A linear lower bound for incrementing a space-optimal integer representation in the bit-probe model

We present the first linear lower bound for the number of bits required to be accessed in the worst case to increment an integer in an arbitrary space- optimal binary representation. The best previously known lower bound was logarithmic. It is known that a logarithmic number of read bits in the worst case is enough to increment some of the integer representations that use one bit of redundancy, therefore we show an exponential gap between space-optimal and redundant counters. Our proof is based on considering the increment procedure for a space optimal counter as a permutation and calculating its parity. For every space optimal counter, the permutation must be odd, and implementing an odd permutation requires reading at least half the bits in the worst case. The combination of these two observations explains why the worst-case space-optimal problem is substantially different from both average-case approach with constant expected number of reads and almost space optimal representations with logarithmic number of reads in the worst case.Comment: 12 pages, 4 figure

Stuttering Min oscillations within E. coli bacteria: A stochastic polymerization model

We have developed a 3D off-lattice stochastic polymerization model to study subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding, and fragmentation of MinD filaments due to MinE. Each of processivity, protection, and fragmentation reduces stuttering, speeds oscillations, and reduces MinD filament lengths. Neither processivity or tip-protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations are consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization in experimental conditions.Comment: 21 pages, 7 figures, missing unit for k_f inserte

Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins

During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description for these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experimental findings. In particular, the temporal period of the oscillations is measured as a function of the cell length and found to be compatible with the theoretical prediction.Comment: 17 pages, 5 figures. Submitted to Physical Biolog

A Regulatory Classification of Digital Assets: Toward an Operational Howey Test for Cryptocurrencies, ICOs, and Other Digital Assets

Digital assets are hot right now. Whether cryptocurrencies, like bitcoin, or initial coin offerings and tokens, this new asset class has captured the imagination of American investors. While it remains to be seen if this phenomenon has staying power, there is no doubt that these assets and their promoters have attracted the attention of the Securities and Exchange Commission. But neither Congress nor the SEC has formally elucidated which digital assets are securities and which are not. This Article seeks to provide clarity in determining which digital assets are securities. It proposes two tests that operationalize the Supreme Court’s test in SEC v. W. J. Howey Co. The first test is the Bahamas Test, which asks whether a digital asset is sufficiently decentralized such that it is not a security. The second test is the Substantial Steps Test which is used to determine whether an investment is made with an expectation of profit. This Article takes a rules-based approach to provide clarity and begin a conversation about crafting more predictable jurisprudence and regulation in this area

The Wandering Jew

Sheet music contains anti-Black, racist language, stereotypes, and/or imagry. Contains advertisements and/or short musical examples of pieces being sold by publisher.https://digitalcommons.library.umaine.edu/mmb-vp/6860/thumbnail.jp

Predictions from a stochastic polymer model for the MinDE dynamics in E.coli

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations -- both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.Comment: 16 page

A review of prospective memory in individuals with acquired brain injury [pre-print]

OBJECTIVE: Prospective memory (PM) deficits have emerged as an important predictor of difficulty in daily life for individuals with acquired brain injury (BI). This review examines the variables that have been found to influence PM performance in this population. In addition, current methods of assessment are reviewed with a focus on clinical measures. Finally, cognitive rehabilitation therapies are reviewed, including compensatory, restorative and metacognitive approaches. METHOD: Preferred reporting items for systematic reviews and meta-analyses guidelines were used to identify studies. Studies were added that were identified from the reference lists of these. RESULTS: Research has begun to elucidate the contributing variables to PM deficits after BI, such as attention, executive function and retrospective memory components. Imaging studies have identified prefrontal deficits, especially in the region of BA10 as contributing to these deficits. There are now several clinical measures available with good psychometric properties. Rehabilitation techniques have mostly focused on compensatory strategies, but, in addition, some restorative and metacognitive approaches have shown preliminary promise. CONCLUSIONS: PM deficits are a common and important deficit after BI. Clinical evaluation is recommended and further understanding of rehabilitation techniques is needed

Low temperature tunneling current enhancement in silicide/Si Schottky contacts with nanoscale barrier width

The low temperature electrical behavior of adjacent silicide/Si Schottky contacts with or without dopant segregation is investigated. The electrical characteristics are very well modeled by thermionic-field emission for non-segregated contacts separated by micrometer-sized gaps. Still, an excess of current occurs at low temperature for short contact separations or dopant-segregated contacts when the voltage applied to the device is sufficiently high. From two-dimensional self-consistent non-equilibrium Green's function simulations, the dependence of the Schottky barrier profile on the applied voltage, unaccounted for in usual thermionic-field emission models, is found to be the source of this deviation