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1

Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma

Rumyantsev A., Shen A.

Fundamenta Informaticae

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2014

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Vol. 132, nr 1

1--14

EN

A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.

2

A Simple Proof of Miller-Yu Theorem

Bienvenu L., Merkle W., Shen A.

Fundamenta Informaticae

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2008

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Vol. 83, nr 1-2

21-24

EN

A few years ago a nice criterion of Martin-Löf randomness in terms of plain (neither prefix nor monotone) Kolmogorov complexity was found (among many other results, it is published in [5]). In fact Martin-Löf came rather close to the formulation of this criterion around 1970 (see [4] and [7], p. 98); a version of it that involves both plain and prefix complexity was proven by Gacs in 1980 ([2], remark after corollary 5.4 on p. 391). We provide a simple proof of this criterion that uses only elementary arguments very close to the original proof of Levin-Schnorr criterion of randomness (1973) in terms of monotone complexity ([3, 6]).

3

GaAs/AlGaAs p-type multiple-quantum wells for infrared detection at normal incidence: model and experiment

Szmulowicz F., Brown G. J., Liu H. C., Shen A., Wasilewski Z. R., Buchanan M.

Opto-Electronics Review

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2001

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Vol. 9, No. 2

164-172

EN

The development of devices for mid-, long-, and very long-wavelength infrared (IR) detection has benefited greatly from advances in band-gap engineering. Recently, there has been great progress in the development of n-type GaAs/AlGaAs quantum well infrared photoconductor (QWIP) detector arrays in all three technologically important wavelength windows. p-type GaAs/AlGaAs QWIPs represent a viable alternative to n-type GaAs/AlGaAs QWIPs, offering the advantage of normal incidence absorption without the need for grating couplers. The maturity of the MBE of GaAs/AlGaAs layered materials offers the possibility of mass producing low cost, high performance, large size, high uniformity, multicolour, high frequency bandwidth, two-dimensional imagine QWIP arrays. This paper describes progress in optimising the performance of p-type GaAs/AlGaAs QWIP through modelling, growth, and characterisation. Using the 8x8 envelope-function approximation (EFA), a number of structures were designed and their optical absorption calculated for comparision with experiment. Samples were grown by MBE based on the theoretical designs and their photoresponse measured. p-type QWIPs were optimised with respect to the well and barrier widths, alloy concentration, and dopant concentration; resonant cavity devices were also fabricated and temperature dependent photoresponse was measured. The quantum efficiences and the background-limited (BLIP) detectivities under BLIP conditions of our p-QWIPs are comparable to those of n-QWIP; however, the responsivities are smaller. For our mid-IR p-QWIPs, the 2D doping densities of (1-2)x10¹² cm⁻² maximised the BLIP temperature and dark current limited detectivity by operating at around 100 K. At 80 K, the detectivity of the optimum doped sample was 3.5x10¹¹ cmHz¹/²/ W at 10 V bias. Barrier widths greater than 200 A were sufficient to impede the tunneling dark current; resonant cavities enhanced absorption fivefold.