We develop methods to evaluate whether a political districting accurately represents the will of the people. To explore and showcase our ideas, we concentrate on the congressional districts for the U.S. House of Representatives and use the state of North Carolina and its redistrictings since the 2010 census. Using a Monte Carlo algorithm, we randomly generate over 24,000 redistrictings that are non-partisan and adhere to criteria from proposed legislation. Applying historical voting data to these random redistrictings, we find that the number of democratic and republican representatives elected varies drastically depending on how districts are drawn. Some results are more common, and we gain a clear range of expected election outcomes. Using the statistics of our generated redistrictings, we critique the particular congressional districtings used in the 2012 and 2016 NC elections as well as a districting proposed by a bipartisan redistricting commission. We find that the 2012 and 2016 districtings are highly atypical and not representative of the will of the people. On the other hand, our results indicate that a plan produced by a bipartisan panel of retired judges is highly typical and representative. Since our analyses are based on an ensemble of reasonable redistrictings of North Carolina, they provide a baseline for a given election which incorporates the geometry of the state's population distribution.

We introduce an optical platform for rapid, high-throughput screening of exogenous molecules that affect cellular mechanotransduction. Our method initiates mechanotransduction in adherent cells using single laser-microbeam generated micro-cavitation bubbles (μCBs) without requiring flow chambers or microfluidics. These μCBs expose adherent cells to a microTsunami, a transient microscale burst of hydrodynamic shear stress, which stimulates cells over areas approaching 1mm2. We demonstrate microTsunami-initiated mechanosignalling in primary human endothelial cells. This observed signalling is consistent with G-protein-coupled receptor stimulation resulting in Ca2+ release by the endoplasmic reticulum. Moreover, we demonstrate the dose-dependent modulation of microTsunami-induced Ca2+ signalling by introducing a known inhibitor to this pathway. The imaging of Ca2+ signalling, and its modulation by exogenous molecules, demonstrates the capacity to initiate and assess cellular mechanosignalling in real-time. We utilize this capability to screen the effects of a set of small molecules on cellular mechanotransduction in 96-well plates using standard imaging cytometry.

Independent component analysis (ICA) has been widely used for electroencephalography (EEG) analyses. However, ICA performance relies on several crucial assumptions about the data. Here, we focus on the granularity of data rank, i.e., the number of linearly independent EEG channels. When the data are rank-full (i.e., all channels are independent), ICA produces as many independent components (ICs) as the number of input channels (rank-full decomposition). However, when the input data are rank-deficient, as is the case with bridged or interpolated electrodes, ICA produces the same number of ICs as the data rank (forced rank deficiency decomposition), introducing undesired ghost ICs and indicating a bug in ICA. We demonstrated that the ghost ICs have white noise properties, in both time and frequency domains, while maintaining surprisingly typical scalp topographies, and can therefore be easily missed by EEG researchers and affect findings in unknown ways. This problem occurs when the minimum eigenvalue λmin of the input data is smaller than a certain threshold, leading to matrix inversion failure as if the rank-deficient inversion was forced, even if the data rank is cleanly deficient by one. We defined this problem as the effective rank deficiency. Using sound file mixing simulations, we first demonstrated the effective rank deficiency problem and determined that the critical threshold for λmin is 10−7 in the given situation. Second, we used empirical EEG data to show how two preprocessing stages, re-referencing to average without including the initial reference and non-linear electrode interpolation, caused this forced rank deficiency problem. Finally, we showed that the effective rank deficiency problem can be solved by using the identified threshold (λmin = 10−7) and the correct re-referencing procedure described herein. The former ensures the achievement of effective rank-full decomposition by properly reducing the input data rank, and the latter allows avoidance of a widely practiced incorrect re-referencing approach. Based on the current literature, we discuss the ambiguous status of the initial reference electrode when re-referencing. We have made our data and code available to facilitate the implementation of our recommendations by the EEG community.

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that adheres to realistic and non-partisan criteria. Using the sampled redistricting plans and historical voting data, we produce an ensemble of elections that reveal geo-political structure within the state. We showcase our methods on the two most recent districtings of NC for the U.S. House of Representatives, as well as a plan drawn by a bipartisan redistricting panel. We find the two state enacted plans are highly atypical outliers whereas the bipartisan plan accurately represents the ensemble both in partisan outcome and in the fine scale structure of district-level results.Gerrymandering | Redistricting | Monte Carlo Sampling I n the 2012 NC congressional election, over half the total votes went to Democratic candidates, yet only four of the thirteen congressional representatives were Democrats. Furthermore, the most Democratic district had 29.63% margin of victory, whereas the most Republican district had a 13.11% margin of victory. These results may be due to political gerrymandering or, alternatively, be natural outcomes of NC's geo-political structure as determined by the spatial distribution of partisan votes.To probe the geo-political structure and its effect on election outcomes we (i) sample from the space of congressional redistricting plans that adheres to non-partisan redistricting criteria; (ii) we simulate an election with each of our sampled redistricting plans using the actual partisan votes cast by North Carolinians in the 2012 and 2016 congressional elections; and (iii) we aggregate election results to construct the distributions of partisan vote balance on each district and of the congressional delegation's partisan composition. Districts that do not respect typical election results are considered gerrymandered. When a districting is gerrymandered, the congressional delegation's partisan composition may be not representative of what is typical.Having probed the impact of the geo-political structure, we analyze three specific districting plans: the two most recent districting plans of NC for the U.S. House of Representatives and a plan proposed by a bipartisan panel of retired NC judges. By situating the election outcomes of these three districting plans in our sampled ensemble, we determine whether the three districting plans contain unlikely partisan favoritism and thwart the underlying geo-political structure, as expressed by the people's votes, by shifting each district's partisan vote balance significantly away from what is typical. MethodsTo sample from the space of congressional redistricting plans, we construct a family of probability distributions that are concentrated on plans adhering to non-partisan design criteria from proposed legislation. The non-partisan design criteria ensures that