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The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random…
By combining the one-way coupled chaotic map lattice system with a bit-reverse operation, we construct a new cryptosystem which is extremely sensitive to the system parameters even for low-dimensional systems. The security of this new…
Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum…
Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why…
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…
This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
Neural network inference typically operates on raw input data, increasing the risk of exposure during preprocessing and inference. Moreover, neural architectures lack efficient built-in mechanisms for directly authenticating input data.…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
Map-based neuron models are an important tool in modelling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their…
Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…
We provide the first step toward developing a hierarchical control-estimation framework to actively plan robot trajectories for anomaly detection in confined spaces. The space is represented globally using a directed region graph, where a…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…