Operator Research Articles

Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations

This paper focuses on the numerical solution of a class of generalized coupled Sylvester-conjugate matrix equations, which are general and contain many significance matrix equations as special cases, such as coupled discrete-time/continuous-time Markovian jump Lyapunov matrix equations, stochastic Lyapunov matrix equation, etc. By introducing the modular operator, a cyclic gradient based iterative (CGI) algorithm is provided. Different from some previous iterative algorithms, the most significant improvement of the proposed algorithm is that less information is used during each iteration update, which is conducive to saving memory and improving efficiency. The convergence of the proposed algorithm is discussed, and it is verified that the algorithm converges for any initial matrices under certain assumptions. Finally, the effectiveness and superiority of the proposed algorithm are verified with some numerical examples.

An algebraic construction technique for codes over Hurwitz integers

Let $\alpha$ be a prime Hurwitz integer. $\mathcal{H}_{\alpha}$, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of $\mathcal{H},$ which is the set of all Hurwitz integers. In this study, we present an algebraic construction technique, which is a modulo function formed depending on two modulo operations, for codes over Hurwitz integers. We consider left congruent modulo $\alpha,$ and the domain of related modulo function is $\mathbb{Z}_{N(\alpha)},$ which is residual class ring of ordinary integers with $N(\alpha)$ elements. Therefore, we obtain the residue class rings of Hurwitz integers with $N(\alpha)$ size. In addition, we present some results for mathematical notations used in two modulo functions, and for the algebraic construction technique formed depending upon two modulo functions. Moreover, we presented graphs obtained by graph layout methods, such as spring, high-dimensional, and spiral embedding, for the set of the residual class obtained with respect to the related modulo function in the rings of Hurwitz integers.

Rupiah exchange rate: the determinants and impact of shocks on the economy

The repetition of policy dynamics on Quantitative Easing (QE) and interest rate by The Fed potentially cause fluctuations in the exchange rate, including in Indonesia. Therefore, this study aims to analyze the determinants and impacts of exchange rate shocks. Inflation (INF), Money Supply (LJUB), Open Market Operations (OPT), Foreign Exchange Reserves (LCD), Expected Inflation (LEHU) and Interest Rates (SB) were used to analyze the determinants of Exchange Rate (NT) through Auto Regressive Distributed Lag (ARDL). The impact of NT shocks was analyzed using Vector Auto Regressive (VAR) by LEHU, Residential Property Price Index (PIHPR), Stock Transactions (LTRANS), and Banking Credit Volume (VK). The Expected Inflation variable and incorporation of ARDL-VAR are novelties in this study. In the secondary time series data for 2014M1 – 2022M9 period, the ARDL results showed that INF and LJUB had positive effect on NT in both long and short run, while OPT, LCD and SB had negative effect. LEHU had negative effect in the short run, but positive in the long run. The speed of adjustment in the model was 49.86% per month. Shock of NT had impacted VK until 15 months, PIHPR at 7 months, LTRANS at 10 months, and LEHU at 14 months. Based on these results, it can be implied that the monetary authority must maintain stability of NT, especially by INF and LJUB transmission. Next, shock's impact must also be overcome, especially on VK. This research is only focused on monetary sector, further research will be refined with other macroeconomic variables.

Burst errors suppression for MLSE in high-speed IM/DD transmission systems using PAM.

Maximum likelihood sequence estimation (MLSE) is the optimal signal sequence detection that can remove the inter-symbol interference (ISI). However, we find that the MLSE causes burst consecutive errors alternating between +2 and -2 in M-ary pulse amplitude modulation (PAM-M) IM/DD systems with large ISI. In this paper, we propose to use precoding to suppress the burst consecutive errors resulted from MLSE. A 2 M modulo operation is employed to guarantee that the probability distribution as well as the peak-to-average power ratio (PAPR) of encoded signal remain unchanged. After the receiver-side MLSE, the decoding process that involves adding the current MLSE output to the previous one and applying a 2 M modulo is implemented to break the burst consecutive errors. We conduct experiments to transmit 112/150-Gb/s PAM-4 or beyond 200-Gb/s PAM-8 signals at C-band to investigate the performance of the proposed MLSE integrated with precoding. The results show that the precoding can break burst errors effectively. For 201-Gb/s PAM-8 signal transmission, the precoding MLSE can achieve 1.4-dB receiver sensitivity gain and reduce the maximum length of burst consecutive errors from 16 to 3.

An efficient null-broadening adaptive beamformer based on magnitude response constraints

To reduce computational complexity of the minimum power distortionless response (MPDR) beamformer, a novel efficient null-broadening method based on magnitude response constraints is proposed in this paper. We convert the original quadratic power constraint to multiple first-order magnitude response constraints using Gauss-Legendre quadrature (GLQ) rather than eigenvalue decomposition (EVD). In addition, the number of first-order constraints only depends on the order of Legendre polynomials. Furthermore, based on the conjugate symmetry of the beamforming weight vector on centro-symmetric array, the nonlinear modular operation in magnitude response constraints is transformed into equivalent linear real operation. Finally, we relax the inequality constraints in the model into equality constraints, which can be solved by Lagrange multiplier method. Simulation shows that the proposed magnitude response constrained MPDR (MRC-MPDR) beamformer can achieve the same dynamic interference suppression capability as other beamformers with shorter calculation time.

Tidal dissipation within an elongated asteroid with satellite, and application to asteroid (216) Kleopatra

(216) Kleopatra is a highly elongated dumbbell shaped asteroid, which is spinning rapidly (spin period 5.38 h), and has two satellites. The tidal migration rate of its outer satellite (related to asteroid tidal despinning) has been measured by Broz et al. (2021), and is used here to deduce the elastic properties of the asteroid, in particular its rigidity μ. For this purpose the satellite is modeled as an homogeneous elongated axisymmetric body, whose shape is described either as a cylinder or more realistically as a dumbbell. Such model asteroid is regarded as a beam (or rod) that undergoes tidal disturbances from the satellite. Due to the deformability of the asteroid, the tidal stresses produced within the body rise a compression tide in the direction of the asteroid's long axis, and a bending tide in the perpendicular direction. We compute the tidal amplitude of the total elastic energy stored within the asteroid, as a function of Young's modulus E. Provided that the tidal quality factor Q is known, this permits to deduce the power tidally dissipated within the asteroid. This is compared to the tidal dissipation deduced from Broz et al. (2022) observations of the tidal migration of Kleopatra's outer satellite. This permits to deduce the asteroid's Young's modulus E (or equivalently the rigidity μ through μ ≈ E/(2.6 ± 0.1)). Using our dumbbell model for Kleopatra, we obtain a rigidity μ ≈ 1.94 × 107 Pa if one assumes Q ≈ 40, or μ ≈ 1.40 × 107 Pa if one assumes Q = 100. Such tidal dissipation is found to be >2 orders of magnitude higher than the tidal dissipation which would occur in a hypothetical spherical asteroid of same density and rigidity as Kleopatra, with radius equal to the volume equivalent radius (RV ≈ 59.1 km). Among model asteroids with same long axis length as Kleopatra (2 L ≈ 267 km), dissipation is also found to be strongly dependent upon the shape of the asteroid (dumbbell, cylinder, or ellipsoid). Here the asteroid is regarded as an elastic solid, whereas it is presumably a weak rubble pile medium. The formalism developed here is however relevant provided that the asteroid may be regarded as a Maxwell material, because tidal frequencies are expected to be much higher than the inverse Maxwell time.

FPGA Implementation for Elliptic Curve Cryptography Algorithm and Circuit with High Efficiency and Low Delay for IoT Applications.

The Internet of Things requires greater attention to the security and privacy of the network. Compared to other public-key cryptosystems, elliptic curve cryptography can provide better security and lower latency with shorter keys, rendering it more suitable for IoT security. This paper presents a high-efficiency and low-delay elliptic curve cryptographic architecture based on the NIST-p256 prime field for IoT security applications. A modular square unit utilizes a fast partial Montgomery reduction algorithm, demanding just a mere four clock cycles to complete a modular square operation. The modular square unit can be computed simultaneously with the modular multiplication unit, consequently improving the speed of point multiplication operations. Synthesized on the Xilinx Virtex-7 FPGA platform, the proposed architecture completes one PM operation in 0.08 ms using 23.1 k LUTs at 105.3 MHz. These results show significantly better performance compared to that in previous works.

On the Mass Dependence of the Modular Operator for a Double Cone

We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in (1+1)- and (3+1)-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum.

A benchmark generator framework for evolving variant-rich software

Software often needs to exist in different variants, which account for varying customer requirements, environments, or non-functional aspects, such as energy consumption. Unfortunately, the number of variants can grow exponentially with the number of features. As such, developing and evolving variant-rich systems is challenging, since they do not only evolve “in time” as single systems, but also “in space” with new variants. Fortunately, many different methods and tools for variant-rich systems have been proposed over the last decades, especially in the field of software product line engineering. However, their level of evaluation varies significantly, threatening their relevance for practitioners and that of future research. Many tools have only been evaluated on ad hoc datasets, minimal examples, or unrealistic and limited evolution scenarios, missing large parts of the actual evolution lifecycle of variant-rich systems.Our long-term goal is to provide benchmarks to increase the maturity of evaluation of methods and tools for evolving variant-rich systems. However, providing manually curated and sufficiently detailed benchmarks that cover the whole evolution lifecycle of variant-rich systems is challenging. We present the framework vpbench, which simulates the evolution of a variant-rich system and thereby generates an evolution enriched with metadata explaining the evolution. The generated benchmarks, i.e., the evolution histories and metadata, can serve as ground truth to check the results of tools applied on it. We formalize the claims we make about the generator and the generated benchmarks as requirements. The design of vpbench comprises modular generators and evolution operators that automatically evolve real codebases. We implement simple and advanced evolution operators—e.g., relying on code transplantation to incorporate features from real projects. We demonstrate how vpbench addresses its claimed requirements, also considering multiple degrees of realism, extensibility and language-independence of the generated benchmarks.

Measuring 3- and 4-Moduli Sets Delay Per Bit in Residue Number System: A Survey

Given the efficiency of the residue number system in high-speed and low-power applications, a wide variety of moduli sets have been introduced in the literature. Selecting an appropriate moduli set is one of the most important issues of using a residue number system. Moduli sets can be evaluated by several factors such as dynamic range, balanced channels, fast and low-power modular operations, and efficient reverse converter. In this paper, 3- and 4-moduli sets are separately reviewed and compared from a different perspective. Furthermore, the most efficient 3- and 4-moduli sets are suggested. A new parameter for average delay comparison is introduced, which shows the delay of every bit in the dynamic range providing a fair comparison of moduli sets with different numbers of moduli. Our comparison showed that either balanced channels or the delay of computations are essential factors for designing an efficient new moduli set.

The compressive response of the filled Kelvin foam

Periodic unit-cell solutions are obtained for the finite-strain, elasto-plastic response of a filled closed-cell Kelvin foam in uniaxial compression. The closed-cell Kelvin foam has edges of equal length, and attention is focussed on the regular Kelvin foam with faces comprising regular hexagons and squares. The elongated Kelvin foam is also studied: its faces comprise elongated hexagons and quadrilaterals. Both the cell walls and core of the Kelvin foam are treated as elastic, ideally plastic von Mises solids. In the first part of the study, the core modulus and strength are sufficiently small for the core to behave as an inviscid, incompressible fluid. Filling of the closed-cell Kelvin foam, in regular or elongated form, with an inviscid, incompressible core elevates its yield strength slightly and stabilises the post-yield response against softening. In the second part of the study, the macroscopic modulus and strength of a filled closed-cell foam are determined as a function of core modulus and deviatoric strength. The deformation mode of the cell edges switches from a bending mode to an affine stretching mode when the core is sufficiently stiff and strong; an analytical model is derived for affine deformation of cell walls and core. Finally, the response of a finite specimen containing an edge imperfection is in good agreement with the periodic, unit cell response of the filled Kelvin foam.

Hip reconstruction in children with cerebral palsy: does magnitude of surgery influence complications and outcomes?

Children with cerebral palsy (CP) and neuromuscular hip dysplasia (NMHD) frequently require hip reconstruction including femoral and pelvic osteotomies. Outcomes and complications in CP patients with NMHD who underwent varying degrees of hip reconstruction surgeries were examined. Ninety-nine patients with a diagnosis of CP who underwent surgical management of NMHD over a 15-year period (2005-2020) were reviewed. Three patient cohorts with varying degrees of surgery were analyzed including: (1) unilateral femoral osteotomy with pelvic osteotomy; (2) bilateral femoral osteotomy with unilateral pelvic osteotomy; and (3) simultaneous bilateral femoral osteotomy and bilateral pelvic osteotomy. Data points included operative (OR) time, length of stay (LOS), estimated blood loss (EBL), and transfusion requirement. Complications during the perioperative and postoperative periods were identified and graded by severity. Increased EBL, need for transfusion, OR time, and LOS were observed more frequently in patients undergoing bilateral reconstruction. Complication rates were high for all three cohorts, with 87% of cases in the bilateral pelvic osteotomy cohort experiencing ≥1 complication. However, 90% of these were considered grade I or II and required no or minimal intervention. The average postoperative migration index at final follow-up for treated hips was significantly less in bilateral pelvic osteotomy cases. Patients with CP and bilateral NMHD can be safely managed with bilateral simultaneous comprehensive reconstruction. The data presented in this study can help both surgeons and families anticipate a more accurate postoperative course. Level of evidence: III.

Modulated Model Predictive Control of Modular Multilevel Converters Operating in a Wide Frequency Range

The finite control set model predictive control (FCS-MPC), which considers corresponding instantaneous power in the cost function, becomes a promising solution that allows modular multilevel converters (MMCs) to operate in a wide frequency range due to its ability to balance the internal energy. However, FCS-MPC usually suffers from a heavy computational burden. The modulated MPC, which combines modulation techniques with MPC methods, is usually employed to overcome such a challenge. In this paper, we propose an exhaustive active-set method to implement the modulated MPC scheme enabling the MMC to operate over a wide frequency range. With the proposed method, the optimal solution can be obtained by enumerating all possible active sets rather than iterating, so the worst-case computational burden (or calculation time) can be determined. Finally, a comparative study of our proposed method with conventional modulated MPC methods and FCS-MPC has been conducted to demonstrate the effectiveness of the proposed method.

A Lightweight, Secure Big Data-Based Authentication and Key-Agreement Scheme for IoT with Revocability

With the rapid development of Internet of Things (IoT), designing a secure two-factor authentication scheme for IoT is becoming increasingly demanding. Two-factor protocols are deployed to achieve a higher security level than single-factor protocols. Given the resource constraints of IoT devices, other factors such as biometrics are ruled out as additional authentication factors due to their large overhead. Smart cards are also prone to side-channel attacks. Therefore, historical big data have gained interest recently as a novel authentication factor in IoT. In this paper, we show that existing big data-based schemes fail to achieve their claimed security properties such as perfect forward secrecy (PFS), key compromise impersonation (KCI) resilience, and server compromise impersonation (SCI) resilience. Assuming a real strong attacker rather than a weak one, we show that previous schemes not only fail to provide KCI and SCI but also do not provide real two-factor security and revocability and suffer inside attack. Then, we propose our novel scheme which can indeed provide real two-factor security, PFS, KCI, and inside attack resilience and revocability of the client. Furthermore, our performance analysis shows that our scheme has reduced modular exponentiation operation and multiplication for both the client and the server compared to Liu et al.’s scheme which reduces the execution time by one third for security levels of λ = 128 . Moreover, in order to cope with the potential threat of quantum computers, we suggest using lightweight XMSS signature schemes which provide the desired security properties with λ = 128 bit postquantum security. Finally, we prove the security of our proposed scheme formally using both the real-or-random model and the ProVerif analysis tool.

High-Performance Multi-RNS-Assisted Concurrent RSA Cryptosystem Architectures

In public-key cryptography, the RSA algorithm is an inevitable part of hardware security because of the ease of implementation and security. RSA Cryptographic algorithm uses many modular arithmetic operations that decide the overall performance of the architecture. This paper proposes VLSI architecture to implement an RSA public-key cryptosystem driven by the Residue Number System (RNS). Modular exponentiation in the RSA algorithm is executed by dividing the entire process into modular squaring and multiplication operations. Based on the RNS employment in modulo-exponential operation, two RSA architectures are proposed. A Verilog HDL code is used to model the entire RSA architecture and ported in Zynq FPGA (XC7Z020CLG484-1) for Proof of Concept (PoC). The Cadence Genus Synthesizer tool characterizes a system’s performance for TSMCs standard Cell library. Partial RNS (Proposed-I)- and Fully RNS (Proposed-II)-based RSA architectures increase the operation speed by 13% and 35%, respectively, compared with the existing RSA. Even though there is an increase in parameters like area, power and PDP for a smaller key size, the improvement in area utilization and encryption/ decryption speed of RSA for a larger key size is evident from the analysis.

A stochastic neural network based approach for metamodelling of mechanical asphalt concrete properties

ABSTRACT This study introduces a stochastic approach based on Convolutional Neural Networks (CNNs) for predicting mechanical Asphalt Concrete (AC) properties with dependency on the mixture composition, temperature and loading frequency. The underlying CNN metamodels were evaluated by a comprehensive database of AC properties with a total of 7400 dynamic modulus records. The CNN approach shows an improved accuracy compared to other state of the art machine learning approaches found in literature. Stochastic CNN based metamodels were developed to take into account the uncertainty of mechanical properties resulting from arbitrarily arranged aggregates and air voids in AC. The data used for the stochastic metamodels contain a total of 3645 dynamic modulus and phase angle values. They were obtained from microscale Finite Element (FE) simulations considering a heterogenous material composition and viscoelastic material behaviour of the AC binder. The developed stochastic CNN metamodels provide highly accurate predictions for the statistical characteristics such as mean values, standard deviations and empirical distribution functions of the dynamic modulus and the phase angle.

Buffeting Chaotification Model for Enhancing Chaos and Its Hardware Implementation

Many shortcomings of chaos-based applications stem from the weak dynamic properties of the chaotic maps they use. To alleviate this problem, inspired by the buffeting effect in aeroelasticity, this article proposes the buffeting chaotification model (BCM). Using the especially designed buffeting and modulo operators, the BCM can generate numerous new chaotic maps with strong dynamic properties from existing one-dimensional chaotic maps. The effectiveness of the BCM is mathematically proven according to the Lyapunov exponent, and further numerical experiments confirm the superiority of the chaotic maps generated by the BCM in terms of the dynamic properties. The field-programmable gate array implementation also shows that the BCM owns simplicity in hardware devices. To investigate the practical application, a scheme for constructing the pseudorandom number generator is designed. Performance analyses indicate that our generators have a strong ability to produce high-quality pseudorandom sequences rapidly.

Process Simulation and Performance Models for Enhanced Modular Refinery Operations in Nigeria

The study aimed at availability of petroleum products in Nigeria through the operation of enhanced modular refinery process due to inefficient conventional major refineries. The enhanced modular refinery converts or processes residue product from conventional modular refinery as feedstock to the hydrocracker reactor for viable and desired products such as liquefied petroleum gas, naphtha and diesel. Therefore, twenty Nigerian crude oil types were classified as sweet, light and medium crude oil, and these crude oil types were categorized based on their recovery volume at true boiling point of 370oC as Group A, Group B and Group C respectively. Thus, based on product output and equipment cost, a modular refinery with 29 trays was used in this study, as light and medium sweet crude oil types were simulated in a modular refinery of various column trays prior to the desired tray. A topping plant with a 30,000 barrel per day capacity and a modified topping plant with 29 trays respectively were used to process different types of Nigerian crude oil. using Aspen Hysys to evaluate their products yield and tray compositions. The modified modular refinery with hydrocracker yielded more valuable from the residue of conventional modular refinery with minimal bottom fraction. Performance models for hydrocracker reactor was developed based on the nature of reaction, kinetic parameters estimated and results compared with experimental data with minimum deviations. The developed performance models predicted feedstock conversion and product yield along the hydrocracker reactor’s dimensionless length by solving a set of ordinary differential equation models. Thus, the hydrocracking process was simulated to evaluate the effects of catalyst effectiveness factor on feedstock conversion and products yield.

Local additivity revisited

We make a number of simplifications in Gour and Friedland’s proof of local additivity of the minimum output entropy of a quantum channel. We follow them in reframing the question as one about the entanglement entropy of bipartite states associated with a dB × dE matrix. We use a different approach to reduce the general case to that of a square positive definite matrix. We use the integral representation of the log to obtain expressions for the first and second derivatives of the entropy, and then exploit the modular operator and functional calculus to streamline the proof following their underlying strategy. We also extend this result to the maximum relative entropy with respect to a fixed reference state, which has important implications for studying the superadditivity of the capacity of a quantum channel to transmit classical information.

Keeping goods moving in the wake of a disaster: a qualitative study of intermodal transport

PurposeThis paper examines what facilitates the swift reconfiguration of freight movements across transport modes in the wake of a major disaster.Design/methodology/approachA qualitative research approach focussing on the New Zealand (NZ) domestic freight transport operations in the wake of the 2016 Kaikōura earthquake is used with data collected through 19 interviews with 27 informants. The interviews are thematically analysed by using the framework method.FindingsThe paper provides rich and detailed descriptions of the ability of a freight transport system to recover from a disaster through rapid modal shifts. This paper identifies nine factors enabling modular transport operations and highlights the critical role of physical, digital, operational and inter-organisational interconnectivity in the aftermath of a disaster.Originality/valueAlthough the management of freight disruptions has become a prevalent topic not only in industry and policy-making circles, but also in the academic literature, qualitative research focussing on the ability of commercial freight systems to adapt and recover from a disaster through rapid modal shifts is limited. This qualitative study sheds light on the mechanisms underlying the continuity of freight operations in the wake of a disaster and provides a comprehensive understanding of modular transport operations and the ability of freight systems to keep goods moving.