We present 3 open challenges in the field of Costas arrays. They are: a) the determination of the number of dots on the main diagonal of a Welch array, and especially the maximal such number for a Welch array of a given order; b) the conjecture that the fraction of Welch arrays without dots on the main diagonal behaves asymptotically as the fraction of permutations without fixed points and henc...

References 1. Levine SR, Welch KMA: Cerebrovascular ischemia associated with lupus anticoagulant. Stroke 1987; 18:257-263 2. Levine SR, Welch KMA: The spectrum of neurological disease associated with antiphospholipid antibodies: Lupus anticoagulants and anticardiolipin antibodies. Arch Neurol 1987;44: 876-883 3. Levine SR, Welch KMA: Antiphospholipid antibodies. Ann Neurol 1989;26:386-389 4. Ya...

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantage...

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantage...

This article re-examines two historic Supreme Court’s decisions—the 1964 Times v. Sullivan and the 1974 Gertz v. Welch—as they apply to the digital era. The Court’s decision in Sullivan established the federal legal guidelines for a victim to prove a libel case including actual malice. In Gertz v. Welch the Court established three categories of public figures who must prove actual malice in a l...

The discrimination technique for estimating parameters of Gaussian mixtures that is based on the Extended Baum-Welch transformations (EBW) has had significant impact on the speech recognition community. In this paper we introduce a general definition of a family of EBW transformations that can be associated with a weighted sum of updated and initial models. We compute a gradient steepness measu...