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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized $1+1$D quantum XY model based on group-valued qudits. This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)\times Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on $G$ for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging $\mathsf{Rep}(G)\times Z(G)$ sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging $\mathsf{Rep}(G)$ symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries., Comment: 64 pages, 2 figures, and featuring SmallGroup(32,49). v2: minor changes and added references

The semiconductor industry's paradigm shift towards fabless integrated circuit (IC) manufacturing has introduced security threats, including piracy, counterfeiting, hardware Trojans, and overproduction. In response to these challenges, various countermeasures, including Logic locking (LL), have been proposed to protect designs and mitigate security risks. LL is likely the most researched form of intellectual property (IP) protection for ICs. A significant advance has been made with the introduction of compound logic locking (CLL), where two LL techniques are concurrently utilized for improved resiliency against attacks. However, the vulnerabilities of LL techniques, particularly CLL, need to be explored further. This paper presents a novel framework, RESAA, designed to classify CLL-locked designs, identify critical gates, and execute various attacks to uncover secret keys. RESAA is agnostic to specific LL techniques, offering comprehensive insights into CLL's security scenarios. Experimental results demonstrate RESAA's efficacy in identifying critical gates, distinguishing segments corresponding to different LL techniques, and determining associated keys based on different threat models. In particular, for the oracle-less threat model, RESAA can achieve up to 92.6% accuracy on a relatively complex ITC'99 benchmark circuit. The results reported in this paper emphasize the significance of evaluation and thoughtful selection of LL techniques, as all studied CLL variants demonstrated vulnerability to our framework. RESAA is also open-sourced for the community at large., Comment: 12 pages, IEEE Transaction format

The low dynamic range (LDR) of common cameras fails to capture the rich contrast in natural scenes, resulting in loss of color and details in saturated pixels. Reconstructing the high dynamic range (HDR) of luminance present in the scene from single LDR photographs is an important task with many applications in computational photography and realistic display of images. The HDR reconstruction task aims to infer the lost details using the context present in the scene, requiring neural networks to understand high-level geometric and illumination cues. This makes it challenging for data-driven algorithms to generate accurate and high-resolution results. In this work, we introduce a physically-inspired remodeling of the HDR reconstruction problem in the intrinsic domain. The intrinsic model allows us to train separate networks to extend the dynamic range in the shading domain and to recover lost color details in the albedo domain. We show that dividing the problem into two simpler sub-tasks improves performance in a wide variety of photographs., Comment: Accepted for ECCV 2024

Intrinsic image decomposition aims to separate the surface reflectance and the effects from the illumination given a single photograph. Due to the complexity of the problem, most prior works assume a single-color illumination and a Lambertian world, which limits their use in illumination-aware image editing applications. In this work, we separate an input image into its diffuse albedo, colorful diffuse shading, and specular residual components. We arrive at our result by gradually removing first the single-color illumination and then the Lambertian-world assumptions. We show that by dividing the problem into easier sub-problems, in-the-wild colorful diffuse shading estimation can be achieved despite the limited ground-truth datasets. Our extended intrinsic model enables illumination-aware analysis of photographs and can be used for image editing applications such as specularity removal and per-pixel white balancing., Comment: 12 pages, 12 figures. Accepted to SIGGRAPH Asia 2024 (TOG). Webpage: https://yaksoy.github.io/ColorfulShading

Class-agnostic image segmentation is a crucial component in automating image editing workflows, especially in contexts where object selection traditionally involves interactive tools. Existing methods in the literature often adhere to top-down formulations, following the paradigm of class-based approaches, where object detection precedes per-object segmentation. In this work, we present a novel bottom-up formulation for addressing the class-agnostic segmentation problem. We supervise our network directly on the projective sphere of its feature space, employing losses inspired by metric learning literature as well as losses defined in a novel segmentation-space representation. The segmentation results are obtained through a straightforward mean-shift clustering of the estimated features. Our bottom-up formulation exhibits exceptional generalization capability, even when trained on datasets designed for class-based segmentation. We further showcase the effectiveness of our generic approach by addressing the challenging task of cell and nucleus segmentation. We believe that our bottom-up formulation will offer valuable insights into diverse segmentation challenges in the literature.

Conversational agents (CA) have become increasingly prevalent in various domains, driving significant interest in understanding the dynamics of trust in CA. This study addresses the need for a comprehensive analysis of research trends in this field, especially given the rapid advancements and growing use of CA technologies like ChatGPT. Through bibliometric analysis, we aim to identify key keywords, disciplines, research clusters, and international collaborations related to CA and trust. We analyzed 955 studies published between 2009 and 2024, all sourced from the Scopus database. Additionally, we conducted a text clustering analysis to identify the main themes in the publications and understand their distribution. Our findings highlight the increasing interest in CA, particularly with the introduction of ChatGPT. The USA leads in research output, followed by Germany, China, and the UK. Furthermore, there is a notable rise in interdisciplinary research, especially in the fields of human-computer interaction and artificial intelligence.

Many results for Banach spaces also hold for quasi-Banach spaces. One important such example is results depending on the Baire Category Theorem (BCT). We use the BCT to explore Lions problem for a quasi-Banach couple $(A_0, A_1)$. Lions problem, posed in 1960's, is to prove that different parameters $(\theta,p)$ produce different interpolation spaces $(A_0, A_1)_{\theta, p}$. We first establish conditions on $A_0$ and $A_1$ so that interpolation spaces of this couple are strictly intermediate spaces between $A_0+A_1$ and $A_0\cap A_1$. This result, together with a reiteration theorem, gives a partial solution to Lions problem for quasi-Banach couples. We then apply our interpolation result to (partially) answer a question posed by Pietsch. More precisely, we show that if $p\neq p^*$ the operator ideals $\mathcal{L}^{(a)}_{p,q}(X,Y)$, $\mathcal{L}^{(a)}_{p^*,q^*}(X,Y)$ generated by approximation numbers are distinct. Moreover, for any fixed $p$, either all operator ideals $\mathcal{L}^{(a)}_{p,q}(X,Y)$ collapse into a unique space or they are pairwise distinct. We cite counterexamples which show that using interpolation spaces is not appropriate to solve Pietsch's problem for operator ideals based on general $s$-numbers. However, the BCT can be used to prove a lethargy result for arbitrary $s$-numbers which guarantees that, under very minimal conditions on $X,Y$, the space $\mathcal{L}^{(s)}_{p,q}(X,Y)$ is strictly embedded into $\mathcal{L}^{\mathcal{A}}(X,Y)$. The paper is dedicated to the memory of Prof. A. Pietsch, who passed away recently., Comment: In the previous version there was an error in a proof and now the corresponding result has been substituted by two other theorems that hopefully are right. We express our thanks to the referee who pointed the error. Also, one reference has been added

Defining distances over finite fields formally by $||x-y||:=(x_1-y_1)^2+\cdots + (x_d-y_d)^2$ for $x,y\in \mathbb{F}_q^d$, distance problems naturally arise in analogy to those studied by Erd\H{o}s and Falconer in Euclidean space. Given a graph $G$ and a set $E\subseteq \mathbb{F}_q^2$, let $\Delta_G(E)$ be the generalized distance set corresponding to $G$. In the case when $G$ is the complete graph on $k+1$ vertices, Bennett, Hart, Iosevich, Pakianathan, and Rudnev showed that when $|E|\geq q^{d-\frac{d-1}{k+1}}$, it follows that $|\Delta_G(E)|\geq cq^{\binom{k+1}{2}}$. In the case when $k=d=2$, the threshold can be improved to $|E|\geq q^{\frac{8}{5}}$. Moreover, Jardine, Iosevich, and McDonald showed that in the case when $G$ is a tree with $k+1$ vertices, then whenever $E\subseteq \mathbb{F}_q^d$, $d\geq 2$ satisfies $|E|\geq C_kq^{\frac{d+1}{2}}$, it follows that $\Delta_G(E)=\mathbb{F}_q^k$. In this paper, we present a technique which enables us to study certain graphs with both rigid and non-rigid components. In particular, we show that for $E\subseteq \mathbb{F}_q^2$, $q=p^n$, $n$ odd, $p\equiv 3 \ \text{mod} \ 4$, and $G$ is the graph consisting of two triangles joined at a vertex, then whenever $|E|\geq q^{\frac{12}{7}}$, it follows that $|\Delta_G(E)|\geq cq^6$., Comment: 14 pages, 3 figures

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models., Comment: 71 pages. v2: minor changes + added references

Existing methods for scale-invariant monocular depth estimation (SI MDE) often struggle due to the complexity of the task, and limited and non-diverse datasets, hindering generalizability in real-world scenarios. This is while shift-and-scale-invariant (SSI) depth estimation, simplifying the task and enabling training with abundant stereo datasets achieves high performance. We present a novel approach that leverages SSI inputs to enhance SI depth estimation, streamlining the network's role and facilitating in-the-wild generalization for SI depth estimation while only using a synthetic dataset for training. Emphasizing the generation of high-resolution details, we introduce a novel sparse ordinal loss that substantially improves detail generation in SSI MDE, addressing critical limitations in existing approaches. Through in-the-wild qualitative examples and zero-shot evaluation we substantiate the practical utility of our approach in computational photography applications, showcasing its ability to generate highly detailed SI depth maps and achieve generalization in diverse scenarios., Comment: To appear in Proc. SIGGRAPH, 2024. Project webpage: https://yaksoy.github.io/sidepth/

A site-specific radio channel representation (SSCR) takes the surroundings of the communication system into account by considering the environment geometry, including buildings, vegetation, and mobile objects with their material and surface properties. We present methods for an SSCR that is spatially consistent, such that mobile transmitter and receiver cause a correlated time-varying channel impulse response and closely spaced antennas are correctly correlated. An SSCR is composed of a dynamically varying number of multipath components solely defined by the environment geometry and the material of the environmental objects. Hence, the environment geometry is the only natural scenario parameterization and specific calibration procedures shall be avoided. 5G and 6G physical layer technologies are increasingly able to exploit the properties of a wide range of environments from dense urban areas to railways, road transportation, industrial automation, and unmanned aerial vehicles. The channel impulse response in this wide range of scenarios has generally non-stationary statistical properties, i.e., the Doppler spectrum, power delay profile, K-factor and spatial correlation are all spatially variant (or time-variant for mobile receivers). SSCRs will enable research and development of emerging 5G and 6G technologies such as distributed multiple-input multiple-output systems, reconfigurable intelligent surfaces, multi-band communication, and joint communication and sensing. We highlight the state of the art and summarize research directions for future work towards an SSCR., Comment: 9 pages, 6 figures, to appear in IEEE Communication Magazine

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $S^{\,}_3$ symmetry and the other with non-invertible $\mathsf{Rep}(S^{\,}_3)$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1D symmetry-topological-order (SymTO) of type $\mathrm{JK}^{\,}_4\boxtimes \overline{\mathrm{JK}}^{\,}_4$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $S^{\,}_3$-symmetric and $\mathsf{Rep}(S^{\,}_3)$-symmetric models., Comment: 49 pages + 42 pages appendix, 17 figures -- minor corrections

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with $\mathrm{U}(1)$ charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments.

The discovery of complex concentrated alloys has unveiled materials with diverse atomic environments, prompting the exploration of solute segregation beyond dilute alloys. Data-driven methods offer promising for modeling segregation in such chemically complex environments, and are employed in this study to understand segregation behavior of a refractory complex concentrated alloy, NbMoTaW. A flexible methodology is developed that uses composable computational modules, with different arrangements of these modules employed to obtain site availabilities at absolute zero and the corresponding density of states beyond the dilute limit, resulting in an extremely large dataset containing 10 million data points. The artificial neural network developed here can rely solely on descriptions of local atomic environments to predict behavior at the dilute limit with very small errors, while the addition of negative segregation instance classification allows any solute concentration from zero up to the equiatomic concentration for ternary or quaternary alloys to be modeled at room temperature. The machine learning model thus achieves a significant speed advantage over traditional atomistic simulations, being four orders of magnitude faster, while only experiencing a minimal reduction in accuracy. This efficiency presents a powerful tool for rapid microstructural and interfacial design in unseen domains. Scientifically, our approach reveals a transition in the segregation behavior of Mo from unfavorable in simple systems to favorable in complex environments. Additionally, increasing solute concentration was observed to cause anti-segregation sites to begin to fill, challenging conventional understanding and highlighting the complexity of segregation dynamics in chemically complex environments.

The conventional Two-Way Fixed-Effects (TWFE) estimator has come under scrutiny lately. Recent literature has revealed potential shortcomings of TWFE when the treatment effects are heterogeneous. Scholars have developed new advanced dynamic Difference-in-Differences (DiD) estimators to tackle these potential shortcomings. However, confusion remains in applied research as to when the conventional TWFE is biased and what issues the novel estimators can and cannot address. In this study, we first provide an intuitive explanation of the problems of TWFE and elucidate the key features of the novel alternative DiD estimators. We then systematically demonstrate the conditions under which the conventional TWFE is inconsistent. We employ Monte Carlo simulations to assess the performance of dynamic DiD estimators under violations of key assumptions, which likely happens in applied cases. While the new dynamic DiD estimators offer notable advantages in capturing heterogeneous treatment effects, we show that the conventional TWFE performs generally well if the model specifies an event-time function. All estimators are equally sensitive to violations of the parallel trends assumption, anticipation effects or violations of time-varying exogeneity. Despite their advantages, the new dynamic DiD estimators tackle a very specific problem and they do not serve as a universal remedy for violations of the most critical assumptions. We finally derive, based on our simulations, recommendations for how and when to use TWFE and the new DiD estimators in applied research.

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks., Comment: 9 pages, 1 figure

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first algorithm uses randomized matrix sketching to compute an initial low-rank input matrix and proceeds to use this input to rapidly compute a SymNMF. The second algorithm uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. We prove theoretically that leverage score sampling can approximately solve nonnegative least squares problems to a chosen accuracy with high probability. Finally we demonstrate that both methods work well in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.