Much Ado About Nothing: How the Securities SRO State Actor Circuit Split Has Been Misinterpreted and What It Means for Due Process at FINRA

Traditionally, the U.S. securities exchanges were self-regulated, governing trading, setting rules, and carryingout disciplinary procedures against member trader-brokers. In the past five decades, however, the SEC hasdivested the exchanges of their regulatory authority,transferring it to independent, private bodies.Concomitantly, the SEC\u27s ability to control the rule-making and enforcement powers of these private bodieshas increased. Recently, this process culminated in thecreation of FINRA, a monopolized, private self-regulatoryorganization (SRO) under comprehensive SEC controlresponsible for regulating the entire U.S. secondarysecurities market. The SEC\u27s ever-growing control oversecurities SROs has called into question whether theregulation of U.S. securities professionals remains aprivate enterprise free from the constitutional constraintson public actors. -This question-whether SROs are private or publicactors-has generated a circuit split so convoluted thatmany courts have misinterpreted it, as the EleventhCircuit\u27s recent opinion in Busacca reveals. Properlyunderstood, however, this Note argues that the pre-FINRASRO state action cases signal very little about whetherFINRA should be deemed a public actor. Yet these casesspeak volumes about what effect a state actordetermination would have on disciplinary procedures atFINRA. Combined with the statutory framework of the Exchange Act, these decisions strongly support theconclusion that constitutionally adequate process isalready guaranteed (and is usually provided) in FINRA\u27sdisciplinary actions. As a result, securities professionalsmay find a judicial ruling requiring constitutional dueprocess difficult to obtain and ultimately ineffective tosecure member trader-brokers additional protections inFINRA\u27s disciplinary actions

Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Modelling diffusional transport in the interphase cell nucleus

In this paper a lattice model for diffusional transport of particles in the interphase cell nucleus is proposed. Dense networks of chromatin fibers are created by three different methods: randomly distributed, non-interconnected obstacles, a random walk chain model, and a self avoiding random walk chain model with persistence length. By comparing a discrete and a continuous version of the random walk chain model, we demonstrate that lattice discretization does not alter particle diffusion. The influence of the 3D geometry of the fiber network on the particle diffusion is investigated in detail, while varying occupation volume, chain length, persistence length and walker size. It is shown that adjacency of the monomers, the excluded volume effect incorporated in the self avoiding random walk model, and, to a lesser extent, the persistence length, affect particle diffusion. It is demonstrated how the introduction of the effective chain occupancy, which is a convolution of the geometric chain volume with the walker size, eliminates the conformational effects of the network on the diffusion, i.e., when plotting the diffusion coefficient as a function of the effective chain volume, the data fall onto a master curve.Comment: 9 pages, 8 figure

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure