A multivariate quadratic public-key cryptography (MQ-PKC) is one of the most promising alternatives for classical PKC after the eventual coming of a quantum computer. We propose a new MQ-signature scheme, ELSA, based on a hidden layer of quadratic equations which is an important role in dramatically reducing the secret key size and computational complexity in signing. We prove existential unforgeability of our scheme against an adaptive chosen-message attack under the hardness of the MQ-problem induced by a public key of ELSA with a specific parameter set in the random oracle model. We analyze the security of ELSA against known attacks and derive a concrete parameter based on the security analysis. Performance of ELSA on a recent Intel processor is the fastest among state-of-the-art signature schemes including classical ones and Post-Quantum ones. It takes 6.3   μ s and 13.39   μ s for signing and verification, respectively. Compared to Rainbow, the secret size of the new scheme has reduced by a factor of 88% maintaining the same public key size.

Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

The Apostol–Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.

We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.

For the assessment of the left ventricle (LV), echocardiography has been widely used to visualize and quantify geometrical variations of LV. However, echocardiographic image itself is not sufficient to describe a swirling pattern which is a characteristic blood flow pattern inside LV without any treatment on the image. We propose a mathematical framework based on an inverse problem for three-dimensional (3D) LV blood flow reconstruction. The reconstruction model combines the incompressible Navier-Stokes equations with one-direction velocity component of the synthetic flow data (or color Doppler data) from the forward simulation (or measurement). Moreover, time-varying LV boundaries are extracted from the intensity data to determine boundary conditions of the reconstruction model. Forward simulations of intracardiac blood flow are performed using a fluid-structure interaction model in order to obtain synthetic flow data. The proposed model significantly reduces the local and global errors of the reconstructed flow fields. We demonstrate the feasibility and potential usefulness of the proposed reconstruction model in predicting dynamic swirling patterns inside the LV over a cardiac cycle.

We consider the standard central finite difference method for solving the Poisson equation with the Dirichlet boundary condition. This scheme is well known to produce second order accurate solutions. From numerous tests, its numerical gradient was reported to be also second order accurate, but the observation has not been proved yet except for few specific domains. In this work, we first introduce a refined error estimate near the boundary and a discrete version of the divergence theorem. Applying the divergence theorem with the estimate, we prove the second order accuracy of the numerical gradient in arbitrary smooth domains.

We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.

We investigate whether the characteristic fund performance indicators (FPI), such as the fund return, the Net asset value (NAV) and the cash flow, are correlated with the asset price ment using information flows estimated by the Granger causality test. First, we find that the information flow of FPI is most sensitive to extreme events of the Korean stock market, which include negative events such as the sub-prime crisis and the impact of QE (quantitative easing) by the US subprime and Europe financial crisis as well as the positive events of the golden period of Korean Composite Stock Price Index (KOSPI), except for the fund cash flow. Second, both the fund return and the NAV exhibit significant correlations with the KOSPI, whereas the cash flow is not correlated with the stock market. This result suggests that the information resulting from the ability of the fund manager should influence stock market. Finally, during market crisis period, information flows between FPI and the Korean stock market are significantly positively correlated with the market volatility.

Maximally synchronizable networks (MSNs) are acyclic directed networks that maximize synchronizability. In this paper, we investigate the feasibility of transforming networks of coupled oscillators into their corresponding MSNs. By tuning the weights of any given network so as to reach the lowest possible eigenratio ${\lambda }_N/{\lambda }_2$ , the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths. We check the robustness of the resulting MSNs with an experimental implementation of a network of nonlinear electronic oscillators and study the propagation of the synchronization errors through the network. Importantly, a method to study the effects of topological uncertainties on the synchronizability is proposed and explored both theoretically and experimentally.

In previous studies, branch length similarity (BLS) entropy was suggested to characterize spatial data, such as an object’s shape and poses. The entropy was defined on a simple network consisting of a single node and branches. The simple network was referred to as the “unit branching network” (UBN). In the present study, I applied the BLS entropy concept to temporal data (e.g., time series) by forming UBNs on the data. The temporal data were obtained from the logistic equation and the ment behavior of Chironomid riparius. Using the UBNs, I calculated a variable, γ, defined as the ratio of the mean entropy value to the standard deviation for the difference values of the sets of two UBNs connected with each other along a given direction. Consequently, I found that ? could be effectively used to characterize temporal data.