Correcting Mandatory Injustice: Judicial Recommendation of Executive Clemency

In 1987, the United States political and social systems lost trust in the judiciary and severely limited its authority by enacting the mandatory Federal Sentencing Guidelines. During this period, many judges were forced to impose sentences they viewed as unjust. Trust in the judiciary was restored in 2005, when United States v. Booker made the Sentencing Guidelines advisory. Despite the increase in judicial discretion, however, judges are still unable to correct sentences imposed during the intervening eighteen years because Booker does not apply retroactively. Unfortunately, the executive and legislative branches are similarly unable to provide adequate remedies. Congressional action is insufficient because it is inflexible, time consuming, and generally nonretroactive. Executive clemency appears more promising due to a flexible and broad nature that allows the president and state governors to pardon or commute sentences at will. But executives have become unwilling to use their clemency power, making it an inadequate remedy. This Note proposes a solution that overcomes the limitations of the current system: judicial recommendation of executive clemency. This solution produces three benefits. First, it provides judges with a discretionary tool to reduce disproportionate mandatory sentences. Second, it revitalizes the exercise of clemency by giving it additional legitimacy. Finally, it refocuses clemency grants on the defendant and the facts of the case rather than on political influences. This Note provides eight illustrative criteria for judicial recommendation of executive clemency that, together, combine the characteristics of three modern cases in which the sentencing judges recommended clemency. This Note seeks to explain how and why each criterion might be important, taking into consideration the goals of judicial discretion, executive clemency, and the criminal justice system overall

Behavior of lacunary series at the natural boundary

We develop a local theory of lacunary Dirichlet series of the form $\sum\limits_{k=1}^{\infty}c_k\exp(-zg(k)), \Re(z)>0$ as $z$ approaches the boundary i\RR, under the assumption $g'\to\infty$ and further assumptions on $c_k$. These series occur in many applications in Fourier analysis, infinite order differential operators, number theory and holomorphic dynamics among others. For relatively general series with $c_k=1$, the case we primarily focus on, we obtain blow up rates in measure along the imaginary line and asymptotic information at $z=0$. When sufficient analyticity information on $g$ exists, we obtain Borel summable expansions at points on the boundary, giving exact local description. Borel summability of the expansions provides property-preserving extensions beyond the barrier. The singular behavior has remarkable universality and self-similarity features. If $g(k)=k^b$, $c_k=1$, $b=n$ or $b=(n+1)/n$, n\in\NN, behavior near the boundary is roughly of the standard form $\Re(z)^{-b'}Q(x)$ where $Q(x)=1/q$ if x=p/q\in\QQ and zero otherwise. The B\"otcher map at infinity of polynomial iterations of the form $x_{n+1}=\lambda P(x_n)$, $|\lambda|<\lambda_0(P)$, turns out to have uniformly convergent Fourier expansions in terms of simple lacunary series. For the quadratic map $P(x) =x-x^2$, $\lambda_0=1$, and the Julia set is the graph of this Fourier expansion in the main cardioid of the Mandelbrot set

Existence and uniqueness for Mean Field Games with state constraints

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption

Fluidization of granular media wetted by liquid 4^4He

We explore experimentally the fluidization of vertically agitated PMMA spheres wetted by liquid $^4$He. By controlling the temperature around the $\lambda$ point we change the properties of the wetting liquid from a normal fluid (helium I) to a superfluid (helium II). For wetting by helium I, the critical acceleration for fluidization ($\Gamma_c$) shows a steep increase close to the saturation of the vapor pressure in the sample cell. For helium II wetting, $\Gamma_c$ starts to increase at about 75% saturation, indicating that capillary bridges are enhanced by the superflow of unsaturated helium film. Above saturation, $\Gamma_c$ enters a plateau regime where the capillary force between particles is independent of the bridge volume. The plateau value is found to vary with temperature and shows a peak at 2.1 K, which we attribute to the influence of the specific heat of liquid helium.Comment: 4 pages, 3 figures, Accepted by Phys. Rev. E as a rapid communicatio