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In the realm of blockchain systems, smart contracts have gained widespread adoption owing to their programmability. Consequently, developing a system capable of facilitating high throughput and scalability is of paramount importance. Directed acyclic graph (DAG) consensus protocols have demonstrated notable enhancements in both throughput and latency, however, the serial execution is now becoming a bottleneck. Numerous approaches prove impractical for smart contracts by assuming that read/write sets are known in prior. This paper introduces Thunderbolt, a novel architecture based on DAG-based protocols, that aims to furnish a scalable and concurrent execution for smart contract transactions. Inspired by Hyperledger, Thunderbolt also expands Execute-Order-Validate architecture in which transactions are distributed into distinct replicas, with execution outcomes determined prior to ordering through the DAG-based protocol. Existing protocols adopt serial executions after the ordering to avoid non-determinism. However, Thunderbolt provides parallel pre-execution before the ordering as well as parallel verifications once any source of non-determinism is removed. Each replica validates the transaction results during the construction of the DAG other than after the ordering following the construction to improve the latency. In an effort to enhance smart contract execution, we implement an execution engine that constructs a dependency graph to dynamically assign transaction orders, thus mitigating abort rates due to execution conflicts. Additionally, we introduce a novel shard reconfiguration to withstand malicious attacks by relocating replicas from the current DAG to a new DAG, and rotating the shards among different replicas. Our comparison of the results on SmallBank with serial execution on Narwhal-Tusk revealed a remarkable 50 times speedup with 64 replicas., Comment: 17 pages

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm., Comment: 24 pages, 12 figures; Chaos, Solitons & Fractals (accepted for publication)

Decentralized systems built around blockchain technology promise clients an immutable ledger. They add a transaction to the ledger after it undergoes consensus among the replicas that run a Proof-of-Stake (PoS) or Byzantine Fault-Tolerant (BFT) consensus protocol. Unfortunately, these protocols face a long-range attack where an adversary having access to the private keys of the replicas can rewrite the ledger. One solution is forcing each committed block from these protocols to undergo another consensus, Proof-of-Work(PoW) consensus; PoW protocol leads to wastage of computational resources as miners compete to solve complex puzzles. In this paper, we present the design of our Power-of-Collaboration (PoC) protocol, which guards existing PoS/BFT blockchains against long-range attacks and requires miners to collaborate rather than compete. PoC guarantees fairness and accountability and only marginally degrades the throughput of the underlying system., Comment: 15 pages, 7 figures

We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear parabolic partial differential equations. Our approach notably extends the one introduced in [Hure Pham Warin 2020] for the implicit Euler scheme to schemes which are more efficient in terms of discrete-time error. We establish some convergence results for our implemented schemes under classical regularity assumptions. We also illustrate the efficiency of our method for different schemes of order one, two and three. Our numerical results indicate that the Crank-Nicolson schemes is a good compromise in terms of precision, computational cost and numerical implementation.

In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants whose matrix elements are elementary Schur polynomials. In the reduction process, three reduction conditions including one index- and two dimension-ones are proved to be consistent by only one constraint relation on parameters of tau-functions of the KP-Toda hierarchy.It is found that the rogue wave solutions in the MT model depend on two background parameters, which influence their orientation and duration. Differing from many other coupled integrable systems, the MT model only admits the rogue waves of bright-type, and the higher-order rogue waves represent the superposition of fundamental ones in which the non-reducible parameters determine the arrangement patterns of fundamental rogue waves. Particularly, the super rogue wave at each order can be achieved simply by setting all internal parameters to be zero, resulting in the amplitude of the sole huge peak of order $N$ being $2N+1$ times the background.Finally, rogue wave patterns are discussed when one of the internal parameters is large. Similar to other integrable equations, the patterns are shown to be associated with the root structures of the Yablonskii-Vorob'ev polynomial hierarchy through a linear transformation., Comment: 26 pages, 8 figures

In the present paper, we are concerned with the tau function and its connection with the Kadomtsev-Petviashvili (KP) theory for the massive Thirring (MT) model. First, we bilinearize the massive Thirring model under both the vanishing and nonvanishing boundary conditions. Starting from a set of bilinear equations of two-component KP-Toda hierarchy, we derive the multi-bright solution to the MT model by the KP hierarchy reductions. Then, we show that the discrete KP equation can generate a set of bilinear equations of a deformed KP-Toda hierarchy through Miwa transformation. By imposing constraints on the parameters of the tau function, the general dark soliton solution to the MT model is constructed from the tau function of the discrete KP equation. Finally, the dynamics and properties of one- and two-soliton for both the bright and dark cases are analyzed in details., Comment: 27 pages, 6 figures

The soft error rate (SER) of integrated circuits (ICs) operating in space environment may vary by several orders of magnitude due to the variable intensity of radiation exposure. To ensure the radiation hardness without compromising the system performance, it is necessary to implement the dynamic hardening mechanisms which can be activated under the critical radiation exposure. Such operating scenario requires the real-time detection of energetic particles responsible for the soft errors. Although numerous particle detection solutions have been reported, very few works address the on-chip particle detectors suited for the self-adaptive fault tolerant microprocessor systems for space missions. This work reviews the state-of-the-art particle detectors, with emphasis on two solutions for the self-adaptive systems: particle detector based on embedded SRAM and particle detector based on pulse stretching inverters.

This work investigates the use of pulse stretching inverters for monitoring the variation of flux and Linear Energy Transfer (LET) of energetic particles. The basic particle detector consists of two cascaded pulse stretching (skew-sized) inverters designed in CMOS technology, and the required sensing area is obtained by connecting multiple two-inverter pulse stretching cells in parallel, and employing the required number of parallel arrays. The particle strikes are detected in terms of the Single Event Transients (SETs), and the detector provides the information on the SET count rate and SET pulse width variation, from which the particle flux and LET can be determined. The main advantage of the proposed solution is the possibility to sense the LET variations using purely digital processing logic. The SPICE simulations done on IHP 130 nm bulk CMOS technology have shown that the SET pulse width at the output of detector changes by 550 ps over the LET range from 1 to 100 MeVcm2mg-1. The proposed solution is intended to operate as an on-chip particle detector within the self-adaptive multiprocessing systems.

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional semi-linear parabolic PDEs. This scheme is inspired by the approach coming from machine learning and developed using deep neural networks in Han and al. [32]. Our algorithm is based on a Picard iteration scheme in which a sequence of linear-quadratic optimisation problem is solved by means of stochastic gradient descent (SGD) algorithm. In the framework of a linear specification of the approximation space, we manage to prove a convergence result for our scheme, under some smallness condition. In practice, in order to be able to treat high-dimensional examples, we employ sparse grid approximation spaces. In the case of periodic coefficients and using pre-wavelet basis functions, we obtain an upper bound on the global complexity of our method. It shows in particular that the curse of dimensionality is tamed in the sense that in order to achieve a root mean squared error of order ${\epsilon}$, for a prescribed precision ${\epsilon}$, the complexity of the Picard algorithm grows polynomially in ${\epsilon}^{-1}$ up to some logarithmic factor $ |log({\epsilon})| $ which grows linearly with respect to the PDE dimension. Various numerical results are presented to validate the performance of our method and to compare them with some recent machine learning schemes proposed in Han and al. [20] and Hur\'e and al. [37].

In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation technique for Markov semigroups, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Among other applications, an unbiased Monte Carlo path simulation method stems from our formulas so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values or Greeks in finance, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.

General rogue waves are derived for the generalized derivative nonlinear Schrodinger (GDNLS) equations by a bilinear Kadomtsev-Petviashvili (KP) reduction method. These GDNLS equations contain the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation as special cases. In this bilinear framework, it is shown that rogue waves to all members of these equations are expressed by the same bilinear solution. Compared to previous bilinear KP reduction methods for rogue waves in other integrable equations, an important improvement in our current KP reduction procedure is a new parameterization of internal parameters in rogue waves. Under this new parameterization, the rogue wave expressions through elementary Schur polynomials are much simpler. In addition, the rogue wave with the highest peak amplitude at each order can be obtained by setting all those internal parameters to zero, and this maximum peak amplitude at order $N$ turns out to be $2N+1$ times the background amplitude, independent of the individual GDNLS equation and the background wavenumber. It is also reported that these GDNLS equations can be decomposed into two different bilinear systems which require different KP reductions, but the resulting rogue waves remain the same. Dynamics of rogue waves in the GDNLS equations is also analyzed. It is shown that the wavenumber of the constant background strongly affects the orientation and duration of the rogue wave. In addition, some new rogue patterns are presented., Comment: 19 pages, 3 figures

The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate and dark ones, whereas the rogue wave for the long wave is always bright type. The higher-order rogue waves correspond to the superposition of fundamental rogue waves. The modulation instability analysis show that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions., Comment: 14 pages, 5 figures

The Yajima-Oikawa (YO) system describes the resonant interaction between long and short waves under certain condition. In this paper, through the KP hierarchy reduction, we construct the breather solutions for the YO system in one- and two-dimensional cases. Similar to Akhmediev and Kuznetsov-Ma breather solutions (the wavenumber k_i->ik_i) for the nonlinear Schrodinger equation, is shown that the YO system have two kinds ofbreather solutions with the relations p_{2k-1}->ip_{2k-1}, p_{2k}->-ip_{2k}, q_{2k-1}->iq_{2k-1} and q_{2k}->-iq_{2k}, in which the homoclinic orbit and dark soliton solutions are two special cases respectively. Furthermore, taking the long wave limit, we derive the rational and rational and rational-exp solutions which contain lump, line rogue wave, soliton and their mixed cases. By considering the further reduction, such solutions can be reduced to one-dimensional YO system.

General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of determinants in which the elements are algebraic expressions. The dynamics of first and higher-order rogue wave are investigated in details for different values of the free parameters. It is shown that the fundamental (first-order) rogue waves can be classified into three different patterns: bright, intermediate and dark ones. The high-order rogue waves correspond to the superposition of fundamental rogue waves. Especially, compared with the nonlinear Schodinger equation, there exists an essential parameter \alpha to control the pattern of rogue wave for both first- and high-order rogue waves since the YO system does not possess the Galilean invariance., Comment: 19 pages,5 figures

A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general $N$-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary dark-dark soliton bound states can exist for all possible combinations of nonlinearity coefficients including all-positive, all-negative and mixed types, while the moving case are possible when they take opposite signs or they are both negative. The dynamics and several interesting structures of the solutions are illustrated through some figures.

In classical shallow water wave (SWW) theory, there exist two integrable one-dimensional SWW equation [Hirota-Satsuma (HS) type and Ablowitz-Kaup-Newell-Segur (AKNS) type] in the Boussinesq approximation. In this paper, we mainly focus on the integrable SWW equation of AKNS type. The nonlocal symmetry in form of square spectral function is derived starting from its Lax pair. Infinitely many nonlocal symmetries are presented by introducing the arbitrary spectrum parameter. These nonlocal symmetries can be localized and the SWW equation is extended to enlarged system with auxiliary dependent variables. Then Darboux transformation for the prolonged system is found by solving the initial value problem. Similarity reductions related to the nonlocal symmetry and explicit group invariant solutions are obtained. It is shown that the soliton-cnoidal wave interaction solution, which represents soliton lying on a cnoidal periodic wave background, can be obtained analytically. Interesting characteristics of the interaction solution between soliton and cnoidal periodic wave are displayed graphically., Comment: 14 pages, 6 figures