Aperiodic Part Research Articles

Cortex-wide topography of 1/f-exponent in Parkinson’s disease

Parkinson’s disease (PD) is a progressive and debilitating brain disorder. Besides the characteristic movement-related symptoms, the disease also causes decline in sensory and cognitive processing. The extent of symptoms and brain-wide projections of neuromodulators such as dopamine suggest that many brain regions are simultaneously affected in PD. To characterise brain-wide disease-related changes in neuronal function, we analysed resting state magnetoencephalogram (MEG) from two groups: PD patients and healthy controls. Besides standard spectral analysis, we quantified the aperiodic components (κ, λ) of the neural activity by fitting a power law κ/fλ – f is the frequency, κ and λ are the fitting parameters—to the MEG power spectrum and studied its relationship with age and Unified Parkinson’s Disease Rating Scale (UPDRS). Consistent with previous results, the most significant spectral changes were observed in the high theta/low-alpha band (7–10 Hz) in all brain regions. Furthermore, analysis of the aperiodic part of the spectrum showed that in all but frontal regions λ was significantly larger in PD patients than in control subjects. Our results indicate that PD is associated with significant changes in aperiodic activity across the whole neocortex. Surprisingly, even early sensory areas showed a significantly larger λ in patients than in healthy controls. Moreover, λ was not affected by the Levodopa medication. Finally, λ was positively correlated with patient age but not with UPDRS-III. Because λ is closely associated with excitation-inhibition balance, our results propose new hypotheses about neural correlates of PD in cortical networks.

Systems-level analysis of local field potentials reveals differential effects of lysergic acid diethylamide and ketamine on neuronal activity and functional connectivity.

Psychedelic substances have in recent years attracted considerable interest as potential treatments for several psychiatric conditions, including depression, anxiety, and addiction. Imaging studies in humans point to a number of possible mechanisms underlying the acute effects of psychedelics, including changes in neuronal firing rates and excitability as well as alterations in functional connectivity between various brain nodes. In addition, animal studies using invasive recordings, have suggested synchronous high-frequency oscillations involving several brain regions as another key feature of the psychedelic brain state. To better understand how the imaging data might be related to high-resolution electrophysiological measurements, we have here analyzed the aperiodic part of the local field potential (LFP) in rodents treated with a classic psychedelic (LSD) or a dissociative anesthetic (ketamine). In addition, functional connectivity, as quantified by mutual information measures in the LFP time series, has been assessed with in and between different structures. Our data suggest that the altered brain states of LSD and ketamine are caused by different underlying mechanisms, where LFP power shifts indicate increased neuronal activity but reduced connectivity following ketamine, while LSD also leads to reduced connectivity but without an accompanying change in LFP broadband power.

Separating Neural Oscillations from Aperiodic 1/f Activity: Challenges and Recommendations

Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law Ppropto 1/{f}^{beta } and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent beta. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them.

Influence of Aperiodic Non‐Tidal Atmospheric and Oceanic Loading Deformations on the Stochastic Properties of Global GNSS Vertical Land Motion Time Series

AbstractMonitoring vertical land motions (VLMs) at the level of 0.1 mm/yr remains one of the most challenging scientific applications of global navigation satellite systems (GNSS). Such small rates of change can result from climatic and tectonic phenomena, and their detection is important to many solid Earth‐related studies, including the prediction of coastal sea‐level change and the understanding of intraplate deformation. Reaching a level of precision allowing to detect such small signals requires a thorough understanding of the stochastic variability in GNSS VLM time series. This paper investigates how the aperiodic part of non‐tidal atmospheric and oceanic loading (NTAOL) deformations influences the stochastic properties of VLM time series. Using the time series of over 10,000 stations, we describe the impact of correcting for NTAOL deformation on 5 complementary metrics, namely: the repeatability of position residuals, the power‐spectrum of position residuals, the estimated time‐correlation properties, the corresponding velocity uncertainties, and the spatial correlation of the residuals. We show that NTAOL deformations cause a latitude‐dependent bias in white noise plus power‐law model parameter estimates. This bias is significantly mitigated when correcting for NTAOL deformation, which reduces velocity uncertainties at high latitudes by 70%. Therefore, removing NTAOL deformation before the statistical analysis of VLM time series might help to detect subtle VLM signals in these areas. Our spatial correlation analysis also reveals a seasonality in the spatial correlation of the residuals, which is reduced after removing NTAOL deformation, confirming that NTAOL is a clear source of common‐mode errors in GNSS VLM time series.

Response time analysis of digraph real-time tasks scheduled with static priority: generalization, approximation, and improvement

Graph-based task models have been studied to better model and analyze the schedulability of real-time systems. Among them, the digraph task model, with its powerful expressiveness to describe the behavior of a large class of real-time tasks, receives a wide range of interests recently. However, the exact schedulability analysis of digraph tasks on a uni-processor with preemptive static-priority scheduling has been shown to be coNP-hard. Approximate analyses based on the request and interference bound functions (\(\textit{rbf}\) and \(\textit{ibf}\)) have been proposed to improve the analysis efficiency. In this work, we summarize the existing results on these analysis techniques, and seek to further improve their generality, complexity, and accuracy. Specifically, we develop analysis techniques for tasks with arbitrary deadlines. We prove the periodicity of interference bound function such that it can be expressed as a finite aperiodic part and an infinite periodic part, which makes the asymptotic complexity of its calculation independent from the length of the time interval. Moreover, we develop a linear upper bound on \(\textit{ibf}\) that is tighter than that of \(\textit{rbf}\), to derive a better response time bound.

Fluctuations of liquid fuel in tanks with oil recovery units

The article presents solutions of problems of natural fluctuations of liquid in cylindrical, conical and spherical tanks, with boundary conditions on the free surface and the surface with resistance, i.e. the drain surface. Particular attention is paid to finding the eigenvalues and eigenfrequencies of equations of oscillations of perturbed motion of fluid with the presence of dissipation on the boundary surfaces. It is shown that low speed of lowering of the free surface and resistance conditions on the surface of the drain can affect both the oscillatory and the aperiodic parts of the solution of the fluid oscillation problem.

Vibrations of a beam‐string complex system under a moving force

AbstractIn this paper, the dynamic response of an Euler‐Bernoulli beam and string system traversed by a constant moving force is considered. The force is moving with a constant velocity on the top beam. The complex system is finite, simply supported, parallel one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a beam‐string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case the aperiodic part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The dynamic influence lines of complex systems may be used for the analysis the complex models of moving load. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Finite generators for countable group actions in the Borel and Baire category settings

For a continuous action of a countable discrete group G on a Polish space X, a countable Borel partition P of X is called a generator if GP:={gP:g∈G,P∈P} generates the Borel σ-algebra of X. For G=Z, the Kolmogorov–Sinai theorem gives a measure-theoretic obstruction to the existence of finite generators: they do not exist in the presence of an invariant probability measure with infinite entropy. It was asked by Benjamin Weiss in the late 1980s whether the nonexistence of any invariant probability measure guarantees the existence of a finite generator. We show that the answer is positive (in fact, there is a 32-generator) for an arbitrary countable group G and σ-compact X (in particular, for locally compact X). We also show that for aperiodic actions there is always a 4-generator on a comeager set, thus giving a positive answer to a question of Alexander Kechris asked the mid-1990s.Furthermore, assuming a positive answer to Weiss's question for arbitrary Polish spaces and G=Z, we prove the following dichotomy: every aperiodic Borel action of Z on a Polish space X admits either an invariant probability measure of infinite entropy or a finite generator. As an auxiliary lemma, we prove the following statement, which may be of independent interest: every aperiodic Borel action of a countable group G on a Polish space X admits a G-equivariant Borel map to the aperiodic part of the shift action G↷2G.We also obtain a number of other related results, among which is a criterion for the nonexistence of non-meager weakly wandering sets for continuous actions of Z. A consequence of this is a negative answer to a question asked by Eigen–Hajian–Nadkarni, which was also independently answered by Benjamin Miller.

A Robust Time-frequency Decomposition Model for Suppression of Mixed Gaussian-impulse Noise in Audio Signals

In this paper, we propose a robust time-frequency decomposition (RTFD) model to restore audio signals degraded by sparse impulse noise mixed with small dense Gaussian noise. This kind of noise is very common especially in old-time recordings. The proposed RTFD model is based on the observation that these degraded audio signals mainly contain four parts, i.e., the quasi-periodic and voiced part, the aperiodic and transient part, the arbitrarily large impulse noise and the small dense Gaussian noise. Sparsity and local correlations of corresponding parts are exploited to solve the RTFD model. We also heuristically develop a discriminative orthogonal matching pursuit (DOMP) algorithm to more precisely estimate sparse representing vectors. Specifically, the DOMP algorithm divides the whole atom set into two subsets, i.e., the active subset and the passive subset. Atoms in two subsets are treated discriminatively since sparsity regularization terms are not equally weighted. Based on RTFD and DOMP, we have developed two algorithms, i.e., the fidelity-oriented algorithm and the articulation-oriented algorithm. The proposed algorithms achieve considerable performance on both synthetic and real noisy signals. Results show that the articulation-oriented algorithm using DOMP obviously outperforms other algorithms in heavier impulse noise situations.

Vibrations of sandwich beam due to a moving force

We study dynamic response of a finite, simply supported sandwich beam subject to a force moving with a constant velocity. The classical solution has a form of an infinite series. The main goal of this paper is to show that the aperiodic part of the solution can be presented in a closed form instead of an infinite series. The presented method of finding the solution in a closed form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The closed solutions take different forms depending if the velocity v of the moving force is smaller or bigger than the shear-wave velocity of the beam. The solution for the dynamic response of the sandwich beam under moving force is important because it can be used also in order to find the solution for other types of moving loads.

Vocal Attractiveness Increases by Averaging

Vocal attractiveness has a profound influence on listeners-a bias known as the "what sounds beautiful is good" vocal attractiveness stereotype [1]-with tangible impact on a voice owner's success at mating, job applications, and/or elections. The prevailing view holds that attractive voices are those that signal desirable attributes in a potential mate [2-4]-e.g., lower pitch in male voices. However, this account does not explain our preferences in more general social contexts in which voices of both genders are evaluated. Here we show that averaging voices via auditory morphing [5] results in more attractive voices, irrespective of the speaker's or listener's gender. Moreover, we show that this phenomenon is largely explained by two independent by-products of averaging: a smoother voice texture (reduced aperiodicities) and a greater similarity in pitch and timbre with the average of all voices (reduced "distance to mean"). These results provide the first evidence for a phenomenon of vocal attractiveness increases by averaging, analogous to a well-established effect of facial averaging [6, 7]. They highlight prototype-based coding [8] as a central feature of voice perception, emphasizing the similarity in the mechanisms of face and voice perception.

Desired Compensation Adaptive Robust Control of a Linear-Motor-Driven Precision Industrial Gantry With Improved Cogging Force Compensation

This paper proposes a new model for cogging forces of linear motor systems. Sinusoidal functions of positions are used to effectively capture the largely periodic nature of cogging forces with respect to position, while B-spline functions are employed to account for the additional aperiodic part of cogging forces. This model is experimentally demonstrated to be able to capture both the periodic and nonperiodic characteristics of cogging force while having a linear parametrization form, which makes the online adaptive compensation of cogging forces possible and effective. A discontinuous-projection-based desired compensation adaptive robust controller (DCARC) is then constructed, which makes full use of the proposed cogging force model for an improved cogging force compensation. Comparative experimental results with various cogging force compensations are obtained on both axes of a linear-motor-driven industrial gantry. The results show that DCARC with the proposed model compensation achieves the best tracking performance among all the three algorithms tested, validating the proposed cogging force model. The excellent tracking performances obtained in the experiments also verify the effectiveness of the proposed ARC control algorithms in practical applications. The proposed model and control algorithm can be applied for other types of motor control systems as well.

Some remarks on aperiodic elements in locally nilpotent groups

In this paper we point out some situations in which one can recognize the local nilpotence of a non-periodic group looking at properties of its aperiodic part. Mathematics Subject Classification: 20F18, 20F19, 20F45 All through this paper, T (G) will denote the set of all periodic elements of a group G. Let G be a non-periodic group, and suppose that T (G) is a subgroup of G. Then G = T (G)∪X, where X is the subgroup generated by all aperiodic elements of G. Therefore G = X since G is non-periodic. This trivial fact is used here in several situations to recognize the local nilpotence of a non- periodic group looking at properties of its aperiodic part. Clearly, the following results make some sense only when the group has both periodic and aperiodic elements. Proposition 1. Let G be a non-periodic group, and let c be any positive in- teger. Then G is nilpotent of class at most c if and only if every aperiodic element of G is contained in Zc(G). Proof. Of course it suffices to prove that T (G) is a subgroup of G, which implies G = T (G) ∪ Zc(G) and G = Zc(G) since G is non-periodic. Suppose not. Hence there exist periodic elements a and b in G with ab aperiodic. Thus ab ∈ Zc(G). Then the subgroup H = � a, ab� = � a, bis nilpotent (of class at most c). Therefore H is finite and ab is periodic, a contradiction.

A novel molecular orbital method for the calculations of polymer systems with local aperiodic part: The combination of the elongation method with the supercell method

In this paper, we propose a new theoretical approach to treat polymer systems with local aperiodic part efficiently. This approach is the combination of the elongation method with the supercell method which has been developed in our group, and we developed this approach to obtain the electronic structure of a polymer having local aperiodicity by considering the locality of the interaction between periodic and local aperiodic parts. In order to confirm the validity of this method, several model calculations were performed at the complete neglect of differential overlap (CNDO/2) level. That is, we applied this method to all-trans polyacetylene interacting with a small molecule, and to all-trans polyacetylene with partial substitution of hydrogen atoms by fluorine atoms. We compared the results obtained by this calculation with those obtained by usual crystal orbital calculation concerning total energy, computational time, and electron density distribution. The charge extension on the polymer chain under the influence of aperiodicity was also discussed.

Oscillation of the water level in a well connected to a confined aquifer

The water in a well, which is connected to a confined aquifer, will oscillate if it is displaced and then released. The motion of the water is composed of a periodic and an aperiodic part. The damping of the periodic part is allways subcritical. The frequency of the periodic part increases with the damping and the inertia of the water in the aquifer. The motion is effectively characterized by two parameters: a non-dimensional transmissivity and the storativity. The inertia of the water in the aquifer has a small influence on the frequency, but negligible influence on the damping.

Decomposition Theorems for Disjointness Preserving Operators

Two different decomposition theorems for disjointness preserving operators on Banach lattices are proved. The first one asserts that a disjointness preserving operator whose spectrum is contained in a sector of angle less than π can be decomposed into a sum of a central operator and a quasi-nilpotent operator. The second one asserts that if T is a disjointness preserving operator on an order complete Banach lattice such that its adjoint T′ is also a disjointness preserving operator, then T can be decomposed into a direct sum of its strictly periodic and aperiodic parts. The latter generalizes an earlier result. Various consequences of these results are given.

The spectrum of quasi-invertible disjointness preserving operators

We study (almost) invertible operators on Banach lattices which take disjoint elements to disjoint elements. We show that these operators may be decomposed into a direct sum of their strictly periodic and aperiodic parts, and then use this result to derive various properties of the spectrum.