The isoperimetric constant of the random graph process

The isoperimetric constant of a graph $G$ on $n$ vertices, $i(G)$, is the minimum of $\frac{|\partial S|}{|S|}$, taken over all nonempty subsets $S\subset V(G)$ of size at most $n/2$, where $\partial S$ denotes the set of edges with precisely one end in $S$. A random graph process on $n$ vertices, $\widetilde{G}(t)$, is a sequence of $\binom{n}{2}$ graphs, where $\widetilde{G}(0)$ is the edgeless graph on $n$ vertices, and $\widetilde{G}(t)$ is the result of adding an edge to $\widetilde{G}(t-1)$, uniformly distributed over all the missing edges. We show that in almost every graph process $i(\widetilde{G}(t))$ equals the minimal degree of $\widetilde{G}(t)$ as long as the minimal degree is $o(\log n)$. Furthermore, we show that this result is essentially best possible, by demonstrating that along the period in which the minimum degree is typically $\Theta(\log n)$, the ratio between the isoperimetric constant and the minimum degree falls from 1 to 1/2, its final value

The New Activist Non-Profits: Four Models Breaking from the Non-Profit Industrial Complex

Twenty-first century activists—inspired by recent social movements and criticisms of the “non-profit industrial complex”—have increasingly sought to avoid pursuing their activism through the hierarchical, professionally managed non-profit corporations that have been the norm for social justice organizations since the 1970s. While many of these activist groups have chosen to remain unincorporated, some activists have been experimenting with new, innovative structures for non-profit organizations, structures that aim to better align activists’ organizations with their values. This Article presents four models of activist non-profits: (1) sociocratic non-profits, (2) worker self-directed non-profits, (3) hub-and-spoke counter-institutions, and (4) swarm organizations. It describes how these approaches increase volunteer participation, deepen organizational democracy, connect more closely with social movements, and aim to maintain accountability among and between organizational members and other stakeholders. It presents legal constraints on the governance structures of these new organizations and concludes with a description of some best practices for these groups and their lawyers

How The 1 Percent Pays Taxes; How The 99 Percent Could: The Subchapter T Worker Cooperative Tax Loophole

The ratification of the Sixteenth Amendment to the United States Constitution granted Congress the right to tax income “from whatever source derived.” Since its inception, the tax code has become long and complicated, filled with broad taxation rules and innumerable exceptions. Over time, the tax code has been amended with the stated purpose of promoting “fairness, efficiency, and enforceability.” However, the complexity of the tax code has led to abuse of “tax loopholes” by wealthy taxpayers who want to avoid paying their fair share of taxes. While abuse is likely to continue, as legislators remain intent on lowering taxes on the wealthy, there exists a “tax loophole” that can benefit the working class. Subchapter T of the Tax Code provides that worker cooperatives, businesses that are jointly owned by their workers, can pass through their income to their worker-owners in the form of patronage dividends, avoiding the entity level taxes that corporations are generally required to pay. However, the IRS has maintained that worker cooperatives must pay their worker-owners a “reasonable salary,” subject to payroll taxes, rather than allowing worker-owners to be paid their entire salaries as patronage dividends to circumvent payroll taxes. This Note argues that the IRS has incorrectly interpreted Subchapter T of the tax code, as Subchapter T allows worker cooperatives to avoid corporate taxes at the entity level and allows worker-owners to avoid payroll taxes on their entire income by structuring their salaries as patronage dividends. Further, this Note argues that, as a matter of policy, the IRS ought to endorse this understanding of Subchapter T, as offering tax incentives to worker cooperatives will benefit the working class

How The 1 Percent Pays Taxes; How The 99 Percent Could: The Subchapter T Worker Cooperative Tax Loophole

The ratification of the Sixteenth Amendment to the United States Constitution granted Congress the right to tax income “from whatever source derived.” Since its inception, the tax code has become long and complicated, filled with broad taxation rules and innumerable exceptions. Over time, the tax code has been amended with the stated purpose of promoting “fairness, efficiency, and enforceability.” However, the complexity of the tax code has led to abuse of “tax loopholes” by wealthy taxpayers who want to avoid paying their fair share of taxes. While abuse is likely to continue, as legislators remain intent on lowering taxes on the wealthy, there exists a “tax loophole” that can benefit the working class. Subchapter T of the Tax Code provides that worker cooperatives, businesses that are jointly owned by their workers, can pass through their income to their worker-owners in the form of patronage dividends, avoiding the entity level taxes that corporations are generally required to pay. However, the IRS has maintained that worker cooperatives must pay their worker-owners a “reasonable salary,” subject to payroll taxes, rather than allowing worker-owners to be paid their entire salaries as patronage dividends to circumvent payroll taxes. This Note argues that the IRS has incorrectly interpreted Subchapter T of the tax code, as Subchapter T allows worker cooperatives to avoid corporate taxes at the entity level and allows worker-owners to avoid payroll taxes on their entire income by structuring their salaries as patronage dividends. Further, this Note argues that, as a matter of policy, the IRS ought to endorse this understanding of Subchapter T, as offering tax incentives to worker cooperatives will benefit the working class

Microfluidic PCR with plasmonic imaging for rapid multiplexed characterization of DNA from microbial pathogens

Bloodstream infections (BSIs) are a critical concern in modern medicine due to their continued prevalence in modern hospitals, along with high costs and attributable mortality, particularly among those who are immunocompromised. The current gold standard for detection and characterization of causative pathogens involves cell culture, which can take 24-48 hours to complete, increasing time to adequate treatment and thus mortality. The rise of antimicrobial resistance in hospital acquired infections has reduced the effectiveness of broad spectrum antimicrobial treatments, resulting in a clear need for a rapid, sensitive technique for characterization of resistance markers in microbial pathogens without cell culture. Here we present the development of a microfluidic platform for polymerase chain reaction (PCR) mediated amplification of microbial gene targets in a continuous flow system for potential coupling with sample preparation systems to reduce time to diagnosis from days to within two hours. This culminated in a thermoelectric cooler mediated fluidic thermocycler with a recirculating assay region for real-time hybridization measurements to minimize assay time. We subsequently demonstrated development of a low-cost optical system for localized surface plasmon resonance imaging using a digital micromirror device and tuned nanoprism monolayers for DNA hybridization with a spectral resolution of 2nm. This LSPR imaging system was integrated in-flow into the microfluidic thermocycler, enabling detection of input E. coli DNA samples at a minimum concentration of 5fg/ [microliter]. We further demonstrated multiplex detection of target markers, indicating potential for assaying target panels for characterization of pathogens. Overall, the studies in this dissertation demonstrate a microfluidic PCR system with built-in sensitive LSPR detection of DNA hybridization. It should serve as a starting point for exploration of and expansion with fluidic sample preparation with a focus on rapid characterization of pathogens.Biomedical Engineerin

Finite size effects and scaling in lattice CP(N-1)

We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency.Comment: 6 pages of text plus 2 pages of figures, Liverpool Preprint LTH28