Miracle-dz/UniFAR-FTUs huggingface dataset:
A Market Mechanism for Virtual Inertia

One of the recognized principal issues brought along by the steadfast migration towards power electronic interfaced energy sources is the loss of rotational inertia. In conventional power systems, the inertia of the synchronous machines plays a crucial role in safeguarding against any drastic variations in frequency by acting as a buffer in the event of large and sudden power generation-demand imbalances. In future power electronic-based power systems, the same role can be played by strategically located virtual inertia devices. However, the question looms large as to how the system operators would procure and pay for these devices. In this article, we propose a market mechanism inspired by the ancillary service markets in power supply. We consider a linear network-reduced power system model along with a robust $\mathcal H_{2}$ performance metric penalizing the worst-case primary control effort. With a social welfare maximization problem for the system operator as a benchmark, we construct a market mechanism in which bids are invited from agents providing virtual inertia, who in turn are compensated via a Vickrey-Clarke-Groves payment rule. The resulting mechanism ensures truthful bidding to be the dominant bidding strategy and guarantees non-negative payoffs for the agents. A three-region case study is considered in simulations, and a comparison with a regulatory approach to the same problem is presented.
Extremes of local times for simple random walks on symmetric trees

We consider local times of the simple random walk on the $b$-ary tree of depth $n$ and study a point process which encodes the location of the vertex with the maximal local time and the properly centered maximum over leaves of each subtree of depth $r_n$ rooted at the $(n-r_n)$ level, where $(r_n)_{n \geq 1}$ satisfies $\lim_{n \to \infty} r_n = \infty$ and $\lim_{n \to \infty} r_n/n \in [0, 1)$. We show that the point process weakly converges to a Cox process with intensity measure $\alpha Z_{\infty} (dx) \otimes e^{-2\sqrt{\log b}~y}dy$, where $\alpha > 0$ is a constant and $Z_{\infty}$ is a random measure on $[0, 1]$ which has the same law as the limit of a critical random multiplicative cascade measure up to a scale factor. As a corollary, we establish convergence in law of the maximum of local times over leaves to a randomly shifted Gumbel distribution.
GOE statistics for Lévy matrices

In this paper we establish eigenvector delocalization and bulk universality for L\'{e}vy matrices, which are real, symmetric, $N \times N$ random matrices $\textbf{H}$ whose upper triangular entries are independent, identically distributed $\alpha$-stable laws. First, if $\alpha \in (1, 2)$ and $E \in \mathbb{R}$ is any energy bounded away from $0$, we show that every eigenvector of $\textbf{H}$ corresponding to an eigenvalue near $E$ is completely delocalized and that the local spectral statistics of $\textbf{H}$ around $E$ converge to those of the Gaussian Orthogonal Ensemble (GOE) as $N$ tends to $\infty$. Second, we show for almost all $\alpha \in (0, 2)$, there exists a $c(\alpha) > 0$ such that the same statements hold if $|E| < c (\alpha)$.
Brieskorn manifolds in contact topology

In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving exotic contact structures, invariants and orderability. The main tool for the required computations is a version of the Morse–Bott spectral sequence. We provide a proof for the particular version that is useful for us.
A quantitative interpretation of the frequent hypercyclicity criterion

We give a quantitative interpretation of the frequent hypercyclicity criterion. Actually we show that an operator which satisfies the frequent hypercyclicity criterion is necessarily $A$ -frequently hypercyclic, where $A$ refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the ‘frequency’ measured by the frequent hypercyclicity criterion. Moreover, we construct an example of a unilateral weighted shift which is frequently hypercyclic but not $A$ -frequently hypercyclic on a particular scale.
Facile and Rapid Electrochemical Conversion of Ni into Ni(OH)2 Thin Film as the Catalyst for Direct Growth of Carbon Nanotubes on Ni Foam for Supercapacitors

In this paper, a facile and rapid aqueous-based electrochemical technique was used for the phase conversion of Ni into Ni(OH)2 thin film. The Ni(OH)2 thin film was directly converted and coated onto the network surface of Ni foam (NF) via the self-hydroxylation process under alkaline conditions using a simple cyclic voltammetry (CV) strategy. The as-formed and coated Ni(OH)2 thin film on the NF was used as the catalyst layer for the direct growth of carbon nanotubes (CNTs). The self-converted Ni(OH)2 thin film is a good catalytic layer for the growth of CNTs due to the fact that the OH− of the Ni(OH)2 can be reduced to H2O to promote the growth of CNTs during the CVD process, and therefore enabling the dense and uniform CNTs growth on the NF substrate. This binder-free CNTs/NF electrode displayed outstanding behavior as an electric double-layer capacitor (EDLC) due to the large surface area of the CNTs, showing excellent specific capacitance values of 737.4 mF cm−2 in the three-electrode configuration and 319.1 mF cm−2 in the two-electrode configuration, at the current density of 1 mA cm−2 in a 6 M KOH electrolyte. The CNTs/NF electrode also displayed good cycling stability, with a capacitance retention of 96.41% after 10,000 cycles, and this the excellent cycling performance can be attributed to the stable structure of the direct growth of CNTs with a strong attachment to the NF current collector, ensuring a good mechanical and electrical connection between the NF collector and the CNTs.
Radio Emission from the Be/Black Hole Binary MWC 656

Context. MWC 656 is the recently discovered first binary system case composed of a Be-type star and an accreting black hole. Its low X-ray luminosity indicates that the system is in a quiescent X-ray state. Aims. The aim of our investigation is to establish if the MWC 656 system has detectable radio emission and if the radio characteristics are consistent with those of quiescent black hole systems. Methods. We used three archived VLA data sets, one hour each, at 3 GHz and seven new VLA observations, two hours each, at 10 GHz to produce very high sensitivity images, down to $\sim$1$\,\mu$Jy. Results. We detected the source twice in the new observations: in the first VLA run, at periastron passage, with a flux density of 14.2$\,\pm\,$2.9 $\mu$Jy and by combining all together the other six VLA runs, with a flux density of $3.7 \pm 1.4$ $\mu$Jy. The resulting combined map of the archived observations has the sensitivity of $1 \sigma = 6.6\, \mu Jy$ but no radio emission is there detected. Conclusions. The radio and X-ray luminosities agree with the behaviour of accreting binary black holes in the hard and quiescent state. In particular, MWC 656 in the $L_X$, $L_R$ plane occupies the same region as A0620$-$00 and XTE J1118+480, the faintest known black holes up to now.
Physical parameters and the projection factor of the classical Cepheid in the binary system OGLE-LMC-CEP-0227

A novel method of analysis of double-lined eclipsing binaries containing a radially pulsating star is presented. The combined pulsating-eclipsing light curve is built up from a purely eclipsing light curve grid created using an existing modeling tool. For every pulsation phase the instantaneous radius and surface brightness are taken into account, being calculated from the disentangled radial velocity curve of the pulsating star and from its out-of-eclipse pulsational light curve and the light ratio of the components, respectively. The best model is found using the Markov Chain Monte Carlo method. The method is applied to the eclipsing binary Cepheid OGLE-LMC-CEP-0227 (Ppuls = 3.80 d, Porb = 309 d). We analyze a set of new spectroscopic and photometric observations for this binary, simultaneously fitting OGLE V-band, I-band and Spitzer 3.6 µm photometry. We derive a set of fundamental parameters of the system significantly improving the precision comparing to the previous results obtained by our group. The Cepheid mass and radius are M1 = 4.165 ± 0.032M⊙ and R1 = 34.92± 0.34R⊙, respectively. For the first time a direct, geometrical and distance-independent determination of the Cepheid projection factor is presented. The value p =1.21 ± 0.03(stat.) ± 0.04(syst.) is consistent with theoretical expectations for a short period Cepheid and interferometric measurements for δ Cep. We also find a very high value of the optical limb darkening coefficients for the Cepheid component, in strong disagreement with theoretical predictions for static atmospheres at a given surface temperature and gravity.
Privacy-Preserving Cross-Area Traffic Forecasting in ITS: A Transferable Spatial-Temporal Graph Neural Network Approach

Traffic forecasting is essential in improving and maintaining safety and orderliness in intelligent transportation systems (ITS). As a deep learning approach, graph neural networks (GNN) based spatial-temporal association mining methods are promising in traffic forecasting. However, current GNN-based methods usually require a high number of training data, and when the sample volume is small, the performance of the model drops dramatically. The existing transfer methods can solve this problem by leveraging knowledge from other data-rich areas, but the domain adaption method with access to source data still faces the non-neglectable problem of private information leakage in the source area. A solution that can solve cross-area transfer without access to source data is still missing. In this paper, to fill the gap, we propose a Transferable Federated Inductive Spatial-Temporal Graph Neural Network (T-ISTGNN) framework to transfer spatial-temporal dependency information in cross-area data to accomplish traffic state forecasting. First, we introduce a multi-source model aggregation scheme based on federated learning to retain the traffic information of the source areas. Second, we propose a transfer method between source and target areas based on hypothesis transfer learning to achieve domain adaption under source domain data protection. Third, we propose a GNN-based method called Inductive Spatial-Temporal Graph Neural Network (ISTGNN) for traffic forecasting. Experiments on real-world datasets demonstrate that T-ISTGNN is capable of cross-area traffic state forecasting under the restriction of preserving the privacy of source areas.
On the harmonic and geometric maximal operators

We examine the harmonic and geometric maximal operators defined for a general basis of open sets in $\R^n$. We prove two weight norm inequalities for the harmonic maximal operator assuming testing conditions over characteristic functions of unions of sets from the basis. We also prove a that a bumped two weight $A_p$-like condition is sufficient for the two weight boundedness of the harmonic maximal operator.
Effects of Intensive Exercise on Cognitive Dysfunction in Patients With Pure Cerebellar Degeneration: A Single-Arm Pilot Study

Objective To clarify the profile of cognitive dysfunction and the effects of intensive exercise in spinocerebellar degeneration (SCD). Methods We enrolled 60 healthy controls and 16 patients with purely cerebellar type SCD without gait disturbance or organic changes other than cerebellar changes. To assess cognitive function, we evaluated the participants using the Mini-Mental State Examination (MMSE), Frontal Assessment Battery (FAB), and Montreal Cognitive Assessment-Japanese (MoCA-J) at admission and after intensive exercise. Results Compared to the controls, SCD patients showed significant cognitive decline. As a result of intensive exercise, significant improvements in motor and cognitive functions were observed: the MMSE score improved from 27.7±1.9 to 29.0±1.3 points (p<0.001); the FAB score improved from 14.8±2.2 to 15.8±2.0 points (p=0.002); and the MoCA-J score improved from 24.6±2.2 to 26.7±1.9 points (p<0.001). For sub-scores, significant improvements were noted in serial 7, lexical fluency, motor series, and delayed recall. Conclusion Our study indicates that intensive exercise can be effective not only for motor dysfunction but also for cognitive dysfunction (Clinical Trial Registration No. UMIN-CTR: UMIN000040079).
Multiparameter Fuss--Catalan numbers with application to algebraic equations

We present an exposition on the Fuss--Catalan numbers, which are a generalization of the well known Catalan numbers. The literature on the subject is scattered (especially for the case of multiple independent parameters, as will be explained in the text), with overlapping definitions by different authors and duplication of proofs. This paper collects the main theorems and identities, with a consistent notation. Contact is made with the works of numerous authors, including the early works of Lambert and Euler. We demonstrate the application of the formalism to solve algebraic equations by infinite series. Our main result in this context is a new necessary and sufficient formula for the domain of absolute convergence of the series solutions of algebraic equations, which corrects and extends previous work in the field. Some historical material is placed in an Appendix.
Numerical Study on Elastic Parameter Identification of Large-Span Steel Truss Structures Based on Strain Test Data

Large-span steel trusses are widely used in public buildings such as large-span factory buildings, exhibition halls, gymnasiums, and bridges because of their fast construction speed and easy industrial manufacturing. Due to construction errors and environmental factors, the material properties may change during their service life, and it is an important prerequisite for the structural safety assessment to identify the true material parameters of the structure. Among the many parameters, the elastic modulus is one that has the greatest impact on the accuracy of structural safety analysis. In this paper, a mathematical analysis model of elastic modulus identification was constructed, based on the strain test data and the improved gradient regularization method. The relationship between the strain test data and elastic moduli was established. A common finite element program based on the method was developed to identify the elastic modulus. A series of numerical simulations was carried out on a 53-element steel truss model to study the availability and numerical stability of the method. The effects of different initial values, numbers of strain tests, and locations of the strain test as well as the number of unknown parameters on the identification results were studied. The results showed that the proposed method had very high accuracy and computational efficiency. For the case of 53 unknown parameters without considering the test error, the identification accuracy could reach a 1 × 10−10 order of magnitude after only several iterations. This paper provides an effective solution to obtain the actual values of the elastic modulus of steel truss structures in practical engineering.
Multi-particle quantum fields for bound states and interactions

The Fock-Hilbert space generated by a single-particle interaction-free Wightman field is augmented by introducing non-trivial multi-particle (that is, multi-point, multilinear) quantum fields, which is justified insofar as Haag's theorem establishes that free field Fock-Hilbert spaces cannot model bound or interacting states. Two Gaussian constructions are given: one that modifies the combinatoric factors and masses associated with products of propagators and a second for which locality is determined by the center of mass of the n-particles and relative separations of the n-particles determine the strength of resonance; it is shown how the two constructions may also be used together. Finally, a method is given for generating non-Gaussian n-particle quantum fields that quite closely tracks familiar interacting quantum fields but that is significantly better-defined and that offers a much richer algebraic structure for future use.
Quantum state transfer through noisy quantum cellular automata

We model the transport of an unknown quantum state on one dimensional qubit lattices by means of a quantum cellular automata (QCA) evolution. We do this by first introducing a class of discrete noisy dynamics, in the first excitation sector, in which a wide group of classical stochastic dynamics is embedded within the more general formalism of quantum operations. We then extend the Hilbert space of the system to accommodate a global vacuum state, thus allowing for the transport of initial on-site coherences besides excitations, and determine the dynamical constraints that define the class of noisy QCA in this subspace. We then study the transport performance through numerical simulations, showing that for some instances of the dynamics perfect quantum state transfer is attainable. Our approach provides one with a natural description of both unitary and open quantum evolutions, where the homogeneity and locality of interactions allow one to take into account several forms of quantum noise in a plausible scenario.
Simultaneous Sensing Error Recovery and Tomographic Inversion Using an Optimization-Based Approach

Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental conditions, which are often beyond the capabilities of the state-of-the-art reconstruction techniques such as regularizations. Because they can lead to reduced spatial resolution and even misinterpretation of the underlying sample structures, these errors present a fundamental obstacle to full realization of the capabilities of next-generation physical imaging. In this work, we develop efficient and explicit recovery schemes of the most common experimental error: movement of the center of rotation during the experiment. We formulate new physical models to capture the experimental setup, and we devise new mathematical optimization formulations for reliable inversion of complex samples. We demonstrate and validate the efficacy of our approach on synthetic data under known perturbations of the center of rotation.
Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.
Screening Method for 23 Alkaloids in Human Serum Using LC/MS/MS with a Pentafluorophenyl Column in Dynamic Multiple Reaction Monitoring Mode

Alkaloids are nitrogen-containing organic compounds, generally basic, and found in plants, fungi, and bacteria. Some alkaloids are used in medicine, but some compounds are highly toxic. Accidental ingestion, homicide, and suicide have occurred due to plants containing alkaloids. The identification of toxic components in biological samples is important for the diagnosis and/or treatment of poisoning cases in forensic and emergency medicine. Alkaloids have a wide variety of structures, such as isoquinoline alkaloid, indole alkaloid, tropane alkaloid, and diterpene alkaloid; therefore, there are few reports of simultaneous analysis methods. We have established a method for the simultaneous analysis of 23 alkaloids in human serum with a liquid chromato-graph-tandem mass spectrometer (LC/MS/MS). A liquid-liquid extraction which was modified from the first step of the QuEChERS AOAC method was used for serum pretreatment. The separation of the compounds was performed using a pentafluorophenyl (PFP) column, CAPCELL CORE PFP (2.1 mm I.D. × 100 mm, 2.7 μm) in gradient mode. Mobile phase A consisted of 10 mM ammonium formate and 0.1% formic acid in ultrapure water, and mobile phase B was 10 mM ammonium formate and 0.1% formic
Magnitude homology of geodesic space.

This paper studies the magnitude homology groups of geodesic metric spaces. We start with a description of the second magnitude homology of a general metric space in terms of the zeroth homology groups of certain simplicial complexes. Then, on a geodesic metric space, we interpret the description by means of geodesics. The third magnitude homology of a geodesic metric space also admits a description in terms of a simplicial complex. Under an assumption on a metric space, the simplicial description allows us to introduce an invariant of third magnitude homology classes as an intersection number. Finally, we provide a complete description of all the magnitude homology groups of a geodesic metric space which fulfils a certain non-branching assumption.
RTNI—A symbolic integrator for Haar-random tensor networks

We provide a computer algebra package called random tensor network integrator (RTNI). It allows to compute averages of tensor networks containing multiple Haar-distributed random unitary matrices and deterministic symbolic tensors. Such tensor networks are represented as multigraphs, with vertices corresponding to tensors or random unitaries and edges corresponding to tensor contractions. Input and output spaces of random unitaries may be subdivided into arbitrary tensor factors, with dimensions treated symbolically. The algorithm implements the graphical Weingarten calculus and produces a weighted sum of tensor networks representing the average over the unitary group. We illustrate the use of this algorithmic tool on some examples from quantum information theory, including entropy calculations for random tensor network states as considered in toy models for holographic duality. Mathematica and Python implementations are supplied.
Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups

We study the existence of various types of gradings on Lie algebras, such as Carnot gradings or gradings in positive integers, and prove that the existence of such gradings is invariant under extensions of scalars. As an application, we prove that if G is a finitely generated nilpotent group, its systolic growth is asymptotically equivalent to its word growth if and only if the Malcev completion of G is Carnot. We also characterize when G is non-cohopfian, in terms of the existence of a non-trivial grading in non-negative integers, and deduce that this property only depends on its real (or even complex) Malcev completion.
Mayer Transfer Operator Approach to Selberg Zeta Function

These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a special situation the dynamical zeta function is defined for a geodesic flow on a hyperbolic plane quotient by an arithmetic cofinite discrete group. More precisely, the flow is defined for the corresponding unit tangent bundle. It turns out that the Selberg zeta function for this group can be expressed in terms of a Fredholm determinant of a classical transfer operator of the flow. The transfer operator is defined in a certain space of holomorphic functions and its matrix representation in a natural basis is given in terms of the Riemann zeta function and the Euler gamma function.