Exact extreme value statistics at mixed order transitions

We study extreme value statistics (EVS) for spatially extended models exhibiting mixed order phase transitions (MOT). These are phase transitions which exhibit features common to both first order (discontinuity of the order parameter) and second order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising (TIDSI) model which is a prototypical model exhibiting MOT, and study analytically the extreme value statistics of the domain lengths. The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size $L$. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length $l_{\max}$ converges, in the large $L$ limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of $l_{\max}$ are governed by novel distributions which we compute exactly. Our main analytical results are verified by numerical simulations.Comment: 25 pages, 6 figures, 1 tabl

Monolithic optoelectronic integration of a GaAlAs laser, a field-effect transistor, and a photodiode

A low threshold buried heterostructure laser, a metal-semiconductor field-effect transistor, and a p-i-n photodiode have been integrated on a semi-insulating GaAs substrate. The circuit was operated as a rudimentary optical repeater. The gain bandwidth product of the repeater was measured to be 178 MHz

How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time $(1+\epsilon)$-approximation algorithm that yields an $(e+\epsilon)$-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with \emph{optimal }cost at $1+\epsilon$ speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most $\log n$ many classes. This algorithm allows the jobs even to have up to $\log n$ many distinct release dates.Comment: 2 pages, 1 figur

High-speed GaAlAs/GaAs p-i-n photodiode on a semi-insulating GaAs substrate

A high-speed, high-responsivity GaAlAs/GaAs p-i-n photodiode has been fabricated on a GaAs semi-insulating substrate. The 75-µm-diam photodiode has a 3-dB bandwidth of 2.5 GHz and responsivity of 0.45 A/W at 8400 Å (external quantum efficiency of 65%). The diode is suitable for monolithic integration with other optoelectronic devices

Gallium Aluminum Arsenide/Gallium Arsenide Integrated Optical Repeater

A low threshold buried heterostructure laser, a metal-semiconductor field effect transistor (MESFET), and a photodiode, have for the first time, been monolithically integrated on a semi-insulating GaAs substrate. This integrated optoelectronic circuit (IOEC) was operated as a rudimentary optical repeater. The incident optical signal is detected by the photodiode, amplified by the MESFET, and converted back to light by the laser. The gain bandwidth product of the repeater was measured to be 178 MHz

AlGaAs lasers with micro-cleaved mirrors suitable for monolithic integration

A technique has been developed for cleaving the mirrors of AlGaAs lasers without cleaving the substrate. Micro-cleaving involves cleaving a suspended heterostructure cantilever by ultrasonic vibrations. Lasers with microcleaved mirrors have threshold currents and quantum efficiencies identical to those of similar devices with conventionally cleaved mirrors

Fast Structuring of Radio Networks for Multi-Message Communications

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Designing efficient communication primitives for radio networks has a rich history that began 25 years ago when Bar-Yehuda et al. introduced fast randomized algorithms for broadcasting and for constructing BFS-trees. Their BFS-tree construction time was $O(D \log^2 n)$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. Since then, the complexity of a broadcast has been resolved to be $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ rounds. On the other hand, BFS-trees have been used as a crucial building block for many communication primitives and their construction time remained a bottleneck for these primitives. We introduce collision free layerings that can be used in place of BFS-trees and we give a randomized construction of these layerings that runs in nearly broadcast time, that is, w.h.p. in $T_{Lay} = O(D \log \frac{n}{D} + \log^{2+\epsilon} n)$ rounds for any constant $\epsilon>0$. We then use these layerings to obtain: (1) A randomized algorithm for gathering $k$ messages running w.h.p. in $O(T_{Lay} + k)$ rounds. (2) A randomized $k$-message broadcast algorithm running w.h.p. in $O(T_{Lay} + k \log n)$ rounds. These algorithms are optimal up to the small difference in the additive poly-logarithmic term between $T_{BC}$ and $T_{Lay}$. Moreover, they imply the first optimal $O(n \log n)$ round randomized gossip algorithm