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Machine learning (ML) has seen tremendous advancements, but its environmental footprint remains a concern. Acknowledging the growing environmental impact of ML this paper investigates Green ML, examining various model architectures and…
Modern astronomical data on galaxy and cosmological scales have revealed powerfully the existence of certain dark sectors of fundamental physics, i.e., existence of particles and fields outside the standard models and inaccessible by…
In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
The finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. However we prove that, in the most general case, the problem is undecidable. We study the case of automaton…
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The…
We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
We derive analytic expressions of the semiclassical energy levels of Sine-Gordon model in a strip geometry with Dirichlet boundary condition at both edges. They are obtained by initially selecting the classical backgrounds relative to the…
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of…
We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for $\mathbb{E}_\infty$ ring spectra. In…
We study fluctuations and finite size corrections for the ferromagnetic thermodynamic limit in the Bethe ansatz for the Heisenberg XXX1/2 spin chain, which is the AdS/CFT dual of semiclassical spinning strings. For this system we derive the…
Using the elements of the so-called $KBc\gamma$ subalgebra, we study a class of analytic solutions depending on a single function $F(K)$ in the modified cubic superstring field theory. We compute the energy associated to these solutions and…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
Uncertainties surrounding the energy transition often lead modelers to present large sets of scenarios that are challenging for policymakers to interpret and act upon. An alternative approach is to define a few qualitative storylines from…
Energy systems optimisation models are a leading tool for informing decisions in the energy transition. However, these models often remain opaque, and results are frequently presented without a clear discussion of their epistemic…
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes…
A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of…