A Migrants\u27 Bill of Rights—Between Restatement and Manifesto

These comments first provide a general perspective on the nature of the proposed International Migrants Bill of Rights (IMBR) and then offer some specific observations on the current draft, in particular its provisions on the subject of equality or nondiscrimination, including but not limited to Article 2

The Multifractal Nature of Volterra-L\'{e}vy Processes

We consider the regularity of sample paths of Volterra-L\'{e}vy processes. These processes are defined as stochastic integrals M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, where $X$ is a L\'{e}vy process and $F$ is a deterministic real-valued function. We derive the spectrum of singularities and a result on the 2-microlocal frontier of $\{M(t)\}_{t\in [0,1]}$, under regularity assumptions on the function $F$.Comment: 21 pages, Stochastic Processes and their Applications, 201

Convex Interpolating Splines of Arbitrary Degree

Shape preserving approximations are constructed by interpolating the data with polynomial splines of arbitrary degree. A regularity condition is formulated on the data which insures the existence of such a shape preserving spline, an algorithm is presented for its construction, and the uniform norm of the error is bound which results when the algorithm is used to produce an approximation to a given f epsilon Ca,b

Functions of nearly maximal Gowers-Host-Kra norms on Euclidean spaces

Let $k\geq 2, n\geq 1$ be integers. Let $f: \mathbb{R}^{n} \to \mathbb{C}$. The $k$th Gowers-Host-Kra norm of $f$ is defined recursively by \begin{equation*} \| f\|_{U^{k}}^{2^{k}} =\int_{\mathbb{R}^{n}} \| T^{h}f \cdot \bar{f} \|_{U^{k-1}}^{2^{k-1}} \, dh \end{equation*} with $T^{h}f(x) = f(x+h)$ and $\|f\|_{U^1} = | \int_{\mathbb{R}^{n}} f(x)\, dx |$. These norms were introduced by Gowers in his work on Szemer\'edi's theorem, and by Host-Kra in ergodic setting. It's shown by Eisner and Tao that for every $k\geq 2$ there exist $A(k,n)< \infty$ and $p_{k} = 2^{k}/(k+1)$ such that $\| f\|_{U^{k}} \leq A(k,n)\|f\|_{p_{k}}$, with $p_{k} = 2^{k}/(k+1)$ for all $f \in L^{p_{k}}(\mathbb{R}^{n})$. The optimal constant $A(k,n)$ and the extremizers for this inequality are known. In this exposition, it is shown that if the ratio $\| f \|_{U^{k}}/\|f\|_{p_{k}}$ is nearly maximal, then $f$ is close in $L^{p_{k}}$ norm to an extremizer

Young entrepreneurs are the future

The Small Business Journalist of the Year for Maine and New England describes producing and hosting “Back to Business” on radio and directing the University of Maine’s Target Technology Incubator.Small business - Maine ; Small business - New England

On the Maximal Displacement of Subcritical Branching Random Walks

We study the maximal displacement of a one dimensional subcritical branching random walk initiated by a single particle at the origin. For each $n\in\mathbb{N},$ let $M_{n}$ be the rightmost position reached by the branching random walk up to generation $n$. Under the assumption that the offspring distribution has a finite third moment and the jump distribution has mean zero and a finite probability generating function, we show that there exists $\rho>1$ such that the function g(c,n):=\rho ^{cn} P(M_{n}\geq cn), \quad \mbox{for each }c>0 \mbox{ and } n\in\mathbb{N}, satisfies the following properties: there exist $0<\underline{\delta}\leq \overline{\delta} < {\infty}$ such that if $c<\underline{\delta}$, then $$0<\liminf_{n\rightarrow\infty} g (c,n)\leq \limsup_{n\rightarrow\infty} g (c,n) {\leq 1},$$ while if $c>\overline{\delta}$, then $$\lim_{n\rightarrow\infty} g (c,n)=0.$$ Moreover, if the jump distribution has a finite right range $R$, then $\overline{\delta} < R$. If furthermore the jump distribution is "nearly right-continuous", then there exists $\kappa\in (0,1]$ such that $\lim_{n\rightarrow \infty}g(c,n)=\kappa$ for all $c<\underline{\delta}$. We also show that the tail distribution of $M:=\sup_{n\geq 0}M_{n}$, namely, the rightmost position ever reached by the branching random walk, has a similar exponential decay (without the cutoff at $\underline{\delta}$). Finally, by duality, these results imply that the maximal displacement of supercritical branching random walks conditional on extinction has a similar tail behavior.Comment: 29 page