影响因子：11.3

JCR分区：Q1 (Mathematics – SCIE)

CiteScre: 26

CiteScore 分区: Q1 (General Mathematics)

CAS分区：数学1区

摘要：Time parallelization, also known as PinT (parallel-in-time) , is a new research direction for the development of algorithms used for solving very large-scale evolution problems on highly parallel computing architectures. Despite the fact that interesting theoretical work on PinT appeared as early as 1964, it was not until 2004, when processor clock speeds reached their physical limit, that research in PinT took off. A distinctive characteristic of parallelization in time is that information flow only goes forward in time, meaning that time evolution processes seem necessarily to be sequential. Nevertheless, many algorithms have been developed for PinT computations over the past two decades, and they are often grouped into four basic classes according to how the techniques work and are used: shooting-type methods; waveform relaxation methods based on domain decomposition; multigrid methods in space–time; and direct time parallel methods. However, over the past few years, it has been recognized that highly successful PinT algorithms for parabolic problems struggle when applied to hyperbolic problems. We will therefore focus on this important aspect, first by providing a summary of the fundamental differences between parabolic and hyperbolic problems for time parallelization. We then group PinT algorithms into two basic groups. The first group contains four effective PinT techniques for hyperbolic problems: Schwarz waveform relaxation (SWR) with its relation to tent pitching; parallel integral deferred correction; ParaExp; and ParaDiag. While the methods in the first group also work well for parabolic problems, we then present PinT methods specifically designed for parabolic problems in the second group: Parareal; the parallel full approximation scheme in space–time (PFASST) ; multigrid reduction in time (MGRiT) ; and space–time multigrid (STMG) . We complement our analysis with numerical illustrations using four time-dependent PDEs: the heat equation; the advection–diffusion equation; Burgers’ equation; and the second-order wave equation.

影响因子：2.9

JCR分区：Q1 (Mathematics – SCIE)

CiteScre: 3.5

CiteScore 分区: Q1 (Algebra and Number Theory)

CAS分区：数学1区

摘要：In this paper, we consider the defocusing nonlinear wave equation ??_t²U+Δu=|u|^p?1u in R×R^d. Building on our companion work (Self-similar imploding solutions of the relativistic Euler equations, arXiv:2403.11471) , we prove that for d=4, p≥29 and d≥5, p≥17, there exists a smooth complex-valued solution that blows up in finite time.

影响因子：1.2

JCR分区：Q1 (Mathematics – SCIE)

CiteScre: 1.9

CiteScore 分区: Q2 (Geometry and Topology)

CAS分区：数学2区

摘要：Let S be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration f:S→B of genus g. We prove a quadratic upper bound on the genus g (i.e., g≤h(χ(O_S) , where h is a quadratic function). We also construct examples showing that the quadratic upper bounds cannot be improved to linear ones. In the special case when p_g(S)=q(S)=1, we show that g≤14.

影响因子：1.4

JCR分区：Q1 (Mathematics – SCIE)

CiteScre:2.1

CiteScore 分区：Q1 (Algebra and Number Theory)

CAS分区：Q1 (Mathematics)

摘要：This paper explores the cohomological consequences of the existence of moduli spaces for flat bundles with bounded rank and irregularity at infinity and gives unconditional proofs. Namely, we prove the existence of a universal bound for the dimension of de Rham cohomology of flat bundles with bounded rank and irregularity on surfaces. In any dimension, we prove a Lefschetz recognition principle stating the existence of hyperplane sections distinguishing flat bundles with bounded rank and irregularity after restriction. We obtain in any dimension a universal bound for the degrees of the turning loci of flat bundles with bounded rank and irregularity. Along the way, we introduce a new operation on the group of b-divisors on a smooth surface  (the partial discrepancy) and prove a closed formula for the characteristic cycles of flat bundles on surfaces in terms of the partial discrepancy of the irregularity b-divisor attached to any flat bundle by Kedlaya.

影响因子：1.0

JCR分区：Q2 (Mathematics – SCIE)

CiteScre: 2.4

CiteScore 分区: Q1 (General Mathematics)

CAS分区：数学2区

摘要：Mukai’s program in [16] seeks to recover a K3 surface X from any curve C on it by exhibiting it as a Fourier–Mukai partner to a Brill–Noether locus of vector bundles on the curve. In the case X has Picard number one and the curve C∈|H| is primitive, this was confirmed by Feyzbakhsh in [11, 13] for g≥11 and g≠12. More recently, Feyzbakhsh has shown in [12] that certain moduli spaces of stable bundles on X are isomorphic to the Brill–Noether locus of curves in |H| if g is sufficiently large. In this paper, we work with irreducible curves in a nonprimitive ample linear system |mH| and prove that Mukai’s program is valid for any irreducible curve when g≠2, mg≥11 and mg≠12. Furthermore, we introduce the destabilising regions to improve Feyzbakhsh’s analysis in [12]. We show that there are hyper-K?hler varieties as Brill–Noether loci of curves in every dimension.

影响因子：1.1

JCR分区：Q2 (Mathematics, Applied – SCIE)

CiteScre: 4.7

CiteScore 分区: Q1 (Applied Mathematics) 

CAS分区：数学4区

摘要：This paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bifurcation theory. Subsequently, by a generalized mountain pass lemma, we successfully demonstrate the existence of steady states with jump discontinuity. Furthermore, the structure of stationary solutions within a one-dimensional domain is investigated and a variety of steady-state solutions are built, which may exhibit monotonicity or symmetry. In the end, we create heterogeneous equilibrium states close to a constant equilibrium state using bifurcation theory and examine their stability.

影响因子：0.9

JCR分区：Q3 (Mathematics, Applied – SCIE)

CiteScre: 1.3

CiteScore 分区: Q2 (Mathematics - miscellaneous) 

CAS分区：数学4区

摘要：Early warning for epilepsy patients is crucial for their safety and well being, in particular, to prevent or minimize the severity of seizures. Through the patients’ electroencephalography (EEG) data, we propose a meta learning framework to improve the prediction of early ictal signals. The proposed bilevel optimization framework can help automatically label noisy data at the early ictal stage, as well as optimize the training accuracy of the backbone model. To validate our approach, we conduct a series of experiments to predict seizure onset in various long-term windows, with long short-term memory (LSTM) and ResNet implemented as the baseline models. Our study demonstrates that not only is the ictal prediction accuracy obtained by meta learning significantly improved, but also the resulting model captures some intrinsic patterns of the noisy data that a single backbone model could not learn. As a result, the predicted probability generated by the meta network serves as a highly effective early warning indicator.

影响因子：0.9

JCR分区：Q1 (Logic – SCIE)

CiteScre: 1.9

CiteScore 分区: Q1 (Philosophy)

CAS分区：数学2区

摘要：In this paper we study logical bilateralism understood as a theory of two primitive derivability relations, namely provability and refutability, in a language devoid of a primitive strong negation and without a falsum constant, ⊥, and a verum constant, ?. There is thus no negation that toggles between provability and refutability, and there are no primitive constants that are used to define an “implies falsity” negation and a “co-implies truth” co-negation. This reduction of expressive power notwithstanding, there remains some interaction between provability and refutability due to the presence of (i) a conditional and the refutability condition of conditionals and (ii) a co-implication and the provability condition of co-implications. Moreover, assuming a hyperconnexive understanding of refuting conditionals and a dual understanding of proving co-implications, neither non-trivial negation inconsistency nor hyperconnexivity is lost for unary negation connectives definable by means of certain surrogates of falsum and verum. Whilst a critical attitude towards ⊥ and ? can be justified by problematic aspects of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations for these constants, the aim to reduce the availability of a toggling negation and observations on undefinability may also give further reasons to abandon ⊥ and ?.

影响因子：0.7

JCR分区：Q1 (Logic – SCIE)

CiteScre: 0.6

CiteScore 分区: Q2 (Philosophy) 

CAS分区：数学3区

摘要：We present a streamlined and simplified exponential lower bound on the length of proofs in intuitionistic implicational logic, adapted to Gordeev and Haeusler’s dag-like natural deduction.

影响因子：0.6

JCR分区：Q3 (Mathematics, Applied – SCIE)

CiteScre: 1.2

CiteScore 分区: Q1 (Philosophy)

CAS分区：数学3区

摘要：In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel Z-orderings. We define a notion of compatibility between such pairs, and prove a dichotomy theorem which characterizes exactly when a pair of Borel Z-orderings are compatible with each other. We show that, if a pair of Borel Z-orderings are incompatible, then a canonical incompatible pair of Borel Z-orderings of E0 can be Borel embedded into the given pair. We then consider hyperfinite-over-finite equivalence relations, which are countable Borel equivalence relations admitting Borel Z²-orderings. We show that if a hyperfinite-over-hyperfinite equivalence relation E admits a Borel Z²-ordering which is self-compatible, then E is hyperfinite.

影响因子：3.1

JCR分区：Q1 (Mathematics, Interdisciplinary applications – SCIE)

CAS分区：心理学2区

摘要：In this paper, we propose a novel and highly effective variational Bayesian expectation maximization-maximization (VBEM-M) inference method for log-linear cognitive diagnostic model (CDM) . In the implementation of the variational Bayesian approach for the saturated log-linear CDM, the conditional variational posteriors of the parameters that need to be derived are in the same distributional family as the priors, the VBEM-M algorithm overcomes this problem. Our algorithm can directly estimate the item parameters and the latent attribute-mastery pattern simultaneously. In contrast, Yamaguchi and Okada’s (2020a) variational Bayesian algorithm requires a transformation step to obtain the item parameters for the log-linear cognitive diagnostic model (LCDM) . We conducted multiple simulation studies to assess the performance of the VBEM-M algorithm in terms of parameter recovery, execution time, and convergence rate. Furthermore, we conducted a series of comparative studies on the accuracy of parameter estimation for the DINA model and the saturated LCDM, focusing on the VBEM-M, VB, expectation-maximization, and Markov chain Monte Carlo algorithms. The results indicated that our method can obtain more stable and accurate estimates, especially for the small sample sizes. Finally, we demonstrated the utility of the proposed algorithm using two real datasets.

影响因子：6.1

JCR分区：Q1 (Mathematical & Computational Biology– SCIE)

CAS分区：生物学2区