Complexity in surfaces of densest packings for families of polyhedra

Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. Here, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three 2-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest packings of more than 55,000 convex shapes. The three families have the symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find that optimal (maximum) packing density surfaces that reveal unexpected richness and complexity, containing as many as 130 different structures within a single family. Our results demonstrate the utility of thinking of shape not as a static property of an object in the context of packings, but rather as but one point in a higher dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we present and interpret our packing results in a consistent and generally applicable way by proposing a method to distinguish regions of packings and classify types of transitions between them.Comment: 16 pages, 8 figure

2022-14 Use It or Lose It: Efficiency and Redistributional Effects of Wealth Taxation

How does wealth taxation differ from capital income taxation? When the return on investment is equal across individuals, a well-known result is that the two tax systems are equivalent. Motivated by recent empirical evidence documenting persistent return heterogeneity, we revisit this question. With heterogeneity, the two tax systems typically have opposite implications for both efficiency and inequality. Under capital income taxation, entrepreneurs who are more productive and therefore generate more income pay higher taxes. Under wealth taxation, entrepreneurs who have similar wealth levels pay similar taxes regardless of their productivity, which expands the tax base, shifts the tax burden toward unproductive entrepreneurs, and raises the savings rate of productive ones. This reallocation increases aggregate productivity and output. In the simulated model parameterized to match the US data, replacing the capital income tax with a wealth tax in a revenue-neutral fashion delivers a significantly higher average welfare. Turning to optimal taxation, the optimal wealth tax (OWT) is positive and yields large welfare gains by raising efficiency and lowering inequality. In contrast, the optimal capital income tax (OKIT) is negative—a subsidy—and delivers lower welfare gains than OWT, owing to the welfare losses from higher inequality. Furthermore, when the transition path is considered, the gains from OKIT turn into significant welfare losses for existing cohorts, whereas OWT continues to deliver robust welfare gains. These results suggest that moderate wealth taxation may be a more appealing alternative than capital income taxation, which can be significantly more distorting under return heterogeneity than under the equal-returns assumption

A neuronal death model: overexpression of neuronal intermediate filament protein peripherin in PC12 cells

<p>Abstract</p> <p>Background</p> <p>Abnormal accumulation of neuronal intermediate filament (IF) is a pathological indicator of some neurodegenerative disorders. However, the underlying neuropathological mechanisms of neuronal IF accumulation remain unclear. A stable clone established from PC12 cells overexpressing a GFP-Peripherin fusion protein (pEGFP-Peripherin) was constructed for determining the pathway involved in neurodegeneration by biochemical, cell biology, and electronic microscopy approaches. In addition, pharmacological approaches to preventing neuronal death were also examined.</p> <p>Results</p> <p>Results of this study showed that TUNEL positive reaction could be detected in pEGFP-Peripherin cells. Swollen mitochondria and endoplasmic reticulum (ER) were seen by electron microscopy in pEGFP-Peripherin cells on day 8 of nerve growth factor (NGF) treatment. Peripherin overexpression not only led to the formation of neuronal IF aggregate but also causes aberrant neuronal IF phosphorylation and mislocation. Western blots showed that calpain, caspase-12, caspase-9, and caspase-3 activity was upregulated. Furthermore, treatment with calpain inhibitor significantly inhibited cell death.</p> <p>Conclusions</p> <p>These results suggested that the cytoplasmic neuronal IF aggregate caused by peripherin overexpression may induce aberrant neuronal IF phosphorylation and mislocation subsequently trapped and indirectly damaged mitochondria and ER. We suggested that the activation of calpain, caspase-12, caspase-9, and caspase-3 were correlated to the dysfunction of the ER and mitochondria in our pEGFP-Peripherin cell model. The present study suggested that pEGFP-Peripherin cell clones could be a neuronal death model for future studies in neuronal IFs aggregate associated neurodegeneration.</p

Nanoparticle-assisted optical tethering of endosomes reveals the cooperative function of dyneins in retrograde axonal transport

Dynein-dependent transport of organelles from the axon terminals to the cell bodies is essential to the survival and function of neurons. However, quantitative knowledge of dyneins on axonal organelles and their collective function during this long-distance transport is lacking because current technologies to do such measurements are not applicable to neurons. Here, we report a new method termed nanoparticle-assisted optical tethering of endosomes (NOTE) that made it possible to study the cooperative mechanics of dyneins on retrograde axonal endosomes in live neurons. In this method, the opposing force from an elastic tether causes the endosomes to gradually stall under load and detach with a recoil velocity proportional to the dynein forces. These recoil velocities reveal that the axonal endosomes, despite their small size, can recruit up to 7 dyneins that function as independent mechanical units stochastically sharing load, which is vital for robust retrograde axonal transport. This study shows that NOTE, which relies on controlled generation of reactive oxygen species, is a viable method to manipulate small cellular cargos that are beyond the reach of current technology.National Institutes of Health (U.S.) (DP2-NS082125)National Science Foundation (U.S.) (Award 1055112)National Science Foundation (U.S.) (Award 1344302

Efficiency of a randomized confirmatory basket trial design constrained to control the family wise error rate by indication

Basket trials pool histologic indications sharing molecular pathophysiology, improving development efficiency. Currently basket trials have been confirmatory only for exceptional therapies. Our previous randomized basket design may be generally suitable in the resource-intensive confirmatory phase, maintains high power even with modest effect sizes, and provides nearly k-fold increased efficiency for k indications, but controls false positives for the pooled result only. Since family-wise error rate by indications (FWER) may sometimes be required, we now simulate a variant of this basket design controlling FWER at 0.025k, the total FWER of k separate randomized trials. We simulated this modified design under numerous scenarios varying design parameters. Only designs controlling FWER and minimizing estimation bias were allowable. Optimal performance results when k=3,4. We report efficiency (expected # true positives/expected sample size) relative to k parallel studies, at 90% power (“uncorrected”) or at the power achieved in the basket trial (“corrected”, because conventional designs could also increase efficiency by sacrificing power). Efficiency and power (percentage active indications identified) improve with higher percentage of initial indications active. Up to 92% uncorrected and 38% corrected efficiency improvement is possible. Even under FWER control, randomized confirmatory basket trials substantially improve development efficiency. Initial indication selection is critical

The Effects of Protein Kinase C Beta II Peptide Modulation on Superoxide Release in Rat Polymorphonuclear Leukocytes

Phorbol 12-myristate 13-acetate (PMA; a diacylglycerol mimetic) is known to augment polymorphonuclear leukocyte (PMN) superoxide (SO) release via protein kinase C (PKC) activation. However, the role of PKC beta II (βII) mediating this response is not known. It’s known that myristic acid (myr-) conjugation facilitates intracellular delivery of the cargo sequence, and that putative PKCβII activator and inhibitor peptides work by augmenting or attenuating PKCβII translocation to cell membrane substrates (e.g. NOX-2). Therefore, we hypothesize that myr- conjugated PKCβII peptide-activator (N-myr-SVEIWD; myr-PKCβ+) would increase PMA-induced rat PMN SO release, whereas, myr-PKCβII peptide-inhibitor (N-myr-SLNPEWNET; myr-PKCβ-) would attenuate this response compared to non-drug treated controls. Rat PMNs (5x106) were incubated for 15min at 370C in the presence/absence of myr-PKCβ+/- (20 μM) or SO dismutase (SOD;10μg/mL; n=8) as positive control. PMA (100nM) induced PMN SO release was measured spectrophotometrically at 550nm via reduction of ferricytochrome c for 390 sec. PMN SO release increased absorbance to 0.39±0.04 in non-drug treated controls (n=28), and 0.49±0.05 in myr-PKCβ+(n=16). This response was significantly increased from 180 seconds to 240 seconds (p\u3c0.05). By contrast, myr-PKCβ- (0.26±0.03; n=14) significantly attenuated PMA-induced SO release compared to non-drug controls and myr-PKCβ+ (p\u3c0.05). SOD-treated samples showed \u3e90% reduction of PMA-induced SO release and was significantly different from all groups (p\u3c0.01). Cell viability ranged between 94± to 98±2% in all groups as determined by 0.2% trypan blue exclusion. Preliminary results suggest that myr-PKCβ- significantly attenuates PMA-induced SO release, whereas myr-PKCβ+ significantly augments PMA-induced SO release, albeit transiently. Additional dose response and western blot experiments are planned with myr-PKCβ+/- in PMA-induced PMN SO release assays. This research was supported by the Department of Bio-Medical Sciences and the Division of Research at PCOM and by Young Therapeutics, LLC