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We study classical spin ice under uniaxial strain along the $[111]$ crystallographic axis. Remarkably, such strain preserves the extensive ice degeneracy and the corresponding classical Coulomb phase. The emergent monopole excitations remain thermodynamically deconfined exactly as in the isotropic case. However, their motion under local heat bath dynamics depends qualitatively on the sign of the strain. In the low-temperature limit for negative strain, the monopoles diffuse, while for positive strain, they localize. Introducing additional ring exchange dynamics into the ice background transforms the localized monopoles into sub-dimensional excitations whose motion is restricted to diffusion in the $(111)$-plane. The phenomena we identify are experimentally accessible in rare-earth pyrochlores under uniaxial pressure as well as in tripod kagome materials. The diffusive versus localized nature of the monopoles manifests in characteristic magnetic noise spectra, which we compute., Comment: 17 pages, 13 figures

In industrial applications Finite State Machines (FSMs) are often used to implement decision making policies for autonomous systems. In recent years, the use of Behavior Trees (BT) as an alternative policy representation has gained considerable attention. The benefits of using BTs over FSMs are modularity and reusability, enabling a system that is easy to extend and modify. However, there exists few published studies on successful implementations of BTs for industrial applications. This paper contributes with the lessons learned from implementing BTs in a complex industrial use case, where a robotic system assembles explosive charges and places them in holes on the rock face. The main result of the paper is that even if it is possible to model the entire system as a BT, combining BTs with FSMs can increase the readability and maintainability of the system. The benefit of such combination is remarked especially in the use case studied in this paper, where the full system cannot run autonomously but human supervision and feedback are needed.

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories (J. Hall\'en et al, Science 378, 1218 (2022)) thus explaining the characteristics of magnetic monopole noise spectra (Dusad, R. et al. Nature 571, 234 (2019); Samarakoon, A. M. et al. Proc. Natl. Acad. Sci. 119, e2117453119 (2022)). Here we apply this new theory to explore the dynamics of field-driven monopole currents, finding them comprised of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss-angle for AC-field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure ${\Phi}(t)$, the time-dependence of magnetic flux threading the sample when a net monopole current $J(t) = \dot{\Phi}(t)/\mu_0$ is generated by applying an external magnetic field $B_0(t)$. These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time-constants before and after $t \approx 600 {\mu}s$ from monopole current initiation. Application of sinusoidal magnetic fields $B_0(t) = Bcos({\omega}t)$ generates oscillating monopole currents whose loss angle ${\theta}(f)$ exhibits a characteristic transition at frequency $f \approx 1.8$ kHz over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after $t \approx 600 {\mu}s$. This complex phenomenology represents a new form of heterogeneous dynamics generated by the interplay of fractionalization and local spin configurational symmetry.

The Ising antiferromagnets on the triangular and on the pyrochlore lattices are two of the most iconic examples of magnetic frustration, paradigmatically illustrating many exotic properties such as emergent gauge fields, fractionalisation, and topological order. In this work, we show that the two instances of frustration can, remarkably, be combined in a single system, where they coexist without inducing conventional long range ordering. We show that the system undergoes a first order phase transition upon lowering the temperature, into a yet different frustrated phase that we characterise to exhibit nematic order. We argue that an extensive degeneracy survives down to zero temperature, at odds with a customary Pauling estimate. Dynamically, we find evidence of anomalous noise in the power spectral density, arising from an effectively anisotropic fractal motion of monopoles at low temperature., Comment: 19 pages, 18 figures

Quantum bits (qubits) are prone to several types of errors due to uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads. A hopeful path forward is to build qubits that are inherently protected against certain types of errors, so that the overhead required to correct remaining ones is significantly reduced. However, the foreseen benefit rests on a severe condition: quantum manipulations of the qubit must not break the protection that has been so carefully engineered. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring continuous and autonomous protection against bit-flips. Here, in a superconducting circuit experiment, we implement a cat-qubit with bit-flip times exceeding 10 seconds. This is a four order of magnitude improvement over previous cat-qubit implementations. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these quantum superpositions without breaking bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.

This paper reports on the deposition of amorphous and crystalline thin films of Ga2O3 by reactive pulsed direct current magnetron sputtering from a liquid gallium target onto fused (f-) quartz and c plane (c-) sapphire substrates, where the temperature of the substrate is varied from room temperature (RT) to 800{\deg}C. The deposition rate (up to 37 nm/min at RT on f-quartz and 5 nm/min at 800{\deg}C on c-sapphire) is two to five times higher than the data given in the literature for radio frequency sputtering. Deposited onto unheated substrates, the films are X-ray amorphous. Well-defined X-ray diffraction peaks of \b{eta}-Ga2O3 start to appear at a substrate temperature of 500{\deg}C. Films grown on c-sapphire at temperatures above 600{\deg}C are epitaxial. However, the high rocking curve full width at half maximum values of {\approx} 2.4-2.5{\deg} are indicative of the presence of defects. A dense and void-free microstructure is observed in electron microscopy images. Composition analysis show stoichiometry close to Ga2O3 and no traces of impurities. The optical properties of low absorptance (<1%) in the visible range and an optical band gap of approximately 5 eV are consistent with the data in the literature for Ga2O3 films produced by other deposition methods., Comment: 15 pages, 6 figures

Fractals -- objects with non-integer dimensions -- occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines. Much effort has been expended to generate fractals for use in many-body physics. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy$_2$Ti$_2$O$_7$, and it resolves a long standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such striking phenomena holds promise of further surprising discoveries in the cooperative dynamics of even simple topological many-body systems., Comment: 13 pages, 11 figures

We develop investment approaches to secure electric power systems against load attacks where a malicious intruder (the attacker) covertly changes reactive power setpoints of loads to push the grid towards voltage instability while the system operator (the defender) employs reactive power compensation (RPC) to prevent instability. Extending our previously reported Stackelberg game formulation for this problem, we develop a robust-defense sequential algorithm and a novel genetic algorithm that provides scalability to large-scale power system models. The proposed methods are validated using IEEE prototype power system models with time-varying load uncertainties, demonstrating that reliable and robust defense is feasible unless the operator's RPC investment resources are severely limited relative to the attacker's resources., Comment: 6 pages, 6 figures, accepted by IEEE CDC 2023

We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and meta-programming quantification. We also investigate the relationship with concepts in intensional logic. We present an extension of first-order logic to support such abstractions, and show that it allows writing expressions of knowledge that are elaboration tolerant. To avoid nonsensical sentences in this formalism, we refine the concept of well-formed sentences, and propose a method to verify well-formedness with a complexity that is linear with the number of tokens in the formula. We have extended FO(.), a Knowledge Representation language, and IDP-Z3, a reasoning engine for FO(.), accordingly. We show that this extension was essential in accurately modelling various problem domains in an elaboration-tolerant way, i.e., without reification., Comment: In Proceedings ICLP 2023, arXiv:2308.14898

The spin ice compound Dy$_2$Ti$_2$O$_7$ is well-known to realise a three-dimensional Coulomb spin liquid with magnetically charged monopole excitations. Its fate at low temperatures, however, remains an intriguing open question. Based on a low-temperature analysis of the magnetic noise and diffuse neutron scattering under different cooling protocols, combined with extensive numerical modelling, we argue that upon cooling, the spins freeze into what may be termed a `structural magnetic glass', without an a priori need for chemical or structural disorder. Specifically, our model indicates the presence of frustration on two levels, first producing a near-degenerate constrained manifold inside which phase ordering kinetics is in turn frustrated. Our results suggest that spin ice Dy$_2$Ti$_2$O$_7$ provides one prototype of magnetic glass formation specifically, and a setting for the study of kinetically constrained systems more generally., Comment: Paper+Sup. Info

The spin ice compound Dy_2Ti_2O_7 stands out as the first topological magnet in three dimensions, with its tell-tale emergent fractionalized magnetic monopole excitations. Its real-time dynamical properties have been an enigma from the very beginning. Using ultrasensitive, non-invasive SQUID measurements, we show that Dy_2Ti_2O_7 exhibits a highly anomalous noise spectrum, in three qualitatively different regimes: equilibrium spin ice, a `frozen' regime extending to ultra-low temperatures, as well as a high-temperature `anomalous' paramagnet. We show that in the simplest model of spin ice, the dynamics is not anomalous, and we present several distinct mechanisms which give rise to a coloured noise spectrum. In addition, we identify the structure of the single-ion dynamics as a crucial ingredient for any modelling. Thus, the dynamics of spin ice Dy_2Ti_2O_7 reflects the interplay of local dynamics with emergent topological degrees of freedom and a frustration-generated imperfectly flat energy landscape, and as such should be relevant for a broad class of magnetic materials., Comment: Article+Sup. Info

A bargaining game is investigated for cooperative energy management in microgrids. This game incorporates a fully distributed and realistic cooperative power scheduling algorithm (CoDES) as well as a distributed Nash Bargaining Solution (NBS)-based method of allocating the overall power bill resulting from CoDES. A novel weather-based stochastic renewable generation (RG) prediction method is incorporated in the power scheduling. We demonstrate the proposed game using a 4-user grid-connected microgrid model with diverse user demands, storage, and RG profiles and examine the effect of weather prediction on day-ahead power scheduling and cost/profit allocation. Finally, the impact of users' ambivalence about cooperation and /or dishonesty on the bargaining outcome is investigated, and it is shown that the proposed game is resilient to malicious users' attempts to avoid payment of their fair share of the overall bill., Comment: 9 pages, 8 figures, published in IEEE Transactions on Industrial Informatics

We present a resource-planning game for cyber-security of networked control systems (NCS). The NCS is assumed to be operating in closed-loop using a linear state-feedback $\mathcal{H}_2$ controller. A zero-sum, two-player Stackelberg game (SG) is developed between an attacker and a defender for this NCS. The attacker aims to disable communication of selected nodes and thereby render the feedback gain matrix to be sparse, leading to degradation of closed-loop performance, while the defender aims to prevent this loss by investing in the protection of targeted nodes. Both players trade their $\mathcal{H}_2$-performance objectives for the costs of their actions. The standard backward induction method is modified to determine a cost-based Stackelberg equilibrium (CBSE) that saves the players' costs without degrading the control performance. We analyze the dependency of a CBSE on the relative budgets of the players as well as on the node "importance" order. Moreover, a robust-defense method is developed for the realistic case when the defender is not informed about the attacker's resources. The proposed algorithms are validated using examples from wide-area control of electric power systems. It is demonstrated that reliable and robust defense is feasible unless the defender's resources are severely limited relative to the attacker's resources. We also show that the proposed methods are robust to time-varying model uncertainties and thus are suitable for long-term security investment in realistic NCSs. Finally, we employ computationally efficient genetic algorithms (GA) to compute the optimal strategies of the attacker and the defender in realistic large power systems., Comment: 16 pages, 14 figures, 2 tables

The susceptibility of millimeter-wave (mmWave) signals to physical blockage and abrupt signal strength variations presents a challenge to reliable 5G communication. This work proposes and examines the feasibility of utilizing lower-frequency signals as early-warning indicators of mobile mmWave signal blockage or recovery. A physics-based channel simulation tool incorporating Fresnel diffraction and image sources is employed to demonstrate that sub-6 GHz signals "lead" mmWave signals in reaching a specific signal-strength threshold by several to tens of milliseconds at mobile speeds, suggesting early-warning systems are viable. This predictive approach stems from frequency-dependent properties of diffraction and does not assume a specific topology or mobile and obstacle speeds. Realistic simulations that include transitions from line of sight (LoS) to non-line of sight (NLoS) and reflection scenarios are employed to verify the proposed prediction capabilities. Moreover, prediction of the strongest multipath component and its angle of arrival (AoA) using sub-6 GHz observations is investigated., Comment: in IEEE Communications Letters

We formulate a Stackelberg game between an attacker and a defender of a power system. The attacker attempts to alter the load setpoints of the power system covertly and intelligently, so that the voltage stability margin of the grid is reduced, driving the entire system towards a voltage collapse. The defender, or the system operator, aims to compensate for this reduction by retuning the reactive power injection to the grid by switching on control devices, such as a bank of shunt capacitors. A modified Backward Induction method is proposed to find a cost-based Stackelberg equilibrium (CBSE) of the game, which saves the players' costs while providing the optimal allocation of both players' investment resources under budget and covertness constraints. We analyze the proposed game extensively for the IEEE 9-bus power system model and present an example of its performance for the IEEE 39-bus power system model. It is demonstrated that the defender is able to maintain system stability unless its security budget is much lower than the attacker's budget., Comment: 6 pages in main paper, 6 pages in supplementary material, 5 figs, Main paper has been accepted by CDC 2020

High frequency signals propagate along the edges of conductors. If the conductors are electroplated, then the seed layer forms at least one edge, so care must be taken to insure the electrical quality of these layers. In this work, we study the initial quality of SAM-based seed layers that are compatible with complex surfaces including through-silicon vias (TSVs), as are used in via-last three-dimensional semiconductor device packaging. The conformal and electrical quality of the seed metal is very important. Also important for a multifunction seed layer is its ability as a barrier layer, which protects the substrate from high temperature diffusion of the deposited metal. Thus, the barrier layer must be robust enough to withstand diffusion, yet thin enough to provide a conformal surface that allows metal seed layer deposition. Standard barrier layer deposition methods such as evaporation or sputtering require either a line of sight from the source or aspect ratios large enough to provide scattering from the background gas within the structure to coat all surfaces. Electrochemical and chemical vapor deposition provide alternatives, but concerns arise about contamination and compatibility with radio frequency or high-speed digital signals. We propose a barrier layer based on an aromatic self-assembled monolayer (SAM) for use in electroless copper seed layer deposition. The viability of the SAM barrier layer is determined by the quality of the deposited copper seed film, judged quantitatively by thin film resistivity and qualitatively by surface adhesion and morphological properties such as cracks and bubbles. Insights to the origins of problems and an optimal scheme are described. Extensions for use as a photolithographic resist layer are suggested. Our SAM approach for TSV applications yields a 'smart' seed layer that can be used with a 'simple,' scalloped, easy to fabricate, via hole., Comment: 11 pages, 5 figures

The National Electrical Manufacturers Association's (NEMA) NU 4-2008 standard specifies methodology for evaluating the performance of small-animal PET scanners. The standard's goal is to enable comparison of different PET scanners over a wide range of technologies and geometries used. In this work, we discuss if the NEMA standard meets these goals and we point out potential flaws and improvements to the standard. For the evaluation of spatial resolution, the NEMA standard mandates the use of filtered backprojection reconstruction. This reconstruction method can introduce star-like artifacts for detectors with an anisotropic spatial resolution, usually caused by parallax error. These artifacts can then cause a strong dependence of the resulting spatial resolution on the size of the projection window in image space, whose size is not fully specified in the NEMA standard. We show that the standard's equations for the estimation of the random rate for PET systems with intrinsic radioactivity are circular and not satisfiable. We compare random rates determined by a method based on the standard to to random rates obtained using a delayed coincidence window and two methods based on the singles rates. We discuss to what extend the NEMA standard's protocol for the evaluation of the sensitivity is unclear and ambiguous, which can lead to unclear interpretations of publicizeded results. The standard's definition of the recovery coefficients in the image quality phantom includes the maximum activity in a region of interest, which causes a positive correlation of noise and recovery coefficients. This leads to an unintended trade-off between desired uniformity, which is negatively correlated with variance (i.e. noise), and recovery. With this work, we want to start a discussion on possible improvements in a next version of the NEMA NU-4 standard.

Covalent amorphous semiconductors, such as amorphous silicon (a-Si) and germanium (a-Ge), are commonly believed to have localized electronic states at the top of the valence band and the bottom of the conduction band. Electrical conductivity is thought to be by the hopping mechanism through localized states. The carrier mobility of these materials is usually very low, in the order of ~10^-3 - 10^-2 cm^2/(Vs) at room temperature. In this study, we present the Hall effect characterization of a-Ge prepared by self-ion implantation of Ge ions. The a-Ge prepared by this method is highly homogenous and has a mass density within 98.5% of the crystalline Ge. The material exhibits an exceptionally high electrical conductivity and carrier mobility (~100 cm^2/(Vs)) for an amorphous semiconductor. The temperature-dependent resistivity of the material is very-well defined with two distinctive regions, extrinsic and intrinsic conductivity, as in crystalline Ge. These results are direct evidence for a largely-preserved band structure and non-localized states of the valence band in a-Ge, as proposed by Tauc et al. from optical characterization alone. This finding is not only significant for the understanding of electrical conductivity in covalent disordered semiconductors, but the exceptionally high mobility we have observed in amorphous Ge opens up device applications not previously considered for amorphous semiconductors., Comment: 10 pages, 3 figures

Multi-agent networked control systems (NCSs) are often subject to model uncertainty and are limited by large communication cost, associated with feedback of data between the system nodes. To provide robustness against model uncertainty and to reduce the communication cost, this paper investigates the mixed $H_2/H_{\infty}$ control problem for NCS under the sparsity constraint. First, proximal alternating linearized minimization (PALM) is employed to solve the centralized social optimization where the agents have the same optimization objective. Next, we investigate a sparsity-constrained noncooperative game, which accommodates different control-performance criteria of different agents, and propose a best-response dynamics algorithm based on PALM that converges to an approximate Generalized Nash Equilibrium (GNE) of this game. A special case of this game, where the agents have the same $H_2$ objective, produces a partially-distributed social optimization solution. We validate the proposed algorithms using a network with unstable node dynamics and demonstrate the superiority of the proposed PALM-based method to a previously investigated sparsity-constrained mixed $H_2/H_{\infty}$ controller.

Full investigation of deep defect states and impurities in wide-bandgap materials by employing commercial transient capacitance spectroscopy is a challenge, demanding very high temperatures. Therefore, a high-temperature deep-level transient spectroscopy (HT-DLTS) system was developed for measurements up to 1100 K. The upper limit of the temperature range allows for the study of deep defects and trap centers in the bandgap, deeper than previously reported by DLTS characterization in any material. Performance of the system was tested by conducting measurements on the well-known intrinsic defects in n-type 4H-SiC in the temperature range 300-950 K. Experimental observations performed on 4H-SiC Schottky diodes were in good agreement with the literatures. However, the DLTS measurements were restricted by the operation and quality of the electrodes.

We formulate a resource-planning game between an attacker and a defender of a network control system. We consider the network to be operating in closed-loop with a linear quadratic regulator (LQR). We construct a general-sum, two-player, mixed strategy game, where the attacker attempts to destroy communication equipment of some nodes, and thereby render the LQR feedback gain matrix to be sparse, leading to degradation of closed-loop performance. The defender, on the other hand, aims to prevent this loss. Both players trade their control performance objectives for the cost of their actions. A Mixed Strategy Nash Equilibrium (MSNE) of the game represents the allocation of the players' respective resources for attacking or protecting the network nodes. We analyze the dependence of a MSNE on the relative budgets of the players as well as on the important network nodes that must be preserved to achieve a desirable LQR performance. MSNE is computed using nonlinear programming. Results are validated using the New England power system model, and it is shown that reliable defense is feasible unless the cost of attack is very low or much smaller than the cost of protection per generator.

Monolithic crystals are examined as an alternative to segmented scintillator arrays in positron emission tomography (PET). Monoliths provide good energy, timing and spatial resolution including intrinsic depth of interaction (DOI) encoding. DOI allows reducing parallax errors (radial astigmatism) at off-center positions within a PET ring. We present a novel DOI-estimation approach based on the supervised machine learning algorithm gradient tree boosting (GTB). GTB builds predictive regression models based on sequential binary comparisons (decision trees). GTB models have been shown to be implementable in FPGA if the memory requirement fits the available resources. We propose two optimization scenarios for the best possible positioning performance: One restricting the available memory to enable a future FPGA implementation and one without any restrictions. The positioning performance of the GTB models is compared with a DOI estimation method based on a single DOI observable (SO) comparable to other methods presented in literature. For a 12 mm high monolith, we achieve an averaged spatial resolution of 2.15 mm and 2.12 mm FWHM for SO and GTB models, respectively. In contrast to SO models, GTB models show a nearly uniform positioning performance over the whole crystal depth., Comment: The accepted version of the article; DOI included; added one citation; results kept unchanged

We review algorithms for protein design in general. Although these algorithms have a rich combinatorial, geometric, and mathematical structure, they are almost never covered in computer science classes. Furthermore, many of these algorithms admit provable guarantees of accuracy, soundness, complexity, completeness, optimality, and approximation bounds. The algorithms represent a delicate and beautiful balance between discrete and continuous computation and modeling, analogous to that which is seen in robotics, computational geometry, and other fields in computational science. Finally, computer scientists may be unaware of the almost direct impact of these algorithms for predicting and introducing molecular therapies that have gone in a short time from mathematics to algorithms to software to predictions to preclinical testing to clinical trials. Indeed, the overarching goal of these algorithms is to enable the development of new therapeutics that might be impossible or too expensive to discover using experimental methods. Thus the potential impact of these algorithms on individual, community, and global health has the potential to be quite significant.

In this paper we present an online wide-area oscillation damping control (WAC) design for uncertain models of power systems using ideas from reinforcement learning. We assume that the exact small-signal model of the power system at the onset of a contingency is not known to the operator and use the nominal model and online measurements of the generator states and control inputs to rapidly converge to a state-feedback controller that minimizes a given quadratic energy cost. However, unlike conventional linear quadratic regulators (LQR), we intend our controller to be sparse, so its implementation reduces the communication costs. We, therefore, employ the gradient support pursuit (GraSP) optimization algorithm to impose sparsity constraints on the control gain matrix during learning. The sparse controller is thereafter implemented using distributed communication. Using the IEEE 39-bus power system model with 1149 unknown parameters, it is demonstrated that the proposed learning method provides reliable LQR performance while the controller matched to the nominal model becomes unstable for severely uncertain systems., Comment: Submitted to IEEE ACC 2019. 8 pages, 4 figures

Microgrids are self-sufficient small-scale power grid systems that can employ renewable generation sources and energy storage devices and can connect to the main grid or operate in a stand-alone mode. Most research on energy-storage management in microgrids does not take into account the dynamic nature of the problem and the need for fully-distributed, multi-step scheduling. First, we address these requirements by extending our previously proposed \textit{multi-step cooperative distributed energy scheduling} (CoDES) algorithm to include both purchasing power from and selling the generated power to the main grid. Second, we model the microgrid as a multi-agent system where the agents (e.g. households) act as players in a cooperative game and employ a distributed algorithm based on the Nash Bargaining Solution (NBS) to fairly allocate the costs of cooperative power management (computed using CoDES) among themselves. The dependency of the day-ahead power schedule and the costs on system parameters, e.g., the price schedule and the user activity level (measured by whether it owns storage and renewable generation devices), is analyzed for a three-agent microgrid example., Comment: 5 pages, 4 figures, submitted into PES general meeting 2017

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining problem as an example of a higher order problem. In short, this problem asks us to find a graph that frequently occurs as a subgraph among a set of example graphs. We start from the problem's mathematical definition to solve it in three state-of-the-art specification systems. For IDP and ASP, which have no native support for higher order logic, we propose the use of encoding techniques such as the disjoint union technique and the saturation technique. ProB benefits from the higher order support for sets. We compare the performance of the three approaches to get an idea of the overhead of the higher order support. We propose higher-order language extensions for IDP-like specification languages and discuss what kind of solver support is needed. Native higher order shifts the burden of rewriting specifications using encoding techniques from the user to the solver itself., Comment: Paper presented at the 9th Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2016), New York City, USA, 16 October 2016