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Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

We study complex CFTs describing fixed points of the two-dimensional $Q$-state Potts model with $Q>4$. Their existence is closely related to the weak first-order phase transition and walking RG behavior present in the real Potts model at…

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the…

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…

Learning the physical dynamics of deformable objects with particle-based representation has been the objective of many computational models in machine learning. While several state-of-the-art models have achieved this objective in simulated…

We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for…

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…

Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…

A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…

The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…

We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to…

Multi-object tracking (MOT) has profound applications in a variety of fields, including surveillance, sports analytics, self-driving, and cooperative robotics. Despite considerable advancements, existing MOT methodologies tend to falter…

Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…

Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

A system, which implements persistent objects, has to provide different opportunities to change the objects in arbitrary ways during their existence. A traditional realization of OO paradigm in modern programming systems has fundamental…

Salient object detection plays an important role in many downstream tasks. However, complex real-world scenes with varying scales and numbers of salient objects still pose a challenge. In this paper, we directly address the problem of…

Robotic manipulation of deformable linear objects (DLOs) is an active area of research, though emerging applications, like automotive wire harness installation, introduce constraints that have not been considered in prior work. Confined…