Despite the apparent cross-disciplinary interactions among scientific fields, a formal description of their evolution is lacking. Here we describe a novel approach to study the dynamics and evolution of scientific fields using a network-based analysis. We build an idea network consisting of American Physical Society Physics and Astronomy Classification Scheme (PACS) numbers as nodes representing scientific concepts. Two PACS numbers are linked if there exist publications that reference them simultaneously. We locate scientific fields using a community finding algorithm, and describe the time evolution of these fields over the course of 1985–2006. The communities we identify map to known scientific fields, and their age depends on their size and activity. We expect our approach to quantifying the evolution of ideas to be relevant for making predictions about the future of science and thus help to guide its development.

Cancer cells alter their migratory properties during tumor progression to invade surrounding tissues and metastasize to distant sites. However, it remains unclear how migratory behaviors differ between tumor cells of different malignancy and whether these migratory behaviors can be utilized to assess the malignant potential of tumor cells. Here, we analyzed the migratory behaviors of cell lines representing different stages of breast cancer progression using conventional migration assays or time-lapse imaging and particle image velocimetry (PIV) to capture migration dynamics. We find that the number of migrating cells in transwell assays, and the distance and speed of migration in unconstrained 2D assays, show no correlation with malignant potential. However, the directionality of cell motion during 2D migration nicely distinguishes benign and tumorigenic cell lines, with tumorigenic cell lines harboring less directed, more random motion. Furthermore, the migratory behaviors of epithelial sheets observed under basal conditions and in response to stimulation with epidermal growth factor (EGF) or lysophosphatitic acid (LPA) are distinct for each cell line with regard to cell speed, directionality, and spatiotemporal motion patterns. Surprisingly, treatment with LPA promotes a more cohesive, directional sheet movement in lung colony forming MCF10CA1a cells compared to basal conditions or EGF stimulation, implying that the LPA signaling pathway may alter the invasive potential of MCF10CA1a cells. Together, our findings identify cell directionality as a promising indicator for assessing the tumorigenic potential of breast cancer cell lines and show that LPA induces more cohesive motility in a subset of metastatic breast cancer cells.

Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental 3D flow fields with particle scale resolution, we calculate the time evolving broken-links network and find that a giant component of this network is formed as shear is applied to this system. We implement a model of link breakages where the probability of a link breaking is proportional to the average rate of longitudinal strain (elongation) in the direction of the edge and find that the model demonstrates qualitative agreement with the data when studying the onset of the giant component. We note, however, that the broken-links network formed in the model is less clustered than our empirical observations, indicating that the model reflects less localized breakage events and does not fully capture the dynamics of the granular flow.

We study echoes and what we call 'revival echoes' for a collection of atoms that are described by a single quantum wavefunction and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two, successive temporally localized potential perturbations to the confining potential, one at time $t=0$, and a smaller one at time $t=\tau$. Pulse-like responses in the expectation value of position $$ are predicted at $t \approx n\tau$ ($n=2,3,...$) and are particularly evident at $t \approx 2\tau$. A novel result of our study is the finding of 'revival echoes'. Revivals (but not echoes) occur even if the second perturbation is absent. In particular, in the absence of the second perturbation, the response to the first perturbation dies away, but then reassembles, producing a response at revival times $mT_x$ ($m=1,2,...$). Including the second perturbation at $t=\tau$, we find temporally localized responses, revival echoes, both before and after $t\approx mT_x$, e.g., at $t\approx m T_x-n \tau$ (pre-revival echoes) and at $t\approx mT_x+n\tau$, (post-revival echoes), where $m$ and $n$ are $1,2,...$ . Depending on the form of the perturbations, the 'principal' revival echoes at $t \approx T_x \pm \tau$ can be much larger than the echo at $t \approx 2\tau$. We develop a perturbative model for these phenomena, and compare its predictions to the numerical solutions of the time-dependent Schr\"odinger Equation. The scaling of the size of the various echoes and revival echoes as a function of the symmetry and size of the perturbations applied at $t=0$ and $t=\tau$ is investigated. We also study the presence of revivals and revival echoes in higher moments of position, $$, $p>1$, and the effect of atom-atom interactions on these phenomena.Comment: 33 pages, 13 figures, corrected typos and added reference

Since the cytoskeleton is known to regulate many cell functions, an increasing amount of effort to characterize cells by their mechanical properties has occured. Despite the structural complexity and dynamics of the multicomponent cytoskeleton, mechanical measurements on single cells are often fit to simple models with two to three parameters, and those parameters are recorded and reported. However, different simple models are likely needed to capture the distinct mechanical cell states, and additional parameters may be needed to capture the ability of cells to actively deform. Our new approach is to capture a much larger set of possibly redundant parameters from cells' mechanical measurement using multiple rheological models as well as dynamic deformation and image data. Principal component analysis and network-based approaches are used to group parameters to reduce redundancies and develop robust biomechanical phenotyping. Network representation of parameters allows for visual exploration of cells' complex mechanical system, and highlights unexpected connections between parameters. To demonstrate that our biomechanical phenotyping approach can detect subtle mechanical differences, we used a Microfluidic Optical Cell Stretcher to mechanically stretch circulating human breast tumor cells bearing genetically-engineered alterations in c-src tyrosine kinase activation, which is known to influence reattachment and invasion during metastasis.