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

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

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

Vocational schooling, occupational matching, and labor market earnings in Israel

The authors conducted a comparative analysis of the earnings of workers in Israel who had last attended vocational schools and those who had last attended academic secondary schools before entering the labor force. Their findings suggest that Israel may provide an example of an educational system in which vocational schooling is economically effective. Vocational schooling in Israel has proven more cost-effective than general academic training. In particular, vocational school attenders who later worked in occupations related to their course of study earned more. Their wages were up to 10 percent more a month than their peers who studied at academic secondary schools and those who attended vocational schools but found employment in other occupations not related to their field of study. These results reinforce similar findings in recent research on vocational schooling in the United States. A caveat is necessary to temper the generally positive findings concerning vocational schooling in Israel. While vocational schooling is cost-effective compared with other forms of secondary schooling, it does not compare favorably with other forms of training for skilled trades, such as apprenticeships and factory-based vocational schools. Another factor is the national consensus in Israel favoring education designed to equip young people for the social and cultural role of integrating the country's heterogenous, largely immigrant population.Teaching and Learning,Gender and Education,Health Monitoring&Evaluation,Education Reform and Management,Primary Education

Iterative optical vector-matrix processors (survey of selected achievable operations)

An iterative optical vector-matrix multiplier with a microprocessor-controlled feedback loop capable of performing a wealth of diverse operations was described. A survey and description of many of its operations demonstrates the versatility and flexibility of this class of optical processor and its use in diverse applications. General operations described include: linear difference and differential equations, linear algebraic equations, matrix equations, matrix inversion, nonlinear matrix equations, deconvolution and eigenvalue and eigenvector computations. Engineering applications being addressed for these different operations and for the IOP are: adaptive phased-array radar, time-dependent system modeling, deconvolution and optimal control

Minimum-fuel turning climbout and descent guidance of transport jets

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft