Small Exponent Research Articles

CHAM-CLAS: A Certificateless Aggregate Signature Scheme with Chameleon Hashing-Based Identity Authentication for VANETs

Vehicular ad hoc networks (VANETs), which are the backbone of intelligent transportation systems (ITSs), facilitate critical data exchanges between vehicles. This necessitates secure transmission, which requires guarantees of message availability, integrity, source authenticity, and user privacy. Moreover, the traceability of network participants is essential as it deters malicious actors and allows lawful authorities to identify message senders for accountability. This introduces a challenge: balancing privacy with traceability. Conditional privacy-preserving authentication (CPPA) schemes are designed to mitigate this conflict. CPPA schemes utilize cryptographic protocols, including certificate-based schemes, group signatures, identity-based schemes, and certificateless schemes. Due to the critical time constraints in VANETs, efficient batch verification techniques are crucial. Combining certificateless schemes with batch verification leads to certificateless aggregate signature (CLAS) schemes. In this paper, cryptanalysis of Xiong’s CLAS scheme revealed its vulnerabilities to partial key replacement and identity replacement attacks, alongside mathematical errors in the batch verification process. Our proposed CLAS scheme remedies these issues by incorporating an identity authentication module that leverages chameleon hashing within elliptic curve cryptography (CHAM-CLAS). The signature and verification modules are also redesigned to address the identified vulnerabilities in Xiong’s scheme. Additionally, we implemented the small exponents test within the batch verification module to achieve Type III security. While this enhances security, it introduces a slight performance trade-off. Our scheme has been subjected to formal security and performance analyses to ensure robustness.

Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a reliable model for frequency-independent Q anelastic behavior. Nonetheless, the numerical resolution of this equation poses considerable challenges due to the requirement of storing a complete time history of wavefields. To address this computational challenge, we present a novel approach: a nearly optimal sum-of-exponentials (SOE) approximation to the Caputo fractional derivative with very small fractional exponent, utilizing the machinery of generalized Gaussian quadrature. This method minimizes the number of memory variables needed to approximate the power attenuation law within a specified error tolerance. We establish a mathematical equivalence between this SOE approximation and the continuous fractional stress-strain relationship, relating it to the generalized Maxwell body model. Furthermore, we prove an improved SOE approximation error bound to thoroughly assess the ability of rheological models to replicate the power attenuation law. Numerical simulations on constant-Q viscoacoustic equation in 3D homogeneous media and variable-order P- and S- viscoelastic wave equations in 3D inhomogeneous media are performed. These simulations demonstrate that our proposed technique accurately captures changes in amplitude and phase resulting from material anelasticity. This advancement provides a significant step towards the practical usage of the time-fractional wave equation in seismic inversion.

Neural-network quantum-state study of the long-range antiferromagnetic Ising chain.

We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent α_{LR}, while the other critical exponents examined are very close to the SR Ising exponents regardless of α_{LR} examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for α_{LR}<2, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as α_{LR} decreases, although a precise breakdown threshold is yet to be determined.

Inhomogeneous long-range percolation in the weak decay regime

We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.

Creep deformation behavior and microstructure of α-Mg/long-period stacking ordered (LPSO) duplex Mg-Y-Zn alloy prepared by hot extrusion and heat treatment

There exists a great demand for improving the creep resistance of α-Mg/long-period stacking ordered (LPSO) duplex alloys. In this study, microstructure control through hot extrusion and heat treatment was employed on Mg-Y-Zn duplex alloys with the aim of achieving superior creep resistance. The extruded Mg-Y-Zn alloy exhibited an enhancement in the creep resistance with increasing heat treatment temperature. Furthermore, the heat-treated samples demonstrated outstanding creep resistance even under high stress. Their creep behavior is characterized by a low minimum creep rate and a relatively small stress exponent (n ∼ 5) even at high stress. Microstructural observations revealed that heat treatment induces grain coarsening and an increase in solute concentration within the recrystallized grains. Additionally, during creep deformation, a plate-like LPSO phase and kink bands formed within the recrystallized grains. Therefore, it is affirmed that the exceptional creep resistance observed in the Mg-Y-Zn alloys in this study can be attributed to the microstructure evolution induced by heat treatment and creep deformation.

Scaling relationships between human leg muscle architectural properties and body size.

A skeletal muscle's peak force production and excursion are based on its architectural properties that are, in turn, determined by its mass, muscle fiber length and physiological cross-sectional area (PCSA). In the classic interspecific study of mammalian muscle scaling, it was demonstrated that muscle mass scales positively allometrically with body mass whereas fiber length scales isometrically with body mass, indicating that larger mammals have stronger leg muscles than they would if they were geometrically similar to smaller ones. Although this relationship is highly significant across species, there has never been a detailed intraspecific architectural scaling study. We have thus created a large dataset of 896 muscles across 34 human lower extremities (18 females and 16 males) with a size range including approximately 90% and 70% of the United States population height and mass, respectively, across the range 36-103 years. Our purpose was to quantify the scaling relationships between human muscle architectural properties and body size. We found that human muscles depart greatly from isometric scaling because muscle mass scales with body mass1.3 (larger exponent than isometric scaling of 1.0) and muscle fiber length scales with negative allometry with body mass0.1 (smaller exponent than isometric scaling of 0.33). Based on the known relationship between architecture and function, these results suggest that human muscles place a premium on muscle force production (mass and PCSA) at the expense of muscle excursion (fiber length) with increasing body size, which has implications for understanding human muscle design as well as biomechanical modeling.

Combinatorial Estimations on Burnside Type Problems

The Burnside problem, formulated by W. Burnside in 1902, is one of the most well-known and important open questions in the field of Group Theory. Despite significant progress made in the past century towards solving this problem, its complete solution remains unknown. In this paper, we investigate one of the approaches to solving the Burnside problem based on the application of an iterative theory of small cancellations and canonical forms developed by E. Rips in recent years. We present a novel self-contained exposition of this theory and utilize it to obtain new estimates on the infiniteness of initial approximations of Burnside groups where only a finite number of periodic relations is used for relatively small odd exponents (n&gt;120).

Factorial growth at low orders in perturbative QCD: control over truncation uncertainties

A method, known as “minimal renormalon subtraction” [Phys. Rev. D97 (2018) 034503, JHEP08 (2017) 62], relates the factorial growth of a perturbative series (in QCD) to the power p of a power correction Λp/Qp. (Λ is the QCD scale, Q some hard scale.) Here, the derivation is simplified and generalized to any p, more than one such correction, and cases with anomalous dimensions. Strikingly, the well-known factorial growth is seen to emerge already at low or medium orders, as a consequence of constraints on the Q dependence from the renormalization group. The effectiveness of the method is studied with the gluonic energy between a static quark and static antiquark (the “static energy”). Truncation uncertainties are found to be under control after next-to-leading order, despite the small exponent of the power correction (p = 1) and associated rapid growth seen in the first four coefficients of the perturbative series.

The Lévy flight foraging hypothesis: comparison between stationary distributions and anomalous diffusion *

We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies. On the one hand, when the prey is uniformly distributed, the best possible strategy for the forager is to be stationary and uniformly distributed in the same region. On the other hand, in several biological settings, foragers cannot be completely stationary, therefore we investigate the best seeking strategy for Lévy foragers in terms of the corresponding Lévy exponent. In this case, we show that the best strategy depends on the region size in which the prey is located: large regions exhibit optimal seeking strategies close to Gaussian random walks, while small regions favor Lévy foragers with small fractional exponent. We also consider optimal strategies in view of the Fourier transform of the distribution of a stationary prey. When this distribution is supported in a suitable volume, then the foraging efficiency functional is monotone increasing with respect to the Lévy exponent and accordingly the optimal strategy is given by the Gaussian dispersal. If instead the Fourier transform of the distribution of a stationary prey is supported in the complement of a suitable volume, then the foraging efficiency functional is monotone decreasing with respect to the Lévy exponent and therefore the optimal strategy is given by a null fractional exponent (which in turn corresponds, from a biological standpoint, to a strategy of ‘ambush’ type). We will devote a rigorous quantitative analysis also to emphasize some specific differences between the one-dimensional and the higher-dimensional cases.

Molybdenum-doped BiVO4 thin films: Facile preparation via hot-spin coating method and the relationship between surface statistical parameters and photoelectrochemical activity

Molybdenum-doped BiVO4 thin films were uniformly coated on indium-doped tin oxide (ITO) substrates via a facile modified hot spin coating (HSC) technique. The prepared layers were used as photoanode in a photoelectrochemical (PEC) cell. Different percentage of Mo dopant was examined to maximize the photo-current density (J) of the layers. The highest J value (872 ± 8 μA/cm2) was obtained by 5 atomic% of Mo doping. After that, the surface topographies of these samples were changed by varying the initial precursor concentration from 27 to 80 mM. The relation between surface topographies and the PEC activity of Mo-doped BiVO4 thin films was investigated from microscopic point of view by calculating the surface roughness exponent of α, and a mechanism for the PEC activity of Mo-doped BiVO4 photoanodes was proposed accordingly. The sample with a small roughness exponent provided a surface with jagged microscopic fluctuations which may trap the air molecules between the electrolyte and sample surface, hindering the fine atomic interaction for photo-generated electron-hole transition. Therefore, the layer with the highest roughness exponent (2α = 0.48 ± 0.03), which means the smoother microscopic surface and better interfacial contact with the electrolyte, exhibited the best PEC activity.

An Algorithm for Construction of the Asymptotic Approximation of a Stable Stationary Solution to a Diffusion Equation System with a Discontinuous Source Function

An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smooth curve lying entirely inside the domain. Each of the equations contains a small parameter as a factor in front of the Laplace operator, and as a result, the system is singularly perturbed. In the vicinity of the curve, the solution of the system has a large gradient. Such a problem statement is used in the model of urban development in metropolitan areas. The discontinuity curves in this model are the boundaries of urban biocenoses or large water pools, which prevent the spread of urban development. The small parameter is the ratio of the city’s outskirts linear size to the whole metropolis linear size. The algorithm includes the construction of an asymptotic approximation to a solution with a large gradient at the media interface as well as the steps for obtaining the existence conditions. To prove the existence and stability theorems, we use the upper and lower solutions, which are constructed as modifications of the asymptotic approximation to the solution. The latter is constructed using the Vasil’yeva algorithm as an expansion of a small parameter exponent.

A CFD-FFT approach to hemoacoustics that enables degree of stenosis prediction from stethoscopic signals

In this paper, we identify a new (acoustic) frequency-stenosis relation whose frequencies lie within the recommended auscultation threshold of stethoscopy (< 120 Hz). We show that this relation can be used to extend the application of phonoangiography (quantifying the degree of stenosis from bruits) to widely accessible stethoscopes. The relation is successfully identified from an analysis restricted to the acoustic signature of the von Karman vortex street, which we automatically single out by means of a metric we propose that is based on an area-weighted average of the Q-criterion for the post-stenotic region. Specifically, we perform CFD simulations on internal flow geometries that represent stenotic blood vessels of different severities. We then extract their emitted acoustic signals using the Ffowcs Williams-Hawkings equation, which we subtract from a clean signal (stenosis free) at the same heart rate. Next, we transform this differential signal to the frequency domain and carefully classify its acoustic signatures per six (stenosis-)invariant flow phases of a cardiac cycle that are newly identified in this paper. We then automatically restrict our acoustic analysis to the sounds emitted by the von Karman vortex street (phase 4) by means of our Q-criterion-based metric. Our analysis of its acoustic signature reveals a strong linear relationship between the degree of stenosis and its dominant frequency, which differs considerably from the break frequency and the heart rate (known dominant frequencies in the literature). Applying our new relation to available stethoscopic data, we find that its predictions are consistent with clinical assessment. Our finding of this linear correlation is also unlike prevalent scaling laws in the literature, which feature a small exponent (i.e., low stenosis percentage sensitivity over much of the clinical range). They hence can only distinguish mild, moderate, and severe cases. Conversely, our linear law can identify variations in the degree of stenosis sensitively and accurately for the full clinical range, thus significantly improving the utility of the relevant scaling laws... Future research will investigate incorporating the vibroacoustic role of adjacent organs to expand the clinical applicability of our findings. Extending our approach to more complex 3D stenotic morphologies and including the vibroacoustic role of surrounding organs will be explored in future research to advance the clinical reach of our findings.

Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

A new route to strange nonchaotic attractors (SNAs) is investigated in a quasiperiodically driven nonsmooth map. It is shown that the smooth quasiperiodic torus becomes nonsmooth (continuous and non-differentiable) due to the border-collision bifurcation of the torus. As the coefficients change, the nonsmooth torus gets gradually fractal, forming strange nonchaotic attractors. It is termed the border-collision bifurcation route to SNAs. A novel feature of this route is that a large number of SNAs are formed, and the parameter area of SNAs makes up about 40 % of the given parameter regions. These SNAs are identified by the largest Lyapunov exponents and the phase sensitivity exponents. They are also characterized by the distribution of finite-time Lyapunov exponents. Unlike other types of SNAs, the distribution of finite-time Lyapunov exponents has its maximum at a relatively small negative Lyapunov exponent, which contributes largely to lead to the abundance of SNAs.

Boundedness of non-local operators with spatially dependent coefficients and $$L_p$$-estimates for non-local equations

We prove the boundedness of the non-local operator $$\begin{aligned} \mathcal {L}^a u(x)=\int _{\mathbb {R}^d} \left( u(x+y)-u(x)-\chi _\alpha (y)\big (\nabla u(x),y\big )\right) a(x,y)\frac{dy}{|y|^{d+\alpha }} \end{aligned}$$ from $$H_{p,w}^\alpha (\mathbb {R}^d)$$ to $$L_{p,w}(\mathbb {R}^d)$$ for the whole range of $$p \in (1,\infty )$$ , where w is a Muckenhoupt weight. The coefficient a(x, y) is bounded, merely measurable in y, and Hölder continuous in x with an arbitrarily small exponent. We extend the previous results by removing the largeness assumption on p as well as considering weighted spaces with Muckenhoupt weights. Using the boundedness result, we prove the unique solvability in $$L_p$$ spaces of the corresponding parabolic and elliptic non-local equations.

Fractional saturable impurity

We examine analytically and numerically the effect of fractionality on a saturable bulk and surface impurity embedded in a one-dimensional lattice. We use a fractional Laplacian introduced previously by us, and by the use of lattice Green functions we are able to obtain the bound state energies and amplitude profiles, as a function of the fractional exponent $s$ and saturable impurity strength $\ensuremath{\chi}$ for both surface and bulk impurity. The transmission is obtained in closed form as a function of $s$ and $\ensuremath{\chi}$, showing strong deviations from the standard case, at small fractional exponent values. The self-trapping of an initially localized excitation is qualitatively similar for the bulk and surface mode, but in all cases complete confinement is obtained at $s\ensuremath{\rightarrow}0$, as shown theoretically and observed numerically.

Gear tribodynamic modeling and analysis considering tooth profile modification

A novel two-part gear tribodynamic model considering tooth profile modification (TPM) is established. One part is a coupling model of gear dynamics and elastohydrodynamic lubrication theory, so that the lubricant-induced backlash reduction and geometry of modified tooth profiles can be described. The other is the Chebyshev subinterval decomposition method that calculates the tribodynamic response intervals efficiently when the correlated uncertainty is considered. Using this model, tribodynamic characteristics of gears with TPM are analyzed. Results show that high viscosity suppresses the torsional and translational vibrations concurrently. Excessive modification amount, length and too small power exponent amplify the vibration and contact pressure. Moreover, the correlated uncertain TPM leads to a nonnegligible influence on the intervals of vibration and contact fatigue life.

Long-range connections and mixed diffusion in fractional networks

Networks with long-range connections, obeying a distance-dependent power law of sufficiently small exponent, display superdiffusion, Lévy flights and robustness properties very different from the scale-free networks. It has been proposed that these networks, found both in society and in biology, be classified as a new structure, the fractional networks. Particular important examples are the social networks and the modular hierarchical brain networks where both short- and long-range connections are present. The anomalous superdiffusive and the mixed diffusion behavior of these networks is studied here as well as its relation to the nature and density of the long-range connections.

Small Private Exponent Attacks on RSA Using Continued Fractions and Multicore Systems

The RSA (Rivest–Shamir–Adleman) asymmetric-key cryptosystem is widely used for encryptions and digital signatures. Let (n,e) be the RSA public key and d be the corresponding private key (or private exponent). One of the attacks on RSA is to find the private key d using continued fractions when d is small. In this paper, we present a new technique to improve a small private exponent attack on RSA using continued fractions and multicore systems. The idea of the proposed technique is to find an interval that contains ϕ(n), and then propose a method to generate different points in the interval that can be used by continued fraction and multicore systems to recover the private key, where ϕ is Euler’s totient function. The practical results of three small private exponent attacks on RSA show that we extended the previous bound of the private key that is discovered by continued fractions. When n is 1024 bits, we used 20 cores to extend the bound of d by 0.016 for de Weger, Maitra-Sarkar, and Nassr et al. attacks in average times 7.67 h, 2.7 h, and 44 min, respectively.

Variable-Precision Approximate Floating-Point Multiplier for Efficient Deep Learning Computation

In this brief, a variable-precision approximate floating-point multiplier is proposed for energy efficient deep learning computation. The proposed architecture supports approximate multiplication with BFloat16 format. As the input and output activations of deep learning models usually follow normal distribution, inspired by the posit format, for numbers with different values, different precisions can be applied to represent them. In the proposed architecture, posit encoding is used to change the level of approximation, and the precision of the computation is controlled by the value of product exponent. For large exponent, smaller precision multiplication is applied to mantissa and for small exponent, higher precision computation is applied. Truncation is used as approximate method in the proposed design while the number of bit positions to be truncated is controlled by the values of the product exponent. The proposed design can achieve 19% area reduction and 42% power reduction compared to the normal BFloat16 multiplier. When applying the proposed multiplier in deep learning computation, almost the same accuracy as that of normal BFloat16 multiplier can be achieved.

State-space renormalization group theory of nonequilibrium reaction networks: Exact solutions for hypercubic lattices in arbitrary dimensions.

Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the steady state. Dynamics of NRNs can be described at different coarse-grained levels. Our previous work showed that the apparent energy dissipation rate at a coarse-grained level follows an inverse power-law dependence on the scale of coarse-graining. The scaling exponent is determined by the network structure and correlation of stationary probability fluxes. However, it remains unclear whether and how the (renormalized) flux correlation varies with coarse-graining. Following Kadanoff's real space renormalization group (RG) approach for critical phenomena, we address this question by developing a state-space renormalization group theory for NRNs, which leads to an iterative RG equationfor the flux correlation function. In square and hypercubic lattices, we solve the RG equationexactly and find two types of fixed point solutions. There is a family of nontrivial fixed points where the correlation exhibits power-law decay, characterized by a power exponent that can take any value within a continuous range. There is also a trivial fixed point where the correlation vanishes beyond the nearest neighbors. The power-law fixed point is stable if and only if the power exponent is less than the lattice dimension n. Consequently, the correlation function converges to the power-law fixed point only when the correlation in the fine-grained network decays slower than r^{-n} and to the trivial fixed point otherwise. If the flux correlation in the fine-grained network contains multiple stable solutions with different exponents, the RG iteration dynamics select the fixed point solution with the smallest exponent. The analytical results are supported by numerical simulations. We also discuss a possible connection between the RG flows of flux correlation with those of the Kosterlitz-Thouless transition.