Related papers: State Space Realization Theorems For Data Mining
An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…
Probabilistic programming combines general computer programming, statistical inference, and formal semantics to help systems make decisions when facing uncertainty. Probabilistic programs are ubiquitous, including having a significant…
Some new results on the module structure of Hopf algebras over a certain class of Hopf subalgebras and right coideal subalgebras are proved.
Symbolic event recognition systems have been successfully applied to a variety of application domains, extracting useful information in the form of events, allowing experts or other systems to monitor and respond when significant events are…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
Declarative process specifications define the behavior of processes by means of rules based on Linear Temporal Logic on Finite Traces (LTLf). In a mining context, these specifications are inferred from, and checked on, multi-sets of runs…
This paper describes a heap construction that supports insert and delete operations in arbitrary (possibly illegitimate) states. After any sequence of at most O(m) heap operations, the heap state is guarantee to be legitimate, where m is…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
Process mining extracts valuable insights from event data to help organizations improve their business processes, which is essential for their growth and success. By leveraging process mining techniques, organizations gain a comprehensive…
Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We…
It is a classical problem in algebraic topology to decide whether a given graded $\mathbb{Z}$-algebra can be realized as the cohomology ring of a space. In this paper, we introduce families of Stanley-Reisner algebras depending on graphs,…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
I present a new method for specifying and verifying the partial correctness of sequential programs. The key observation is that, in Hoare logic, assertions are used as selectors of states, that is, an assertion specifies the set of program…
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…
The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…
We consider the conditions under which the $q$-oscillator algebra becomes a Hopf $*$-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown…
In model based development, embedded systems are modeled using a mix of dataflow formalism, that capture the flow of computation, and hierarchical state machines, that capture the modal behavior of the system. For safety analysis, existing…
Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different…