Hybrid Sleep Stage Classification for Clinical Practices across Different Polysomnography Systems Using Frontal EEG

Automatic bio-signal processing and scoring have been a popular topic in recent years. This includes sleep stage classification, which is time-consuming when carried out by hand. Multiple sleep stage classification has been proposed in recent years. While effective, most of these processes are trained and validated against a singular set of data in uniformed pre-processing, whilst in a clinical environment, polysomnography (PSG) may come from different PSG systems that use different signal processing methods. In this study, we present a generalized sleep stage classification method that uses power spectra and entropy. To test its generality, we first trained our system using a uniform dataset and then validated it against another dataset with PSGs from different PSG systems. We found that the system achieved an accuracy of 0.80 and that it is highly consistent across most PSG records. A few samples of NREM3 sleep were classified poorly, and further inspection showed that these samples lost crucial NREM3 features due to aggressive filtering. This implies that the system’s effectiveness can be evaluated by human knowledge. Overall, our classification system shows consistent performance against PSG records that have been collected from different PSG systems, which gives it high potential in a clinical environment.

Structure of singular sets of some classes of subharmonic functions

In this paper, we survey the recent results on removable singular sets for the classes of $m$-subharmonic ($m-sh$) and strongly $m$-subharmonic ($sh_m$), as well as $\alpha$-subharmonic functions, which are applied to study the singular sets of $sh_{m}$ functions. In particular, for strongly $m$-subharmonic functions from the class $L_{loc}^{p}$, it is proved that a set is a removable singular set if it has zero $C_{q,s}$-capacity. The proof of this statement is based on the fact that the space of basic functions, supported on the set $D\backslash E$, is dense in the space of test functions defined in the set $D$ on the $L_{q}^{s}$-norm. Similar results in the case of classical (sub)harmonic functions were studied in the works by L. Carleson, E. Dolzhenko, M. Blanchet, S. Gardiner, J. Riihentaus, V. Shapiro, A. Sadullaev and Zh. Yarmetov, B. Abdullaev and S. Imomkulov.

Contra invidentium effascinationes: Prophylaxis and the evil eye in some gems of the republican Roman era with grotesque subjects

In the glyptic repertoire of roman-republican age, numerous subjects that must be recognized as amulets with probaskanica function. These objects are designed to protect the owner from the negative effects of the evil eye. The ridiculous and caricatural aspect often seen in these engraved gems characterized the grotesque and/or deformed beings such as hunchbacks, bald, dwarfs, pygmies. A further common typical element is the sexual hypertrophy, another characteristic that, in literature, has always been associated with a clear apotropaic function. From a functional perspective, all these features would contribute to identify these characters as useful expedients to ward off the charm. Instead, from a perspective of antithetical analogy, they communicate positive symbolic concepts, such as the fullness of life, fertility, rebirth and victory over death. Thanks to the analytical study of some pictures engraved in gems conducted by the authors, it has been possible to define a singular set similar for style, subject and type of material, produced between the second and first century BC in the Italian peninsula. The paper intends to explain the figurative and material elements, both constant or variable, that contribute to reinforce the symbolic and amuletic meaning of these gems.

On the existence of four or more curved foldings with common creases and crease patterns

Consider an oriented curve $$\Gamma $$ Γ in a domain D in the plane $${\varvec{R}}^2$$ R 2 . Thinking of D as a piece of paper, one can make a curved folding in the Euclidean space $${\varvec{R}}^3$$ R 3 . This can be expressed as the image of an “origami map” $$\Phi :D\rightarrow {\varvec{R}}^3$$ Φ : D → R 3 such that $$\Gamma $$ Γ is the singular set of $$\Phi $$ Φ , the word “origami” coming from the Japanese term for paper folding. We call the singular set image $$C:=\Phi (\Gamma )$$ C : = Φ ( Γ ) the crease of $$\Phi $$ Φ and the singular set $$\Gamma $$ Γ the crease pattern of $$\Phi $$ Φ . We are interested in the number of origami maps whose creases and crease patterns are C and $$\Gamma $$ Γ , respectively. Two such possibilities have been known. In the authors’ previous work, two other new possibilities and an explicit example with four such non-congruent distinct curved foldings were established. In this paper, we determine the possible values for the number N of congruence classes of curved foldings with the same crease and crease pattern. As a consequence, if C is a non-closed simple arc, then $$N=4$$ N = 4 if and only if both $$\Gamma $$ Γ and C do not admit any symmetries. On the other hand, when C is a closed curve, there are infinitely many distinct possibilities for curved foldings with the same crease and crease pattern, in general.

On the structure of the singular set of solutions in one class of 3D time-optimal control problems

A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.

Regularity and global structure for Hamilton–Jacobi equations with convex Hamiltonian

We consider the multidimensional Hamilton–Jacobi (HJ) equation [Formula: see text] with [Formula: see text] being a constant and for bounded [Formula: see text] initial data. When [Formula: see text], this is the typical case of interest with a uniformly convex Hamiltonian. When [Formula: see text], this is the famous Eikonal equation from geometric optics, the Hamiltonian being Lipschitz continuous with homogeneity [Formula: see text]. We intend to fill the gap in between these two cases. When [Formula: see text], the Hamiltonian [Formula: see text] is not uniformly convex and is only [Formula: see text] in any neighborhood of [Formula: see text], which causes new difficulties. In particular, points on characteristics emanating from points with vanishing gradient of the initial data could be “bad” points, so the singular set is more complicated than what is observed in the case [Formula: see text]. We establish here the regularity of solutions and the global structure of the singular set from a topological standpoint: the solution inherits the regularity of the initial data in the complement of the singular set and there is a one-to-one correspondence between the connected components of the singular set and the path-connected components of the set [Formula: see text].