Future link prediction is a fundamental challenge in various real-world dynamic systems. To address this, numerous temporal graph neural networks (temporal GNNs) and benchmark datasets have been developed. However, these datasets often feature excessive repeated edges and lack complex sequential dynamics, a key characteristic inherent in many real-world applications such as recommender systems and ``Who-To-Follow'' on social networks. This oversight has led existing methods to inadvertently downplay the importance of learning sequential dynamics, focusing primarily on predicting repeated edges. In this study, we demonstrate that existing methods, such as GraphMixer and DyGFormer, are inherently incapable of learning simple sequential dynamics, such as ``a user who has followed OpenAI and Anthropic is more likely to follow AI at Meta next.'' Motivated by this issue, we introduce the Temporal Graph Benchmark with Sequential Dynamics (TGB-Seq), a new benchmark carefully curated to minimize repeated edges, challenging models to learn sequential dynamics and generalize to unseen edges. TGB-Seq comprises large real-world datasets spanning diverse domains, including e-commerce interactions, movie ratings, business reviews, social networks, citation networks and web link networks. Benchmarking experiments reveal that current methods usually suffer significant performance degradation and incur substantial training costs on TGB-Seq, posing new challenges and opportunities for future research. TGB-Seq datasets, leaderboards, and example codes are available at https://tgb-seq.github.io/.

The rapid growth of location acquisition technologies makes Point-of-Interest(POI) recommendation possible due to redundant user check-in records. In this paper, we focus on next POI recommendation in which next POI is based on previous POI. We observe that time plays an important role in next POI recommendation but is neglected in the recent proposed translating embedding methods. To tackle this shortage, we propose a time-adaptive translating embedding model (TransTARec) for next POI recommendation that naturally incorporates temporal influence, sequential dynamics, and user preference within a single component. Methodologically, we treat a (previous timestamp, user, next timestamp) triplet as a union translation vector and develop a neural-based fusion operation to fuse user preference and temporal influence. The superiority of TransTARec, which is confirmed by extensive experiments on real-world datasets, comes from not only the introduction of temporal influence but also the direct unification with user preference and sequential dynamics.

In this section, we won't delve into the depths of neuroscience, but rather aim to illuminate a fundamental concept: action potential. Understanding the behavior of neurons and the process that gives rise to a spike lays a crucial foundation. This rudimentary insight serves as a key building block, enriching our comprehension of the Neural Network models and its mathematical underpinnings. The action potential AP, a pivotal concept in neuronal function, is a neuronal phenomenon in which we see the neuron fires. Transmission of a neuronal signal is entirely dependent of the movement of ions, such as Sodium (Na+), Potassium (K+) and Chloride (CI), that are unequally distributed between the inside and the outside of the cell body. The presence and the movement of these ions creates a chemical gradient across the membrane which we define as electro-chemical gradient ECG .

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are tested for instances in the Euclidean plane. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean-average-percentage error of two of these models is below 3%.

Modeling user preferences (long-term history) and user dynamics (short-term history) is of greatest importance to build efficient sequential recommender systems. The challenge lies in the successful combination of the whole user's history and his recent actions (sequential dynamics) to provide personalized recommendations. Existing methods capture the sequential dynamics of a user using fixed-order Markov chains (usually first order chains) regardless of the user, which limits both the impact of the past of the user on the recommendation and the ability to adapt its length to the user profile. In this article, we propose to use frequent sequences to identify the most relevant part of the user history for the recommendation. The most salient items are then used in a unified metric model that embeds items based on user preferences and sequential dynamics. Extensive experiments demonstrate that our method outperforms state-of-the-art, especially on sparse datasets. We show that considering sequences of varying lengths improves the recommendations and we also emphasize that these sequences provide explanations on the recommendation.

We present exact analytical equilibrium solutions for a class of recurrent neural network models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour and long-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.

We present exact analytical equilibrium solutions for a class of recurrent neural network models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour and long-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.

We present exact analytical equilibrium solutions for a class of recurrent neuralnetwork models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour andlong-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.

For an n-neuron recurrent network, a much--studied and Widely-used continuous-time (CT) model is the leaky integrator model (Hertz, et 01., 1991; Hopfield, 1984),