Miracle-dz/UniFAR-FTUs huggingface dataset:
Reinforcement Learning-Based Physical Cross-Layer Security and Privacy in 6G

Sixth-generation (6G) cellular systems will have an inherent vulnerability to physical (PHY)-layer attacks and privacy leakage, due to the large-scale heterogeneous networks with booming time-sensitive applications. Important wireless techniques including non-orthogonal multiple access, mobile edge computing, millimeter-wave, massive multiple-input and multiple-output, visible light communication, terahertz, and intelligent reflecting surface can improve the spectrum efficiency and quality-of-service but will raise challenges for the 6G PHY and cross-layer security and privacy protection. Existing optimization based PHY and cross-layer security and privacy protection schemes such as the convex optimization method have to rely on accurate attack patterns and strategies and thus suffer from performance degradation in 6G systems that have shorter communication latency, more devices and higher spectrum efficiency than 5G. Reinforcement learning (RL) algorithms help wireless devices optimize their security policies to enhance the security performance in dynamic networks against smart attacks without depending on the attack model. Therefore, this article provides a comprehensive survey on the RL based 6G PHY cross-layer security and privacy protection. In this article, we investigate the potential attacks in 6G systems and discuss the PHY cross-layer security solutions. A brief overview of reinforcement learning algorithms is provided. Afterward, we review the RL based PHY-layer security and privacy protection and discuss how to apply RL algorithms in 6G security scenarios, especially focusing on the game with jammers, eavesdroppers, spoofers and inference attackers. The RL based security solutions for unmanned aerial vehicles (UAVs) and cross-layer scenarios are also reviewed. The future research directions are identified and the corresponding RL based potential solutions are discussed for 6G.
Gabor Tight Fusion Frames: Construction and Applications in Signal Retrieval Modulo Phase

Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness. As tight frames are a very important topic within standard frame theory, tight fusion frames are similarly important; however, only trivial examples of tight fusion frames are hitherto known. In this paper, we apply ideas from Gabor analysis to demonstrate a non-trivial construction of tight fusion frames. We then use this construction to further show their applicability in some cases for the retrieval of signals modulo phase.
Nonsingular spacetimes with a negative cosmological constant: Stationary solutions with matter fields

Generalising the results in arXiv:1612.00281, we construct infinite-dimensional families of non-singular stationary space times, solutions of Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function

In this paper, a novel indirect adaptive fuzzy controller is proposed for a class of uncertain nonlinear systems with input and output constrains. To address output and input constraints, a barrier Lyapunov function and an auxiliary design system are employed, respectively. The proposed approach is explored by employing fuzzy logic systems to tackle unknown nonlinear functions and combining the adaptive backstepping technique with adaptive fuzzy control design. Especially, the number of the online learning parameters are reduced to 2n in the closed‐loop system. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded, and the input and output constraints are circumvented simultaneously. A numerical example with comparisons is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.
Results on the development of mid-infrared integrated optics for the Darwin Mission

To detect earth-like planets orbiting around solar-type stars in the mid-infrared spectral range, a typical rejection ratio of 106 of the stellar flux must be achieved. Space missions like Darwin/TPF aim at achieving such contrasts using nulling interferometry between 4 μm and 20 μm. The instrumental constraints on beam combination, spatial filtering, intensity and phase mismatches must then be accurately considered. This paper presents the first characterization results of mid-infrared waveguides for integrated optics (IO) developed in the frame of an ESA contract. Taking into account the scientific achievements already obtained with IO components in the near infrared range, results demonstrate that these technologies can also be used for future nulling devices as an alternative to bulk optics instrumentation in the mid-infrared spectral range. Good waveguiding behaviour has been obtained on dielectric waveguides based on Chalcogenide or Zinc Selenide glasses and Hollow Metallic Waveguides. The single-mode behavior, spatial filtering and polarization control capabilities of the hollow metallic channel waveguides have been also demonstrated. This paper focuses on the methods used to validate the waveguide behaviour and the first laboratory results obtained with the different technologies used in the mid-infrared.
Global fixed points for nilpotent actions on the torus

An isotopic to the identity map of the 2-torus, that has zero rotation vector with respect to an invariant ergodic probability measure, has a fixed point by a theorem of Franks. We give a version of this result for nilpotent subgroups of isotopic to the identity diffeomorphisms of the 2-torus. In such a context we guarantee the existence of global fixed points for nilpotent groups of irrotational diffeomorphisms. In particular, we show that the derived group of a nilpotent group of isotopic to the identity diffeomorphisms of the 2-torus has a global fixed point.
Testing for Periodicity and Trend in Long-Memory Processes

This thesis presents methods of testing the periodicity and trend for the time series, which exhibit dependence over long periods of time. Many such processes can be modeled by a class of models called fractionally differenced processes. The first approach we consider to analyse such processes is by using the band periodogram, which divides the periodogram into different intervals or bands, matching the band-pass of the discrete wavelet transform (DWT). In other words, we have a number of high frequency bands and one low frequency band. We investigate the distribution of statistics based on these bands of the long memory processes at high frequency bands, and we show that these distributions are similar to those derived from white noise processes. The next approach for analysing long memory processes is by using the DWT. For long memory processes, the properties of the periodogram of the wavelet scales are similar to those of the band periodograms. We propose two tests for testing the periodicity in the case of long memory processes. The two tests are based on the two methods mentioned above. We develop the Fisher test in the case of simple periodicity, and the Siegel test when we have multiple periodicities. We use simulations to study properties of the tests; in particular we provide results on size and power of the tests. We also investigate the testing of trends in long memory processes. We suggest two test statistics. The first one is based on the quotient of the low frequency band in the periodogram and the high frequency bands. The second one is based on the ratio of low frequency band periodogram to the sum of other ordinates in the periodogram. We also use the DWT method for testing the trend. By the use of simulation we compare our tests with alternative tests. We further investigate the impact of periodicity and trend on different methods of estimating the long memory parameter. We provide a simulation study that shows how the periodicity and trend may affect such methods. We apply our methodology to several environmental time series.
Semi-parametric X2 Testing in Mean Structure and Covariance Structure Analysis Using Projections

Mean structures form a basis for mean, covariance, and other forms of moment structure analysis including structural equation modeling. It is shown how to analyze mean structures using projections. These are used to derive a simple general goodness of fit test statistic that is asymptotically chi-squared and robust to departures from normality. Projections are also used to derive two goodness of fit test statistics for mean structures that are substructures of a more general mean structure. One of these uses the difference of two goodness of fit test statistics, one for the general structure and one for the substructure. It is shown how to use the mean structure results for covariance structure analysis. Best generalized least squares, or ADF estimates are not required. Any asymptotically normal estimates may be use. The primary methods used for testing mean and covariance structures are orthogonal complement methods. A basic difficulty with using these is identified. Specific examples show how the general results may be applied to generalized nonlinear regression and to autoregression with measurement errors. Simulation studies investigate the type one errors and power of the test statistics involved. An appendix contains a review of the basic asymptotic and projection methods used. It also gives conditions that lead to the commonly made assumption that the asymptotic covariance matrix of a vectorized form of a sample covariance matrix is positive definite and that this is a very mild assumption.
Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions

We consider the standard model of distributed optimization of a sum of functions F(z)=∑i=1nfi(z), where node i in a network holds the function fi(z). We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node i is capable of generating gradients of its function fi(z) corrupted by zero-mean bounded–support additive noise at each step, (ii) F(z) is strongly convex, and (iii) each fi(z) has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions f1(z), …, fn(z) at each step.
Using k-MST, k-EC, and k-VC neighbor graphs construction methods with spatial coherent distance for manifold learning in hyperspectral image processing

Dimensionality reduction is a key step in hyperspectral image processing. Recent investigations are looking into nonlinear manifold learning for dimensionality reduction in hyperspectral imagery. Nonlinear manifold learning methods such as Isomap, and Local Linear Embedding are use to recover the low dimensional representation of an unknown nonlinear manifold for high dimensional data where it is important to retain the neighborhood structure of the manifold. Although these algorithms use different philosophies for recovering the nonlinear manifold, they all incorporate neighborhood information from each data point to construct a weighted graph having the data points as vertices. Thus the performance of these methods highly depends on how well these neighborhoods are selected, since all subsequent steps rely on it. The k-NN algorithm is the most widely used technique for neighbor selection in manifold learning. However, it can result in a disconnected graph and it does not fully exploit spatial neighborhood information from the image in selecting points to form the neighborhoods. In this paper, recently proposed methods for constructing the weighted graph in manifold learning are studied: k-VC, k-EC and k-MST, which have the advantage of creating connected graphs and have performed well in artificial data sets. Spatial information of the hyperspectral images is included in the manifold learning process by using spatial coherence. Experiments are conducted with artificial data and hyperspectral images. For hyperspectral images, classification accuracy was used as an indirect measure to understand how the low dimensional embedding of the data reduces dimensionality while still maintaining good discrimination performance.
Inefficient weights from pairwise comparison matrices with arbitrarily small inconsistency

Having a pairwise comparison matrix in a multi-attribute decision problem, two basic problems arise: how to compute the weight vector, and, how to associate an inconsistency index to the matrix. Two key concepts of the Analytic Hierarchy Process, the eigenvector method and inconsistency index are discussed. (In)efficiency is a well-known property in multiple objective optimization. We introduce a restriction of it in the paper. Given a pairwise comparison matrix, a weight vector is called internally inefficient if there exists another weight vector such that every pairwise ratio of the latter’s components is between the corresponding element of the pairwise comparison matrix and the pairwise ratio of the former’s components, and there exists at least one position, where the latter’s approximation is strictly better than the former’s. A class of pairwise comparison matrices with arbitrarily small inconsistency is provided such that the eigenvector method yields an internally inefficient weight vector. The paper is closed by another pairwise comparison matrix with an internally inefficient eigenvector and open questions.
Auslander orders over nodal stacky curves and partially wrapped Fukaya categories

It follows from the work of Burban and Drozd [Math. Ann. 351 (2011) 665–709] that for nodal curves C , the derived category of modules over the Auslander order AC provides a categorical (smooth and proper) resolution of the category of perfect complexes Perf (C) . On the A‐side, it follows from the work of Haiden–Katzarkov–Kontsevich [Publ. Math. Inst. Hautes Études Sci. 126 (2017) 247–318] that for punctured surfaces X with stops Λ at their boundary, the partially wrapped Fukaya category W(X,Λ) provides a categorical (smooth and proper) resolution of the compact Fukaya category F(X) . Inspired by this analogy, we establish an equivalence between the derived category of modules over the Auslander orders over certain nodal stacky curves and partially wrapped Fukaya categories associated to punctured surfaces of arbitrary genus equipped with stops at their boundary. As an application, we deduce equivalences between derived categories of coherent sheaves (respectively perfect complexes) on such nodal stacky curves and the wrapped (respectively compact) Fukaya categories of punctured surfaces of arbitrary genus.
Stability in Bounded Cohomology for Classical Groups, I: The Symplectic Case

We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as $(\mathrm{Sp}_{2r}(\mathbb{Z}))_{r \geq 1}$ or $(\mathrm{Sp}_{2r}(\mathbb{Z}[i]))_{r \geq 1}$. Our method is based on a general stability criterion which extends Quillen's method to the functional analytic setting of bounded cohomology. This criterion is then applied to a new family of complexes associated to symplectic polar spaces, which we call symplectic Stiefel complexes; similar complexes can also be defined for other families of classical groups acting on polar spaces.
A novel hybrid method for equilibrium problems and fixed point problems

The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the extra-steps as in some previously known methods. The strongly convergence theorem is established and some numerical examples are presented to illustrate its convergence.
On the rational homology of high dimensional analogues of spaces of long knots

We study high-dimensional analogues of spaces of long knots. These are spaces of compactly-supported embeddings (modulo immersions) of $\mathbb{R}^m$ into $\mathbb{R}^n$. We view the space of embeddings as the value of a certain functor at $\mathbb{R}^m$, and we apply manifold calculus to this functor. Our first result says that the Taylor tower of this functor can be expressed as the space of maps between infinitesimal bimodules over the little disks operad. We then show that the formality of the little disks operad has implications for the homological behavior of the Taylor tower. Our second result says that when $2m+1<n$, the singular chain complex of these spaces of embeddings is rationally equivalent to a direct sum of certain finite chain complexes, which we describe rather explicitly.
H I Profiles in IRAS Galaxies

H-I line profiles have been obtained for a sample of 37 galaxies. Thirty of these galaxies have IRAS fluxes representing a wide range of infrared luminosites and spectra. The galaxies also represent five levels of optical activity, nonactive, LINERs, H-II galaxies, Sy 2, and Sy 1. They also have a wide range of tidal interaction activity with other galaxies. The behavior of H-I is studied within a scenario that relates tidal events with star formation, dust formation, IR luminosity, and nuclear activity in galaxies. A strong correlation is found between H-I and IR luminosity, which appears to be in the form of an excess of H-I emission related to the interaction events. Detached weak extra H-I components are common, and H-I absorption components are seen in several objects. H-I outflow is indicated in most cases. Relative velocities are of the order of a few hundred km/s. The most strongly disturbed galaxies also have peculiar H-I profiles. A fit to the Tully-Fisher relation indicates a mean extinction of about 1 mag for the group, and a general spread in the relation with no systematic effects. 17 refs.
Deep Contrastive Principal Component Analysis Adaptive to Nonlinear Data

Principal component analysis (PCA) is one of the most fundamental techniques for Big Data analytics in e.g, smart manufacturing and biostatistics, which is capable of extracting the most essential information from a dataset. However, when it encounters multiple datasets, PCA cannot reveal the specific inherent data structure hidden in one dataset relative to the other(s), which we term contrastive data analytics in this paper. Although a number of proposals such as contrastive or discriminative PCA have been suggested, they require fine-tuning of hyper-parameters or cannot effectively deal with nonlinear data. In this context, we advocate deep contrastive (Dc) PCA for nonlinear contrastive data analytics, which leverages the power of deep neural networks to explore the hidden nonlinear relationships in the datasets and extract the desired contrastive features. An alternating minimization algorithm is developed for simultaneously seeking the best nonlinear transformations for the data as well as the associated contrastive projections, tantamount to performing an eigenvalue decomposition and a back-propagation step. Substantial numerical tests using both synthetic and real datasets from protein expression, electroencephalography, wearable human motion, and smart manufacturing, are conducted, which corroborate the superior adaptivity of DcPCA in dealing with nonlinear data relative to state-of-the-art alternatives.
Investigation of thermal denaturation of DNA molecules based on non-equilibrium transport approach

Using nonequilibrium transport theory, the thermal denaturation of DNA molecules is investigated as a preliminary step to clarify the dynamical process of DNA transcription. The distribution functions of the displacement of base pairs at different temperatures are calculated. A modified model is also proposed which can reproduce the essential features of the denaturation process. Calculations show that the Langevin equation is an effective tool for describing the dynamical process of DNA molecules, and it seems to be more advantageous than the Nose method.
Dynamic Evolution with Limited Learning Information on a Small-World Network

This paper investigates the dynamic evolution with limited learning information on a small-world network. In the system, the information among the interaction players is not very lucid, and the players are not allowed to inspect the profit collected by its neighbors, thus the focal player cannot choose randomly a neighbor or the wealthiest one and compare its payoff to copy its strategy. It is assumed that the information acquainted by the player declines in the form of the exponential with the geographical distance between the players, and a parameter V is introduced to denote the inspect-ability about the players. It is found that under the hospitable conditions, cooperation increases with the randomness and is inhibited by the large connectivity for the prisoner's dilemma; however, cooperation is maximal at the moderate rewiring probability and is chaos with the connectivity for the snowdrift game. For the two games, the acuminous sight is in favor of the cooperation under the hospitable conditions; whereas, the myopic eyes are advantageous to cooperation and cooperation increases with the randomness under the hostile condition.
Derivation of Kurtosis and Option Pricing Formulas for Popular Volatility Models with Applications in Finance

This article discusses some topics relevant to financial modeling. The kurtosis of a distribution plays an important role in controlling tail-behavior and is used in edgeworth expansion of the call prices. We present derivations of the kurtosis for a number of popular volatility models useful in financial applications, including the class of random coefficient GARCH models. Option pricing formulas for various classes of volatility models are also derived and a simple proof of the option pricing formula under the Black–Scholes model is given.
The complexity of propositional proofs

In this paper, we consider the complexity of propositional proofs of classical and intuitionistic tautologies. In fact, we describe a nondeterministic polynomial-time decision procedure for intuitionistic implicational tautologies. For this purpose, we reduce a decision problem for intuitionistic implicational tautologies to a decision problem for deductive proof diagrams which are a short form for representing of proofs in the intuitionistic implicational calculus. Next, we transform deductive proof diagrams to a special form in which any proof has the size bounded by a polynomial in the length of input formula. Also, we show that this procedure can be extended to all classical and intuitionistic tautologies, and deduce some corollaries including results about complexity classes and polynomially bounded proof systems.