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STUDY OBJECTIVES: Polysomnography is the gold standard in identifying sleep stages; however, there are discrepancies in how technicians use the standards. Because organizing meetings to evaluate this discrepancy and/or reach a consensus among multiple sleep centers is time-consuming, we developed an artificial intelligence system to efficiently evaluate the reliability and consistency of sleep scoring and hence the sleep center quality. METHODS: An interpretable machine learning algorithm was used to evaluate the interrater reliability (IRR) of sleep stage annotation among sleep centers. The artificial intelligence system was trained to learn raters from 1 hospital and was applied to patients from the same or other hospitals. The results were compared with the experts’ annotation to determine IRR. Intracenter and intercenter assessments were conducted on 679 patients without sleep apnea from 6 sleep centers in Taiwan. Centers with potential quality issues were identified by the estimated IRR. RESULTS: In the intracenter assessment, the median accuracy ranged from 80.3%–83.3%, with the exception of 1 hospital, which had an accuracy of 72.3%. In the intercenter assessment, the median accuracy ranged from 75.7%–83.3% when the 1 hospital was excluded from testing and training. The performance of the proposed method was higher for the N2, awake, and REM sleep stages than for the N1 and N3 stages. The significant IRR discrepancy of the 1 hospital suggested a quality issue. This quality issue was confirmed by the physicians in charge of the 1 hospital. CONCLUSIONS: The proposed artificial intelligence system proved effective in assessing IRR and hence the sleep center quality. CITATION: Liu G-R, Lin T-Y, Wu H-T, et al. Large-scale assessment of consistency in sleep stage scoring rules among multiple sleep centers using an interpretable machine learning algorithm. J Clin Sleep Med. 2021;17(2):159–166.

We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based algorithms, diffusion map (DM), and alternating diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep dynamics by reorganizing the spectral information of an electroencephalogram (EEG) extracted from a nonlinear-type time frequency analysis tool, the synchrosqueezing transform (SST). The visualization is achieved by the nonlinear dimension reduction properties of DM and AD. Moreover, the reconstructed nonlinear geometric structure of the sleep dynamics allows us to achieve the automatic annotation purpose. The hidden Markov model is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC∗ and ST∗, with the leave-one-subject-out cross-validation. The overall accuracy and macro F1 achieve 82.57% and 76% in Sleep-EDF SC∗ and 77.01% and 71.53% in Sleep-EDF ST∗, which is compatible with the state-of-the-art results by supervised learning-based algorithms. The results suggest the potential of the proposed algorithm for clinical applications.

We study bond prices in Black–Cox model with jumps in asset value. We assume that the jump size distribution is arbitrary and, if default occurs, following Longstaff and Schwartz [A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance 50 (1995), 789–819] and Zhou [The Term Structure of Credit Spreads with Jump Risk. Journal of Banking & Finance 26 (2001), 2015–2040], the payoff at maturity date depends on a general write-down function. Under this general setting, we propose an integral equation approach for the bond prices. As an application of this approach, we study the analytic properties of the bond prices. Also we derive an infinite series expression for the bond prices.

Based on the well-established biopotential theory, we hypothesize that the high frequency spectral information, like that higher than 100Hz, of the EEG signal recorded in the off-the-shelf EEG sensor contains muscle tone information. We show that an existing automatic sleep stage annotation algorithm can be improved by taking this information into account. This result suggests that if possible, we should sample the EEG signal with a high sampling rate, and preserve as much spectral information as possible., Sensors, 20 (7), ISSN:1424-8220

Background: Polysomnography is the gold standard in identifying sleep stages; however, there are discrepancies in the standards used by technicians. Because organizing meetings to reach a consensus among multiple sleep centers is time consuming, we developed an artificial intelligence (AI) system to evaluate the reliability and consistency of sleep scoring. Methods: An interpretable machine learning algorithm was used to evaluate interrater reliability (IRR) among sleep centers. Intra-center and inter-center assessments were conducted on 679 subjects without sleep apnea in six sleep centers in Taiwan. IRR was estimated based on prediction outcomes. Findings: In the intra-center assessment, the median accuracy of the databases ranged from 78·8% to 81·9% with the exception of one hospital (designated E) with an accuracy of 72·5%. In the inter-center assessment, the median accuracy ranged from 74·4% to 79·9% when hospital E was excluded from testing and training. The performance of the proposed method was higher for N2, awake, and REM, compared to N1 and N3. There was a significant difference in the prediction models learned from hospital E and others. Interpretation: The proposed AI system proved highly effective in assessing IRR. Increasing the interrater agreement rate would lead to further improvements in the accuracy of the proposed sleep stage annotation system. Funding: This research was supported by grants from the Ministry of Science and Technology, Taiwan (MOST-109-2119-M-002-014), and the Chang Gung Medical Research Program (CMRPG3K0201). Declaration of Interest: The authors declare no competing interests. Ethical Approval: The study protocol was approved by the Institutional Review Board of each hospital (Chang Gung Memorial Hospital’s IRB No: 201800609B0; MacKay Memorial Hospital’s IRB No: 18MMHIS142e; Shuanh-Ho Hospital’s IRB No: N201911007, N201903142; Taipei Tzu Chi Hospital’s IRB No: 07-XD-083; Taichung Tzu Chi Hospital’s IRB No: REC107-37, and Taipei Veterans General Hospital’s IRB No: 2018-12-009AC).

We study the first exit from a general open set for a one-dimensional Levy process, where the Levy measure is proportional to a two-sided matrix-exponential distribution. Under appropriate conditions on the Levy measure, we obtain an explicit solution for the joint distribution of the first-exit time and the position of the Levy process upon first exit, in terms of the zeros and poles of the corresponding Laplace exponent. The present result complements several earlier works on the use of exit sets for Levy processes with algebraically similar Laplace exponents, where exits from open intervals are the main focus.

We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information from two electroencephalograms (EEG). The diffusion geometry approach helps organize the nonlinear dynamical structure hidden in the EEG signal. The visualization is achieved by the nonlinear dimension reduction capability of the chosen diffusion geometry algorithms. For the automatic annotation purpose, the support vector machine is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC* (SC = Sleep Cassette) and ST* (ST = Sleep Telemetry), with the leave-one-subject-out cross validation. When we have a single EEG channel (Fpz-Cz), the overall accuracy, macro F1 and Cohen's kappa achieve 82.72%, 75.91% and 76.1% respectively in Sleep-EDF SC* and 78.63%, 73.58% and 69.48% in Sleep-EDF ST*. This performance is compatible with the state-of-the-art results. When we have two EEG channels (Fpz-Cz and Pz-Oz), the overall accuracy, macro F1 and Cohen's kappa achieve 84.44%, 78.25% and 78.36% respectively in Sleep-EDF SC* and 79.05%, 74.73% and 70.31% in Sleep-EDF ST*. The results suggest the potential of the proposed algorithm in practical applications.

This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of these perpetual American compound options. Explicit formulae for the rational prices and the optimal boundaries are also obtained for hyper-exponential jump-diffusion models.

We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra's replica symmetry breaking scheme, we establish this at the level of the free energy as well as the Gibbs measure irrespective the presence or absence of the external field., 12 pages

In this article, we considers reversible Markov chains of which $L^{2}$-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [J. Funct. Anal. 258 (2010) 2246–2315], while we provide here a completely different pathway to analyze the $L^{2}$-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between discrete time lazy chains and continuous time chains. For an illustration, we consider product chains, a rather complicated model which could be involved to analyze using the method in [J. Funct. Anal. 258 (2010) 2246–2315], and derive the equivalence of their $L^{2}$-cutoffs.

An American option is an option that can be exercised at any time prior to its expiration. For an American call option (written on an underlying stock without dividends) with a finite expiration ti...

We consider families of Ehrenfest chains and provide a simple criterion on the L p -cutoff and the L p -precutoff with specified initial states for 1 ≤ p ∞ . For the family with an L p -cutoff, a cutoff time is described and a possible window is given. For the family without an L p -precutoff, the exact order of the L p -mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where only downward jumps are allowed.

We study defaultable bond prices in the Black–Cox model with jumps in the asset value. The jump-size distribution is arbitrary, and following Longstaff and Schwartz (1995) and Zhou (2001) we assume that, if default occurs, the recovery at maturity depends on the ‘severity of default’. Under this general setting, the vehicle for our analysis is an integral equation. With the aid of this, we prove some properties of the bond price which are consistent numerically and empirically with earlier works. In particular, the limiting credit spread as time to maturity tends to 0 is nonzero. As a byproduct, we show that the integral equation implies an infinite-series expansion for the bond price.

We study defaultable bond prices in the Black–Cox model with jumps in the asset value. The jump-size distribution is arbitrary, and following Longstaff and Schwartz (1995) and Zhou (2001) we assume that, if default occurs, the recovery at maturity depends on the ‘severity of default’. Under this general setting, the vehicle for our analysis is an integral equation. With the aid of this, we prove some properties of the bond price which are consistent numerically and empirically with earlier works. In particular, the limiting credit spread as time to maturity tends to 0 is nonzero. As a byproduct, we show that the integral equation implies an infinite-series expansion for the bond price.

Boyle and Vorst work in the framework of the binomial model and derive self-financing strategies perfectly replicating the final payoffs to long and short positions in call and put options, assuming proportional transactions costs on trades in the stock and no transactions costs on trades in the bond. Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Bensaid et al. gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalized by Stettner, Rutkowski and Palmer to the case of asymmetric transaction costs. In this paper, we first determine the number of replicating portfolios and then compute the least cost super replicating portfolio for any contingent claim in a one-period binomial model. By using the fundamental theorem of linear programming, we show that there are only finitely many possibilities for a least cost super replicating portfolio for any contingent claim in a two-period binomial model. As an application of our results, we give an example in which we compute the least cost super replicating portfolio for a butterfly spread in a two-period model.

Under martingale and joint-normality assumptions, various optimal hedge ratios are identical to the minimum variance hedge ratio. As empirical studies usually reject the joint-normality assumption, we propose the generalized hyperbolic distribution as the joint log-return distribution of the spot and futures. Using the parameters in this distribution, we derive several widely used optimal hedge ratios: minimum variance, maximum Sharpe measure, and minimum generalized semivariance. Under mild assumptions on the parameters, we find that these hedge ratios are identical. Regarding the equivalence of these optimal hedge ratios, our analysis suggests that the martingale property plays a much important role than the joint distribution assumption.

Consider an (L, α)-superdiffusion X, 1 < α [les ] 2, in a smooth cylinder Q = ℝ+ × D. Where L is a uniformly elliptic operator on ℝ+ × ℝd and D is a bounded smooth domain in ℝd. Criteria for determining which (internal) subsets of Q are not hit by the graph [Gscr ] of X were established by Dynkin [5] in terms of Bessel capacity and according to Sheu [14] in terms of restricted Hausdorff dimension (partial results were also obtained by Barlow, Evans and Perkins [3]). While using Poisson capacity on the lateral boundary ∂Q of Q, Kuznetsov [10] recently characterized complete subsets of ∂Q which have no intersection with [Gscr ]. In this work, we examine the relations between Poisson capacity and restricted Hausdorff measure. According to our results, the critical restricted Hausdorff dimension for the lateral [Gscr ]-polarity is d − (3 − α)/(α − 1). (A similar result also holds for the case d = (3 − α)/(α − 1)). This investigation provides a different proof for the critical dimension of the boundary polarity for the range of X (as established earlier by Le Gall [12] for L = Δ, α = 2 and by Dynkin and Kuznetsov [7] for the general case).

Consider an (L, a)-superdiffusion X on Rd, where L is an uniformly elliptic differential operator in Rd, and 1 < a < 2. The G-polar sets for X are subsets of R x Rd which have no intersection with the graph G of X, and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the G-polarity of a general analytic set A C R x Rd in term of the Bessel capacity of A, and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the G-polarity of sets of the form E x F, where E and F are two Borel subsets of R and Rd respectively. We establish a relationship between the restricted Hausdorff dimension of E x F and the usual Hausdorff dimensions of E and F. As an application, we obtain a criterion for G-polarity of E x F in terms of the Hausdorff dimensions of E and F, which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures.

This investigation concerns the hyper-exponential jump-diffusion processes. Following the exposition of the two-sided exit problem by Kyprianou, A. E., and Asmussen, S. and Albrecher, H., this study investigates first passage functionals for these processes.The corresponding boundary value problems are solved to obtain an explicit formula for the first passage functionals.

By using connections between superdiffusions and partial differential equations (established recently by Dynkin, 1991), we study the structure of the set of all positive (bounded or unbounded) solutions for a class of nonlinear elliptic equations. We obtain a complete classification of all bounded solutions. Under more restrictive assumptions, we prove the uniqueness property of unbounded solutions, which was observed earlier by Cheng and Ni (1992).

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

We establish relations betweenG-polar sets of superdiffusions and the restricted Hausdorff dimension. As an application, we give new proofs of Dynkin's criteria for theS-polarity andH-polarity (established earlier by Dawson, Iscoe, Perkins, and Le Gall under more restrictive assumptions.)

In this paper, we study the discounted penalty in a perturbed compound Poisson model with two sided jumps. We prove second-order regularity of this function and investigate its asymptotic behavior at infinity. Next, based on Boyarchenko and Levendorskii (2002), we justify an integro-differential equation for the discounted penalty.

Under the assumption that the asset value follows a phase-type jump diffusion, we show the expected discounted penalty satisfies an ODE and obtain a general form ?for the expected discounted penalty. In particular, if only downward jumps are allowed, we get an explicit formula in terms of the penalty function and jump distribution. On the other hand, if downward jump distribution is a mixture of exponential distributions (and upward jumps are determined by a general Levy measure), we obtain closed form solutions for the expected discounted penalty. As an application, we work out an example in Leland’s structural model with jumps. For earlier and related results, see Gerber and Landry [Insurance: Mathematics and Economics 22:263–276, 1998], Hilberink and Rogers [Finance Stoch 6:237–263, 2002], Asmussen et al. [Stoch. Proc. and their App. 109:79–111, 2004] and Kyprianou and Surya [Finance Stoch 11:131–152, 2007].

In this note we give semi-explicit solutions for $r$-balayages of matrix-exponential-Levy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in [11], Asmussen, Avram and Pistorius in [3], Chen, Lee and Sheu in [7], and many others

Since Black and Scholes (1973) introduced their option-pricing model in frictionless markets, many authors have attempted to develop models incorporating transaction costs. The groundwork of modeling the effects of transaction costs was done by Leland (1985). The Leland model was put into a binomial setting by Boyle and Vorst (1992). Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist superreplicating portfolios of lower cost. However, it is known that there is no superreplicating portfolio for long calls and puts of lower cost than the replicating portfolio. Nevertheless, this is not true for short calls and puts. As the negative of the cost of the least cost superreplicating portfolios for such a position is a lower bound for the call or put price, it is important to determine this least cost. In this paper, we consider two-period binomial models and show that, for a special class of claims including short call and put options, there are just four possibilities so that the least cost superreplicating portfolios can be easily calculated for such positions. Also we show that, in general, the least cost superreplicating portfolio is path-dependent.

We consider the exit measures of $(L,\alpha)$-superdiffusions, $1 < \alpha \leq 2$, from a bounded smooth domain D in R d. By using analytic results about solutions of the corresponding boundary value problem, we study the states of the exit measures. (Abraham and Le Gall investigated earlier .this problem for a special case $L = \Delta$ and $\alpha = 2$). Also as an application of these analytic results, we give a different proof for the critical Hausdorff. dimension of boundary polarity (established earlier by Le Gall under more restrictive assumptions and by Dynkin and Kuznetsov for general situations).

Consider the simple random walk on the n-cycle Zn. For this example, Diaconis and Saloff-Coste (Ann. Appl. Probab. 6 (1996) 695) have shown that the log-Sobolev constant α is of the same order as the spectral gap λ. However the exact value of α is not known for n>4. (For n=2, it is a well known result of Gross (Amer. J. Math. 97 (1975) 1061) that α is 12. For n=3, Diaconis and Saloff-Coste (Ann. Appl. Probab. 6 (1996) 695) showed that α=12log2

Let X be a super-Brownian motion with a general (time-space) homogeneous branching mechanism. We study a relation between lifetime and compactness of range for X . Under a restricted condition on the branching mechanism, we show that the set X survives is the same as that the range of X is unbounded. (For α-branching super-Brownian motion, 1 α ⩽ 2, similar results were obtained earlier by Iscoe (1988) and Dynkin (1991).) We also give an interesting example in that case X dies out in finite time, but it has an unbounded range.