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Background: We previously found that vagus nerve stimulation (VNS) strengthened stimulus-evoked activity in the superficial layer of the sensory cortex but not in the deep layer, suggesting that VNS altered the balance between the feedforward (FF) and feedback (FB) pathways. Band-specific oscillatory activities in the cortex could serve as an index of the FF-FB balance, but whether VNS affects cortical oscillations along sensory pathways through neuromodulators remains unclear. Hypothesis: VNS modulates the FF-FB balance through the cholinergic and noradrenergic systems, which modulate stimulus gain in the cortex. Methods: We investigated the effects of VNS using electrocorticography in the auditory cortex of 34 Wistar rats under general anesthesia while presenting click stimuli. In the time-frequency analyses, the putative modulation of the FF and FB pathways was estimated using high- and low-frequency power. We assessed, using analysis of variance, how VNS modulates auditory-evoked activities and how the modulation changes with cholinergic and noradrenergic antagonists. Results: VNS increased auditory cortical evoked potentials, consistent with results of our previous work. Furthermore, VNS increased auditory-evoked gamma and beta powers and decreased theta power. Local administration of cholinergic antagonists in the auditory cortex selectively disrupted the VNS-induced increase in gamma and beta power, while noradrenergic antagonists disrupted the decrease in theta power. Conclusions: VNS might strengthen the FF pathway through the cholinergic system and attenuate the FB pathway through the noradrenergic system in the auditory cortex. Cortical gain modulation through the VNS-induced neuromodulatory system provides new mechanistic insights into the effect of VNS on auditory processing.

Numerical Study on Vortices in Collision of Flow with Circular, Square, Triangular, and Pentagonal Barriers of Different DiametersStructures constructed on rivers induce downstream oscillating vortices. These vortices apply oscillating loads on the structure and harm its stability. This paper carried out numerical simulations in SOLIDWORKS to explore the effects of the barrier shape and size on the load applied by the vortex on structures constructed in water streams. It was found that a reduction in the barrier size diminished the vortices. The highest Strouhal number was calculated to be 5.2 at a Reynolds number of 5000 and a barrier diameter of 0.09. The maximum downstream vortices were induced by the triangular barrier, and the maximum Strouhal number occurred to be 7.8 at a velocity of 0.4 and a barrier diameter of 0.05. The maximum vortices induced by the square barrier occurred at a barrier diameter of 0.05. Keywords: Strouhal number, Reynolds number, Barrier, Physical model, Oscillation

In this paper, we study various types of exponents of oscillation (upper or lower, strong or weak) of non-strict signs, zeros, and roots of non-zero solutions of linear homogeneous differential equations of the third order with continuous and bounded coefficients on the positive semi-axis. A nonzero solution of a linear homogeneous equation cannot be zeroed due to the existence and uniqueness theorem. Therefore, the spectra of all the listed exponents of oscillation (i.e. their sets of values on nonzero solutions) consist of one zero value. In addition, it is known that the spectra of the oscillation exponents of linear homogeneous equations of the second order also consist of a single value. Consequently, on the set of solutions of equations up to the second order there is a residual of all exponents of oscillation. On the set of solutions of third-order equations, strong exponents vibrations of hyper roots are not residual, i.e. are not invariant with respect to the change in the solution at any finite section of the half-axis of time. In this article, it is proved that on the set of solutions of third-order equations, strong oscillation indices of non-strict signs, zeros, and roots are not residual. In parallel, the existence of a function from the specified set with the following properties is proved: all listed exponents of oscillation are accurate, but not absolute. At the same time, all strong exponents like all weak ones, are equal to each other.

In this paper, we offer new technique for investigation of the even order linear differential equations of the form \begin{equation*}\label{E} y^{(n)}(t)=p(t)y(\tau(t)). \tag{$E$} \end{equation*} We establish new criteria for bounded and unbounded oscillation of \eqref{E} which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicities for the positive solutions of \eqref{E} than those presented in known works. We illustrate the improvement over known results by applying and comparing our technique with the other known methods on the particular examples.

Abstract We use an improved technique to establish new sufficient criteria of product type for the oscillation of the delay differential equation x ′ ( t ) + ∑ l = 1 m b l ( t ) x ( σ l ( t ) ) = 0 , t ≥ t 0 , $$\begin{aligned} x'(t)+\sum_{l=1}^{m} b_{l}(t)x\bigl(\sigma _{l}(t)\bigr)= 0,\quad t\geq t_{0}, \end{aligned}$$ with b l , σ l ∈ C ( [ t 0 , ∞ ) , [ 0 , ∞ ) ) $b_{l},\sigma _{l}\in C([t_{0},\infty ),[0,\infty ))$ such that σ l ( t ) ≤ t $\sigma _{l}(t)\leq t$ and lim t → ∞ σ l ( t ) = ∞ $\lim_{t \rightarrow \infty} \sigma _{l}(t)=\infty $ , l = 1 , 2 , … , m $l=1,2,\ldots,m$ . The obtained results are applicable for the nonmonotone delay case. Their strength is supported by a detailed practical example.

Abstract The distance between consecutive zeros of a first-order differential equation with several variable delays is studied. Here, we show that the distribution of zeros of differential equations with variable delays is not an easy extension of the case of constant delays. We obtain new upper bounds for the distance between zeros of all solutions of a differential equation with several delays, which extend and improve some existing results. Two illustrative examples are given to show the advantages of the proposed results over the known ones.

In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇α+1χ(κ)⋅∇αχ(κ)−p(κ)г(∇αχ(κ))+q(κ)G∑μ=κ−α+1∞(μ−κ−1)(−α)χ(μ)=0,{\nabla }^{\alpha +1}\chi \left(\kappa )\cdot {\nabla }^{\alpha }\chi \left(\kappa )-p\left(\kappa )г\left({\nabla }^{\alpha }\chi \left(\kappa ))+q\left(\kappa ){\mathcal{G}}\left(\mathop{\sum }\limits_{\mu =\kappa -\alpha +1}^{\infty }{\left(\mu -\kappa -1)}^{\left(-\alpha )}\chi \left(\mu )\right)=0, where κ∈N0\kappa \in {{\mathbb{N}}}_{0}, ∇α{\nabla }^{\alpha } denotes the Liouville fractional difference operator of order α∈(0,1)\alpha \in \left(0,1), pp, and qq are nonnegative sequences, and гг and G{\mathcal{G}} are real valued continuous functions, all of which satisfy certain assumptions. Using the generalized Riccati transformation technique, mathematical inequalities, and comparison results, we have found a number of new oscillation results. A few examples have been built up in this context to illustrate the main findings. The conclusion of this study is regarded as an expansion of continuous time to discrete time in fractional contexts.

A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.

The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for testing whether the studied equation exhibits oscillatory behavior or converges to zero. Our results contribute uniquely to oscillation theory by presenting some theorems that improve and expand upon the results found in the existing literature. We also provide an example to corroborate the validity of our proposed criteria.

In this paper, a survey of the most interesting conditions for the oscillation of all solutions to first-order linear differential equations with a retarded argument is presented in chronological order, especially in the case when well-known oscillation conditions are not satisfied. The essential improvement and the importance of these oscillation conditions is also indicated.

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.

In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend the range of the neutral coefficient. Therefore, our results generalize to some of the results presented in the literature. Furthermore, several examples are provided to illustrate our conclusions.

Due to the influence of parasitic internal parameters and junction capacitance, the silicon carbide (SiC) power devices are frequently marred by significant overshoots in current and voltage, as well as high-frequency oscillations during the switching process. These phenomena can severely compromise the reliability of SiC-based power electronic converters during operation. This study delves into the switching transient of the SiC MOSFET with the goal of establishing a quantitative correlation between the gate driving current and the overshoot in both the drain-source voltage and the drain current. In light of these findings, the innovative active gate drive (AGD) circuit, which features an adjustable gate current, is introduced. Throughout the switching process, the AGD circuit employs a dynamic monitoring and feedback mechanism that is responsive to the gate voltage and rate of change in the drain-source voltage and drain current of the SiC MOSFET. This adjustment enables gate driving current to be actively modified, thereby effectively mitigating the occurrence of overshoots and oscillations. To empirically validate the efficacy of the proposed AGD circuit in curbing voltage and current overshoots and oscillations, a double-pulse experimental setup was meticulously constructed and tested.

This paper focuses on establishing new criteria to guarantee the oscillation of solutions for second-order differential equations with a superlinear and a damping term. New sufficient conditions are presented, aimed at analysing the oscillatory properties of the solutions to the equation under study. To prove these results, we employed various analysis methods, establishing new relationships to address certain problems that have hindered previous research. Consequently, by applying the principles of comparison and the Riccati transformation, we obtained findings that develop and complement those reported in earlier literature. The significance of our results is illustrated with several examples.

Phase change material (PCM) based thermal energy storage (TES) is an important solution to the waste of heat and intermittency of new energy sources. However, the thermal conductivity of most PCMs is low, which severely affects the thermal energy storage performance. Oscillation of the tube bundles in a TES unit can intensify the convection of liquid PCM and, therefore, enhance heat transfer. However, the energy storage performance of bundled-tube TES systems in response to oscillation at different amplitudes and frequencies has not been well understood yet, and the optimum time to apply the oscillation during phase transition remains unexplored. To address this issue, this present study was carried out. First, the melting behaviour of PCM with oscillation starting at different times was investigated. Then, the influences of oscillation frequency and amplitude on the melting performance were explored. Finally, the solidification behaviour of PCM with oscillation starting at different times was examined. Results show that the oscillation can accelerate the phase transition process by enhancing convective heat transfer. Compared to the case without oscillation, the complete melting and solidification times are reduced by 8.2 and 6.7% for the case with oscillation starting at 200 s, respectively. The effect of oscillation frequency on the melting enhancement is negligible, while the oscillation amplitude has an important effect on the melting enhancement.

In this paper, we discuss the oscillatory behavior of solutions of two general classes of nonlinear second-order differential equations. New criteria are obtained using Riccati transformations and the integral averaging techniques. The obtained results improve and generalize some recent criteria in the literature. Moreover, a traditional condition is relaxed. Three examples are given to justify the results.

The purpose of this paper is to study the oscillatory properties of solutions to a class of delay differential equations of even order. We focus on criteria that exclude decreasing positive solutions. As in this paper, this type of solution emerges when considering the noncanonical case of even equations. By finding a better estimate of the ratio between the Kneser solution with and without delay, we obtain new constraints that ensure that all solutions to the considered equation oscillate. The new findings improve some previous findings in the literature.

Abstract In the era of precision measurements of the neutrino oscillation parameters, upcoming neutrino experiments will also be sensitive to physics beyond the Standard Model. KM3NeT/ORCA is a neutrino detector optimised for measuring atmospheric neutrinos from a few GeV to around 100 GeV. In this paper, the sensitivity of the KM3NeT/ORCA detector to neutrino decay has been explored. A three-flavour neutrino oscillation scenario, where the third neutrino mass state ν 3 decays into an invisible state, e.g. a sterile neutrino, is considered. We find that KM3NeT/ORCA would be sensitive to invisible neutrino decays with 1/α 3 = τ 3 /m 3 < 180 ps/eV at 90% confidence level, assuming true normal ordering. Finally, the impact of neutrino decay on the precision of KM3NeT/ORCA measurements for θ 23, Δ m 31 2 $$ \Delta {m}_{31}^2 $$ and mass ordering have been studied. No significant effect of neutrino decay on the sensitivity to these measurements has been found.

We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D_3y(n)+f(n)y^\beta(\sigma(n))=0, where $D_3 y(n)=\Delta(b(n)\Delta(a(n)(\Delta y(n))^\alpha))$ is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results.

The paper focuses on two literary periods located at opposite ends of the twentieth century and examines the relationship between utopian ideas of Victorian fin de siècle and the re-emergence of utopian desires within a metamodernist context. The two periods discussed, while separated by a century of what is typically understood as progress, are both permeated by impending change and in dire need of alternatives to their respective forms of capitalism, making the appearance of utopian discourse almost inevitable. While their understanding of utopia certainly differs in many aspects, I will argue that they both recognize its oscillatory potential and neither focuses on bare facilitation of escapism or provision of blueprints, instead consciously employing hope-based utopian impulses as a method and a process by means of which various alternatives can be continuously investigated.

I propose that there exists in natural and artificial environments a class of resonant oscillations that can be excited directly by a steady, zero-frequency force such as that of wind, water, electric field. A member of this class comprises two normally independent oscillating modes of a system, for example, a building or bridge, which, separately, cannot be driven by a zero-frequency force. Agreeing on terms of collaboration, the two modes engage in a joint oscillation powered by the steady zero-frequency force in which they drive each other, one directly and the other parametrically. I observed a bimodal vibration belonging to this class in a home shower where the two modes are the pendulum excursion and the torsional twisting of a freely suspended showerhead which break into a joint oscillation above a threshold value of the water flow rate. I advance a theoretical model which predicts and explains the main features of the observations. The model constitutes an extension to two modes of a proposal and demonstration in 1883 by Lord Rayleigh and Michael Faraday for the excitation of a single resonant mode by modulating a system parameter at twice the resonance frequency. The proposal is credited with the launching of parametric physics. The Experiments section of this report consists of three linked video clips photographed in the home shower which support the basic theoretical assumptions. The ubiquity of zero-frequency forces, such as that of wind, and their direct conversion to alternating on-resonance system vibrations endows the class with an amplified destructive potential with implications for structural stability. [ABSTRACT FROM AUTHOR]

Alpha rhythmic activity is often suggested to exert an inhibitory influence on information processing. However, relatively little is known about how reported alpha-related effects are influenced by a potential confounding element of the neural signal, power-law scaling. In the current study, we systematically examine the effect of accounting for 1/f activity on the relation between prestimulus alpha power and human behavior during both auditory and visual detection (N 5 27; 19 female, 6 male, 2 nonbinary). The results suggest that, at least in the scalp-recorded EEG signal, the difference in alpha power often reported before visual hits versus misses is probably best thought of as a combination of narrowband alpha and broadband shifts. That is, changes in broadband parameters (exponent and offset of 1/f-like activity) also appear to be strong predictors of the subsequent awareness of visual stimuli. Neither changes in posterior alpha power nor changes in 1/f-like activity reliably predicted detection of auditory stimuli. These results appear consistent with suggestions that broadband changes in the scalp-recorded EEG signal may account for a portion of prior results linking alpha band dynamics to visuospatial attention and behavior, and suggest that systematic re-examination of existing data may be warranted. [ABSTRACT FROM AUTHOR]

In this paper, we study various types of oscillation exponents for solutions of linear homogeneous differential systems with continuous bounded coefficients. The calculation of the oscillation exponents is carried out by averaging the number of zeros (signs, roots, or hyperroots) of the projection of a solution 푥 of a differential system onto any straight line, and this line is chosen so that the resulting average value is minimal: if the minimization is performed before (after) the averaging, then weak (strong, respectively) oscillation exponents are obtained. In the calculation of the oscillation exponents for a solution 푦 of a linear homogeneous 푛 th-order differential equation, a transition to the vector function 푥 푦 ˙ 푦 ... superscript 푦 푛 1 is carried out. In the first part of the paper, for any preassigned positive integer 푁 , a two-dimensional periodic linear differential system is constructed, which has the property that its spectra of all upper and lower strong and weak oscillation exponents of strict and nonstrict signs, zeros, roots, and hyperroots contain the same set consisting of 푁 different essential values, both metrically and topologically. Moreover, all these values are implemented on the same set of solutions of the constructed system; that is, for each solution from this set, all the oscillation exponents coincide with each other. In the second part of the paper, a similar theorem on the existence of a two-dimensional differential system with a countable set of essential (both metrically and topologically) values of oscillation exponents is proved. In constructing the mentioned systems and proving the required results, we use analytical methods of the qualitative theory of differential equations and methods of the theory of perturbations of solutions of linear differential systems, in particular, the author's technique for controlling the fundamental matrix of solutions of such systems in one special case. [ABSTRACT FROM AUTHOR]

Cognitive and behavioral processes are often accompanied by changes within well-defined frequency bands of the local field potential (LFP i.e., the voltage induced by neuronal activity). These changes are detectable in the frequency domain using the Fourier transform and are often interpreted as neuronal oscillations. However, aside some well-known exceptions, the processes underlying such changes are difficult to track in time, making their oscillatory nature hard to verify. In addition, many non-periodic neural processes can also have spectra that emphasize specific frequencies. Thus, the notion that spectral changes reflect oscillations is likely too restrictive. In this study, we use a simple yet versatile framework to understand the frequency spectra of neural recordings. Using simulations, we derive the Fourier spectra of periodic, quasi-periodic and non-periodic neural processes having diverse waveforms, illustrating how these attributes shape their spectral signatures. We then show how neural processes sum their energy in the local field potential in simulated and real-world recording scenarios. We find that the spectral power of neural processes is essentially determined by two aspects: (1) the distribution of neural events in time and (2) the waveform of the voltage induced by single neural events. Taken together, this work guides the interpretation of the Fourier spectrum of neural recordings and indicates that power increases in specific frequency bands do not necessarily reflect periodic neural activity. [ABSTRACT FROM AUTHOR]

Background: It is well known that motor features of Parkinson’s disease (PD) commonly begin on one side of the body and extend to the other side with disease progression. The onset side generally remains more severely affected over the course of the disease. However, the pathophysiology underlying the asymmetry of motor manifestations remains unclear. The purpose of the present study is to examine whether alterations in neuronal activity in the subthalamic nucleus (STN) associate with PD severity. Methods: Microelectrode recording was performed in the STN during targeting for 30 patients in the treatment of deep brain stimulation. The mean spontaneous firing rate (MSFR), power density spectral analysis, and correlations were calculated. Characteristics of subthalamic oscillatory activity were compared between two hemispheres. UPDRS III scores during “Off” and “On” states were obtained for the body side of initial symptoms (BSIS) and the body side of extended symptoms (BSES). Results: There were significant differences of MSFR (41.3 ± 11.0 Hz vs 35.2 ± 10.0 Hz) and percentage of ß frequency oscillatory neurons (51.3% vs 34.9%) between BSIS and BSES. The percentage of ß frequency oscillatory neurons correlated with the bradykinesia/rigidity scores for both sides (p < 0.05). In contrast, the percentage of tremor frequency oscillatory neurons was significantly higher in the BSES than that in the BSIS. In particular, these neurons only correlated with the tremor scores of the BSES (p < 0.05). Conclusion: The results suggest that increased neuronal firing rate and ß frequency oscillatory neurons in the STN are associated with contralateral side motor severity and its progression. Tremor frequency oscillatory neurons are less observed in the STN of the BSIS suggesting that ß oscillatory activity dominates and tremor frequency oscillatory activity reciprocally declines. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Long-baseline neutrino oscillation experiments, which are among the largest neutrino experiments in the world, have extensive physics programs to make precision measurements of three-flavor oscillation parameters, search for physics beyond the Standard Model, and study neutrinos from astrophysical sources. In this article, experimental considerations, including oscillation phenomenology, detector and experiment design, and analysis strategies, are described, with a focus on the three-flavor oscillation measurements. Current and future experiments are discussed, and significant sources of systematic uncertainty, along with mitigation strategies, are emphasized as control of systematic uncertainty is critical for success in precise measurement of long-baseline oscillation parameters. This article is structured as a primer for those new to this area of experimental work. [ABSTRACT FROM AUTHOR]

We investigate the oscillation of the fourth-order differential equation for a class of functional differential equations of the neutral type. We obtain a new single-oscillation criterion for the oscillation of all the solutions of our equation. We establish new monotonic properties for some cases of positive solutions of the studied equation. Moreover, we improve these properties by using an iterative method. This development of monotonic properties contributes to obtaining new and more efficient criteria for verifying the oscillation of the equation. The results obtained extend and improve previous findings in the literature by using an Euler-type equation as an example. The importance of the results was clarified by applying them to some special cases of the studied equation. The fourth-order delay differential equations have great practical importance due to their wide applications in civil, mechanical, and aeronautical engineering. Research on this type of equation is still ongoing due to its remarkable importance in many fields. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the oscillatory behavior of solutions of second-order differential equations with a superlinear neutral term and a damping term in noncanonical forms. We do not place any additional conditions on the damping term. Therefore, our results apply to new classes of equations that were not covered by the previous criteria. According to symmetry between the negative and positive solutions of the studied equation, we present some new criteria that ensure the oscillation of all solutions by using the Riccati transformation and comparison method. We provide an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

We previously found that vagus nerve stimulation (VNS) strengthened stimulus-evoked activity in the superficial layer of the sensory cortex but not in the deep layer, suggesting that VNS altered the balance between the feedforward (FF) and feedback (FB) pathways. Band-specific oscillatory activities in the cortex could serve as an index of the FF-FB balance, but whether VNS affects cortical oscillations along sensory pathways through neuromodulators remains unclear. VNS modulates the FF-FB balance through the cholinergic and noradrenergic systems, which modulate stimulus gain in the cortex. We investigated the effects of VNS using electrocorticography in the auditory cortex of 34 Wistar rats under general anesthesia while presenting click stimuli. In the time-frequency analyses, the putative modulation of the FF and FB pathways was estimated using high- and low-frequency power. We assessed, using analysis of variance, how VNS modulates auditory-evoked activities and how the modulation changes with cholinergic and noradrenergic antagonists. VNS increased auditory cortical evoked potentials, consistent with results of our previous work. Furthermore, VNS increased auditory-evoked gamma and beta powers and decreased theta power. Local administration of cholinergic antagonists in the auditory cortex selectively disrupted the VNS-induced increase in gamma and beta power, while noradrenergic antagonists disrupted the decrease in theta power. VNS might strengthen the FF pathway through the cholinergic system and attenuate the FB pathway through the noradrenergic system in the auditory cortex. Cortical gain modulation through the VNS-induced neuromodulatory system provides new mechanistic insights into the effect of VNS on auditory processing. • Auditory-evoked responses are modulated by vagus nerve stimulation (VNS). • VNS increases auditory-evoked gamma and beta powers through the cholinergic system. • VNS decreases auditory-evoked theta power through the noradrenergic system. • VNS possibly modulates the balance of feedforward-feedback pathways in the neocortex. [ABSTRACT FROM AUTHOR]

Structures constructed on rivers induce downstream oscillating vortices. These vortices apply oscillating loads on the structure and harm its stability. This paper carried out numerical simulations in SOLIDWORKS to explore the effects of the barrier shape and size on the load applied by the vortex on structures constructed in water streams. It was found that a reduction in the barrier size diminished the vortices. The highest Strouhal number was calculated to be 5.2 at a Reynolds number of 5000 and a barrier diameter of 0.09. The maximum downstream vortices were induced by the triangular barrier, and the maximum Strouhal number occurred to be 7.8 at a velocity of 0.4 and a barrier diameter of 0.05. The maximum vortices induced by the square barrier occurred at a barrier diameter of 0.05. [ABSTRACT FROM AUTHOR]

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type. [ABSTRACT FROM AUTHOR]

The characteristics of local surface wind are closely related to the assessment of wind power resources and the oscillation period of offshore wind turbines. In this research, we analyzed near-surface wind observation data from the southern coast of Sri Lanka, comparing the surface wind variation characteristics across different seasons. Through spectral analysis, we discuss the wind stability and oscillation period, aiming to provide information for the management strategies and oscillation issues of offshore wind turbines in the North Equatorial Indian Ocean to ensure their stable operation. Our findings showed that the Indian summer monsoon dominated the seasonal surface wind variation in the southern coast of Sri Lanka. The local monsoon period began in mid-May and ended in mid-October, during which stable southwest winds prevailed with an average maximum 10 m wind speed exceeding 6.0 m/s. In contrast, surface wind was unstable and weaker during autumn and winter. The surface wind speed exhibited a clear diurnal oscillation throughout the year. The wind speed power spectral density exhibited clear peaks at periods of 24 h, 12 h, and 6 h. [ABSTRACT FROM AUTHOR]

In the paper, we present some new oscillation results for the second order nonlinear delay dynamic equation of the form r (θ) (z Δ (θ)) α Δ + q (θ) z ν (ω (θ)) = 0 for θ ∈ T 0 = [ θ 0 , ∞) ∩ T. We derive new monotonic properties of the nonoscillatory solutions and utilizing them to linearize the considered equation. The presented results are verified by some illustrative examples. [ABSTRACT FROM AUTHOR]

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β‐cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re‐thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory (‘pacemaking’) mechanisms at the cellular, tissue and system levels. [ABSTRACT FROM AUTHOR]

The distance between consecutive zeros of a first-order differential equation with several variable delays is studied. Here, we show that the distribution of zeros of differential equations with variable delays is not an easy extension of the case of constant delays. We obtain new upper bounds for the distance between zeros of all solutions of a differential equation with several delays, which extend and improve some existing results. Two illustrative examples are given to show the advantages of the proposed results over the known ones. [ABSTRACT FROM AUTHOR]

We use an improved technique to establish new sufficient criteria of product type for the oscillation of the delay differential equation x ′ (t) + ∑ l = 1 m b l (t) x (σ l (t)) = 0 , t ≥ t 0 , with b l , σ l ∈ C ([ t 0 , ∞) , [ 0 , ∞)) such that σ l (t) ≤ t and lim t → ∞ σ l (t) = ∞ , l = 1 , 2 , ... , m . The obtained results are applicable for the nonmonotone delay case. Their strength is supported by a detailed practical example. [ABSTRACT FROM AUTHOR]

This research leads with the analysis of a structural joint. Different arrays of steel sheets were joined using bolts. The structures were built in a metallic box filled with Granitic 0/3 sand. This box was used as a rigid body to transmit impacts and the sand as a medium to interact between the body and the structure. Then, an optical set-up was placed to measure the interaction of the impact along the different arrays. Measurements were made 5 cm before and 5 cm after the bolt. Results were analyzed by performing signal filtering and approaching a mathematical solution revealing that impact interaction can be harmonic or damped oscillations with more than 98 % accuracy. [ABSTRACT FROM AUTHOR]

During early development, brains undergo profound changes in structure at the molecular, synaptic, cellular and circuit level. At the same time, brains need to perform adaptive function. How do structurally immature brains process information? How do brains perform stable and reliable function despite massive changes in structure? The rodent olfactory system presents an ideal model for approaching these poorly understood questions. Rodents are born deaf and blind, and rely completely on their sense of smell to acquire resources essential for survival during the first 2 weeks of life, such as food and warmth. Here, we review decades of work mapping structural changes in olfactory circuits during early development, as well as more recent studies performing in vivo electrophysiological recordings to characterize functional activity patterns generated by these circuits. The findings demonstrate that neonatal olfactory processing relies on an interacting network of brain areas including the olfactory bulb and piriform cortex. Circuits in these brain regions exhibit varying degrees of structural maturity in neonatal animals. However, despite substantial ongoing structural maturation of circuit elements, the neonatal olfactory system produces dynamic network-level activity patterns that are highly stable over protracted periods during development. We discuss how these findings inform future work aimed at elucidating the circuit-level mechanisms underlying information processing in the neonatal olfactory system, how they support unique neonatal behaviors, and how they transition between developmental stages. [ABSTRACT FROM AUTHOR]

ESSnuSB is a design study for an experiment to measure the CP violation in the leptonic sector at the second neutrino oscillation maximum using a neutrino beam driven by the uniquely powerful ESS linear accelerator. The reduced impact of systematic errors on sensitivity at the second maximum allows for a very precise measurement of the CP violating parameter. This review describes the fundamental advantages of measurement at the second maximum, the necessary upgrades to the ESS linac in order to produce a neutrino beam, the near and far detector complexes, and the expected physics reach of the proposed ESSnuSB experiment, concluding with the near future developments aimed at the project realization. [ABSTRACT FROM AUTHOR]

In this paper new oscillatory criteria for odd order linear functional differential equations of the type y (n) (t) + p (t) y (τ (t)) = 0 have been established. Deviating argument τ(t) is supposed to have dominating delay part. [ABSTRACT FROM AUTHOR]

During spatial exploration, neural circuits in the hippocampus store memories of sequences of sensory events encountered in the environment. When sensory information is absent during 'offline' resting periods, brief neuronal population bursts can 'replay' sequences of activity that resemble bouts of sensory experience. These sequences can occur in either forward or reverse order, and can even include spatial trajectories that have not been experienced, but are consistent with the topology of the environment. The neural circuit mechanisms underlying this variable and flexible sequence generation are unknown. Here we demonstrate in a recurrent spiking network model of hippocampal area CA3 that experimental constraints on network dynamics such as population sparsity, stimulus selectivity, rhythmicity and spike rate adaptation, as well as associative synaptic connectivity, enable additional emergent properties, including variable offline memory replay. In an online stimulus‐driven state, we observed the emergence of neuronal sequences that swept from representations of past to future stimuli on the timescale of the theta rhythm. In an offline state driven only by noise, the network generated both forward and reverse neuronal sequences, and recapitulated the experimental observation that offline memory replay events tend to include salient locations like the site of a reward. These results demonstrate that biological constraints on the dynamics of recurrent neural circuits are sufficient to enable memories of sensory events stored in the strengths of synaptic connections to be flexibly read out during rest and sleep, which is thought to be important for memory consolidation and planning of future behaviour. Key points: A recurrent spiking network model of hippocampal area CA3 was optimized to recapitulate experimentally observed network dynamics during simulated spatial exploration.During simulated offline rest, the network exhibited the emergent property of generating flexible forward, reverse and mixed direction memory replay events.Network perturbations and analysis of model diversity and degeneracy identified associative synaptic connectivity and key features of network dynamics as important for offline sequence generation.Network simulations demonstrate that population over‐representation of salient positions like the site of reward results in biased memory replay. [ABSTRACT FROM AUTHOR]

In this paper, we characterize a new second-order Hardy-type inequality and find a two-sided estimate for its least constant. As applications of this new inequality, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. [ABSTRACT FROM AUTHOR]

In this paper, we aim to contribute to the increasing interest on the study of neutral differential equations by obtaining some new oscillation results for second-order forced functional differential equations involving superlinear neutral terms. The results presented here do not been covered by previous existing ones, and they are new even for the linear neutral function. The applicability of the results is illustrated with several examples. [ABSTRACT FROM AUTHOR]

This study purposes to present some new sufficient conditions for the oscillation of all solutions to a second order noncanonical Emden-Fowler differential equation with mixed neutral term i.e., the neutral term contains both retarded and advanced arguments. The obtained results show that different definitions of neutral term can cause or destroy oscillatory properties of the solutions. This impact of the deviating arguments on the oscillatory behavior is illustrated with examples in which equations including unbounded neutral coefficients. [ABSTRACT FROM AUTHOR]

Introduction: Psychosis is in part defined by disturbances in perception. Recent investigations have implicated the speed of alpha oscillations observed in brain electrical activity as reflective of a sampling rate of the visual environment and perception. Although both slowed alpha oscillations and aberrant percept formation are evident in disorders of psychotic psychopathology such as schizophrenia it is unclear whether slow alpha accounts for abnormal visual perception in these disorders. Methods: To examine the role of the speed of alpha oscillations in perception in psychotic psychopathology we gathered resting-state magneto-encephalography data from probands with psychotic psychopathology (i.e., schizophrenia, schizoaffective disorder, and bipolar disorder with a history of psychosis), their biological siblings, and healthy controls. We appraised visual perceptual function without the confound of cognitive ability and effort through the use of a simple binocular rivalry task. Results: We found a slowed pace of alpha oscillations in psychotic psychopathology that was associated with longer percept durations during binocular rivalry, consistent with the assertion that occipital alpha oscillations govern the rate of accumulation of visual information used to generate percepts. Alpha speed varied widely across individuals with psychotic psychopathology and was highly stable across several months indicating that it is likely a trait characteristic of neural function that is relevant to visual perception. Finally, a lower speed of alpha oscillation was associated with a lower IQ and greater disorder symptomatology implying that the effects of the endogenous neural oscillation on visual perception may have wider consequences for everyday functioning. Discussion: Slowed alpha oscillations in individuals with psychotic psychopathology appear to reflect altered neural functions related to percept formation. [ABSTRACT FROM AUTHOR]

Parkinson's disease (PD) is one of the leading neurodegenerative disorders. It is considered a movement disorder, although it is accepted that many nonmotor symptoms accompany the classic motor symptoms. PD exhibits heterogeneous and overlaying clinical symptoms, and the overlap of motor and nonmotor symptoms complicates the clinical diagnosis and management. Loss of modulation secondary to the absence of dopamine due to degeneration of the substantia nigra compacta produces changes in firing rates and patterns, oscillatory activity, and higher interneuronal synchronization in the basal ganglia–thalamus–cortex and nigrovagal network involvement in motor and nonmotor symptoms. These neurophysiological changes can be monitored by electrophysiological assessment. The purpose of this review was to summarize the results of neurophysiological changes, especially in the network oscillation in the beta-band level associated with parkinsonism, and to discuss the use of these methods to optimize the diagnosis and management of PD. [ABSTRACT FROM AUTHOR]

This paper deals with obtaining some sufficient conditions for oscillation of high-order neutral fractional integro-differential equations. The obtained results are mentioned for the first time in the literature for the oscillation of Caputo–Fabrizio fractional integro-differential equations. Finally, some illustrative examples are given to verify our main results. [ABSTRACT FROM AUTHOR]

We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or ∞. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works. [ABSTRACT FROM AUTHOR]