arXiv subjects

Johannes Schmidt

Publications and source records attributed to Johannes Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

Representative Sets in Propositional Abduction

The propositional abduction problem is a well-known form of non-monotonic reasoning where we are asked to find an explanation of a given manifestation. Recently, there has been an influx of results asking more refined questions about the solution space rather than only individual solutions. For example, we might be interested in finding two solutions that are sufficiently far from each other (diverse solutions) in the solution space. In this paper we consider a related representation question where we ask if a given set of explanations S can represent any other explanation (that is, whether their symmetric difference is smaller than a given k). We first study this problem from a classical complexity perspective and obtain a complete classification. While only a handful of cases are tractable, the increase in complexity compared to classical abduction is often smaller than expected. We then study the parameterized complexity for several parameters and obtain new tractable and hard cases. Interestingly, a full parameterized complexity classification would require resolving the parameterized complexity of the covering radius problem from coding theory. To the best of our knowledge, no useful relationship between coding theory and non-monotonic reasoning has previously been established, but such connections seemingly become important when asking more complex questions about solution spaces.

cs.CC↗

arXiv2026

Universality in driven systems with a multiply-degenerate umbilic point

We investigate a driven particle system, a multilane asymmetric exclusion process, where the particle number in every lane is conserved, and stationary state is fully uncorrelated. The phase space has, starting from three lanes and more, an umbilic manifold where characteristic velocities of all the modes but one coincide, thus allowing us to study a weakly hyperbolic system with arbitrarily large degeneracy. We then study space-time fluctuations in the steady state, at the umbilic manifold, which are expected to exhibit universal scaling features. We formulate an effective mode-coupling theory (MCT) for the multilane model within the umbilic subspace and test its predictions. Unlike in the bidirectional two-lane model with an umbilic point studied earlier, here we find a robust $z=3/2$ dynamical exponent for the umbilic mode. The umbilic scaling function, obtained from Monte-Carlo simulations appears to have a universal shape for a range of interaction parameters and depends only on umbilic mode degeneracy. Remarkably, the shape and dynamic exponent of the non-degenerate mode can be analytically predicted on the base of effective MCT, up to non-universal scaling factor. Our findings suggest the existence of novel universality classes with dynamical exponent $3/2$, appearing in long-lived hydrodynamic modes with equal characteristic velocities.

cond-mat.stat-mech↗

arXiv2025

Complexity of Faceted Explanations in Propositional Abduction

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional abduction, we focus on specifying knowledge by a propositional formula. The computational complexity of tasks in propositional abduction has been systematically characterized - even with detailed classifications for Boolean fragments. Unsurprisingly, the most insightful reasoning problems (counting and enumeration) are computationally highly challenging. Therefore, we consider reasoning between decisions and counting, allowing us to understand explanations better while maintaining favorable complexity. We introduce facets to propositional abductions, which are literals that occur in some explanation (relevant) but not all explanations (dispensable). Reasoning with facets provides a more fine-grained understanding of variability in explanations (heterogeneous). In addition, we consider the distance between two explanations, enabling a better understanding of heterogeneity/homogeneity. We comprehensively analyze facets of propositional abduction in various settings, including an almost complete characterization in Post's framework.

cs.AI↗

arXiv2025

Universality in many-body driven systems with an umbilic point

We study stationary fluctuations of conserved slow modes in a two-lane model of hardcore particles which are expected to show universal behaviour. Specifically, we focus on the properties of fluctuations at a special umbilic point where the characteristic velocities coincide. At large space and time scales, fluctuations are described by a system of stochastic Burgers equations studied recently in [13]. Our data suggest coupling-dependent scaling functions and, even more surprisingly, coupling-dependent dynamical scaling exponents, distinct from KPZ scaling exponent typical for surface growth processes.

cond-mat.stat-mech↗

arXiv2025

Little to lose: the case for a robust European green hydrogen strategy

The EU targets 10 Mt of green hydrogen production by 2030, but has not committed to targets for 2040. Green hydrogen competes with carbon capture and storage, biomass and imports in reaching emissions reductions; earlier studies have demonstrated the great uncertainty in future cost-optimal development of green hydrogen. In spite of this, we show that Europe risks little by setting green hydrogen production targets at around 25 Mt by 2040. Employing an extensive scenario analysis combined with novel near-optimal techniques, we find that this target results in systems that are within 10% of cost-optimal in most considered scenarios. Setting concrete targets is important in order to resolve significant uncertainty which hampers investments. Targeting green hydrogen reduces the dependence on carbon capture and storage and green fuel imports, making for a more robust European climate strategy.

eess.SY↗

arXiv2025

A Fine-Grained Complexity View on Propositional Abduction -- Algorithms and Lower Bounds

The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning, e.g., abductive reasoning, comparably little is known outside classic complexity theory. In this paper we take a first step of bridging the gap between monotonic and non-monotonic reasoning by analyzing the complexity of intractable abduction problems under the seemingly overlooked but natural parameter n: the number of variables in the knowledge base. We obtain several positive results for $Σ^P_2$- as well as NP- and coNP-complete fragments, which implies the first example of beating exhaustive search for a $Σ^P_2$-complete problem (to the best of our knowledge). We complement this with lower bounds and for many fragments rule out improvements under the (strong) exponential-time hypothesis.

cs.CC↗

arXiv2025

Learning Tree Pattern Transformations

Explaining why and how a tree $t$ structurally differs from another tree $t^\star$ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we explore how to learn explanations for structural differences between pairs of trees from sample data: suppose we are given a set $\{(t_1, t_1^\star),\dots, (t_n, t_n^\star)\}$ of pairs of labelled, ordered trees; is there a small set of rules that explains the structural differences between all pairs $(t_i, t_i^\star)$? This raises two research questions: (i) what is a good notion of "rule" in this context?; and (ii) how can sets of rules explaining a data set be learned algorithmically? We explore these questions from the perspective of database theory by (1) introducing a pattern-based specification language for tree transformations; (2) exploring the computational complexity of variants of the above algorithmic problem, e.g. showing NP-hardness for very restricted variants; and (3) discussing how to solve the problem for data from CS education research using SAT solvers.

cs.LG↗

arXiv2024

HOLa: HoloLens Object Labeling

In the context of medical Augmented Reality (AR) applications, object tracking is a key challenge and requires a significant amount of annotation masks. As segmentation foundation models like the Segment Anything Model (SAM) begin to emerge, zero-shot segmentation requires only minimal human participation obtaining high-quality object masks. We introduce a HoloLens-Object-Labeling (HOLa) Unity and Python application based on the SAM-Track algorithm that offers fully automatic single object annotation for HoloLens 2 while requiring minimal human participation. HOLa does not have to be adjusted to a specific image appearance and could thus alleviate AR research in any application field. We evaluate HOLa for different degrees of image complexity in open liver surgery and in medical phantom experiments. Using HOLa for image annotation can increase the labeling speed by more than 500 times while providing Dice scores between 0.875 and 0.982, which are comparable to human annotators. Our code is publicly available at: https://github.com/mschwimmbeck/HOLa

cs.CV↗

arXiv2024

Impact of terahertz short pulses on the oxygen defect state in TiO$_{2-x}$

Oxygen deficient titanium dioxide (TiO$_{2-x}$) is a very attractive material for several applications ranging from photocatalysis to resistive switching. Oxygen vacancies turn insulating anatase titanium dioxide into a polaronic conductor, while creating a defect state band below the ultraviolet semiconducting gap. Here we employ a combination of broadband infrared (IR) reflectivity and THz-pump/IR-probe measurements to investigate the relationship between localized defect states and delocalized conducting polaronic states. We show that the THz pump allows to convert deeply localized electrons into metastable polarons with a lifetime in the ns range. These long-lived metastable states may find application in novel opto-electronic applications exploiting the interplay of dc resistivity, with terahertz and infrared signals.

cond-mat.mtrl-sci↗

arXiv2024

Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class

The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings we demonstrate scale invariance at different times and heights using large-scale Monte-Carlo simulations of the totally asymmetric simple exclusion process (TASEP) which belongs to the KPZ universality class. Here we focus on current/height fluctuations in the steady state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by super-diffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.

cond-mat.stat-mech↗

arXiv2024

Universal anomalous fluctuations in charged single-file systems

Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical universality reflected in anomalous statistical properties of macroscopic fluctuating observables such as charge transfer. We find that stringent dynamical constraints lead to universal anomalous statistics of cumulative charge currents manifested both on the timescale characteristic of typical fluctuations and also in the rate function describing rare events. By computing the full counting statistics of net transferred charge between two extended subsystems, we establish a number of unorthodox dynamical properties in an analytic fashion. Most prominently, typical fluctuations in equilibrium are governed by a universal distribution that markedly deviates from the expected Gaussian statistics, whereas large fluctuations are described by an exotic large-deviation rate function featuring an exceptional triple critical point. Far from equilibrium, competition between dynamical phases leads to dynamical phase transitions of first and second order and spontaneous breaking of fluctuation symmetry of the univariate charge large-deviation function. The rich phenomenology of the outlined dynamical universality is exemplified on an exactly solvable classical cellular automaton of charged hardcore particles. We determine the dynamical phase diagram in the framework of Lee-Yang's theory of phase transitions and exhibit a hyper-dimensional diagram of distinct dynamical regimes. Our findings lead us to conclude that the conventional classification of dynamical universality classes based on the algebraic dynamical exponents and asymptotic scaling functions that characterize hydrodynamic relaxation of the dynamical structure factor is incomplete and calls for refinement.

cond-mat.stat-mech↗

arXiv2023

Dynamical criticality of magnetization transfer in integrable spin chains

Recent studies have found that fluctuations of magnetization transfer in integrable spin chains violate the central limit property. Here we revisit the problem of anomalous counting statistics in the Landau-Lifshitz field theory by specializing to two distinct anomalous regimes featuring a dynamical critical point. By performing optimized numerical simulations using an integrable space-time discretization we extract the algebraic growth exponents of time-dependent cumulants which attain their threshold values. The distinctly non-Gaussian statistics of magnetization transfer in the easy-axis regime is found to converge towards the universal distribution of charged single-file systems. At the isotropic point we infer a weakly non-Gaussian distribution, corroborating the view that superdiffusive spin transport in integrable spin chains does not belong to any known dynamical universality class.

cond-mat.stat-mech↗

arXiv2023

Terahertz Saturable Absorption from Relativistic High-Temperature Thermodynamics in Black Phosphorus

Thanks to its tunable infrared band-gap and to its anisotropic conduction properties, black phosphorus represents a very unique 2D material, whose potential in the engineering of new devices still needs to be fully explored. We investigate here the nonlinear terahertz (THz) electrodynamics of black phosphorus along the more conducting armchair direction. Similarly to the case of other 2D systems like graphene and topological insulators, the THz saturable absorption properties of black phosphorus can be understood within a thermodynamic model by assuming a fast thermalization of the electron bath. While black phosphorus does not display the presence of massless fermions at ambient pressure and temperature, our analysis shows that its anomalous THz nonlinear properties can be accounted for by a relativistic massive Dirac dispersion, provided the Fermi temperature is low enough. An optimal tuning of the Fermi level therefore represents a strategy to engineer strong THz nonlinear response in other massive Dirac materials as in transition metal dichalchogenides or high-temperature superconductors.

cond-mat.mtrl-sci↗

arXiv2023

Explaining the decline of US wind output power density

US wind power generation has grown significantly over the last decades, in line with the number and average size of operating turbines. However, wind power density has declined, both measured in terms of wind power output per rotor swept area as well as per spacing area. To study this effect, we present a decomposition of US wind power generation data for the period 2001--2021 and examine how changes in input power density and system efficiency affected output power density. Here, input power density refers to the amount of wind available to turbines, system efficiency refers to the share of power in the wind flowing through rotor swept areas which is converted to electricity and output power density refers to the amount of wind power generated per rotor swept area. We show that, while power input available to turbines has increased in the period 2001--2021, system efficiency has decreased. In total, this has caused a decline in output power density in the last 10 years, explaining higher land-use requirements. The decrease in system efficiency is linked to the decrease in specific power, i.e. the ratio between the nameplate capacity of a turbine and its rotor swept area. Furthermore, we show that the wind available to turbines has increased substantially due to increases in the average hub height of turbines since 2001. However, site quality has slightly decreased in this period.

stat.AP↗

arXiv2023

Complexity of Reasoning with Cardinality Minimality Conditions

Many AI-related reasoning problems are based on the problem of satisfiability of propositional formulas with some cardinality-minimality condition. While the complexity of the satisfiability problem (SAT) is well understood when considering systematically all fragments of propositional logic within Schaefer's framework (STOC 1978) this is not the case when such minimality condition is added. We consider the CardMinSat problem, which asks, given a formula F and an atom x, whether x is true in some cardinality-minimal model of F. We completely classify the computational complexity of the CardMinSat problem within Schaefer's framework, thus paving the way for a better understanding of the tractability frontier of many AI-related reasoning problems. To this end we use advanced algebraic tools developed by (Schnoor & Schnoor 2008) and (Lagerkvist 2014).

cs.CC↗

arXiv2022

Temperature-independent non-linear terahertz transmission by liquid water

Liquid water is one of the most studied substances, yet many of its properties are difficult to rationalize. The uniqueness of water is rooted in the dynamic network of hydrogen-bonded molecules with relaxation time constants of about one picosecond. Terahertz fields oscillate on a picosecond timescale and are inherently suited to study water. Recent advances in non-linear terahertz spectroscopy have revealed large signals from water, which have been interpreted with different, sometimes competing, theoretical models. Here we show that the non-linear transmission of liquid water at ~1 THz is equal at 21 °C and 4 °C, thus suggesting that the most appropriate microscopic models should depend weakly on temperature. Among the different mechanisms proposed to date, the resonant reorientation of hydrogen-bonded water molecules might be the most appropriate to describe all of the currently available experimental results.

physics.chem-ph↗

arXiv2022

Exact anomalous current fluctuations in a deterministic interacting model

We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.

cond-mat.stat-mech↗

arXiv2021

The perils of automated fitting of datasets: the case of a wind turbine cost model

Rinne et al. conduct an interesting analysis of the impact of wind turbine technology and land-use on wind power potentials, which allows profound insights into each factors contribution to overall potentials. The paper presents a detailed model of site-specific wind turbine investment cost (i.e. road- and grid access costs) complemented by a model used to estimate site-independent costs. We believe that propose a cutting edge model of site-specific investment costs. However, the site-independent cost model is flawed in our opinion. This flaw most likely does not impact the results presented in the paper, although we expect a considerable generalization error. Thus the application of the wind turbine cost model in other contexts may lead to unreasonable results. More generally, the derivation of the wind turbine cost model serves as an example of how applications of automated regression analysis can go wrong.

stat.AP↗