spectroscopy (STS) at different stages depict a broad distribution of defect states in the bandgap region of n-Si(111) which presumably facilitates tunneling through otherwise insulating DNA layer

New approach towards imaging λ-DNA using scanning tunneling microscopy/spectroscopy (STM/STS)

Abstract. A new methodology to anchor λ-DNA to silanized n-Si(111) surface using Langmuir Blodget trough was developed. The n-Si (111) was silanized by treating it with low molecular weight octyltrichlorosilane in toluene. Scanning tunneling microscopy (STM) image of λ-DNA on octyltrichlorosilane deposited Si substrate shows areas exhibiting arrayed structures of 700 nm length and 40 nm spacing. Scanning tunneling spectroscopy (STS) at different stages depict a broad distribution of defect states in the bandgap region of nSi(111) which presumably facilitates tunneling through otherwise insulating DNA layer

A study of mechanical properties and WEDM machinability of spark plasma sintered ZrB2-B4C ceramic composites

Four different compositions of ZrB2-B4C composites (i.e., 5, 15, 20, 25 Wt. % of B4C) were fabricated by Spark Plasma Sintering Technique (SPS) at 2000 degrees C temperature. The composites were characterized by the evolution of physical and mechanical properties; X-Ray Diffraction (XRD) analysis was also done for phase analysis of the composites. The relative density values were obtained in the range of 96.14-97.78 % of all the composites. The addition of B4C in ZrB2 matrix led to an enhancement in hardness (15.38 GPa at 5 wt.% B4C to 20.49 GPa at 25 wt.% B4C measured at 1.0 kgf load) and fracture toughness (from 2.93 MPa-m(0.5) at 5 wt.% B4C to 4.13 MPa-m(0.5) at 25 wt.% B4C measured at 1.0 kgf load). The composite samples were processed by wire electrical discharge machining (WEDM) process with three different parameters set for the study of machining speed, surface roughness. The composite with 25 wt.% of B4C shows highest machining speed of 10.56 mm(2)/min. The average surface roughness (R-a) of the WEDM processed composite surfaces lies in the range of 1.26-5.64 mu m

Phase determination of ZrB2-B4C ceramic composite material using XRD and rietveld refinement analysis

In this work, the Spark plasma sintering technique has been used to sinter ZrB2-B4C (20 wt%) composite at 2100 degrees C and 50 MPa uniaxial pressure for 15 min soaking in an argon atmosphere. XRD analysis has been carried out on the sintered sample to analyze the different phases present in the ZrB2-B4C composite. The Rietveld refinement technique has been used to analyze the crystal structure, the unit cell information such as space group, cell position, cell angles and atomic distances of the composite material using FULLPROF software. (C) 2019 Elsevier Ltd. All rights reserved

Dendrite regeneration in C. elegans is controlled by the RAC GTPase CED-10 and the RhoGEF TIAM-1.

Neurons are vulnerable to physical insults, which compromise the integrity of both dendrites and axons. Although several molecular pathways of axon regeneration are identified, our knowledge of dendrite regeneration is limited. To understand the mechanisms of dendrite regeneration, we used the PVD neurons in C. elegans with stereotyped branched dendrites. Using femtosecond laser, we severed the primary dendrites and axon of this neuron. After severing the primary dendrites near the cell body, we observed sprouting of new branches from the proximal site within 6 hours, which regrew further with time in an unstereotyped manner. This was accompanied by reconnection between the proximal and distal dendrites, and fusion among the higher-order branches as reported before. We quantified the regeneration pattern into three aspects-territory length, number of branches, and fusion phenomena. Axonal injury causes a retraction of the severed end followed by a Dual leucine zipper kinase-1 (DLK-1) dependent regrowth from the severed end. We tested the roles of the major axon regeneration signalling hubs such as DLK-1-RPM-1, cAMP elevation, let-7 miRNA, AKT-1, Phosphatidylserine (PS) exposure/PS in dendrite regeneration. We found that neither dendrite regrowth nor fusion was affected by the axon injury pathway molecules. Surprisingly, we found that the RAC GTPase, CED-10 and its upstream GEF, TIAM-1 play a cell-autonomous role in dendrite regeneration. Additionally, the function of CED-10 in epidermal cell is critical for post-dendrotomy fusion phenomena. This work describes a novel regulatory mechanism of dendrite regeneration and provides a framework for understanding the cellular mechanism of dendrite regeneration using PVD neuron as a model system

Seeing the vibrational breathing of a single molecule through time-resolved coherent anti-Stokes Raman scattering

The motion of chemical bonds within molecules can be observed in real time, in the form of vibrational wavepackets prepared and interrogated through ultrafast nonlinear spectroscopy. Such nonlinear optical measurements are commonly performed on large ensembles of molecules, and as such, are limited to the extent that ensemble coherence can be maintained. Here, we describe vibrational wavepacket motion on single molecules, recorded through time-resolved, surface-enhanced, coherent anti-Stokes Raman scattering. The required sensitivity to detect the motion of a single molecule, under ambient conditions, is achieved by equipping the molecule with a dipolar nano-antenna (a gold dumbbell). In contrast with measurements in ensembles, the vibrational coherence on a single molecule does not dephase. It develops phase fluctuations with characteristic statistics. We present the time evolution of discretely sampled statistical states, and highlight the unique information content in the characteristic, early-time probability distribution function of the signal