Differential Approximation Research Articles

Optimizing S-box generation based on the Adaptive Agent Heroes and Cowards Algorithm

This paper introduces a new variant of a metaheuristic algorithm based on Agent Heroes and Cowards Algorithm (AHC), called Adaptive Agent Heroes and Cowards Algorithm (AAHC). The main feature of AAHC is the fact that the algorithm allows adaptive assignment of its population agents into cowards and heroes based on the exponential controlling functions. Furthermore, unlike its predecessor, AAHC also permits systematic manipulation of candidate solutions around the global best agent via the swap operator to boost its search intensification process. Meanwhile, to further enhance the diversification its solution, AHC also exploit the Tent map as the pseudo random generator replacement during its initial population initialization. Experimental results based on the generation of 8 × 8 substitution-box demonstrate that the proposed AAHC outperforms other competing metaheuristic algorithms in two main S-box criteria namely nonlinearity and strict avalanche criteria whilst maintaining commendable performances on bits independence criteria, differential approximation probability, linear approximation probability and transparency order.

S-Box Construction Method Based on the Combination of Quantum Chaos and PWLCM Chaotic Map

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

Symbolic Music Generation with Transformer-GANs

Autoregressive models using Transformers have emerged as the dominant approach for music generation with the goal of synthesizing minute-long compositions that exhibit large-scale musical structure. These models are commonly trained by minimizing the negative log-likelihood (NLL) of the observed sequence in an autoregressive manner. Unfortunately, the quality of samples from these models tends to degrade significantly for long sequences, a phenomenon attributed to exposure bias. Fortunately, we are able to detect these failures with classifiers trained to distinguish between real and sampled sequences, an observation that motivates our exploration of adversarial losses to complement the NLL objective. We use a pre-trained Span-BERT model for the discriminator of the GAN, which in our experiments helped with training stability. We use the Gumbel-Softmax trick to obtain a differentiable approximation of the sampling process. This makes discrete sequences amenable to optimization in GANs. In addition, we break the sequences into smaller chunks to ensure that we stay within a given memory budget. We demonstrate via human evaluations and a new discriminative metric that the music generated by our approach outperforms a baseline trained with likelihood maximization, the state-of-the-art Music Transformer, and other GANs used for sequence generation. 57% of people prefer music generated via our approach while 43% prefer Music Transformer.

Approximation of the Double Traveling Salesman Problem with Multiple Stacks

The Double Traveling Salesman Problem with Multiple Stacks, DTSPMS, deals with the collect and delivery of n commodities in two distinct cities, where the pickup and the delivery tours are related by LIFO constraints. During the pickup tour, commodities are loaded into a container of k rows, or stacks, with capacity c. This paper focuses on computational aspects of the DTSPMS, which is NP-hard. We first review the complexity of two critical subproblems: deciding whether a given pair of pickup and delivery tours is feasible and, given a loading plan, finding an optimal pair of pickup and delivery tours, are both polynomial under some conditions on k and c. We then prove a (3k)/2 standard approximation for the Min Metric k DTSPMS, where k is a universal constant, and other approximation results for various versions of the problem. We finally present a matching-based heuristic for the 2 DTSPMS, which is a special case with k=2 rows, when the distances are symmetric. This yields a 1/2−o(1), 3/4−o(1) and 3/2+o(1) standard approximation for respectively Max 2 DTSPMS, its restriction Max 2 DTSPMS(1,2) with distances 1 and 2, and Min 2 DTSPMS(1,2), and a 1/2−o(1) differential approximation for Min 2 DTSPMS and Max 2 DTSPMS.

Smooth approximation of probability and quantile functions: vector generalization and its applications

In this paper, we provide an approximation method for probability function and its derivatives, which allows using the first order numerical algorithms in stochastic optimization problems with objectives of that type. The approximation is based on the replacement of the indicator function with a smooth differentiable approximation – the sigmoid function. We prove the convergence of the approximation to the original function and the convergence of their derivatives to the derivatives of the original ones. This approximation method is highly universal and can be applied in other problems besides stochastic optimization – the approximation of the kernel of the probability measure, considered in the present article as an example, and the confidence absorbing set approximations.

Joint Inversion of Multiphysical Parameters Based on a Combination of Cosine Dot-Gradient and Joint Total Variation Constraints

The joint inversion of structural constraints is a new and rapidly developing detection technology in comprehensive geophysical interpretation. In this article, a new structural constraint 2-D multiphysical parameter joint inversion algorithm for magnetotelluric (MT), gravity, and magnetic data is developed. The structural constraint term is a combination of cosine dot-gradient (CDG) and joint total variation (JTV) constraints, which not only has characteristics of traditional dot product and cross-gradient structure constraints but also avoids the uncertainty of dot product constraints predicting the gradient direction of the model parameters, overcomes the need for high-order differential approximation of the cross-gradient constraint, ignores the influence of the gradient amplitude of different model parameters on the weight of the structural constraint of different regions, and enhances the reconstruction accuracy of the underground discontinuous interface. To more easily combine multiple optimization algorithms to improve the resolution and computational efficiency of joint inversion, an adaptive inexact structural resemblance (IESR) algorithm is developed to minimize numerical solutions to the objective function. Experimental results have demonstrated that the CDG constraint has a wider use range than the traditional structural constraint, the addition of the JTV constraint can recover the underground discontinuous interface, and an inversion result of higher resolution can be obtained using the adaptive IESR algorithm.

Improving robustness of deep neural networks via large-difference transformation

Recent research shows that previous model-agnostic methods that transform the input images before feeding them into the classifiers fail to defend against the adversarial examples. We assume that the small-difference transformations commonly used are the blame and therefore propose a new model-agnostic defense using a large-difference transformation. Specifically, we try to apply the novel primitive-based transformation that re-builds the input images by primitives of colorful triangles. In terms of the distortions required to completely break the defenses, our experiments on the ImageNet subset show that significantly large distortions (0.12) are needed to break the defense compared to other state-of-the-art model-agnostic defenses (0.05–0.06) under the strong attack method Backward Pass Differentiable Approximation (BPDA). This finding indicates that large difference transformation can improve the adversarial robustness, suggesting a promising new direction towards solving the challenge of adversarial robustness.

Phase Object Tomography Reconstruction Based on high-order Transport of Intensity Equation

The phase of the object contains the depth, shape, refractive index and other information of the object surface, which is more important than the intensity. As a classical phase retrieval algorithm, the Transport of Intensity Equation(TIE) can directly obtain the phase calculated from the known intensity. In this paper, a new algorithm is proposed to reconstruct the three-dimensional phase information of an object by tomography. The algorithm obtains high-precision phase input through the high-order TIE, and then reconstructs the three-dimensional phase information of the object by using Fourier slice theorem backprojection tomography. The experimental results show that the algorithm can solve the problem of low phase accuracy caused by intensity differential approximation constraints, and can obtain high-precision 3D phase reconstruction results of objects.

Panel quantile regression neural network for electricity consumption forecasting in China: a new framework

ABSTRACT Accurate electricity consumption forecasting (ECF) is challenging due to its complexity, and it is more challenging for a provincial ECF in China when it comes to the great heterogeneity among provinces. To depict and predict electricity consumption, a new framework, the panel quantile regression neural network (PQRNN), is developed by adding an artificial neural network structure to a panel quantile regression model. The PQRNN can account for the complex nonlinear relationship and the latent provincial heterogeneity simultaneously. In addition, a differential approximation of the quantile loss function and a quasi-Newton optimization based on the backpropagation algorithm is developed. The prediction accuracy is evaluated by an empirical analysis of the provincial panel dataset from 1999 to 2017 in China, which shows that the ECF based on the PQRNN performs well. Finally, the provincial electricity consumptions over the next 5 years (2018–2022) are predicted by utilizing the PQRNN model.

Improved chance index and its solutions for quantifying the structural safety degree under twofold random uncertainty

For the twofold random uncertainty problem of the random input variables with random distribution parameters, there still lacks a reasonable index to measure its safety degree. Aiming to this issue and starting from the characteristics of the failure probability function varying with the random distribution parameters under the twofold random uncertainty, an improved chance index (ICI) is proposed to quantify the safety degree of the structure. The proposed ICI takes into account the bilateral information of the statistical distribution of the failure probability function, and it uses the average of the upper and lower bilateral fractiles of the failure probability function with respect to a given confidence as the ICI. Compared with the existing primitive chance index (PCI), the information extracted by the ICI is more comprehensive. The ICI has self-duality, which can avoid the self-contradiction judgement resulted from the PCI. After the specific properties of the proposed ICI are proved, a differential interval approximation combined with numerical simulation is established for solving ICI, in which an adaptive Kriging model is nested for improving the efficiency, and multi-training-point based on cluster analysis and candidate sample pool reduction strategy are employed to improve the efficiency of constructing the Kriging model.

An Integrated Approach to Design and Develop High-Performance Polymer-Composite Thermal Interface Material.

A computational framework based on novel differential effective medium approximation and mean-field homogenization is used to design high-performance filler-laden polymer thermal interface materials (TIMs). The proposed design strategy has the capability to handle non-dilute filler concentration in the polymer matrix. The effective thermal conductivity of intended thermal interface composites can be tailored in a wide range by varying filler attributes such as size, aspect ratio, orientation, as well as filler–matrix interface with an upper limit imposed by the shear modulus. Serval potential polymers and fillers are considered at the design stage. High-density polyethylene (HDPE) and thermoplastic polyurethane (TPU) with a non-dilute concentration (~60 vol%) of ceramic fillers exhibit high thermal conductivity (4–5 W m−1 K−1) without compromising the high compliance of TIMs. The predicted thermal conductivity and coefficient of thermal expansion are in excellent agreement with measured data of various binary composite systems considering HDPE, TPU, and polypropylene (PP) loaded with Al2O3 and AlN fillers in varying sizes, shapes, and concentrations, prepared via the melt-mixing and compression-molding route. The model also validates that manipulating filler alignment and aspect ratio can significantly contribute to making heat-conducting networks in composites, which results in ultra-high thermal conductivity.

A novel finite rings based algebraic scheme of evolving secure S-boxes for images encryption

Substitution-boxes have significant role in block ciphers as they are the only component which offers nonlinearity in the anticipated symmetric encryption systems. This paper proposed to present a novel algebraic scheme to generate secure 8 × 8 substitution-boxes. We find the finite rings of integers with exactly 256 unit elements which are utilized to construct S-boxes. Firstly, the unit elements of the selected rings are used to create the initial random sequence of 256 elements. Secondly, the newly defined bijective polynomial maps are applied to create two initial seed S-boxes of decent cryptographic strength. Lastly, appropriate permutations of a symmetric group of degree 16 are employed to evolve two more S-boxes. The performances of the generated S-boxes are tested through the standard analyses consisting of criterions such as nonlinearity test, probability tests (linear and differential approximation), strictly avalanche criteria, and output bits independence criteria. Moreover, we examine the strength of generated S-boxes for symmetric image encryption applications through various performance measures. The simulation outcomes confirm the effectiveness of proposed scheme for secure communication.

Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection

Penalized factor analysis is an efficient technique that produces a factor loading matrix with many zero elements thanks to the introduction of sparsity-inducing penalties within the estimation process. However, sparse solutions and stable model selection procedures are only possible if the employed penalty is non-differentiable, which poses certain theoretical and computational challenges. This article proposes a general penalized likelihood-based estimation approach for single- and multiple-group factor analysis models. The framework builds upon differentiable approximations of non-differentiable penalties, a theoretically founded definition of degrees of freedom, and an algorithm with integrated automatic multiple tuning parameter selection that exploits second-order analytical derivative information. The proposed approach is evaluated in two simulation studies and illustrated using a real data set. All the necessary routines are integrated into the R package penfa.

Анализ межрегиональных миграционных потоков в России в проекции отдельных видов миграции

The impact of interregional migration on regional economic and social sphere necessitates the determination of migration factors. An analysis of existing studies has shown that gravity models can be considered the most effective tool for migration flows analysis. At the same time existing studies show a weak elaboration of approaches that involve the separation of migration into different types depending on the goal of the relocation. The purpose of the article is to analyze the interregional migration flows in the context of types of migration identifying a set of factors that determine a particular type of migration. The main result obtained by the authors is the determination of three regional clusters that attract a certain type of migrants. Clustering was carried out using a set of indicators with a model-oriented clustering methods. The main conclusions made in the article are related to improving the quality of models when dividing regions into clusters and including different variables for certain types of migration. However, the authors note that the input data for the analysis is somewhat noisy, since it contains migrants of all ages. Therefore, the obtained regional groupings by type of migration are only the first approximation of differentiation by type of arriving or departing citizens. The results of the study can be used for further work on the definition of the determinants of interregional migration, as well as for studies on the impact of migration on regional labor markets and socioeconomic situation of regions.

14‐Bit Fully Differential SAR ADC with PGA Used in Readout Circuit of CMOS Image Sensor

This paper proposes a 14‐bit fully differential Successive Approximation Register (SAR) Analog‐to‐Digital Converter (ADC) with a programmable gain amplifier (PGA) used in the readout circuit of CMOS image sensor (CIS). SAR ADC adopts two‐step scaled‐reference voltages to realize 14‐bit conversion, aimed at reducing the scale of capacitor array and avoiding using calibration to mitigate the impact of offset and mismatch. However, the reference voltage self‐calibration algorithm is applied on the design to guarantee the precision of reference voltages, which affects the results of conversion. The three‐way PGA provides three types of gains: 3x, 4x, and 6x, and samples at the same time to get three columns of pixel signal and increase the system speed. The pixel array of the mentioned CIS is 1026 × 1024, and the pixel pitch is 12.5 μm × 12.5 μm. The prototype chip is fabricated in the 180 nm CMOS process, and both digital and analog voltages are 3.3 V. The total area of the chip is 6.25 × 18.38 mm2. At 150 kS/s sampling rate, the SNR of SAR ADC is 71.72 dB and the SFDR is 82.91 dB. What is more, the single SAR ADC consumes 477.2 uW with the 4.8 VPP differential input signal and the total power consumption of the CIS is about 613 mW.

Phoneme Level Lyrics Alignment and Text-Informed Singing Voice Separation

The goal of singing voice separation is to recover the vocals signal from music mixtures. State-of-the-art performance is achieved by deep neural networks trained in a supervised fashion. Since training data are scarce and music signals are extremely diverse, it remains challenging to achieve high separation quality across various recording and mixing conditions as well as music styles. In this paper, we investigate to which extent the separation can be improved when lyrics transcripts are used as additional information. To this end, we propose a joint approach to phoneme level lyrics alignment and text-informed singing voice separation. It is based on DTW-attention, a new monotonic attention mechanism including a differentiable approximation of dynamic time warping. Experimental results show that the method can align phonemes with mixed singing voice with high precision given accurate transcripts. It also achieves competitive results on challenging word level alignment test sets using less training data than state-of-the-art methods. Sequential alignment and informed separation lead to improved separation quality according to objective measures. Text information helps preserving spectral phoneme properties in the separated voice signals.

Construction of S-Boxes Using Different Maps Over Elliptic Curves for Image Encryption

In this article, we present an encryption technique that can encrypt any digital data. The proposed scheme basically depends on a substitution-permutation network. Two separate bijective maps are used in the proposed algorithm. Firstly, the substitution boxes are used to perform the substitution process. This technique uses elliptic curves (ECs) to create several substitution boxes with good cryptographic properties. The generated substitution boxes are utilized to replace the arrange data that produces the most uncertainty in the plain image data. Further, we used the permutation process to generate strong randomness in the proposed technique. For the evaluation of the stability of the proposed algorithm; nonlinearity, linear approximation probability, bit independence criterion, strict avalanche criterion and differential approximation probability were performed on the substitution boxes. Differential attacks ( Number of Changing Pixel Rate (NPCR), Uniform Average Change Intensity (UACI)) and statistical tests ( Entropy, Correlation) were performed on the encrypted images to check their resistance against different attacks. The execution and image analysis reveals that the proposed scheme attains good encryption results while requiring minimal computing ability and has efficient potential in real-time image encryption applications.

Nonparametric estimation of the fragmentation kernel based on a partial differential equation stationary distribution approximation

AbstractWe consider a stochastic individual‐based model in continuous time to describe a size‐structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We here address the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier techniques we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the nonstandard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling.

Compact and efficient structure of 8-bit S-box for lightweight cryptography

In this paper, we design an inversion-based S-box with better hardware implementation than the AES S-box with similar cryptographic properties. The proposed S-box computation involves basically two steps, the field inversion, and the affine transformation. The constructed S-box uses a cost-efficient affine transformation with low area resources and low critical path delay (CPD). The sub-blocks of the S-box, such as field inversion in F24, are implemented based on the efficient circuits. A large number of gates, in the structure, have been implemented by 2-input NAND and 2-input NOR gates to reduce delay and area. The cryptographic strength of the proposed S-boxes is analyzed by studying the properties of S-box such as Nonlinearity, Differential uniformity (DU), Strict avalanche criterion (SAC), Algebraic degree (AD), Differential approximation probability (DAP), and Linear approximation probability (LAP) in SAGE. Security analysis of the proposed S-box shown that the structure has the security level equal to the AES S-box. Therefore, this structure can be used in the lightweight block ciphers. Also, the implementation results, in 180 nm and 65 nm CMOS technologies, show the proposed S-box is comparable in terms of area, delay, and area×delay than most of the famous S-boxes.

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.