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This chapter presents the Laplace transform, which is as fundamental to continuous-time systems as the z-transform is to discrete-time systems. Several properties and examples are presented. Similar to the z-transform, the Laplace transform can be regarded as a generalization of the appropriate Fourier transform. In continuous time, the Laplace transform is very useful in the study of systems represented by linear constant-coefficient differential equations (i.e., rational LTI systems). Frequency responses, resonances, and oscillations in electric circuits (and in mechanical systems) can be studied using the Laplace transform. The application in electrical circuit analysis is demonstrated with the help of an LCR circuit. The inverse Laplace transformation is also discussed, and it is shown that the inverse is unique only when the region of convergence (ROC) of the Laplace transform is specified. Depending on the ROC, the inverse of a given Laplace transform expression may be causal, noncausal, two-sided, bounded, or unbounded. This is very similar to the theory of inverse z-transformation. Because of these similarities, the discussion of the Laplace transform in this chapter is brief.
The paper looks at the question of measuring the importance of shocks to cycles. We consider two types of cycles - oscillations and those summarized by the NBER that require a study of growth in activity to establish turning points in the level of activity. The latter demarcate expansions and contractions. We establish a connection between these two concepts of cycles that shows shocks may have very different effects on each. As an application we look at a question that has often been asked over how important technology shocks are to cycles in activity? Some recent research concludes that total factor productivity (TFP) shocks are not important for oscillations and therefore models should be designed to reflect that. Using the same data we show that TFP shocks are very important to both types of cycles.
Cognitive control deficits are one of the main symptoms of psychosis. The basic neural oscillation patterns associated with cognitive control are already present in early adolescence. However, as previous studies have focused on adults with psychosis, it is unclear whether neurobiological impairments in cognitive control are present in children and adolescents with first-episode psychosis (FEP) or clinical high-risk (CHR) state for psychosis.
Aims
To explore the deficits of electroencephalogram related to cognitive control tasks in children and adolescents with FEP and CHR.
Method
Electroencephalogram was recorded in untreated 48 patients with FEP, 24 patients with CHR and 42 healthy controls aged 10–17 years, while performing the visual oddball task. The N2 amplitude, theta and alpha oscillations were then analysed and compared between groups.
Results
There was no significant group difference in N2 amplitude (P = 0.099). All groups showed increased theta and alpha oscillations relative to baseline before the stimulus in the frontal, central, left fronto-central and right fronto-central areas. These changes differed significantly between groups, with the FEP group showing significantly smaller theta (P < 0.001) and alpha (P < 0.01) oscillation than healthy controls. Theta and alpha oscillations in the CHR group did not differ significantly from the FEP group and healthy controls.
Conclusions
These results suggest that neural damage has already occurred in the early stage of psychosis, and that abnormal rhythmic activity of neurons may constitute the pathophysiological mechanism of cognitive dysfunction related to early-onset psychosis.
An extended catalog of long-periodic terms of the Sun tide-generating potential (STGP ver.2) is released. It contains 2.5 times of such terms than in the first version of the STGP catalog (Cionco et al. 2023). The analysis of the new data is done in order to re-examine the existence of tidal forces of ≈ 11.0-yr and ≈ 22.0-yr period able to excite the observed solar-activity cycles. In several recent studies, such tidal forcings are claimed to be a result of certain combinations of Venus, Earth and Jupiter mean motions with the multipliers (6, −10, 4) and (3, −5, 2), respectively. So, in this contribution, we specifically look for the periodic terms related to these combinations. As a result of these additional investigation we do not confirm any noticeable tidal forcing factors of ≈ 11.0-yr nor ≈ 22.0-yr period in the extended STGP spectrum either.
The architecture of the thalamus and its reciprocal connections with multiple cortical and subcortical structures are essential to the generation of the thalamo-cortical network oscillations associated with attention, sleep, and consciousness. This chapter provides an overview of the cellular mechanisms underlying thalamo-cortical network oscillations occurring during sleep and their contribution to the architecture of the sleep–wake cycle, including the onset and stability of non–rapid eye movement (NREM) and rapid eye movement (REM) sleep. It further summarizes the influence of the brainstem neuromodulatory system on thalamo-cortical network activity during wakefulness and sleep. Finally, the association between these mechanisms and synaptic plasticity in thalamo-cortical networks is described in the context of sleep-dependent consolidation, or weakening, of previously acquired information in health and disease.
This chapter applies a perspective from biophysically grounded computational modeling to explore how the intrinsic properties of thalamic microcircuits support the computational roles that the thalamus plays in perceptual and cognitive functions. A key focus is on the modeling of neurophysiological activity in the thalamus as nonlinear dynamical systems. Dynamical modeling can give insight into thalamic function across levels of analysis, including cellular channel properties, synaptic plasticity, and anatomical connectivity. This chapter reviews how the interplay between cellular and circuit mechanisms supports thalamic contributions to neural oscillations, regulation of brain state, top-down attentional control of sensory processing, and other cognitive functions. Understanding circuit function through biophysically grounded computational modeling and dynamical systems perspectives can also provide insight into how cellular and synaptic alterations caused by pharmacology or disease can impair thalamic function.
In the preceding chapter on rigid-body motion we took a step beyond single-particle mechanics to explore the behavior of a more complex system containing many particles bonded rigidly together. Now we will explore additional sets of many-particle systems in which the individual particles are connected by linear, Hooke’s-law springs. These have some interest in themselves, but more generally they serve as a model for a large number of coupled systems that oscillate harmonically when disturbed from their natural state of equilibrium, such as elastic solids, electric circuits, and multi-atom molecules. We will begin with the oscillations of a few coupled masses and end with the behavior of a continuum of masses described by a linear mass density. The mathematical techniques required to analyze such coupled oscillators are used throughout physics, including linear algebra and matrices, normal modes, eigenvalues and eigenvectors, and Fourier series and Fourier transforms.
Ultra-massive (⩾M⊙) oxygen/neon (ONe) core white dwarfs (WDs) are the result of the evolution of isolated progenitor stars with masses above 6−M⊙. It is expected that hydrogen-rich (DA) ultra-massive WDs harbor crystallized cores at the typical temperatures of the ZZ Ceti instability strip. These stars offer a unique opportunity to study the processes of crystallization and to infer their core chemical composition. We present a study of the evolution and asteroseismology of ultra-massive DA WDs. We found that all pulsating WDs known to date with M⩾1.1M⊙ should have more than 80% of their mass crystallized, if a ONe-core is assumed. Finally, we present a complete asteroseismological analysis to the well known ZZ Ceti BPM 37093 and a preliminary analysis to GD 518 and SDSS J0840+5222.
Asteroseismology of white dwarf stars has led to a number of interesting results pertaining to the long term evolution and present state of white dwarf interiors. I will review recent results and will give a not necessarily comprehensive view of the prospects for further progress in this area. Two – but only two white dwarf stars - have shown the expected cooling as they age. Careful observations of a few white dwarfs with rich pulsational properties reveal interior compositions as well as the thickness of their surface layers. A few very well observed stars have revealed changes in their pulsational spectra which we don’t understand yet.
Convection is a highly turbulent, three dimensional process that is traditionally treated using a simple, local, time independent description. Convection is one of the largest sources of theoretical uncertainty in stellar modeling. We outline recent progress in studies using pulsating white dwarfs to constrain convection and calibrate mixing length theory.
The chapter discusses numerical discretization of first-order quasilinear hyperbolic PDEs, so-called conservation laws. We start by briefly reviewing some of the theory for these equations, including weak solutions, discontinuities, and entropy conditions. We then present a general family of conservative finite-volume methods that includes centered as well as upwind and Godunov-type schemes. We demonstrate typical deficiencies in classical schemes including smearing of discontinuities and creation of nonphysical oscillations. We end the chapter by presenting the implicit, upstream-mobility scheme, which is the most widespread method in reservoir simulation.
Despite the critical role of working memory (WM) in neuropsychiatric conditions, there remains a dearth of available WM-targeted interventions. Gamma and theta oscillations as measured with electroencephalography (EEG) or magnetoencephalography (MEG) reflect the neural underpinnings of WM. The WM processes that fluctuate in conjunction with WM demands are closely correlated with WM test performance, and their EEG signatures are abnormal in several clinical populations. Novel interventions such as transcranial magnetic stimulation (TMS) have been shown to modulate these oscillations and subsequently improve WM performance and clinical symptoms. Systematically identifying pathological WM-related gamma/theta oscillatory patterns with EEG/MEG and developing ways to target them with interventions such as TMS is an active area of clinical research. Results hold promise for enhancing the outcomes of our patients with WM deficits and for moving the field of clinical neuropsychology towards a mechanism-based approach.
Non-smooth approximations of steep sigmoidal switching networks, such as those used as qualitative models of gene regulation, lead to analytic and computational challenges that arise as a result of the discontinuities in the vector fields. In order to highlight the need for care in dealing with such systems, several particular phenomena are presented here through illustrative examples, including ‘Zeno breaking’, or computing beyond the finite time convergence of an infinite sequence of threshold transitions; the ‘Contact’ effect, in which in the discontinuous limit, trajectories can pass through a ‘saddle point’ without stopping, though these solutions are not unique and other solutions stop for arbitrary time intervals; and sensitive behaviour that arises from exotic dynamics within switching regions.
New observations of Kepler δ Scuti stars show that our understanding of pulsation in these stars is incomplete. A large fraction of A and B stars exhibit rotational modulation in light, suggesting that spots exist in stars with radiative envelopes. Flares are seen in some A stars, as may be expected if starspots are present. Differential rotation shear increases from M to F but decreases for A stars; it reaches a maximum among the γ Doradus variables. Current views of stars with radiative envelopes may need to be reviewed in the light of these observations.
Following the LAMOST Spectroscopic Survey and Xuyi's Photometric Survey of the Galactic anti-center (GAC), we plan to conduct a time-domain survey of GAC to study the variable sky using Nanshan 1m telescope. The survey will be conducted during winter (in Nov., Dec., and Jan.). The first goal of the survey is to cover 270 sq.deg. of sky area in three years. The survey intends to detect some strong transient events of stars and find some short time-scale variable stars of different types. In this paper, we introduce the survey and present the preliminary results already carried out.
Two cases of filament oscillations induced by large-scale coronal shock waves are presented. For the first case, a chain of transverse oscillating filaments are observed in a proper order after the passing of a shock wave, and it is found that the they were triggered by the surface component of the dome-shaped shock wave. For the second case, simultaneous transverse oscillation of a limb prominence and longitudinal oscillation in an on-disk filament are launched by a single shock wave. It is found that the interaction angle between the shock wave and the prominence axis is the key to launch transverse or longitudinal filament oscillations. In addition, filament magnetic fields are estimated, using the measured parameters.
We present a brief progress report in our quest for deriving seismic models of pulsating white dwarfs that can account simultaneously for all the observed periods at the precision of the observations. We point out that this is possible from a pratical point of view only if parametrized models are used to complement evolutionary models. We adopt a double optimization procedure that insures that the best possible model in parameter space is found objectively and automatically. Our ultimate goal is to be able to account for the exquisite period data gathered with Kepler and Kepler-2 on key pulsating white dwarfs of both the DA (ZZ Ceti) and DB (V777 Her) type.
Coronal quasi-periodic fast-propagating (QFP) magnetosonic waves are scare in previous studies due to the relative low temporal and spatial resolution of past telescopes. Recently, they are detected by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Here, two cases of QFP waves are presented. The analysis results indicate that QFP waves are tightly associated with the associated flares. It is indicate that QFP waves and the associated flares are possibly driven by the same physic process such as quasi-periodic magnetic reconnection process in producing flares.
Triple supermassive black holes (SMBH) can form during the hierarchical mergers of massive galaxies with an existing binary. Perturbations by a third black hole may accelerate the merging process of an inner binary, for example through the Kozai mechanism. We analyze the evolution of simulated hierarchical triple SMBHs in galactic centers, and find resonances in the evolution of the semi-major axis, the eccentricity and the inclination, for both the inner and the outer orbits of the triple system, which are not only Kozai like. Through resonant oscillations, SMBH can trigger a significant increase of the inner SMBH binary eccentricity shortening the merger timescale expected from gravitational wave (GW) emission. As hierarchical triple SMBHs may be frequent in massive galaxies, the influence of orbital resonances is of great importance to our understanding of black hole coalescence and gravitational wave detection. Although Kozai mechanism is believed to play an important role in this process, detailed studies on the pattern of these resonances is necessary.
Be stars are B-type stars near the main sequence which undergo episodic mass loss events detected by emission lines, whose line shape and intensity vary with a timescale of the order of decades. Spectroscopic observations show a large rotation velocity such that one of the prevailing scenarios for the formation of the equatorial disk consists in an increasing equatorial rotation velocity to the break-up limit where gravity is challenged by the centrifugal force. We investigate here a new scenario recently suggested by Ishimatsu & Shibahashi (2013), in which the transport of angular momentum through the photosphere would be achieved by leaky waves, keeping the rotation velocity still below the break-up limit.