Miracle-dz/UniFAR-FTUs huggingface dataset:
A New Method to Mine Classification Rules

This paper makes use of knowledge granular to present a new method to mine rules based on granule. First, use the measure to measure the importance of attribute, and get the granularity of the universe, and then repeat this procedure to every granule of the granularity, until the decision attribute has only one value for all granules, then we will describe every granule to get the rule. The analysis of the algorithm and the experiment show that the method presented is effective and reliable.Classification rules is the main target of association rule,decision tree and rough sets.a new algorithm to mine classification rules based on the importance of attribute value supported.this algorithm views the importance as the number of tuple pair that can be discernible by it,and the rules obtained from the constructed decision tree is equivalent to those obtained from ID3,which can be proved by the idea of rule fusion.however, this method is of low computation,and is more suitable to large database . rough sets is a techniques applied to data mining problems. This paper presents a new method to extract efficiently classification rules from decision table. The new model uses rough set theory to help in decreasing the computational effort needed for building decision tree by using what is called reduct algorithm and a rules set (knowledge) is generated from the decision table. reliable classifier architecture is obtained and its effectiveness is verified by the experiments comparing with traditional rough set approaches. Data mining research has made much effort to apply various mining algorithms efficiently on large databases.
The reflectarray antenna

A class of antennas that utilizes arrays of elementary antennas as reflecting surfaces has been investigated. An antenna of this type is here called a Reflectarray. It has been found that the Reflectarray combines much of the simplicity of the reflector-type antenna with the performance versatility of the array type. The reflecting surfaces employed in these antennas are characterized by a surface impedance that can be synthesized to produce a variety of radiation patterns. The equations of the surface impedance as a function of the desired reflected phase front is derived for the lossless case and methods of realizing this surface impedance are presented. Experimental results of a waveguide array type Reflectarray are given including pencil beam, broad beam and scanning modes. Data on the effects of specific phase errors are presented.
Group divisible designs with block size 4 and type gum1

Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type gum1 are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m>0 and m≠g are sufficient in the following cases: g≡0( mod 6) , g=2 with one exception, 2651, g=10 , and g=11 .
Tensor Networks in a Nutshell

Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and pictorially reason about quantum circuits, channels, protocols, open systems and more. Our goal is to explain tensor networks and some associated methods as quickly and as painlessly as possible. Beginning with the key definitions, the graphical tensor network language is presented through examples. We then provide an introduction to matrix product states. We conclude the tutorial with tensor contractions evaluating combinatorial counting problems. The first one counts the number of solutions for Boolean formulae, whereas the second is Penrose's tensor contraction algorithm, returning the number of $3$-edge-colorings of $3$-regular planar graphs.
Summation arithmetic functions with asymptotically independent summands

The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is also prove that the limiting distribution of the summation arithmetic function with asymptotically independent summands is normal under certain conditions for summands of the summation arithmetic function.
Characteristics of a Supersonic Plasma Flow in a Magnetic Nozzle

A high-density and high-speed flowing helium-plasma is produced quasi-steadily (1 ms) by use of a magneto-plasma-dynamic arcjet (MPDA) in various external magnetic field configurations. In a uniform magnetic field configuration, an ion acoustic Mach number Mi of the plasma flow is limited to be nearly unity. In a divergent magnetic nozzle configuration, on the other hand, the Mach number increases up to almost 3. The Mach number increases in proportion to the gradient of the magnetic field. Spatial variations of Mi are well predicted by an isentropic model of compressible flow. The Mach number decreases in the downstream region due to charge-exchange collisional processes that are caused by a limited pumping capability of surface-recombined neutral gases.
Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential

We study the existence, regularity and so-called `strict physicality' of weak solutions of a coupled Navier-Stokes Q-tensor system which is proposed as a model for the incompressible flow of nematic liquid crystal materials. An important contribution to the dynamics comes from a singular potential introduced by John Ball and Apala Majumdar (Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst., Vol. 525: pp. 1-11, 2010) which replaces the commonly employed Landau-de Gennes bulk potential. This is built into our model to ensure that a natural physical constraint on the eigenvalues of the Q-tensor order parameter is respected by the dynamics of the system.
Chow motive of Fulton-MacPherson configuration spaces and wonderful compactifications

We study the Chow groups and the Chow motives of the wonderful compactifications $Y_{\mathcal{G}}$ of arrangements of subvarieties. We prove a natural decomposition of the Chow motive of $Y_\mathcal{G}$, in particular of the Fulton-MacPherson configuration space $X[n]$. As a consequence, we prove a decomposition of the Chow motive of $X[n]/\frak{S}_n$. A generating function for the Chow groups and for the Chow motive of $X[n]$ is given.
Structure-Preserving {\Gamma}QR and {\Gamma}-Lanczos Algorithms for Bethe-Salpeter Eigenvalue Problems

To solve the Bethe-Salpeter eigenvalue problem with distinct sizes, two efficient methods, called {\Gamma}QR algorithm and {\Gamma}-Lanczos algorithm, are proposed in this paper. Both algorithms preserve the special structure of the initial matrix $H=\begin{bmatrix}A & B-\overline{B} & -\overline{A}\end{bmatrix}$, resulting the computed eigenvalues and the associated eigenvectors still hold the properties similar to those of $H$. Theorems are given to demonstrate the validity of the proposed two algorithms in theory. Numerical results are presented to illustrate the superiorities of our methods.
General Integral Inequalities Including Weight Functions

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many existing inequalities in the published literature, including those with free matrix variables, are the special cases of our inequalities. An relation on the lower bounds of the proposed inequalities is also established. For specific applications, our inequalities are applied to construct a Liapunov-Krasovskii functional for the stability analysis of a linear coupled differential-difference system with a distributed delay, which gives to equivalent stability conditions based on the properties of the proposed inequalities. Finally, it is worthy to note that the inequalities in this note can be applied in general contexts such as the stability analysis of PDE-related systems or sampled-data systems.
An Abstract Linking Theorem Applied to Indefinite Problems Via Spectral Properties

Abstract An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite-dimensional Hilbert Spaces. The applications are given to Schrödinger equations. Here spectral properties inherited by the potential features are exploited in order to establish a linking structure, and hence hypotheses of monotonicity on the nonlinearities are discarded.
Vector Contraction Analysis for Nonlinear Dynamical Systems

This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently induces a vector distance between any pair of trajectories of the system, offers an amenable framework as each component of vector-valued norm function satisfies fewer strict conditions as that of standard contraction analysis. Particularly, every element of vector-valued norm derivative need not be strictly negative definite for convergence of any pair of trajectories of the system. Moreover, vector-valued norm derivative satisfies a component-wise inequality employing some comparison system. In fact, the convergence analysis is performed by comparing the relative distances between any pair of the trajectories of the original nonlinear system and the comparison system. Comparison results are derived by utilizing the concepts of quasi-monotonicity property of the function and vector differential inequalities. Moreover, the results are also derived in the framework of the cone ordering instead of utilizing component-wise inequalities between vectors. In addition, the proposed framework is illustrated by examples.
Global linear convergent algorithm to compute the minimum volume enclosing ellipsoid

The minimum volume enclosing ellipsoid (MVEE) problem is an optimization problem in the basis of many practical problems. This paper describes some new properties of this model and proposes a first-order oracle algorithm, the Adjusted Coordinate Descent (ACD) algorithm, to address the MVEE problem. The ACD algorithm is globally linear convergent and has an overwhelming advantage over the other algorithms in cases where the dimension of the data is large. Moreover, as a byproduct of the convergence property of the ACD algorithm, we prove the global linear convergence of the Frank-Wolfe type algorithm (illustrated by the case of Wolfe-Atwood's algorithm), which supports the conjecture of Todd. Furthermore, we provide a new interpretation for the means of choosing the coordinate axis of the Frank-Wolfe type algorithm from the perspective of the smoothness of the coordinate axis, i.e., the algorithm chooses the coordinate axis with the worst smoothness at each iteration. This finding connects the first-order oracle algorithm and the linear optimization oracle algorithm on the MVEE problem. The numerical tests support our theoretical results.
Equilibrium properties of a partially ionized plasma

A model for a partially-ionized, partially-dissociated plasma has been formulated using known theoretical concepts to describe both bound and free electron states, internal molecular degrees of freedom and Coulomb interactions. It has been applied to a system of particles arising from the hydrogen molecule. The Coulomb interaction is treated in the classical Debye approximation. However, a distance of closest approach between ions and electrons depending on the kinetic energy of the electrons is included to avoid the short range divergence of the Coulomb potential. The kinetic energy of the free electrons is calculated from the partition function for a perfect Fermi gas. The vibrational and rotational motion is treated in the harmonic oscillator and rigid rotor approximation with the number of energy levels counted for a given electronic state depending on the dissociation energy of the state. A volume dependence of the bound electronic energy eigenvalues is included by considering the effect of surrounding particles as a confinement of a given particle to a spherical box of variable size. For the counting of the bound electronic states, a given state is bound until its energy increases to zero due to confinement. From the partition function for the entire system, the free energy is calculated. By a minimization of the free energy of the system, the equilibrium composition as a function of temperature and volume is obtained. Then not only can thermodynamic quantities be calculated, but it is believed that a reasonable approximation to the correct balance of molecular, ionic and free electonic states is achieved over a wide range of V-T space. Consequently, regions where incomplete ionization and dissociation are important are delineated. In addition, for different regions of V-T space, the relative contributions of charged particle interactions, non-classical behaviour of electrons, internal degrees of freedom and translation to the total energy of the system can be determined.
Lyapunov graphs of nonsingular Smale flows on $S^{1}\times S^{2}$

In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on $S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on $S^1 \times S^2$. We also study the singular type vertices in Lyapunov graphs of nonsingular Smale flows on 3-manifolds.
Localized charge trapping due to adsorption in nanotube field-effect transistor and its field-mediated transport

Ambient adsorption is known to cause hysteretic behavior and irreproducible transport phenomena in carbon nanotubes and their corresponding field-effect transistors. The authors report that pulsed measurements, with a time constant below 500μs, provide reproducible characteristics of carbon nanotube field-effect transistor with minimal hysteresis. Transient measurements of fabricated devices in air reveal multiple time constants whose origins are linked to adsorption processes and the local electric field environment of the carbon nanotube surface. Additional measurements in vacuum allow them to further elaborate on distinct effects on device transport characteristics due to adsorption.
Noise-equivalent power characterization of an uncooled microbolometer-based THz imaging camera

A THz camera based on an uncooled microbolometer 160X120 pixel array with nominal pitch of 52 μm has been developed at INO and initial transmission and reflection images showed promise. In the present paper, the characterization of both standard infrared and THz-optimized uncooled microbolometer pixel arrays are presented at both infrared and THz wavelengths. Measurements in the THz region has been performed using non-uniform low-power quantum-cascade laser (QCL) and uniform high-power far-infrared laser (FIR laser) beams at 3 THz and 4.25 and 2.54 THz, respectively. A measurement comparison has been achieved in the infrared using a blackbody radiation. Different methods for noise-equivalent power (NEP) measurements have been investigated. These characterization methods are promising especially for non-uniform laser beams irradiated on pixel arrays. The NEP results obtained from the different methods are in good agreement independent of the method used in the experiments. The results show a high sensitivity of the THz-optimized pixel array in the THz region. Large beam area reflection imaging of obscured materials at 2.54 THz have been performed at video rates of 30 frames per second using the THz-optimized pixel array equipped with a semi-custom fast THz objective, proving that the INO THz camera provides a promising solution for stand-alone imaging systems.
Variational methods for Dirac wave equations

Several difficulties associated with the use of the Dirac operator in atomic and molecular structure calculations are analysed. The physical stability of the ground states of atoms and molecules requires the use of Dirac's 'hole' (positron) theory to prevent the decay of bound electrons into the lower continuum. Thus relativistic bound-state calculations for atoms or molecules can, in practice, more or less ignore the negative energy states. A rigorous theorem on the eigenvalue distribution in finite-basis-set variational calculations with one-body Dirac operators is presented, and its implications for many-body atomic or molecular systems are described. The theory shows that the basis sets must satisfy suitable boundary conditions to ensure acceptable results. The theory is illustrated with numerical studies of convergence to hydrogenic solutions using finite basis sets, and to closed-shell Dirac-Fock problems. In all cases, the bound-state variational energies are rigorous upper bounds. Finally, the author presents the first results of a calculation in which the Breit interaction has been included in the self-consistent field instead of being treated as a first-order perturbation.
A unifying framework for the analysis of proportionate NLMS algorithms

Despite being a de facto standard in sparse adaptive filtering, the two most important members of the class of proportionate normalised least mean square (PNLMS) algorithms are introduced empirically. Our aim is to provide a unifying framework for the derivation of PNLMS algorithms and their variants with an adaptive step‐size. These include algorithms with gradient adaptive learning rates and algorithms with adaptive regularisation parameters. Convergence analysis is provided for the proportionate least mean square (PLMS) algorithm in both the mean and mean square sense and bounds on its parameters are derived. An alternative, more insightful approach to the convergence analysis is also presented and is shown to provide an estimate of the optimal step‐size of the PLMS. Incorporating the so obtained step‐size into the PLMS gives the standard PNLMS together with a unified framework for introducing other adaptive learning rates. Simulations on benchmark sparse impulse responses support the approach. Copyright © 2014 John Wiley & Sons, Ltd.
A hypercyclicity criterion for non-metrizable topological vector spaces

We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Doma\'nski \cite{bd12}, and the "snake shift" constructed in \cite{bfpw} on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space $Y$ for which the operator restricted to $Y$ is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces.
Closures of exponential families

The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential family, introduced previously by the authors, and a new concept of accessible faces of a convex set. Two other closures related to the information divergence are also characterized.
Delay-Minimizing Capacity Allocation in an Infinite Server-Queueing System

We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is an infinite sequence of service rates. We study the probabilistic properties of this system by considering overflows from sub-systems with a finite number of servers. Several stability measures are suggested and analysed. The tail of the series of service rates that minimizes the average expected delay (service time) is shown to be approximately geometrically decreasing. We use this property in order to approximate the optimal allocation of service rates by constructing an appropriate dynamic program.
Diagnosis of climate models in terms of transient climate response and feedback response time

Climate models have traditionally been characterised by their climate sensitivity (equilibrium response to a doubling of CO2) and their ocean heat uptake. Together these determine a third property: the transient climate response to a linear increase in radiative forcing. A fourth property, the feedback response time is introduced here and shown to provide a complementary diagnostic of climate model behaviour. In particular, it demonstrates that the discrepancy between recent climate observations and the general circulation models in the ‘IPCC ensemble’ primarily arises because the models are undersampling the range of transient climate responses consistent with recent attributable greenhouse warming. Copyright © 2007 Royal Meteorological Society
Some Alternatives to the Box-Cox Regression Model

A nonlinear regression model is proposed as an alternative to the Box-Cox regression model for nonnegative variables. The functional form contains linear, exponential, and reciprocal models as special cases. Unlike Box-Cox type approaches, the proposed estimators of the conditional mean function are robust to conditional variance and other distributional misspecifications. Computationally simple, robust Lagrange multiplier statistics for restricted versions of the model are derived. Scale invariant t-statistics are proposed and the Lagrange multiplier statistic for exclusion restrictions is shown to be scale invariant. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
Ameboid cell migration through regular arrays of micropillars under conﬁnement

Migrating cells often encounter a wide variety of topographic features—including the presence of obstacles— when navigating through crowded biological environments. Unraveling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study the impact of geometrical cues on ameboid migration of HL-60 cells differentiated into neutrophils. A microﬂuidic device is designed to track the cells in conﬁning geometries between two parallel plates with distance h , in which identical micropillars are arranged in regular pillar forests with pillar spacing e . We observe that the cells are temporarily captured near pillars, with a mean contact time that is independent of h and e . By decreasing the vertical conﬁnement h , we ﬁnd that the cell velocity is not affected, while the persistence reduces; thus, cells are able to preserve their velocity when highly squeezed but lose the ability to control their direction of motion. At a given h , we show that by decreasing the pillar spacing e in the weak lateral conﬁnement regime, the mean escape time of cells from effective local traps between neighboring pillars grows. This effect, together with the increase of cell-pillar contact frequency, leads to the reduction of diffusion constant D . By disentangling the contributions of these two effects on D in numerical simulations, we verify that the impact of cell-pillar contacts on cell diffusivity is more pronounced at smaller pillar spacing. micropillars while the vertically between two parallel squeezing, control of of motion. effects of cell-pillar interactions