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Multi-objective evolutionary algorithms (MOEAs) are widely used to solve multi-objective optimization problems. The algorithms rely on setting appropriate parameters to find good solutions. However, this parameter tuning could be very computationally expensive in solving non-trial (combinatorial) optimization problems. This paper proposes a framework that integrates MOEAs with adaptive parameter control using Deep Reinforcement Learning (DRL). The DRL policy is trained to adaptively set the values that dictate the intensity and probability of mutation for solutions during optimization. We test the proposed approach with a simple benchmark problem and a real-world, complex warehouse design and control problem. The experimental results demonstrate the advantages of our method in terms of solution quality and computation time to reach good solutions. In addition, we show the learned policy is transferable, i.e., the policy trained on a simple benchmark problem can be directly applied to solve the complex warehouse optimization problem, effectively, without the need for retraining.

Achieving efficient, high-power harmonic generation in the terahertz spectral domain has technological applications, for example in sixth generation (6G) communication networks. Massless Dirac fermions possess extremely large terahertz nonlinear susceptibilities and harmonic conversion efficiencies. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene. Here, we demonstrate room-temperature terahertz harmonic generation in a Bi$_2$Se$_3$ topological insulator and topological-insulator-grating metamaterial structures with surface-selective terahertz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW - an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip terahertz (opto)electronic applications.

Characterising the correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory. The seminal work [M. Navascu\'es et al, NJP 10,7,073013 (2008)], known as the NPA hierarchy, reformulated this question as a polynomial optimisation problem over noncommutative variables and proposed a convergent hierarchy of necessary conditions, each testable using semidefinite programming. More recently, the problem of characterising the quantum network correlations, which arise when locally measuring several independent quantum systems distributed in a network, has received considerable interest. Several generalisations of the NPA hierarchy, such as the Scalar Extension [Pozas-Kerstjens et al, Phys. Rev. Lett. 123, 140503 (2019)], were introduced while their converging sets remain unknown. In this work, we introduce a new hierarchy, prove its equivalence to the Scalar Extension, and characterise its convergence in the case of the simplest network, the bilocal scenario, and explore its relations with the known generalisations., Comment: Comments welcome! Mar. 2024 update: another major revision/fix is made. In particular, a correct new definition of scalar extension hierarchy with a convergent proof, paper restructured accordingly. 27 pages + appendices, 3 figures

We present the dynamical spin structure factor of the antiferromagnetic spin-$\frac{1}{2}$ $J_1-J_2$ Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest and next-to-nearest neighbour interactions yields a rich phase diagram. We resolve the low-energy excitations both in the $120^{\circ}$-ordered phase and in the putative spin liquid phase at $J_2/J_1 = 0.125$. In the ordered phase, we observe an avoided decay of the lowest magnon-branch, demonstrating the robustness of this phenomenon in the presence of gapless excitations. Our findings in the spin-liquid phase chime with the field-theoretical predictions for a gapless Dirac spin liquid, in particular the picture of low-lying monopole excitations at the corners of the Brillouin zone. We comment on possible practical difficulties of distinguishing proximate liquid and solid phases based on the dynamical structure factor.

Several chronic lung diseases, like idiopathic pulmonary fibrosis (IPF) are characterised by abnormal dilatation of the airways. Quantification of airway features on computed tomography (CT) can help characterise disease progression. Physics based airway measurement algorithms have been developed, but have met with limited success in part due to the sheer diversity of airway morphology seen in clinical practice. Supervised learning methods are also not feasible due to the high cost of obtaining precise airway annotations. We propose synthesising airways by style transfer using perceptual losses to train our model, Airway Transfer Network (ATN). We compare our ATN model with a state-of-the-art GAN-based network (simGAN) using a) qualitative assessment; b) assessment of the ability of ATN and simGAN based CT airway metrics to predict mortality in a population of 113 patients with IPF. ATN was shown to be quicker and easier to train than simGAN. ATN-based airway measurements were also found to be consistently stronger predictors of mortality than simGAN-derived airway metrics on IPF CTs. Airway synthesis by a transformation network that refines synthetic data using perceptual losses is a realistic alternative to GAN-based methods for clinical CT analyses of idiopathic pulmonary fibrosis. Our source code can be found at https://github.com/ashkanpakzad/ATN that is compatible with the existing open-source airway analysis framework, AirQuant., Comment: 11 Pages, 4 figures. Source code available: https://github.com/ashkanpakzad/ATN. Initial submission version, to be published in MICCAI Workshop on Deep Generative Models 2022

In research concerning quantum networks, it is often assumed that the parties can classically communicate with each other. However, classical communication might introduce a substantial delay to the network, especially if it is large. As the latency of a network is one of its most important characteristics, it is interesting to consider quantum networks in which parties cannot communicate classically and ask what limitations this assumption imposes on the possibility of preparing multipartite states in such networks. We show that graph states of an arbitrary prime local dimension known for their numerous applications in quantum information cannot be generated in a quantum network in which parties are connected via sources of bipartite quantum states and the classical communication is replaced by some pre-shared classical correlations. We then generalise our result to arbitrary quantum states that are sufficiently close to graph states., Comment: 15 pages (4.5 + appendices) and 4 figures; See also the related work by Y.-X. Wang et al. arXiv:2208.12100

Machine learning (ML) continues to permeate all layers of academia, industry and society. Despite its successes, mental frameworks to capture and represent machine learning workflows in a consistent and coherent manner are lacking. For instance, the de facto process modeling standard, Business Process Model and Notation (BPMN), managed by the Object Management Group, is widely accepted and applied. However, it is short of specific support to represent machine learning workflows. Further, the number of heterogeneous tools for deployment of machine learning solutions can easily overwhelm practitioners. Research is needed to align the process from modeling to deploying ML workflows. We analyze requirements for standard based conceptual modeling for machine learning workflows and their serverless deployment. Confronting the shortcomings with respect to consistent and coherent modeling of ML workflows in a technology independent and interoperable manner, we extend BPMN's Meta-Object Facility (MOF) metamodel and the corresponding notation and introduce BPMN4sML (BPMN for serverless machine learning). Our extension BPMN4sML follows the same outline referenced by the Object Management Group (OMG) for BPMN. We further address the heterogeneity in deployment by proposing a conceptual mapping to convert BPMN4sML models to corresponding deployment models using TOSCA. BPMN4sML allows technology-independent and interoperable modeling of machine learning workflows of various granularity and complexity across the entire machine learning lifecycle. It aids in arriving at a shared and standardized language to communicate ML solutions. Moreover, it takes the first steps toward enabling conversion of ML workflow model diagrams to corresponding deployment models for serverless deployment via TOSCA., Comment: 105 pages 3 tables 33 figures

The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree-Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field, since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.

We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes. The devices are fabricated from high-mobility two-dimensional electron gases in which quasi-one-dimensional wires are defined by electrostatic gates. These devices enable measurements of local and non-local transport properties and have been optimized via extensive simulations to ensure robustness against non-uniformity and disorder. Our main result is that several devices, fabricated according to the design's engineering specifications, have passed the topological gap protocol defined in Pikulin et al. [arXiv:2103.12217]. This protocol is a stringent test composed of a sequence of three-terminal local and non-local transport measurements performed while varying the magnetic field, semiconductor electron density, and junction transparencies. Passing the protocol indicates a high probability of detection of a topological phase hosting Majorana zero modes as determined by large-scale disorder simulations. Our experimental results are consistent with a quantum phase transition into a topological superconducting phase that extends over several hundred millitesla in magnetic field and several millivolts in gate voltage, corresponding to approximately one hundred micro-electron-volts in Zeeman energy and chemical potential in the semiconducting wire. These regions feature a closing and re-opening of the bulk gap, with simultaneous zero-bias conductance peaks at both ends of the devices that withstand changes in the junction transparencies. The extracted maximum topological gaps in our devices are 20-60 $\mu$eV. This demonstration is a prerequisite for experiments involving fusion and braiding of Majorana zero modes., Comment: Final version

Tree ensembles are powerful models that are widely used. However, they are susceptible to adversarial examples, which are examples that purposely constructed to elicit a misprediction from the model. This can degrade performance and erode a user's trust in the model. Typically, approaches try to alleviate this problem by verifying how robust a learned ensemble is or robustifying the learning process. We take an alternative approach and attempt to detect adversarial examples in a post-deployment setting. We present a novel method for this task that works by analyzing an unseen example's output configuration, which is the set of predictions made by an ensemble's constituent trees. Our approach works with any additive tree ensemble and does not require training a separate model. We evaluate our approach on three different tree ensemble learners. We empirically show that our method is currently the best adversarial detection method for tree ensembles.

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for $J_1 > |J_2|, |J_3|$ based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate ground-state phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller $J_3$ interactions, an indication of a very strong competition between low-energy states in this model., Comment: Accepted version for PRB; 23 pages (16 main text), 20 figures

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

We consider the following variational problem: minimize the $(n+1)$st polynomial conserved quantity of KdV over $H^n(\mathbb{R})$ with the first $n$ conserved quantities constrained. Maddocks and Sachs used that $n$-solitons are local minimizers for this problem in order to prove that $n$-solitons are orbitally stable in $H^n(\mathbb{R})$. Given $n$ constraints that are attainable by an $n$-soliton, we show that there is a unique set of $n$ amplitude parameters so that the corresponding multisolitons satisfy the constraints. Moreover, we prove that these multisolitons are the unique global constrained minimizers. We then use this variational characterization to provide a new proof of the orbital stability result of Maddocks and Sachs via concentration compactness. In the case when the constraints can be attained by functions in $H^n(\mathbb{R})$ but not by an $n$-soliton, we discover new behavior for minimizing sequences.

The recent advent of topological states of matter spawned many significant discoveries. The quantum anomalous Hall effect[1-3] is a prime example due to its potential for applications in quantum metrology[4, 5] as well as its influence on fundamental research into the underlying topological and magnetic states[6-11] and axion electrodynamics[2, 12-14]. Here, we perform electronic transport studies on a (V,Bi,Sb)2Te3 ferromagnetic topological insulator nanostructure in the quantum anomalous Hall regime. This allows us access to the dynamics of an individual ferromagnetic domain. The volume of the domain is estimated to be about 85 000 nm3, containing some 50 000 vanadium atoms, spread over a macroscopic distance of 115 nm. Telegraph noise resulting from the magnetization fluctuations of this domain is observed in the Hall signal. Careful analysis of the influence of temperature and external magnetic field on the domain switching statistics provides evidence for quantum tunneling of magnetization[15-22] in a macrospin state. This ferromagnetic macrospin is not only the largest magnetic object in which quantum tunneling has been observed, but also the first observation of the effect in a topological state of matter.

Energy system models underpin decisions by energy system planners and operators. Energy system modelling faces a transformation: accounting for changing meteorological conditions imposed by climate change. To enable that transformation, a community of practice in energy-climate modelling has started to form that aims to better integrate energy system models with weather and climate models. Here, we evaluate the disconnects between the energy system and climate modelling communities, then lay out a research agenda to bridge those disconnects. In the near-term, we propose interdisciplinary activities for expediting uptake of future climate data in energy system modelling. In the long-term, we propose a transdisciplinary approach to enable development of (1) energy-system-tailored climate datasets for historical and future meteorological conditions and (2) energy system models that can effectively leverage those datasets. This agenda increases the odds of meeting ambitious climate mitigation goals by systematically capturing and mitigating climate risk in energy sector decision making., Comment: MTC, JW and LPS contributed equally to this manuscript. 25 pages, 2 figures. Fixed typos in manuscript title. This perspective is based on the discussion held at the 2021 Next Generations Challenges in Energy-Climate Modelling (NextGenEC'21) workshop

It is increasingly common to solve combinatorial optimisation problems that are partially-specified. We survey the case where the objective function or the relations between variables are not known or are only partially specified. The challenge is to learn them from available data, while taking into account a set of hard constraints that a solution must satisfy, and that solving the optimisation problem (esp. during learning) is computationally very demanding. This paper overviews four seemingly unrelated approaches, that can each be viewed as learning the objective function of a hard combinatorial optimisation problem: 1) surrogate-based optimisation, 2) empirical model learning, 3) decision-focused learning (`predict + optimise'), and 4) structured-output prediction. We formalise each learning paradigm, at first in the ways commonly found in the literature, and then bring the formalisations together in a compatible way using regret. We discuss the differences and interactions between these frameworks, highlight the opportunities for cross-fertilization and survey open directions.

Hybrid samples combining superconductors with magnetic topological insulators are a promising platform for exploring exotic new transport physics. We examine a Josephson junction of such a system, based on the dilute magnetic topological insulator (Hg,Mn)Te and the type II superconductor MoRe. In the zero and very low field limit, to the best of our knowledge, the device shows, for the first time, induced supercurrent through a magnetically doped semiconductor, in this case a topological insulator. At higher fields, a rich and hysteretic magnetoresistance is revealed. Careful analysis shows that the explanation of this behaviour can be found in magnetic flux focusing stemming from the Meissner effect in the superconductor, without invoking any role of proximity induced superconductivity. The phenomena is important, as it will ubiquitously co-exist with any exotic new physics that may be present in this class of devices., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright \c{opyright} 2022 American Chemical Society after peer review. To access the final edited and published work see doi.org/10.1021/acs.nanolett.1c04903

The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity \'a la Einstein, the gravitational interaction is geometrized in terms of the spacetime curvature. However, if we embrace the geometrical character of gravity, two alternative, though equivalent, formulations of General Relativity emerge in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity. The latter allows a much simpler formulation of General Relativity oblivious to the affine spacetime structure, the Coincident General Relativity. The entropy of a black hole can be computed using the Euclidean path integral approach, which strongly relies on the addition of boundary or regulating terms in the standard formulation of General Relativity. A more fundamental derivation can be performed using Wald's formula, in which the entropy is directly related to Noether charges and is applicable to general theories with diffeomorphism invariance. In this work we extend Wald's Noether charge method for calculating black hole entropy to spacetimes endowed with non-metricity. Using this method, we show that Coincident General Relativity with an improved action principle gives the same entropy as the well-known entropy in standard General Relativity. Furthermore the first law of black hole thermodynamics holds and an explicit expression for the energy appearing in the first law is obtained., Comment: 30 pages

We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry. This characterization yields a set of quantities satisfying the coupled pentagon equations, associated with a module category over the fusion category that describes the MPO symmetry. Equivalence classes of these quantities provide complete invariants for an MPO symmetry protected phase: they are robust under continuous deformations of the MPS tensor, and two phases with the same equivalence class can be connected by a symmetric gapped path. Our techniques match and extend the known renormalization fixed point classifications and facilitate the numerical study of these systems. For MPO symmetries described by a group, we recover the symmetry protected topological order classification for unique and degenerate ground states. Moreover, we study the interplay between time reversal symmetry and an MPO symmetry and we also provide examples of our classification, together with explicit constructions based on groups. Finally, we elaborate on the connection between our setup and gapped boundaries of two-dimensional topological systems, where MPO symmetries also play a key role., Comment: v2 Introduction changed, one figure added v3 Main result improved: complete classification (connection and separation of phases) outside RG fixed points

Adipose tissue (AT) transcriptome studies provide holistic pictures of adaptation to weight and related bioclinical settings changes. Objective To implement AT gene expression profiling and investigate the link between changes in bioclinical parameters and AT gene expression during 3 steps of a 2-phase dietary intervention (DI). Methods AT transcriptome profiling was obtained from sequencing 1051 samples, corresponding to 556 distinct individuals enrolled in a weight loss intervention (8-week low-calorie diet (LCD) at 800 kcal/day) followed with a 6-month ad libitum randomized DI. Transcriptome profiles obtained with QuantSeq sequencing were benchmarked against Illumina RNAseq. Reverse transcription quantitative polymerase chain reaction was used to further confirm associations. Cell specificity was assessed using freshly isolated cells and THP-1 cell line. Results During LCD, 5 modules were found, of which 3 included at least 1 bioclinical variable. Change in body mass index (BMI) connected with changes in mRNA level of genes with inflammatory response signature. In this module, change in BMI was negatively associated with changes in expression of genes encoding secreted protein (GDF15, CCL3, and SPP1). Through all phases of the DI, change in GDF15 was connected to changes in SPP1, CCL3, LIPA and CD68. Further characterization showed that these genes were specific to macrophages (with LIPA, CD68 and GDF15 expressed in anti-inflammatory macrophages) and GDF15 also expressed in preadipocytes. Conclusion Network analyses identified a novel AT feature with GDF15 upregulated with calorie restriction induced weight loss, concomitantly to macrophage markers. In AT, GDF15 was expressed in preadipocytes and macrophages where it was a hallmark of anti-inflammatory cells.

The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to $h/e^2$. By tuning the disorder using different fabrication processes, we find evidence that this unexpected $\nu=1$ plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device., Comment: 8+3 pages, 5+2 figures