Analytical Explanation Research Articles

Deciphering the Instability of the Black Hole Ringdown Quasinormal Spectrum.

The spectrum of the quasinormal modes of the gravitational waves emitted during the ringdown phase following the merger of two black holes is of primary importance in gravitational astronomy. However, the spectrum is extremely sensitive to small disturbances of the system, thus potentially jeopardizing the predictions of the gravitational-wave observables. We offer an analytical and intuitive explanation of such an instability and its properties based on the transfer matrix approach of quantum mechanics. We also give a simple interpretation of the fact that the prompt ringdown response in the time domain and the black hole greybody factor receive parametrically small corrections, thus being robust observables.

Mechanisms of middle-frequency oscillations in an offshore wind farm induced by the converter current inner loops

Abstract Middle-frequency oscillation instability is one of the important issues that threats the safe integration of offshore wind farms. However, analytical explanations to key affecting factors and laws for the middle-frequency oscillation are not clear yet, which makes it difficult to avoid this kind of oscillation effectively. Therefore, in this paper, mechanism for the middle-frequency oscillation induced by the dynamics of converter current inner loops is studied in-depth. First, small-signal transfer function model for a general offshore wind farm integrated via AC submarine cable is established. Then impact of the AC submarine cable and control parameters of the converter current inner loops on oscillation stability of the wind farm is analysed via eigenvalue analysis. It is found that with the length of AC submarine cable increases, frequency for the open-loop pole of the AC grid decreases. When open-loop pole of the AC grid gets close that of the PMSGs on complex plane, the near strong mode resonance can cause middle-frequency oscillation of the system. Finally, effectiveness of the conclusions drawn is evaluated through nonlinear simulations.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

Thermodynamic Effects Are Essential for Surface Entrapment of Bacteria.

The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is not well understood. We demonstrate that it is crucial to include a commonly neglected thermodynamic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α_{1} the ratio of thermal energy to self-propulsion, and α_{2} an intrinsic shape factor. For α_{1} and α_{2} that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α_{1},α_{2}}.

Scattering model of scintillation arcs in pulsar secondary spectra

ABSTRACT The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend beyond the traditional Fresnel–Kirchhoff method by using the Green’s function of the Helmholtz equation, i.e. we consider spherical waves originating from three-dimensional space, not from a two-dimensional screen. Secondly, the discrete structures observed in the secondary spectrum result from discrete scatterer configurations, namely plasma concentrations in the interstellar medium, and not from the selection of points by the stationary phase approximation. Through advanced numerical techniques, we model both the dynamic and secondary spectra, providing a comprehensive framework that describes all components of the latter spectra in terms of physical quantities. Additionally, we provide a thorough analytical explanation of the secondary spectrum.

Analytical Explanations of the Concept of the Fixed Term and the Random Error Term in Econometric Models

The error term or disturbance term plays an important role in the econometric model, and there are several reasons for including it in the econometric model, including issues related to measurement problems, the omission of variables from the econometric model, or for contingency reasons or related to abnormal human behavior from the general rule, or for inaccurate description of the models or inaccurate preparation of the data. The fixed term or intercept also has different meanings in the econometric model, such as the mathematical meaning, the econometric meaning, the fixed term without meaning, or the fixed term with a negative sign, and others.

Hardness of Random Reordered Encodings of Parity for Resolution and CDCL

Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We provide an analytical explanation for their hardness by showing that they require exponential resolution refutations with high probability when the variable order is chosen at random. We obtain this result by proving that these formulas, which are known to be Tseitin formulas, have Tseitin graphs of linear treewidth with high probability. Since such Tseitin formulas require exponential resolution refutations, our result follows. We generalize this argument to a new class of formulas that capture a basic form of parity reasoning involving a sum of two random parity constraints with random orders. Even when the variable order for the sum is chosen favorably, these formulas remain hard for resolution. In contrast, we prove that they have short DRAT refutations. We show experimentally that the running time of CDCL SAT solvers on both classes of formulas grows exponentially with their treewidth.

Explaining Generalization Power of a DNN Using Interactive Concepts

This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been proved, i.e., the output score of a DNN can be well explained by a small number of interactions between input variables. In this way, to some extent, we can consider such interactions as interactive concepts encoded by the DNN. Therefore, in this paper, we derive an analytic explanation of inconsistency of concepts of different complexities. This may shed new lights on using the generalization power of concepts to explain the generalization power of the entire DNN. Besides, we discover that the DNN with stronger generalization power usually learns simple concepts more quickly and encodes fewer complex concepts. We also discover the detouring dynamics of learning complex concepts, which explains both the high learning difficulty and the low generalization power of complex concepts. The code will be released when the paper is accepted.

Exploring the nonclassical dynamics of the “classical” Schrödinger equation

The introduction of nonlinearities into the Schrödinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, we explore the nonlinear effects induced by subtracting a term proportional to Bohm’s quantum potential to the usual (linear) Schrödinger equation, which generates the so-called “classical” Schrödinger equation. Although a simple nonlinear transformation allows us to recover the well-known classical Hamilton–Jacobi equation, by combining a series of analytical results (in the limiting cases) and simulations (whenever the analytical treatment is unaffordable), we find an analytical explanation to why the dynamics in the nonlinear “classical” regime is still strongly nonclassical. This is even more evident by establishing a one-to-one comparison between the Bohmian trajectories associated with the corresponding wave function and the classical trajectories that one should obtain. Based on these observations, it is clear that the transition to a fully classical regime requires extra conditions in order to remove any trace of coherence, which is the truly distinctive trait of quantum mechanics. This behavior is investigated in three paradigmatic cases, namely, the dispersion of a free propagating localized particle, the harmonic oscillator, and a simplified version of Young’s two-slit experiment.

DETERMINATION OF THE CAPACITY OF PIPELINES TRANSPORTING LIQUID PRODUCTS, DEPENDING ON THE THERMOBARIC CONDITIONS

The article discusses the issues of calculating the capacity of pipelines through which liquid hydrocarbon products are transported, depending on thermobaric conditions. These calculations are important for such urgent tasks of pipeline transport practice as carrying out an inventory and establishing the fact of illegal withdrawal of oil/oil products from the pipeline. The work provides a fundamental equation of the state of the stopped pipeline, in consideration of which the focus of attention is on changing the geometric capacity of the pipeline depending on the change in temperature and pressure of the pumped medium. When considering the change in volume, from the classical equations of mechanics, refined dependencies were obtained for two cases: underground and above-ground laying. A comparison of the obtained relationships has been made, in which it has been found that a number of effects such as a change in gas volume and a temperature factor «mask» the effect of leakage/illegal sampling, preventing their identification from the pressure/temperature change data. An analytical explanation of the processes occurring in the shut down pipeline will allow further quantification of the uncertainties that arise, which will facilitate the decision and allow adjustments to be made to the software used.

The Power to Contract and the Offer-and-Acceptance Analysis of Contract Formation

Abstract The offer-and-acceptance analysis has long been questioned as not (easily) applicable to certain methods of contracting. This paper looks at this analysis through the prism of normative powers and identifies much deeper problems with the analytic explanation of how such unilateral normative powers as offer and acceptance can generate such a normative result as concluding a contract. It argues that even if the powers to offer and accept are exercised, as they are in certain methods of contracting, these are not the normative powers that create contractual obligations; such obligations are always created by the jointly exercised power to contract. The paper substantiates an account of the power to contract as a sui generis normative power and explains the role the unilateral powers to offer and to accept play when they are exercised, while also explaining why there is no need to ‘invent’ offering and accepting where there are none.

Novel rapid treatment options for adolescent depression

There is an urgent need for novel fast-acting antidepressants for adolescent treatment-resistant depression and/or suicidal risk, since the selective serotonin reuptake inhibitors that are clinically approved for that age (i.e., fluoxetine or escitalopram) take weeks to work. In this context, one of the main research lines of our group is to characterize at the preclinical level novel approaches for rapid-acting antidepressants for adolescence. The present review summarizes the potential use in adolescence of non-pharmacological options, such as neuromodulators (electroconvulsive therapy and other innovative types of brain stimulation), as well as pharmacological options, including consciousness-altering drugs (mainly ketamine but also classical psychedelics) and cannabinoids (i.e., cannabidiol), with promising fast-acting responses. Following a brief analytical explanation of adolescent depression, we present a general introduction for each therapeutical approach together with the clinical evidence supporting its potential beneficial use in adolescence (mainly extrapolated from prior successful examples for adults), to then report recent and/or ongoing preclinical studies that will aid in improving the inclusion of these therapies in the clinic, by considering potential sex-, age-, and dose-related differences, and/or other factors that might affect efficacy or long-term safety. Finally, we conclude the review by providing future avenues to maximize treatment response, including the need for more clinical studies and the importance of designing and/or testing novel treatment options that are safe and fast-acting for adolescent depression.

Algorithm it Quantitative Physics Coding Quantum Astrospace Timeline

We propose a novel formalism for physical quantifiability based on a rank-4 tensor time matrix that abstracts informational observables in different domains of reality. We show that our formalism can reveal two types of time representations: arithmetic and algebraic and provide analytical explanations for their properties and relations. We also demonstrate how our formalism can account for various physical phenomena, such as spin, rotation, revolution, and angular gauge momentum, and provide correlative proofs from quantum, mesoscopic, and astrophysical domains. Our formalism contributes to the ongoing quest for a unified theory of physics and has implications for the future of science and technology.

CRESPR: Modular sparsification of DNNs to improve pruning performance and model interpretability

Modern DNNs often include a huge number of parameters that are expensive for both computation and memory. Pruning can significantly reduce model complexity and lessen resource demands, and less complex models can also be easier to explain and interpret. In this paper, we propose a novel pruning algorithm, Cluster-Restricted Extreme Sparsity Pruning of Redundancy (CRESPR), to prune a neural network into modular units and achieve better pruning efficiency. With the Hessian matrix, we provide an analytic explanation of why modular structures in a sparse DNN can better maintain performance, especially at an extreme high pruning ratio. In CRESPR, each modular unit contains mostly internal connections, which clearly shows how subgroups of input features are processed through a DNN and eventually contribute to classification decisions. Such process-level revealing of internal working mechanisms undoubtedly leads to better interpretability of a black-box DNN model. Extensive experiments were conducted with multiple DNN architectures and datasets, and CRESPR achieves higher pruning performance than current state-of-the-art methods at high and extremely high pruning ratios. Additionally, we show how CRESPR improves model interpretability through a concrete example.

Correspondence of L. N. Tolstoy and Yu. F. Samarin: New Contexts and Problems of Relations between Two Contemporaries

Purpose. The purpose of this article is an analytical study of the correspondence between Tolstoy and Samarin, the introduction into scientific circulation of three letters that are stored in the Department of Manuscripts of the State Museum of Leo Tolstoy in Moscow and have not been published until that time. Results. The problem of creative and personal connections between Tolstoy and Samarin, their interaction and especially correspondence is comprehended in many ways. The authors of this article present a detailed scientific commentary on the letters of Tolstoy and Samarin, and explain many realities and facts that have not been given attention in Tolstoy studies. The dating of three Samarin's letters introduced into scientific circulation with analytical explanations of their place and role in the communication of correspondents has been carried out. The work uses biographical, comparative, historical and typological methods, hermeneutic and ontological methods. Conclusion. Despite the fact that Tolstoy could not find a best friend in Samarin, as he really wanted in the early 1860s, it was thanks to communication with him that he deeply comprehended the ambiguity and complexity of a number of Slavophiles’ beliefs in their application to real life.

Induced synchronization by endogenous noise modulation in finite-size random neural networks: A stochastic mean-field study.

Event-related synchronization and desynchronization (ERS/ERD) are well-known features found experimentally in brain signals during cognitive tasks. Their understanding promises to have much better insights into neural information processes in cognition. Under the hypothesis that neural information affects the endogenous neural noise level in populations, we propose to employ a stochastic mean-field model to explain ERS/ERD in the γ-frequency range. The work extends previous mean-field studies by deriving novel effects from finite network size. Moreover, numerical simulations of ERS/ERD and their analytical explanation by the mean-field model suggest several endogenous noise modulation schemes, which may modulate the system's synchronization.

Chinese chess competition strategy analysis based on the zero-sum game

As a desktop game with a long history, Chinese chess has been widely circulated. In recent years, Chinese chess championships have become increasingly popular. During the competition, in addition to the individual abilities of the participants, the use of different strategies in the competition also become another major factor affecting the outcome of the competition. Based on the fixed ability values of the contestants, this research focuses on discussing the selection of strategies. This paper will adopt points-based match rules in common competitions and quantify the player's ability values for making a data analysis about nine different strategies. Due to the use of a point system in the competition, this research could use zero-sum game for analysis. According to zero-sum game and Nash equilibrium, the payoff matrix could be obtained. Furthermore, a precise linear program model is built. After the calculation, this research presents a result about which strategies should be used in the competition and provide an analytical explanation.

Qur'anic Interpretation in the Form of Sundanese Poetry: K.H. Ahmad Dimyati's Interpretation of Q.S. al-A'lá/87

This article focuses on Quranic interpretation in the form of Sundanese poetry or Sundanese nadoman. The object is Kitāb al-Tabyīn al-Ajlá wa al-Ahlá fī Tafsīr Sūrah al-A'lá written by K.H. Ahmad Dimyati (1886-1946) a famous scholar from the Sukamiskin Islamic Boarding School (Pesantren) in Bandung. This book is a tafsir of surah al-A'la (Q.87: 1-19) in Sundanese with pegon style letters. Compared to Qur'anic translations, poeticized forms of interpretation are not widely practiced in Indonesia, given their attachment to strict poetic rules, such as the number of chants, syllables, and the final rhyme in each chant. However, for Ahmad Dimyati, this type of composition was chosen because, in addition to being popular, the lyrics are also concise, easy to read, and the song is pleasant to hear. This form of pupujian poetry is generally sung in mosques waiting for prayer time to arrive. This study shows that the use of pupujian poetry in interpretation adds to the diversity of interpretation literature in West Java. The provisions of the pupujian rules make it unfree to use extensive and analytical explanations. As a poetry-like composition, this type of Qur'anic interpretation contributes not only to the teaching of the Qur'ān but also to the development of Qur'ānic studies that adapt the poetic form of poetry to the Sundanese literary tradition

The Dating Dupe―The Limits of Biosocially Unfriendly Sociology

Curington, Lundquist, and Lin’s book, The Dating Divide: Race and Desire in the Era of Online Romance, demonstrates the limits of a moralizing sociological approach to courting behavior shorn of biosocial insight. In this essay, I summarize the book’s central findings and claims regarding the roots of systematic, racially exclusionary patterns in online dating. I question the adequacy of their social constructionist, power analytic explanation of such patterns; and I suggest additional interpretations from a multidimensional, biosocial perspective. I argue that reducing dating discrimination to “racism,” based on a totally constructed view of romantic desire, is both scientifically and politically shortsighted in today’s polarized ideological environment.

A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications

Fixed point theory is a branch of mathematics that studies solutions that remain unchanged under a given transformation or operator, and it has numerous applications in fields such as mathematics, economics, computer science, engineering, and physics. In the present article, we offer a quicker iteration technique, the D** iteration technique, for approximating fixed points in generalized α-nonexpansive mappings and nearly contracted mappings. In uniformly convex Banach spaces, we develop weak and strong convergence results for the D** iteration approach to the fixed points of generalized α-nonexpansive mappings. In order to demonstrate the effectiveness of our recommended iteration strategy, we provide comprehensive analytical, numerical, and graphical explanations. Here, we also demonstrate the stability consequences of the new iteration technique. We approximately solve a fractional Volterra–Fredholm integro-differential problem as an application of our major findings. Our findings amend and expand upon some previously published results.