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An all-sky sample of 1227 visual binaries based on Washington Double Star catalogue is constructed to infer the IMF, mass ratio, and projected distance distribution with a dedicated population synthesis model. Parallaxes from Gaia DR2 and Hipparcos are used to verify the distance distribution. The model is validated on the single-star Tycho-2 sample and successfully reproduces the observed magnitudes and angular separations. The projected separation distribution follows $f(s)\sim s^{-1.2}$ in $10^2 - 2\cdot10^3$ AU range for 1--4.5 $m_{\odot}$ primary stars. Several algorithms are explored as pairing functions. Random pairing is confidently rejected. Primary-constrained (PCP) and split-core pairing (SCP), the scenarios adopting primary component's or total system's mass as fundamental, are considered. The preferred IMF slope is $\alpha \sim 2.8$ either way. A simple power-law mass ratio distribution is unlikely, but the introduction of a twin excess provides a favourable result. PCP with $f(q) \sim q^{-1}$ is preferred with a tiny twin fraction, models with $f(q) \sim q^{-1.5}$ are acceptable when a larger twin excess is allowed. SCP is similar to PCP when a larger slope of the power law is adopted: $f(q)\sim q^{\beta+0.7}$., Comment: 16 pages, 14 figures. MNRAS, Accepted 2020 November 13

For secure transmission of digital images, existing cryptographic algorithms transform coherent visual information into a noise-like appearance prompting an adversary of the presence of a possible cipher. This paper proposes an algorithm that produces a visually coherent and meaningful cipher image. The proposed algorithm consists of a permutation-substitution subroutine to obtain a partial cipher. The Arnold-3D map does the permutation, and a delayed logistic map performs the substitution in this subroutine. The hiding of this partial cipher is done in the reference image using an integer wavelet transform. The pixels of the partial cipher are embedded in the four sub-bands of the decomposed reference image as 4 to 1-pixel encoding using Cantor-like pairing function. In addition to the lossless encryption scheme, the integer nature of all the sub-bands in the wavelet decomposition and the invertible pairing function facilitates the perfect reconstruction of the reference image. One of the significant novelty of this work lies in the subtle use of simple pairing functions, which prohibits the unnecessary increase in the size of the cipher, thereby reducing the storage and transmission costs., Highlights • A novel compression and embedding scheme for generating VMCI. • Subtle use of pairing functions and Integer Wavelet transform in the scheme. • Facilitates perfect decryption/reconstruction of both the original/reference image. • The VMCI transmission cost is reduced by four times as compared to earlier schemes. • Robust and secure against traditional cryptanalysis and steganalysis.

For secure transmission of digital images, existing cryptographic algorithms transform images into a noise-like appearance. One obvious inference that an adversary could draw is that the noise-like texture is a cipher, prompting to apply classical cryptanalysis. This article proposes an efficient algorithm that produces a visually coherent and meaningful cipher image to bypass the cryptanalysis. In the partial-encryption phase, the Arnold-3D map drives the permutation mechanism, whereas the implementation of the diffusion phase is done by harnessing the iterates of the chaotic Logistic map. The partial cipher is compressed using a Cantor-like pairing function that does a 4 to 1 pixel encoding to facilitate embedding. The embedding phase is implemented in the spatial domain by applying Multi-resolution singular value decomposition on the reference image and replacing the vertical, horizontal, diagonal sub-band with the encoded cipher. The encoding of pixels facilitates the transmission of the visually meaningful cipher image to be of the same size as the original image rather than four-times the original image as reported in earlier schemes. Simulation results confirm the security of the scheme.

Recent experiments suggest a multi-component pairing function in Sr2RuO4, which appears to be inconsistent with the absence of an apparent cusp in the transition temperature (Tc) as a function of the uniaxial strain. We show, however, that the theoretical cusp in Tc for a multi-component pairing can be easily smeared out by the spatial inhomogeneity of strain, and the experimental data can be reproduced qualitatively by a percolation model. This shed new light on multi-component pairings. We then perform a thorough group-theoretical classification of the pairing functions, taking the spin-orbit coupling into account. We list all 13 types of two-component spin-singlet pairing functions, with 8 of them belonging to the Eg representation. In particular, we find two types of intra-orbital pairings in the Eg representation ($k_xk_z$, $k_yk_z$) are favorable in view of most existing experiments., 10 pages, 4 figures, 3 tables

This paper proposes an eye control interaction method for digital interface function icons. The method is divided into three steps: 1. Preprocessing of function icons and precoding of eye movement signals. Pairing function icons through the rectangular coordinate system of the two-dimensional image of the eye with the digital code of the eye movement signal, the eye movement signal array of the function icon is generated. 2. The collection of the eye movement signal. The subject performs eye movement according to the digital code of the function icon to complete the start and stop of signal recording. 3. Eye movement signal Output, calculation, recognition and confirmation. Calculate the quadrant position of the pupil center coordinate point, compile the function icon trigger command, and confirm by blinking. This method directly uses the subject’s eye movement signal on the function icon to realize the icon-to-digital interface eye machine Interactive.

Delegation of pairings from a computationally weaker client to a computationally stronger server has been advocated to expand the applicability of pairing-based cryptographic protocols to computation paradigms with resource-constrained devices. Important requirements for such delegation protocols include privacy of the client’s inputs and security of the client’s output, in the sense of detecting, with high probability, any malicious server’s attempt to convince the client of an incorrect pairing result. In this paper we show that pairings with inputs only available in the online phase can be efficiently, privately and securely delegated to a single, possibly malicious, server. We present new protocols in 2 different scenarios: (1) the two pairing inputs are publicly known; (2) privacy of both pairing inputs needs to be maintained (left open in previous papers; e.g., [27]). In both cases, we improve the online-phase client’s runtime with respect to previous work. In the latter case, we show the first protocol where the client’s online-phase runtime is faster than non-delegated computation for all of the most practical known curves. In previous work, the client’s runtime was worse, especially for one of the most practical elliptic curves underlying the pairing function (i.e., BN-12).

The distribution of the spin-singlet component, the short-range spin-triplet component with zero projection, and the long-range spin-triplet component with projection ±1 of the superconducting pairing function has been obtained for different regimes of switching of a spin valve with a three-layer heterostructure (superconductor/ferromagnet/ferromagnet). The distribution of the components is discussed as the main reason for the behavior of the superconducting transition temperature as a function of the angle between the magnetic moments of the ferromagnetic layers in these regimes.

An important challenge in condensed matter physics is understanding iron-based superconductors. Among these systems, the iron selenides hold the record for highest superconducting transition temperature and pose especially striking puzzles regarding the nature of superconductivity. The pairing state of the alkaline iron selenides appears to be of $d$-wave type based on the observation of a resonance mode in neutron scattering, while it seems to be of $s$-wave type from the nodeless gaps observed everywhere on the Fermi surface (FS). Here we propose an orbital-selective pairing state, dubbed $s \tau_{3}$, as a natural explanation of these disparate properties. The pairing function, containing a matrix $\tau_{3}$ in the basis of $3d$-electron orbitals, does not commute with the kinetic part of the Hamiltonian. This dictates the existence of both intraband and interband pairing terms in the band basis. A spin resonance arises from a $d$-wave-type sign change in the intraband pairing component whereas the quasiparticle excitation is fully gapped on the FS due to an $s$-wave-like form factor associated with the addition in quadrature of the intraband and interband pairing terms. We demonstrate that this pairing state is energetically favored when the electron correlation effects are orbitally selective. More generally, our results illustrate how the multiband nature of correlated electrons affords unusual types of superconducting states, thereby shedding new light not only on the iron-based materials but also on a broad range of other unconventional superconductors such as heavy fermion and organic systems., Comment: 9 pages, 5 figures, plus supplementary material; finalized version with a more streamlined presentation; to appear in Npj Quantum Materials. arXiv admin note: text overlap with arXiv:1505.04170

We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Due to the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data., Comment: 6 pages, 3 figures, revised version

Non-magnetic impurity scattering effects on the vortex core states are theoretically studied to clarify the contributions from the sign-change of the pairing function in anisotropic superconductors. The vortex states are calculated by the Eilenberger theory in superconductors with p x -wave pairing symmetry, as well as the corresponding anisotropic s-wave symmetry. From the spatial structure of the pair potential and the local electronic states around a vortex, we examine the differences between anisotropic superconductors with and without sign-change of the pairing function, and estimate how twofold symmetric vortex core images change with increasing the impurity scattering rate both in the Born and the unitary limits. We found that twofold symmetric vortex core image of zero-energy local density of states changes the orientation of the twofold symmetry with increasing the scattering rate when the sign change occurs in the pairing function. Without the sign change, the vortex core shape reduces to circular one with approaching dirty cases. These results of the impurity effects are valuable for identifying the pairing symmetry by observation of the vortex core image by the STM observation.

The Eliashberg theory of superconductivity is based on a dynamical electron-phonon interaction as opposed to a static interaction present in BCS theory. The standard derivation of Eliashberg theory is based on an equation of motion approach, which incorporates certain assumptions such as Migdal's approximation for the pairing vertex. In this paper we provide a functional-integral-based derivation of Eliashberg theory and we also consider its Gaussian-fluctuation extension. The functional approach enables a self-consistent method of computing the mean-field equations, which arise as saddle-point conditions, and here we observe that the conventional Eliashberg self-energy and pairing function both appear as Hubbard-Stratonovich auxiliary fields. An important consequence of this fact is that it provides a systematic derivation of the Cooper and density-channel interactions in the Gaussian-fluctuation response. We also investigate the fluctuation contribution to the diamagnetic susceptibility near the critical temperature.

In this paper $\mathrm{NFU}^{-\mathrm{AC}}$ is used to denote Ronald Jensen's modification of Quine's `New Foundations' Set Theory ($\mathrm{NF}$) fortified with a type-level pairing function but without the Axiom of Choice. The axiom $\mathrm{AxCount}_\geq$ is the variant of the Axiom of Counting which asserts that no finite set is smaller than its own set of singletons. This paper shows that $\mathrm{NFU}^{-\mathrm{AC}}+\mathrm{AxCount}_\geq$ proves the consistency of the Simple Theory of Types with Infinity ($\mathrm{TSTI}$). This result implies that $\mathrm{NF}+\mathrm{AxCount}_\geq$ proves that consistency of $\mathrm{TSTI}$, and that $\mathrm{NFU}^{-\mathrm{AC}}+\mathrm{AxCount}_\geq$ proves the consistency of $\mathrm{NFU}^{-\mathrm{AC}}$., 14 pages

In this paper, we construct an explicit pairing in Cartier series for formal Lorentz groups of the form (X + Y + XY)/(1 + c 2 XY), where c is a unit of the ring of integers of the local field. We prove the basic properties of this pairing, namely, bilinearity and invariance, which make it possible to explicitly construct the generalized Hilbert symbol for formal Lorentz groups over rings of integers of local fields with the use of the obtained pairing.

In [Bue76] , [Bue77] a non-trivial homomorphism δ was constructed from Q -rational points on an elliptic curve to the ideal class group of a quadratic field K = Q ( D ) . In [MT83] it was conjectured that δ was related to a pairing on points of E ( K ) , which has come to be known as the ideal class pairing. In this paper we will show how to write the ideal class pairing in an explicit and easy-to-compute manner, and we will prove by direct calculation that the homomorphism δ is identical to the ideal class pairing with one argument fixed. For any elliptic curve E over a number field K, we will show how to extend the ideal class pairing to a full pairing on E ( K ) , called simply the elliptic curve class pairing, which maps into an extension of the idele class group of K. The explicit formulas we will derive for the elliptic curve class pairing will enable us to prove that there is a natural relationship between this pairing and the Weil descent pairing. The kernel of the elliptic curve class pairing will be determined in many cases where one argument is taken to be a fixed torsion point and, as a corollary, the kernel of δ will be computed for a class of elliptic curves over imaginary quadratic fields.

High-Tc cuprates, iron-based superconductors, heavy-fermion superconductors and κ-type layered organic superconductors share some common features − the proximity of the superconducting state to the magnetic ordered state and the non-s-wave superconducting pairing function. It is generally believed that the Cooper pairings in these unconventional superconductors are mediated by spin fluctuations. In this paper, we present a brief overview on the spin dynamics and unconventional pairing, focusing on high-Tc cuprates and iron-based superconductors. In particular, we will overview the properties of the neutron spin resonance and its possible origin, the pairing mechanism in Hubbard model within the weak-coupling framework and its application to the aforesaid unconventional superconductors. We point out that the interplay between magnetism and superconductivity is still an area of active research.

A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. We propose a certificateless proxy signature (CLPS) scheme, and prove it's security under a stronger security model. Although some good results were achieved in speeding up the computation of pairing function in recent years, it is still interesting to design cryptosystem with less pairing operations. Taken into account the computational costs, our scheme only requires 2 pairing operations in delegation and signing, respectively.

present days electronic communication is a fundamental method of exchanging information. Secure communication is a major concern by which people can share information with varying degrees of certainty that third parties cannot capture the information that is transmitted over network. With the introduction of internet and distributed systems security issues are more challenging and complex. Hence information security is an important consideration in these days. Cryptography and information security is helping to develop more number of practical approaches to enforce security for networks. In this paper the proposed algorithm which uses basic encryption techniques like substitution, transposition, bitwise logical operations along with pairing function to encrypt the data. The algorithm itself generates the key from plain text and hides within plaintext.

Allowing for dynamic information control in Crawford and Sobel’s (1982) cheap-talk game can significantly improve the informativeness of communication. While the constructions offered in Ivanov (2014, 2015) significantly increase the amount of information transmitted in equilibrium, they rely on very demanding assumptions regarding the receiver’s ability to alter the sender’s information during the interim stages of communication. This note offers a new construction and shows that, for the uniform quadratic specification with constant sender’s bias, if the sender’s bias is sufficiently small, there exists a fully revealing equilibrium that does not require interim information control. Only the first-period signal is controlled ex ante, prior to any communication. The sender becomes completely informed at the end of period 2 regardless of his reporting strategy.

This work is based on the double correlated linear aggregations of holes in checkerboard geometry. It is proved that the pairing function symmetry is - d(x*x-y*y), as been observed experimentally. It is also shown that there is a "superconductive spin gap" for the observation of the magnetic incommensurate modulation peaks, in agreement with experiment. In addition, the unperturbed Hamiltonian is reanalyzed and modified.

To defend intelligent transportation networks’ security and privacy, existing standards employ the Public Key Infrastructure (PKI) authentication framework. However, the high associated PKI computation and communication overheads break ground for utilizing an alternative candidate, the Identity-based Cryptographic (IBC) authentication. Most of the underlined calculations of the IBC approaches rely on the elliptic curves’ pairing operation. Since the pairing function is a complex and computation intensive operation, several studies have developed pairingless IBC authentications and applied the hardware security of tamper-proof devices to secure the cryptographic parameters at user-end. Motivated by this trend, we compose a Pairingless Modified Efficient Conditional Privacy-Preserving Authentication Scheme (PME-CPPAS). Our scheme omits the utilization of the complex pairing operation as well as the demand for expensive tamper-proof devices. When analyzing the performance of the presented design, its effectiveness, in comparison to the available pairing-based and pairingless approaches, is proved in terms of computation complexity, communication overhead, and storage overhead. PME-CPPAS achieves less signing computational cost and comparable verification computational performance.

Xiang Qi association in the world has quite large members, so that when organizing a tournament with many participants caused a scheduling problem. Round-robin system which is commonly used in tournament cannot be efficiently used regarding to the number of participant. The higher the number of participant, the longer and the more exhausted the players. This paper suggests Swiss pairing system to do scheduling in Xiang Qi tournament. The capacity of the tournament can be increased, but the player can still compete with the optimal result. The pairing function considers the player's record, the ‘bye’ notes, the player's color preferences, and the origin of the player's club. The time complexity of Swiss pairing and Round-robin is shown in the evaluation where the Swiss-pairing is more efficient than Round-robin system.

A novel method for packet forwarding in MANETs has been proposed in this paper. A node in the network acts as both host and router. Energy utilization of the node increases as all nodes in MANET operate as source, destination, and router to forward packets to the next hop ultimately to reach destination. Routers execute a variety of functions from simple packet classification for forwarding to complex payload revision. As the number of tasks and complexity increases, processing time required also increases resulting in significant processing delay in routers. The proposed work optimizes packet header at transport and network layer by calculating Unique Identifier using pairing function for the fields which do not change for a source–destination pair. This technique optimizes the processing cost of each packet header thereby conserving energy and reducing delay. It also simplifies the task of system administration. This paper elucidates an extension to basic AODV protocol, allowing routing of most packets without an explicit header, reducing the overhead of the protocol while still conserving its basic properties. The proposed method improves the network performance significantly compared to AODV, MTPR, and S-AODV protocol.

In this study, we show how to construct a function from the set [image omitted] of natural numbers that explicitly counts the set [image omitted] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance without any prior knowledge of the Unique Prime Factorization Theorem or other nonelementary results. Unlike Cantor's function, the one we propose makes it very easy to determine what rational number, in unreduced form, is in a given position on the list and vice versa.

Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments (see, e.g., Blaauw 1991, and references therein). Binarity is also a key ingredient in stellar population studies, and is a prerequisite to calibrate the binary evolution channels. In this paper we present an overview of several commonly used methods to pair individual stars into binary systems, which we refer to as pairing functions. These pairing functions are frequently used by observers and computational astronomers, either for their mathematical convenience, or because they roughly describe the expected outcome of the star forming process. We discuss the consequences of each pairing function for the interpretation of observations and numerical simulations. The binary fraction and mass ratio distribution generally depend strongly on the selection of the range in primary spectral type in a sample. The mass ratio distribution and binary fraction derived from a binarity survey among a mass-limited sample of targets is thus not representative for the population as a whole. Neither theory nor observations indicate that random pairing of binary components from the mass distribution, the simplest pairing function, is realistic. It is more likely that companion stars are formed in a disk around a star, or that a pre-binary core fragments into two binary components. The results of our analysis are important for (i) the interpretation of the observed mass ratio distribution and binary fraction for a sample of stars, (ii) a range of possible initial condition algorithms for star cluster simulations, and (iii) how to discriminate between the different star formation scenarios., 43 pages, 18 figures, accepted for publication in A&A

Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments. Binarity is also a key ingredient in stellar population studies and is a prerequisite to calibrate the binary evolution channels. In these proceedings we present an overview of several commonly used methods to pair individual stars into binary systems, which we refer to as the pairing function. Many pairing functions are frequently used by observers and computational astronomers, either for the mathematical convenience, or because they roughly describe the expected outcome of the star forming process. We discuss the consequences of each pairing function for the interpretation of observations and numerical simulations. The binary fraction and mass ratio distribution generally depend strongly on the selection of the range in primary spectral type in a sample. These quantities, when derived from a binary survey with a mass-limited sample of target stars, are thus not representative for the population as a whole., Comment: 4 pages, 2 figures, in: Galactic and stellar dynamics in the era of high-resolution surveys, Boily C., Combes F., Hensler G., eds., Strasbourg (France), March 2008, in press (Astron. Nachr.)

The process of distributing information in a secured way is called Secured Communication. Secured information involves Encryption procedure at the sender side and Decryption process at the receiver side of the communication system. Many Ciphers have been developed to provide data guard. The effectiveness of the Ciphers that are being used depends mainly on their throughput and memory constraint. The proposed method encrypts two messages at a time with the help pairing function so that it reduces the size to half of original length. The key is embedded within the cipher text with the help of transposition ciphers. The proposed method decrypts the single message (which is transmitted) into two messages with the help of depairing functions.

In Mathematics is megethology (Lewis (1993). Philosophia Mathematica, 1(1), 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification.

In [1] the class of safe recursive functions over an arbitrary structure is defined. We prove that in this class, one cannot define a total pairing function independently of the structure. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Pairings are typically implemented using ordinary pairing-friendly elliptic curves. The two input groups of the pairing function are groups of elliptic curve points, while the target group lies in the multiplicative group of a large finite field. At moderate levels of security, at least two of the three pairing groups are necessarily proper subgroups of a much larger composite-order group, which makes pairing implementations potentially susceptible to small-subgroup attacks. To minimize the chances of such attacks, or the effort required to thwart them, we put forward a property for ordinary pairing-friendly curves called subgroup security. We point out that existing curves in the literature and in publicly available pairing libraries fail to achieve this notion, and propose a list of replacement curves that do offer subgroup security. These curves were chosen to drop into existing libraries with minimal code change, and to sustain state-of-the-art performance numbers. In fact, there are scenarios in which the replacement curves could facilitate faster implementations of protocols because they can remove the need for expensive group exponentiations that test subgroup membership.