Related papers: A topological chaos framework for hash functions
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…
We present a differentiable framework capable of learning a wide variety of compositions of simple policies that we call skills. By recursively composing skills with themselves, we can create hierarchies that display complex behavior. Skill…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Topological invariants, including the Chern numbers, can topologically classify parameterized Hamiltonians. We find that topological invariants can be properly defined and calculated even if the parameter space is discrete, which is done by…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of…
We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…
For systems that involve particle production through branching processes the concept of chaos is explored. The measures that can describe their behaviors are investigated. Monte Carlo simulation is used to generate events according to…
The two-gene Andrecut-Kauffman model describes gene expression within cells by a two-dimensional discrete dynamical system. Using periodic orbits of an one dimensional subsystem we, rigourously prove the existence of topological chaos in…
Hashing techniques are in great demand for a wide range of real-world applications such as image retrieval and network compression. Nevertheless, existing approaches could hardly guarantee a satisfactory performance with the extremely…
The application of synchronization theory to build up new cryptosystems has been a hot topic during the last two decades. In this paper we analyze a recent proposal in this field. We pinpoint the main limitations of the software…
In this paper we introduce a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics. The designs of the major components of the cipher are given. Its cryptographic properties of period, auto- and…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Given a set $S$ of $n$ distinct keys, a function $f$ that bijectively maps the keys of $S$ into the range $\{0,\ldots,n-1\}$ is called a minimal perfect hash function for $S$. Algorithms that find such functions when $n$ is large and retain…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
In this paper the chaotic properties of the TCP congestion avoidance mechanism are investigated. The analysis focuses on the origin of the complex behavior appearing in deterministic TCP/IP networks. From the traffic modeling point of view…
A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the…
The linear response of synchronized time-delayed chaotic systems to small external perturbations, i.e., the phenomenon of chaos pass filter, is investigated for iterated maps. The distribution of distances, i.e., the deviations between two…