Miracle-dz/UniFAR-FTUs huggingface dataset:
Multi-dimensional Sublinear Sparse Fourier Algorithm

In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In "Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with empirically $O(k\log k)$ runtime and $O(k)$ sampling complexity for the one-dimensional sparse FFT was developed for signals of bandwidth $N$, where $k$ is the number of significant modes such that $k\ll N$. In this work we develop an efficient algorithm for sparse FFT for higher dimensional signals, extending some of the ideas in the paper mentioned above. Note a higher dimensional signal can always be unwrapped into a one dimensional signal, but when the dimension gets large, unwrapping a higher dimensional signal into a one dimensional array is far too expensive to be realistic. Our approach here introduces two new concepts; "partial unwrapping" and "tilting". These two ideas allow us to efficiently compute the sparse FFT of higher dimensional signals.
Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics

Controlling the time evolution of the population of two states in cavity quantum electrodynamics is necessary by tuning the modified Rabi frequency in which the extra classical effect of electromagnetic field is taken into account. The theoretical explanation underlying the perturbation of potential on spatial regime of bloch sphere is by the use of Bagrov–Baldiotti–Gitman–Shamshutdinova–Darboux transformations [Bagrov et al., “Darboux transformation for two-level system,” Ann. Phys. 14, 390 (2005)] on the electromagnetic field potential in one-dimensional stationary Dirac model in which the Pauli matrices are the central parameters for controlling the collapse and revival of the Rabi oscillations. It is shown that by choosing σ1 in the transformation generates the parabolic potential causing the total collapse of oscillations, while {σ2,σ3} yield the harmonic oscillator potentials ensuring the coherence of qubits.
A Garden of Eden theorem for principal algebraic actions

Let $\Gamma$ be a countable abelian group and $f \in \Z[\Gamma]$, where $\Z[\Gamma]$ denotes the integral group ring of $\Gamma$. Consider the Pontryagin dual $X_f$ of the cyclic $\Z[\Gamma]$-module $\Z[\Gamma]/\Z[\Gamma] f$ and suppose that the natural action of $\Gamma$ on $X_f$ is expansive and that $X_f$ is connected. We prove that if $\tau \colon X_f \to X_f$ is a $\Gamma$-equivariant continuous map, then $\tau$ is surjective if and only if the restriction of $\tau$ to each $\Gamma$-homoclinicity class is injective. This is an analogue of the classical Garden of Eden theorem of Moore and Myhill for cellular automata with finite alphabet over $\Gamma$.
Non-Abelian SU ( 3 ) k ?> anyons: inversion identities for higher rank face models

The spectral problem for an integrable system of particles satisfying the fusion rules of SU ( 3 ) k ? > is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused A 2 ( 1 ) ? > interaction round a face model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang–Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the separation of variables approach to integrable vertex models.
Holocene glacier readvances on the Fildes Peninsula, King George Island (Isla 25 de Mayo), NW Antarctic Peninsula

1Alfred-Wegener-Institut Helmholtz-Zentrum für Polarund Meeresforschung, Geosciences Division, Am Alten Hafen 26, 27568 Bremerhaven, Germany. 2University of Bremen, Department of Geosciences, Klagenfurterstr. 2–4, 28359 Bremen, Germany. 3Centro de Investigaciones en Ciencias de la Tierra (CONICET-UNC), Vélez Sársfield 1611, X5016GCA, Córdoba, Argentina. 4British Antarctic Survey (BAS), Natural Environmental Research Council (NERC), High Cross, Madingley Road, Cambridge CB3 0ET, UK. 5Institute for Geology und Mineralogy, University of Cologne, Zuelpicher Str. 49b, Cologne D-50674, Germany. 6ETH Zürich, Laboratory of Ion Beam Physics, Schafmattstrasse 20, CH-8093 Zürich, Switzerland. 7ECRC Dept. of Geography, University College London, North West Wing, Gower St, London WC1E 6BT, UK. 8Dept. of Geography, Royal Holloway, University of London, Egham, Surrey, TW20 OEX, UK. 9School of Geography, Politics and Sociology, Newcastle University, Newcastle-upon-Tyne, NE1 7RU, UK. 10Aberystwyth University, Department of Geography and Earth Sciences, Aberystwyth, SY23 3DB, UK. 11Department of Geography, University of Exeter, Exeter EX4 4RJ, UK. 12Department of Geography, Northumbria University, Ellison Building, Newcastle-upon-Tyne NE1 8ST, UK. 13Department of Geography, Durham University, Durham DH1 3LE, UK. 14School of Geosciences, Grant Institute, University of Edinburgh, The King's Buildings, James Hutton Road, Edinburgh EH9 3FE. 15Centro de Investigación en Ecosistemas de la Patagonia, Coyhaique, Aysén, Chile. 16Instituto Antártico Argentino, Convenio MREC Universidad Nacional de Córdoba, Vélez Sársfield 1611, X5016GCA, Córdoba, Argentina.
3D simulations of the early stages of AGN jets: Geometry, thermodynamics and backflow

We investigate the interplay between jets from Active Galactic Nuclei (AGNs) and the surrounding InterStellar Medium (ISM) through full 3D, high resolution, Adaptive Mesh Refinement simulations performed with the FLASH code. We follow the jet- ISM system for several Myr in its transition from an early, compact source to an extended one including a large cocoon. During the jet evolution, we identify three major evolutionary stages and we find that, contrary to the prediction of popular theoretical models, none of the simulations shows a self-similar behavior. We also follow the evolution of the energy budget, and find that the fraction of input power deposited into the ISM (the AGN coupling constant) is of order of a few percent during the first few Myr. This is in broad agreement with galaxy formation models employing AGN feedback. However, we find that in these early stages, this energy is deposited only in a small fraction (< 1%) of the total ISM volume. Finally we demonstrate the relevance of backflows arising within the extended cocoon generated by a relativistic AGN jet within the ISM of its host galaxy, previously proposed as a mechanism for self-regulating the gas accretion onto the central object. These backflows tend later to be destabilized by the 3D dynamics, rather than by hydrodynamic (Kelvin- Helmholtz) instabilities. Yet, in the first few hundred thousand years, backflows may create a central accretion region of significant extent, and convey there as much as a few millions of solar masses.
Electromagnetic response of LaO_0.94F_0.06FeAs: AC susceptibility and microwave surface resistance

We discuss on the electromagnetic response of a polycrystalline sample of LaO0.94F0. 06FeAs exposed to DC magnetic fields up to 10 kOe. The low- and high-frequency responses have been investigated by measuring the AC susceptibility at 100 kHz and the microwave surface resistance at 9.6 GHz. At low as well as high DC magnetic fields, the susceptibility strongly depends on the amplitude of the AC driving field, highlighting enhanced nonlinear effects. The field dependence of the AC susceptibility exhibits a magnetic hysteresis that can be justified considering the intragrain-field-penetration effects on the intergrain critical current density. The microwave surface resistance exhibits a clockwise magnetic hysteresis, which cannot be justified in the framework of the critical-state models of the Abrikosov-fluxon lattice; it may have the same origin as that detected in the susceptibility.
An HMM-based approach exploiting crowd wisdom for rumour veracity classiﬁcation

Prior manual studies of rumours suggested that crowd stance can give insights into the actual rumour veracity. Even though numerous studies of automatic ve-racity classiﬁcation of social media rumours have been carried out, none explored the effectiveness of leveraging crowd stance to determine veracity. We model the veracity of rumours on Twitter using Hidden Markov Models (HMM) while using collective stance information extracted from replying tweets as the only feature. This paper demonstrates that processing of collective stances can lead to substantial performance boost over commonly used features. Furthermore, we show that HMMs using stance as the only feature for modelling rumour veracity achieve signiﬁcantly better results than those approaches where stance
on Machine Intelligence

Intelligent intrusion detection systems are one of the important research fields in computer network security. The purpose of the intrusion detection system is to detect and identify attacks and detect security problems in computer systems and networks and notify security managers. The main algorithm used in this article is the random forest algorithm. To check the effectiveness of the proposed algorithm in intelligent intrusion detection, the NSL-KDD dataset has been used, which includes 125,973 samples and has 41 features. Since the random forest algorithm is a hybrid algorithm and is created from several decision trees, it achieves high accuracy in intelligent intrusion detection. By using this algorithm, we were able to increase the accuracy of intelligent intrusion detection by 99.89%.
Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups

In this PhD thesis we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove that $C^{\infty }$-reducible cocycles are dense in the $C^{\infty }$ topology, for a full measure set of frequencies. We will firstly define two invariants of the dynamics, which we will call energy and degree and which give a preliminary distinction between reducible and non-reducible cocycles. We will then take up the proof of the density theorem. We will show that an algorithm of renormalization converges to perturbations of simple models, indexed by the degree. Finally, we will analyse these perturbations using methods inspired by K.A.M. theory. In this context we will prove that if a $C^{\infty }$ cocycle is measurably reducible to a diophantine constant, it is actually $C^{\infty }$-reducible.
Is Event-Related Desynchronization variability correlated with BCI performance?

Despite current research, the relationship between the variability of Event-Related Desynchronization (ERD) generated during Motor Imagery (MI) tasks and MI-BCI performances is still not well understood. Indeed, numerous studies have previously shown that there is a lot of inter-subject and intra-subject variability in ERD patterns, but difficulties remain to understand the origin of such variability. This lack of knowledge about variability of cerebral motor patterns limits the possibilities of improving the performance of BCIs, which remains quite poor on average. We believe that a better understanding of the variability of ERDs during BCI use is crucial for developing effective interfaces. Indeed, analysis of intertrial ERDs and their variability throughout the experimental session during MI are largely neglected in most studies, which have mainly focused on identifying ERD patterns averaged across trial and possibly across participants. In this study, we propose to analyze large MI-BCI databases (n=75 subjects) and investigate how the inter/intra-individual variability of the cerebral motor patterns underlying the right-hand and left-hand MIs task (i.e., ERDs) is associated to BCI performance. Our study revealed that although ERD amplitude and baseline power are correlated with BCI performances, variability of ERD amplitude or baseline power are not.
Intermediary asset pricing: Capital constraints and market power ∗

We study if and how the capitalization of financial intermediaries affects asset demand and prices in a framework that allows for intermediary market power. We show that weaker capital requirements lead to lower yields (higher prices) but greater market power. We test these predictions and calibrate the model with data on the Canadian primary market for government bonds, where we can link asset demand to balance sheet information of individual intermediaries. A counterfactual analysis shows that relaxing capital constraints can reduce bond yields but increases markups; each on the order of 23–49%. This implies lower funding costs at an implicit cost of higher yield distortion.
UWS Academic Portal Impact of bariatric surgery on renal function

we aim to look at bariatric surgery’s effect on renal function at post This is a retrospective cross-sectional single-center study of patients who underwent bariatric surgery between 11/2008 and 06/2018. Renal function was calculated by using Cockroft-Gault equation, expressed as Creatinine Clearance (CrCl). Statistical analysis used was one-way ANOVA (Welch’s) with Games-Howell Post-Hoc Test. 145 were studied. 30.3% (n=44) were male. The average age and body mass index (BMI) at referral were 48.1±8.6 years and 47.96±7.9 kgm 2 respectively, while the average age and BMI at surgery were 49.1±8.8 years and 40.62±4.2 kgm 2 respectively. Mean CrCl at surgery, year 1, year 2, and year 3 post-op were 172.35±53.29 mL/min, 179.20±57.87 mL/min, 142.35±46.05 mL/min, and 119.56±42.46 mL/min. Marginal improvement of CrCl at year one post-op (172.35±53.29mL/min to 179.20±57.87mL/min) was statistically insignificant (p=0.731). Meanwhile, there was statistically significant CrCl decline observed from year 1 to year 3 post-op (p<0.001). Statistically insignificant marginal improvement in CrCl at year one post-op was noted. Beyond this, there was steady CrCl decline, albeit remained higher than the lower limit for respective gender. We recommend for further studies that take into account additional factors affecting renal function. this study, we explore the impact of bariatric surgery (Gastric sleeve (SG) and Roux-en-Y bypass (RYBG))
Continuous representations of scalar products of Bethe vectors

We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at one’s convenience. Here we consider Bethe vectors in two versions of the six-vertex model: the case with boundary twists and the case with open boundaries.
Effects of Biochar on the C Use Efficiency of Soil Microbial Communities: Components and Mechanisms

Biochar production and incorporation into soil is gaining momentum as a sustainable strategy for climate change mitigation, supported by ever increasing reports of significant carbon (C) sequestration in soil and reduction in greenhouse gas (GHG) emissions from the amended soils. With the progression in biochar testing and use, there is also emerging evidence that biochar induces C sequestration in soil, and that it may not be solely caused by its inherent chemical stability, but also by the complex microbially driven processes and an increase in C use efficiency (CUE) through soil microbial metabolism. This evidence contradicts the current paradigm that sees the microbial CUE decrease during the degradation of recalcitrant material due to thermodynamic constraints, as observed only in several short-term and pilot-scale trials. As the CUE in soil results from interactions between several abiotic and biotic factors, in this paper we examine the link between the biochar properties, soil physico-chemical properties and microbial physiology to explain the CUE increase reported for biochar-amended soils. Based on the large body of physico-chemical literature, and on the high functional diversity and metabolic flexibility of soil microbial communities, we hypothesize that the long-term stabilization of biochar-borne C in the soil systems is not only controlled by its inherent recalcitrance, but also by the cooperative actions of improved soil status and increased microbial CUE. Given that the current knowledge on this specific aspect is still poor, in this feature paper we summarize the state of knowledge and examine the potential impact of biochar on some factors contributing to the whole-soil CUE. We conclude that, beside its inherent recalcitrance, biochar weathering and oxidation in soil create physical and chemical conditions that can potentially increase the microbial CUE. While these processes stabilize the microbial processed C in soil and increase soil fertility, more data from long-term field trials are needed to model the relationship between the CUE and the MRT of biochar-borne C. Based on our hypotheses and relying upon analysis of the available literature, we also suggest possible research approaches that may contribute to filling the gaps in the current knowledge on the topic.
Discrete-time probabilistic approximation of path-dependent stochastic control problems

We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or non-Markovian) case for a general stochastic control problem. A general convergence result is obtained by a weak convergence method in the spirit of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time (1992) Springer]. We also get a rate of convergence using the invariance principle technique as in Dolinsky [Electron. J. Probab. 17 (2012) 1-5], which is better than that obtained by viscosity solution method. Finally, by approximating the conditional expectations arising in the numerical scheme with simulation-regression method, we obtain an implementable scheme.
A Discrete Model for Nonlocal Transport Equations with Fractional Dissipation

In this note, we propose a discrete model to study one-dimensional transport equations with non-local drift and supercritical dissipation. The inspiration for our model is the equation $$ \theta_t + (H\theta) \theta_x +(-\Delta)^\alpha \theta =0 $$ where $H$ is the Hilbert transform. For our discrete model, we present blow-up results that are analogous to the known results for the above equation. In addition, we will prove regularity for our discrete model which suggests supercritical regularity in the range $1/4<\alpha<1/2$ in the continuous setting.
On a Discretization of Confocal Quadrics. A Geometric Approach to General Parametrizations

We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system may be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics. Various sequences correspond to various discrete parametrizations. The coordinate functions of discrete confocal quadrics are computed explicitly. The theory is illustrated with a variety of examples in two and three dimensions. These include confocal coordinate systems parametrized in terms of Jacobi elliptic functions. Connections with incircular nets and a generalized Euler–Poisson–Darboux system are established.
On the simplicity of multigerms

We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where one of the branches is a non stable primitive germ. Using our results we obtain a list which includes all simple multigerms from $\mathbb C^3$ to $\mathbb C^3$.
Gaussian martingale inequality applies to random functions and maxima of empirical processes

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi and Massart (2000,2003), we show that our result can be applied to the concentration of random functions, Erdos-Renyi random graph, and maxima of empirical processes. Several interesting Gaussian concentration inequalities have been obtained.
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability

We characterize the long‐time asymptotic behavior of the focusing nonlinear Schrödinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity by using a variant of the recently developed inverse scattering transform (IST) for such problems and by employing the nonlinear steepest‐descent method of Deift and Zhou for oscillatory Riemann‐Hilbert problems. First, we formulate the IST over a single sheet of the complex plane without introducing the uniformization variable that was used by Biondini and Kovačič in 2014. The solution of the focusing NLS equation with nonzero boundary conditions is thereby associated with a matrix Riemann‐Hilbert problem whose jumps grow exponentially with time for certain portions of the continuous spectrum. This growth is the signature of the well‐known modulational instability within the context of the IST. We then eliminate this growth by performing suitable deformations of the Riemann‐Hilbert problem in the complex spectral plane. The results demonstrate that the solution of the focusing NLS equation with nonzero boundary conditions remains bounded at all times. Moreover, we show that, asymptotically in time, the xt‐plane decomposes into two types of regions: a left far‐field region and a right far‐field region, where the solution equals the condition at infinity to leading order up to a phase shift, and a central region in which the asymptotic behavior is described by slowly modulated periodic oscillations. Finally, we show how, in the latter region, the modulus of the leading‐order solution, initially obtained as a ratio of Jacobi theta functions, can be reduced to the well‐known elliptic solutions of the focusing NLS equation. These results provide the first characterization of the long‐time behavior of generic perturbations of a constant background in a modulationally unstable medium. © 2017 Wiley Periodicals, Inc.
A short guide to pure point diffraction in cut-and-project sets

We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner’s theorem from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.
Fair Universal Representations using Adversarial Models

We present a data-driven framework for learning fair universal representations (FUR) that guarantee statistical fairness for any learning task that may not be known a priori . Our framework leverages recent advances in adversarial learning to allow a data holder to learn representations in which a set of sensitive attributes are decoupled from the rest of the dataset. We formulate this as a constrained minimax game between an encoder and an adversary where the constraint ensures a measure of usefulness (utility) of the representation. For appropriately chosen adversarial loss functions, our framework precisely clarifies the optimal adversarial strategy against strong information-theoretic adversaries; it also achieves the fairness measure of demographic parity for the resulting constrained representations. We high-light our results for the UCI Adult and UTKFace datasets.