Konstantin Ziegler

• Prof. Dr.
• Professor at University of Applied Sciences Landshut

The integration of renewable energy resources transforms traditional energy systems, introducing prosumers-entities that both produce and consume energy-as key participants in modern Smart Grids. Effective load forecasting is mandatory for optimizing energy resources and grid stability. Federated Learning (FL) has emerged as a promising approach fo...

The rising tide of single household prosumers leads to a paradigm shift for power grid operators. Those prosumers are characterized by their consumption, production and storage capabilities. Via buying and selling electricity, every prosumer becomes a rational agent in the smart grid, trying to maximize one's utility. The optimal short-and long-ter...

The functional (de)composition of polynomials is a topic in pure and computer algebra with many applications. The structure of decompositions of (suitably normalized) polynomials f=g∘h in F[x] over a field F is well understood in many cases, but less well when the degree of f is divisible by the positive characteristic p of F. This work investigate...

In an ego-network, an individual (ego) organizes its friends (alters) in different groups (social circles). This social network can be efficiently analyzed after learning representations of the ego and its alters in a low-dimensional, real vector space. These representations are then easily exploited via statistical models for tasks such as social...

The functional (de)composition of polynomials is a topic in pure and computer algebra with many applications. The structure of decompositions of (suitably normalized) polynomials f(x) = g(h(x)) in F[x] over a field F is well understood in many cases, but less well when the degree of f is divisible by the positive characteristic p of F. This work in...

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward strategy, large, mostly fully connected architectures are selected, thereby relying on a good optimization strategy...

Due to the growing volume of electronic payments, the monetary strain of credit-card fraud is turning into a substantial challenge for financial institutions and service providers, thus forcing them to continuously improve their fraud detection systems. However, modern data-driven and learning-based methods, despite their popularity in other domain...

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward strategy, large, mostly fully connected architectures are selected, thereby relying on a good optimization strategy...

A univariate polynomial f over a field is decomposable if f=go h=g(h) with nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field Fq. The tame case, where the characteristic of Fq does not divide n=deg. f, is fairly well understood, and we have reasona...

Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA. Please send abstracts to the CCA editors <editors_SIGSAM@acm.org> f...

Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gauß count the remaining ones, approximately and exactly. For polynomials in two or more variables, the situation changes dramatically. Most multivariate polynomials are irreducible. This survey presents...

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The tame case, where the characteristic of Fq does not divide n = deg f, is fairly well-understood, and we have reaso...

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one has to know the number of equal-degree collisions, that is f = g o h = g^* o h^* with (g,h) != (g^*, h^*) and deg(g) = deg(g^*). Such collisions only occur in the wild case, where the field character...

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f = g o h in Fq[x] is well understood in many cases, but quite poorly when the degrees of both components are divisible by the character...

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields is well understood in many cases, but quite poorly when the degrees of both components are divisible by the ch...

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another on...

We define formal ΟK-modules and their heights, following Drinfeld. To describe their universal deformations we introduce a formal cohomology group.

The formalism of raising and lowering operators is developed for the difference operator analogue of a quantum harmonic oscillator which acts on functions on a discrete support. The grid under consideration is a mixed version of an equidistant lattice and a q-linear grid. Several properties of the grid are described. The grids under consideration a...