Finite Input Sequences Research Articles

Universal adaptive beamforming for moving interferers

Loud moving interferers challenge adaptive beamformers (ABFs) attempting attenuate these interferers while detecting quiet sources. Specifically, moving interferers create a dynamic tension in choosing the best window length for estimating the sample covariance matrix (SCM) from received snapshots. If the window is too short, the ABF does not accurately steer its nulls toward the interferers, diminishing its effectiveness in attenuating the interferers. If the window is too long, the interferers transit multiple beamwidths, splitting their power across multiple eigenvectors, also diminishing the ABF's effectiveness (Baggeroer and Cox, 1999). Previously proposed approaches to address this challenge include Multirate Adaptive Beamforming (Cox, 2000) and Null-Broadening (Song et al., 2003). This talk proposes a universal adaptive beamformer (UABF) exploiting online learning techniques to adapt the length of the SCM averaging window. The UABF's array weights blend the array weights of several competing ABFs. The recent performance of each fixed-window ABF determines its contribution to the UABF array weights. The UABF's performance provably converges to rival the best fixed-length window ABF for every finite power input sequence, without assuming a specific probability distribution. In nonstationary environments where interferers change speed, the UABF may outperform all of the competing fixed-window ABFs. [Supported by ONR 321US.]Loud moving interferers challenge adaptive beamformers (ABFs) attempting attenuate these interferers while detecting quiet sources. Specifically, moving interferers create a dynamic tension in choosing the best window length for estimating the sample covariance matrix (SCM) from received snapshots. If the window is too short, the ABF does not accurately steer its nulls toward the interferers, diminishing its effectiveness in attenuating the interferers. If the window is too long, the interferers transit multiple beamwidths, splitting their power across multiple eigenvectors, also diminishing the ABF's effectiveness (Baggeroer and Cox, 1999). Previously proposed approaches to address this challenge include Multirate Adaptive Beamforming (Cox, 2000) and Null-Broadening (Song et al., 2003). This talk proposes a universal adaptive beamformer (UABF) exploiting online learning techniques to adapt the length of the SCM averaging window. The UABF's array weights blend the array weights of several competing ABFs. ...

Numerical and Non-Asymptotic Analysis of Elias's and Peres's Extractors with Finite Input Sequences.

Many cryptographic systems require random numbers, and the use of weak random numbers leads to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias’s extractor achieves the optimal rate (i.e., information-theoretic upper bound) if the block size tends to infinity, where is the binary entropy function and p is the probability that each bit of input sequences occurs. Peres’s extractor achieves the optimal rate if the length of the input and the number of iterations tend to infinity. Previous research related to both extractors has made no reference to practical aspects including running time and memory size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres’s extractor, and we show that Elias’s extractor is better than Peres’s extractor in terms of the maximum redundancy (or the rates) if we do not pay attention to the time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. To do so, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres’s extractor is much better than Elias’s extractor for given finite input sequences under a very similar running time. As a consequence, Peres’s extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.

Determination of distinguishing input sequences for the diagnosis of discrete-event systems

The paper deals with the determination of input sequences for which the faults occurring in discrete-event systems described by deterministic I/O automata can be detected and identified. The basis for this method is provided by diagnosability criteria that show that faults can be found whenever the automata describing the faultless and the faulty system do not have equivalent initial states. The absence of equivalent states implies that there exist finite input sequences for which the output sequences distinguish for all faults. The paper describes a method to find these input sequences.

Diagnosability of deterministic I/O automata

The paper deals with the relation between diagnosability of deterministic I/O automata and state equivalence. Diagnosability criteria are formulated in terms of the existence of equivalent automaton states. The absence of equivalent states implies that there exist finite input sequences for which the output sequences distinguish for all faults. and, hence, make it possible to identify the fault.

Temporal self-imaging effects for periodic optical pulse sequences of finite duration

Integer and fractional temporal self-imaging phenomena occur when an ideal (infinite-duration) periodic optical pulse sequence propagates through a suitable dispersive medium under the first-order dispersion approximation. I analytically and numerically investigate the impact of nonidealities in the input periodic pulse sequence, especially finite duration of the sequences as well as intensity and phase fluctuations between pulses, on the temporal self-imaging phenomena. I derive conditions for which effects associated with these nonidealities can be neglected. Under these conditions, the intensity of the input nonideal finite sequence can also be self-imaged—integer and fractional self-imaging are also possible—by propagation through a suitable dispersive medium. The resulting self-images of the input signal not only maintain the temporal features of the original individual pulses (temporal shape and duration) but also the total temporal duration of the finite input sequence and the original intensity fluctuations between pulses. The analytical results are confirmed by means of numerical simulations.

On-Line Multi-Threaded Paging

In this paper we introduce a generalization of Paging to the case where there are many threads of requests. This models situations in which the requests come from more than one independent source. Hence, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities.Four different on-line problems arise depending on whether we consider fairness restrictions or not, with finite or infinite input sequences. We study all of them, proving lower and upper bounds for the competitiveness of on-line algorithms.The main competitiveness results presented in this paper state that when no fairness restrictions are imposed it is possible to obtain competitive algorithms for finite and infinite inputs. On the other hand, for the fair case in general there exist no competitive algorithms.In addition, we consider three definitions of competitiveness for infinite inputs. One of them forces algorithms to behave efficiently at every finite stage, while the other two aim at comparing the algorithms' steady-state performances. A priori, the three definitions seem different. We study them and find, however, that they are essentially equivalent. This suggests that the competitiveness results that we obtain reflect the intrinsic difficulty of the problem and are not a consequence of a too strict definition of competitiveness.