The Hitting Times with Taboo for a Random Walk on an Integer Lattice

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x, the hitting state y and the taboo state z. We find the probability that these passages times are finite and analyze the tails of their cumulative distribution functions. In particular, it turns out that for the random walk on Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the tail decrease is specified by dimension d only. In contrast, for a simple random walk on Z, the asymptotic properties of hitting times with taboo essentially depend on the mutual location of the points x, y and z. These problems originated in our recent study of branching random walk on Z^d with a single source of branching

Designing Legal Experiences

Technological advancements are improving how courts operate by changing the way they handle proceedings and interact with litigants. Court Innovations is a socially minded software startup that enables citizens, law enforcement, and courts to resolve legal matters through Matterhorn, an online communication and dispute resolution platform. Matterhorn was conceived at the University of Michigan Law School and successfully piloted in two Michigan district courts beginning in 2014. The platform now operates in over 40 courts and in at least eight states, and it has facilitated the resolution of more than 40,000 cases to date. These numbers will continue to grow as new categories of disputes and other legal matters become eligible for online management and resolution and as more court systems recognize the economic and social benefits of adopting online platform technology. This case study chronicles the development, implementation, and refinement of Matterhorn. Implementing software in the legal world can be cumbersome, especially when adoption requires the coordination and agreement of multiple public entities with overlapping – but not identical – goals. We hope that by sharing the story of Matterhorn’s creation and growth over the last few years, we can light the way for the next generation of court-focused technology and e-governance tools, especially those that relate to the criminal justice system. We also hope to offer valuable lessons for transitioning ideas for progress into realized change. First, we outline the social problem that Matterhorn was initially designed to address – minor warrants – and how that focus led to Matterhorn’s now-broader aim of improving court access generally. Second, we describe Matterhorn and how it works in practical terms. Third, we present an analysis of the platform’s underlying design philosophy and objectives. Fourth, we address two challenges that Court Innovations encountered and overcame in implementing Matterhorn in a variety of courts with diverse stakeholders. We conclude that Matterhorn has demonstrated the value of using online platform technology to resolve disputes in courts and has succeeded in producing measurable improvements in court accessibility and efficienc

Online Case Resolution Systems: Enhancing Access, Fairness, Accuracy, and Efficiency

Online case resolution (OCR) systems have the potential to dramatically increase access to our justice system. Part I introduces the concept of an OCR system, how it might work in practice, and its likely impact on courts and citizens. Part II argues that OCR systems can lower many of the barriers to going to court by reducing the need for face-to-face resolution of disputes; cutting the amount of time needed for hearings; mitigating litigant confusion and fear; allowing asynchronous scheduling that can accommodate work and child-care schedules; and offering a more reliable and easier-to-use means for litigants to voice their views. These advantages should especially benefit those of lower socioeconomic status, who often suffer disproportionality under the status quo. Part III contends that OCR systems need not compromise a judge’s or a prosecutor’s decision-making process but can actually enhance both. OCR systems can provide more, better, and easier-to-use information, and by removing a litigant’s appearance (race, gender, weight, etc.) from a judge’s consideration, can render outcomes less subject to implicit biases

Online Case Resolution Systems: Enhancing Access, Fairness, Accuracy, and Efficiency

Online case resolution (OCR) systems have the potential to dramatically increase access to our justice system. Part I introduces the concept of an OCR system, how it might work in practice, and its likely impact on courts and citizens. Part II argues that OCR systems can lower many of the barriers to going to court by reducing the need for face-to-face resolution of disputes; cutting the amount of time needed for hearings; mitigating litigant confusion and fear; allowing asynchronous scheduling that can accommodate work and child-care schedules; and offering a more reliable and easier-to-use means for litigants to voice their views. These advantages should especially benefit those of lower socioeconomic status, who often suffer disproportionality under the status quo. Part III contends that OCR systems need not compromise a judge’s or a prosecutor’s decision-making process but can actually enhance both. OCR systems can provide more, better, and easier-to-use information, and by removing a litigant’s appearance (race, gender, weight, etc.) from a judge’s consideration, can render outcomes less subject to implicit biases

The extreme HBL behaviour of Markarian 501 during 2012

A multiwavelength campaign was organized to take place between March and July of 2012. Excellent temporal coverage was obtained with more than 25 instruments, including the MAGIC, FACT and VERITAS Cherenkov telescopes, the instruments on board the Swift and Fermi spacecraft, and the telescopes operated by the GASP-WEBT collaboration. Mrk 501 showed a very high energy (VHE) gamma-ray flux above 0.2 TeV of $\sim$0.5 times the Crab Nebula flux (CU) for most of the campaign. The highest activity occurred on 2012 June 9, when the VHE flux was $\sim$3 CU, and the peak of the high-energy spectral component was found to be at $\sim$2 TeV. This study reports very hard X-ray spectra, and the hardest VHE spectra measured to date for Mrk 501. The fractional variability was found to increase with energy, with the highest variability occurring at VHE, and a significant correlation between the X-ray and VHE bands. The unprecedentedly hard X-ray and VHE spectra measured imply that their low- and high-energy components peaked above 5 keV and 0.5 TeV, respectively, during a large fraction of the observing campaign, and hence that Mrk 501 behaved like an extreme high-frequency- peaked blazar (EHBL) throughout the 2012 observing season. This suggests that being an EHBL may not be a permanent characteristic of a blazar, but rather a state which may change over time. The one-zone synchrotron self-Compton (SSC) scenario can successfully describe the segments of the SED where most energy is emitted, with a significant correlation between the electron energy density and the VHE gamma-ray activity, suggesting that most of the variability may be explained by the injection of high-energy electrons. The one-zone SSC scenario used reproduces the behaviour seen between the measured X-ray and VHE gamma-ray fluxes, and predicts that the correlation becomes stronger with increasing energy of the X-rays

Nerve growth factor induces neurite outgrowth of PC12 cells by promoting Gβγ-microtubule interaction

Background: Assembly and disassembly of microtubules (MTs) is critical for neurite outgrowth and differentiation. Evidence suggests that nerve growth factor (NGF) induces neurite outgrowth from PC12 cells by activating the receptor tyrosine kinase, TrkA. G protein-coupled receptors (GPCRs) as well as heterotrimeric G proteins are also involved in regulating neurite outgrowth. However, the possible connection between these pathways and how they might ultimately converge to regulate the assembly and organization of MTs during neurite outgrowth is not well understood. Results: Here, we report that Gβγ, an important component of the GPCR pathway, is critical for NGF-induced neuronal differentiation of PC12 cells. We have found that NGF promoted the interaction of Gβγ with MTs and stimulated MT assembly. While Gβγ-sequestering peptide GRK2i inhibited neurite formation, disrupted MTs, and induced neurite damage, the Gβγ activator mSIRK stimulated neurite outgrowth, which indicates the involvement of Gβγ in this process. Because we have shown earlier that prenylation and subsequent methylation/demethylation of γ subunits are required for the Gβγ-MTs interaction in vitro, small-molecule inhibitors (L-28 and L-23) targeting prenylated methylated protein methyl esterase (PMPMEase) were tested in the current study. We found that these inhibitors disrupted Gβγ and ΜΤ organization and affected cellular morphology and neurite outgrowth. In further support of a role of Gβγ-MT interaction in neuronal differentiation, it was observed that overexpression of Gβγ in PC12 cells induced neurite outgrowth in the absence of added NGF. Moreover, overexpressed Gβγ exhibited a pattern of association with MTs similar to that observed in NGF-differentiated cells. Conclusions: Altogether, our results demonstrate that βγ subunit of heterotrimeric G proteins play a critical role in neurite outgrowth and differentiation by interacting with MTs and modulating MT rearrangement. Electronic supplementary material The online version of this article (doi:10.1186/s12868-014-0132-4) contains supplementary material, which is available to authorized users

Cytokine preconditioning of engineered cartilage provides protection against interleukin-1 insult

Research reported in this publication was supported in part by the National Institute of Arthritis and Musculoskeletal and Skin Diseases and National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health under Award Number R01AR60361, R01AR061988, P41EB002520). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. ART was supported by a National Science Foundation Graduate Fellowship